Determine the axis of symmetry of the quadratic function whose graph is y = - 2x2 - 8x - 4.
Responses

x = 4
x = 4

y = 4
y = 4

x = -2
x = -2

y = -2
y = -2

Answers

Answer 1

The axis of symmetry of the given quadratic function is the vertical line x = -2. The correct answer would be an option (C).

What is Parabola?

A parabola is a U-shaped curve this is drawn for a quadratic function,

Determine the axis of symmetry of the quadratic function whose graph is y = - 2x² - 8x - 4.

The axis of symmetry of a parabolic function of the form y = ax² + bx + c is given by the formula x = -b/(2a).

In this case, a = -2, b = -8, and c = -4, so:

x = -(-8)/(2 × -2)

x = - 2

So, the axis of symmetry is the vertical line x = -2.

Learn more about the parabola here:

brainly.com/question/4074088

#SPJ1

Determine The Axis Of Symmetry Of The Quadratic Function Whose Graph Is Y = - 2x2 - 8x - 4.Responsesx

Related Questions

Drag and drop the constant of proportionality into the box to match the table. If the table is not proportional, drag and drop "not proportional" into the box. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. x 0 3 6 9 y 0 2 4 6

Answers

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

x      y

0     0

3      2

6      4

9      6

The variable 'y' is directly proportional to the variable 'x'. Then we have

y ∝ x

y = k x

At (9, 6), the value of the constant 'k' is given as,

6 = 9k

k = 6 / 9

k = 2/3

The proportionality is given as,

y = (2/3) x

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ1

how to solve the congruency of triangle MNO and triangle XYZ using a reflection across the line bisecting OZ

Answers

The following two-column proof can be used to demonstrate the congruency of triangles MNO and XYZ:

What in mathematics is congruence?

Two figures are said to be "congruent" if they can be perfectly positioned over each other. When stacked on top of each other, both bread slices are the same size and shape. Things that are exactly the same size and shape are said to be congruent.

Given: Line segment OZ bisects line segment MN and line segment XZ, and MNO is reflected across line OZ to form XYZ.

Prove: Triangles MNO and XYZ are congruent.

Statements | Reasons

OZ bisects MN, OZ bisects XZ | Given

Angle MOZ = Angle XOZ, Angle NOZ = Angle YOZ | Definition of angle bisector

∠MOZ = ∠XOZ, ∠NOZ = ∠YOZ | Using Corresponding angles postulate

∠MON = ∠XOY, ∠NOZ = ∠YOZ | Using definition of angle bisector

m∠MON = m∠XOY, m∠NOZ = m∠YOZ | Using Angle addition postulate

MN = XZ, MO = XO, NO = YO | Using Segment addition postulate

MNO ≅ XYZ | Using SAS congruence theorem

Therefore, we can conclude that the triangles MNO and XYZ are congruent.

Learn more about congruence at

brainly.com/question/2938476

#SPJ1

Write ration for Tan A(pic included)

Answers

The ratio for Tan A is 9/40.

Trigonometric ratios:

Trigonometric ratios are determined by the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

The six Trigonometric Ratios and their formulas are given below

Sin θ = Opposite Side/Hypotenuse

Cos θ = Adjacent Side /Hypotenuse

Tan θ = Opposite Side/Adjacent Side

Cot θ = Adjacent Side/Opposite Side

Sec θ = Hypotenuse/Adjacent Side

Cosec θ = Hypotenuse/Opposite Side

Here we have

Right-angled triangle ABC and the right angle at C

From angle A,  

Opposite side = BC and Adjacent side = AC

As we know tan θ = Opposite side /Adjacent side

=> Tan A = BC/AC = 9/40  

Therefore,

The ratio for Tan A is 9/40.

Learn more about Trigonometric ratios at

https://brainly.com/question/29156330

#SPJ1

The expression c=30m + 400, models the total cost (c) to buy a wireless
phone with a data plan for (m) months. Which of the following is not a true statement
about this situation?
1) The phone costs $400.
2) If you spent a total of $1,200, you had the phone for 20 months.
3) If you have the plan for a year, you have paid $760,
4) The data plan costs $30 per month.

Answers

Answer:

2) If you spent a total of $1,200, you had the phone for 20 months.

Step-by-step explanation:

From the equation, the cost of the phone is 400 and the monthly data plan costs $30 per month

For 20 months, you would have paid:
30 x20 + 400 = 600 + 400 = $1000

and not $1200

So statement 2 is false

Which graph shows a function whose inverse is also a function?

On a coordinate plane, 2 curves are shown. f (x) is a curve that starts at (0, 0) and opens down and to the right in quadrant 1. The curve goes through (4, 2). The inverse of f (x) starts at (0, 0) and curves up sharply and opens to the left in quadrant 1. The curve goes through (2, 4).

On a coordinate plane, 2 parabolas are shown. f (x) opens up and goes through (negative 2, 5), has a vertex at (0, negative 2), and goes through (2, 5). The inverse of f (x) opens right and goes through (5, 2), has a vertex at (negative 2, 0), and goes through (5, negative 2).

Answers

A graph which shows a function whose inverse is also a function include the following: A. On a coordinate plane, 2 curves are shown. f (x) is a curve that starts at (0, 0) and opens down and to the right in quadrant 1. The curve goes through (4, 2). The inverse of f (x) starts at (0, 0) and curves up sharply and opens to the left in quadrant 1. The curve goes through (2, 4).

What is a vertical line test?

In Mathematics, a vertical line test can be defined as a technique which is typically used to determine whether or not a given relation is a function.

According to the vertical line test, a vertical line must cut through the x-coordinate (x-axis) on the graph of a function at only one (1) point, in order for it to represent a function. Else, the relation does not represent a function because it can only have one output value (y) for a unique input value (x).

In conclusion, we can reasonably infer and logically deduce that the relation graphed in graph 1 represents a function whose inverse is also a function because it passed the vertical line test, unlike the other graph.

Read more on function here: brainly.com/question/9795474

#SPJ1

Make each equation true by converting the numbers to tenths hundredth or thousandths as needed 3+6+2

Answers

the equation of the true by converting the numbers is 362.

What is Tenths?

The place value of the digit that follows the decimal is tenths. It denotes the digit's 1/10th position. The denominator and numerator are the two components of a fraction. Therefore, if a fraction has 10 as the denominator, we can represent it as a decimal number with a digit in the tenths place. The place value of the digits that come after a decimal point is defined in mathematics as tenths and hundredths. When we count from right to left, the place values of the digits in a number are ones, tens, hundreds, and thousands.

x*100+y*10+z*1

=3*100+6*10+2*1

=362.

Hence the equation of the true by converting the numbers is 362.

Learn more about Tenths, by the following link

https://brainly.com/question/25829061

#SPJ1

Broadcasters use a parabolic microphone on football sidelines to pick up field audio for broadcasting purposes. A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches. If the receiver of the microphone is located at the focus of the reflector​ dish, how far from the vertex should the receiver be​ positioned?

Answers

The receiver should be positioned 3.0625 inches from the vertex.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that:

A certain parabolic microphone has a reflector dish with a diameter of 14 inches and a depth of 4 inches.

Here, we have;

Diameter = 14 inches

Depth = 4 inches

So, Radius = 14 / 2 = 7 inches

Hence, The coordinate is, (x, y) → (7, 4)

So, By the equation of parabola we get;

⇒ y = 1/4c × x²

⇒ 4 = 1/4c × 7²

⇒ 4 × 4c = 49

⇒ 16c = 49

⇒ c = 49/16

⇒ c = 3.0625 inches

Thus, The receiver should be positioned 3.0625 inches from the vertex.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The following set is in set-builder notation. Convert it to roster notation.

{x|x is a season of the year}

Answers

Roster notation is a straightforward way to represent a set in mathematical form. Within the curly brackets, the components (or members) of a set are listed in a row in the roster form.

What is set-builder notation?Set-builder notation, used in set theory and its applications to logic, mathematics, and computer science, is a mathematical notation for describing a set by listing its components or specifying the conditions that each member of the set must meet. Roster notation is a straightforward way to represent a set in mathematical form. Within the curly brackets, the components (or members) of a set are listed in a row in the roster form. If the set has more than one element, a comma is used to denote the separation of every pair of elements in a roster notation.

A set's roster method is fairly straightforward and consists of of a list of the set's components encircled by curly brackets. It is easier to construct sets with large or even infinite cardinalities using set-builder notation because it specifies the constituents of the set rather than just listing them. I'll start with the roster technique for my response, followed by the set-builder approach.

A. S = 15 (-15, -5, -3, -1, 1, 3, 5) = x (Z) | 15 (x (Z)

By using the set-builder notation, I am creating a set of all integers where x is a factor of 15 and 15/x is an integer.

b. S = {0} = {x ∈ R | 8x = 0}

c. S = {-2, 2} = {x ∈ Z | 2x^2 = 8}

The complete quesyion is,

Write the following sets using roster method and set builder notation.

A.     Write the following sets using roster method and set builder notation.

a.        Set of all factors of 15

b.       Set of all solution of the equation 8x=0

c.        Set of all integer’s solution of 2x^2 = 8

To learn more about  set-builder notation refer to;

https://brainly.com/question/14657951

#SPJ4

Assume that in 2018, the first edition of a comic book was sold at auction for $609,000. the comic book was originally sold in 1935 for $.05. For this to have been true, what was the annual increase in the value of the comic book?

Answers

The annual increase in the value of the comic book is 21.7%

What was the anual increase?

If each year the increase is X (a percentage), the initial value is A, and we define "t" as the number of years, then the value is given by the exponential function.

f(t) = A*(1 + X/100%)^t

Here we know that the initial value is A = 0.05

And after 83 years, the new value is 609,000 dollars, then we can write the equation:

609,000 = 0.05*(1 + X/100%)^83

609,000/0.05 = (1 + X/100%)^83

12,180,000 =  (1 + X/100%)^83

Now we can apply the exponent 1/83 in both sides:

(12,180,000)^(1/83) =  1 + X/100%

1.217 = 1 + X/100%

1.217 - 1 = X/100%

0.217*100% = X

21.7% = X

That is the increase per year.

Laern more about exponential functions at:

https://brainly.com/question/2456547

#SPJ1

Which piecewise function represents the graph?

Answers

We can write the piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →  {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

What is piecewise function?

In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.

A piecewise function is continuous on a given interval in its domain if the following conditions are met:

Its constituent functions are continuous on the corresponding intervals (subdomains).There is no discontinuity at each endpoint of the subdomains within that interval.

For a piecewise function to be differentiable on a given interval in its domain, the following conditions have to fulfilled in addition to those for continuity above:

Its constituent functions are differentiable on the corresponding open intervals.The one-sided derivatives exist at all intervals endpoints,At the points where two subintervals touch, the corresponding one -sided derivatives of the two neighboring subintervals coincide.

Give is a piecewise function in the graph.

We can write the piecewise function as follows.

For the interval (- ∞, 1)

The line passes through the point -

(- 1, 0) and (0, 1)

We can write slope of the line -

{m} = (1 - 0)/(0 + 1) = 1

{m} = 1

and

{c} = 1

So, we can write f(x) as -

f(x) = x + 1

For the interval (1, 4)

f(x) = 5

For the interval [5, ∞)

The line passes through the point -

(4, 3) and (5, 4)

We can write slope of the line -

{m} = (4 - 3)/(5 - 4) = 1/1

{m} = 1

and

For the point (5, 4), we can write -

4 = 1 x 5 + c

c = 4 - 5

{c} = - 1

So, we can write f(x) as -

f(x) = x - 1

Combining all the parts, we can write piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →   {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

Therefore, we can write the piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →  {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

To solve more questions on piecewise functions, visit the link below -

https://brainly.com/question/12561612

#SPJ1

Many calculators express very large and very similar numbers in Scientific notation if the number 4.32×104 appears in the display of the calculator what is the value of this number 

Answers

Answer:

options d is the correct answer of this

Find 135.1% of 338. Round to the nearest tenth.

Answers

456.638 so would be 456.6

Can someone help on these? I only need the ones that are circled.

Answers

(I) x+ y=5,2x+2y=10

(ii) x−y=8,3x−3y=16

How to calculate  x, y?

Step 1

I) x +y=5   …(i)

2x+2y=10    …(ii)

⇒x +y=5

⇒y=5−x

x  0  3

y  5  2

Plot (0,5) and (3,5) on graph and join them to get equation x +y=5.

2x+2y=10

⇒2y=(10−2x)

⇒y=

2

10−2x

​ =5−x   …(iii)

x  5  2

y  0  3

So, the equation is consistent and has infinitely many solution

Step 2

ii) x−y=8   ….(i)

3x−3y=16   ….(ii)

⇒x−y=8

⇒−x +y=−8

⇒y=−8+x

⇒y=x−8

x  8  0

y  0  -8

3x−3y=16   …(ii)

⇒3x=16+3y

⇒3x−16=3y

⇒y= 3x−16/3

⇒y=x− 16/3

x 16/3  0

y  0  -16/3

Plotting both the equation in graph, we see that the lines are parallel , so inconsistent.

To learn more about linear equation refers to;

https://brainly.com/question/26310043

#SPJ1

Lucy and Tanya rent an apartment together. The monthly total amount they owe includes $950 for rent, $100 for parking and $50 for utilities. If Lucy and Tanya spit the total amount they owe evenly between the two of them, how much does Lucy owe each month?

Answers

Lucy owe $550 each month.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The monthly total amount they owe includes $950 for rent, $100 for parking and $50 for utilities.

So, the total they have spend on all assets

= 950+ 100 + 50

= 1100

So, they will split the amount

= 1100/2

= $550

Hence, Lucy owe $550.

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ1

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPp

Answers

Answer:

x=35

Step-by-step explanation:

3x+16=5x-54

-2x=-70

x=35

Answer:

35

Step-by-step explanation:

the given two unknown angles are co-interior angles and for the lines to be parallel, they must be equal . So on equating them , we have ,

5x - 54 = 3x + 16

5x - 3x = 54 + 16

2x = 70

x = 70/2 = 35 [ required answer]

and we are done!

-Rishabh

HELP IM BEGGING YOUUUU HELP

Answers

Answer:

B. $52.50

Step-by-step explanation:

Just multiply the initial value by 1.05...

Use f(x) = 1
2
x and f -1(x) = 2x to solve the problems.

Answers

Answer:

Step-by-step explanation:

The function is described as f(x) = 1/2x, while the inverse is defined as f-1(x) = 2x.

The inverse function "undoes" the original function given a function. To get the inverse of a function, we must first swap the x and y variables before solving for y.

We may obtain the inverse function of f(x) = 1/2x by exchanging x and y: y = 1/2x.

then calculate x: x = 2y

As a result, the inverse function f-1(x) = 2x.

We may now employ these functions to solve issues by undoing the original function with the inverse function.

The function is defined as f(x) = 1/2x, and the inverse as f-1(x) = 2x.

The inverse function of a function "undoes" the original function. To get the inverse of a function, swap the x and y variables before solving for y.

By exchanging x and y, we may derive the inverse function of f(x) = 1/2x: y = 1/2x.

then compute x: x = 2y

The inverse function f-1(x) Equals 2x as a result.

By redoing the original function with the inverse function, we may now use these functions to solve problems.

Answer:

1,2,2 then -4,-2, -2 and for the last one is x

Step-by-step explanation:

engenuity

Which point is a solution to the system of linear equations?
y = -x + 1
3x - y = 3

Answers

The point (1,0) is a solution to the system of linear equations.

What is a linear system of equations?

A system of linear equations consists of two or further equations made up of two or further variables similar that all equations in the system are considered contemporaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

We are given a system of linear equations i.e. y = -x + 1 and 3x - y = 3.

In order to check that which point is a solution to the system of linear equations, we need to put the values in the given system.

1. (3/2 , -1/2)

Here, x = 3/2 and y = -1/2

Putting these values in the equations, we get

y = -x + 1

1/2= -3/2+1

1/2=1/2

3x - y = 3

3(3/2)-(-1/2) ≠ 3

9/2+1/2 ≠ 3

5 ≠ 3

Thus, it is not a solution to the system of linear equations.

2. (1 , 0)

Here, x = 1 and y = 0

Putting these values in the equations, we get

y = -x + 1

0= -1+1

0=0

3x - y = 3

3(1)-(0) = 3

3=3

Thus, it is a solution to the system of linear equations.

3. (-1/2, 3/2)

Here, x = -1/2  and y = 3/2

Putting these values in the equations, we get

y = -x + 1

3/2= -(-1/2)+1

3/2=1/2+1

3/2=3/2

3x - y = 3

3(-1/2)-(3/2) ≠ 3

-3/2-3/2 ≠ 3

-3 ≠ 3

Thus, it is not a solution to the system of linear equations.

4. (0, 1)

Here, x = 0  and y = 1

Putting these values in the equations, we get

y = -x + 1

1= -0+1

1=1

3x - y = 3

3(0)-(1) ≠ 3

0-1 ≠ 3

-1 ≠ 3

Thus, it is not a solution to the system of linear equations.

Hence, the point (1,0) is a solution to the system of linear equations.

Learn more about the linear system of equations from the given link:

brainly.com/question/27664510

#SPJ1

Malia is on a hike down a cliff. She begins at an elevation of 8 feet and descends at the rate of 4 feet per minute. She is above the bottom of the cliff, which is at −32 feet. How many minutes has she been hiking?
Write an inequality to represent the situation. Use x to represent the number of minutes Malia has been hiking

Answers

An inequality to represent Malia's situation is 4x ≤ 40. The time for which Malia has been hiking is 10 minutes.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

While hiking on a cliff Malia elevates at a distance = 8 feet

Then Malia descends at a distance = 4 feet

The bottom of the cliff is at the distance of -32 feet from Malia.

Let x represent the number of minutes Malia has been hiking.

The diagram is drawn for the situation.

A right-angled triangle ABC is formed -

Where the total measure of AB is 40 feet.

The time for which Malia has been hiking is AB' = 4x.

So, now the inequality becomes -

4x ≤ 40

On dividing both sides by 4 -

x  ≤ 40

Therefore, Malia has been hiking from 10 minutes.

To learn more about inequality from the given link

https://brainly.com/question/28230245

#SPJ1

find the value of each variable in the parallelogram.

Answers

The value of each variable in the parallelogram:

u = 63° and g = 60°.

What is parallelogram?

A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Given:

The shape is a parallelogram.

That means, the opposite sides are parallel and equal.

u=66°

3v°

u=66°=3v°

3v - u =66

u = 66 -  3v

u = 66-3v

u=63v

And opposite angles of a parallelogram are also equal.

v=63 -3

v = 60°

To learn more about parallelogram refers to:

https://brainly.com/question/21782549

#SPJ1

equivalent fraction to 3/4

Answers

Answer:

6/8 is equivalent to 3/

The answer is 6/8

3/4 x 2/2 = 6/8

Find the approximate perimeter and area of the figure below.

Answers

Answer:

perimeter: 40.48 mmarea: 110.55 mm²

Step-by-step explanation:

You want the perimeter and area of a composite figure that has an isosceles triangle atop a semicircle of diameter 12 mm. The triangle's height is 9 mm.

Perimeter

The length of the semicircle is half the circumference of the circle with the same diameter:

  C = 1/2πd . . . . circumference of semicircle

  C = 1/2π(12 mm) = 6π mm ≈ 18.85 mm

When the two straight sides are added, the perimeter is found to be ...

  P = (2×10.82 +18.85) mm ≈ 40.48 mm

The perimeter of the figure is about 40.48 mm.

Area

The area is the sum of the areas of the triangle and the semicircle:

  A = 1/2bh +1/2πr²

  A = 1/2(12 mm)(9 mm) +1/2π(6 mm)² = 1/2(108 mm² +36π mm²)

  A = (54 +18π) mm² ≈ 110.55 mm²

The area of the figure is about 110.55 mm².

what is the constant of proportionality for the relationship between x and y

Answers

The constant of proportionality for the relationship between x and y is defined as,

⇒ y = kx

Where, k is constant of proportionality.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We know that;

If y is directly proportion to x, then we can defined as;

⇒ y = kx

Where, k is constant of proportionality.

Hence, The constant of proportionality for the relationship between x and y is defined as,

⇒ y = kx

Where, k is constant of proportionality.

Learn more about the proportion visit:

https://brainly.com/question/1496357

#SPJ1

The vertex of a parabola is at the point (3,1), and its focus is at (3,5). What function does the graph represent?
A. f(x)=(x - 3)² - 1
B. f(x)=(x + 3)² - 1
C. f(x)=(x - 3)² - 1
D. f(x) = (x - 3)² + 1

Answers

Answer:

[tex]\textrm{In terms of f(x),}\\\\f(x) = \dfrac{(x-3)^2}{16} + 1\\\\[/tex]

Unable to match any of the answer choices provided. There has to be a mistake in the typing of the answer choice equations

Step-by-step explanation:

The equation of a vertical upward parabola given vertex (h, k) and focus(f, k) is :

(x-h)² = 4a(y-k)

a is the vertical distance between the y-coordinate of the focus and the y-coordinate of the vertex

The given parameters are vertex = (h, k) with h = 3, k = 1

Focus is (f, k) with f = 3, k = 5
(y-coordinate of a vertical parabola's vertex = y-coordinate of its focus)

a = 5- 1 = 4

Apply the equation:

[tex](x-h)^2 = 4a(y-k)\\\\(x - 3)^2= 4\cdot4(y - 1)\\\\(x - 3)^2= 16(y - 1)\\\\(x - 3)^2= 16y - 16\\\\[/tex]

Switch sides and add 16 to both sides:

[tex]16y = (x-3)^2 + 16\\\\\\\textrm{Divide throughout by 16:}\\\\y = \dfrac{(x-3)^2}{16} + 1\\\\[/tex]

[tex]\textrm{In terms of f(x),}\\\\f(x) = \dfrac{(x-3)^2}{16} + 1\\\\[/tex]


Find the quadratic equation whose root are -6 and 1.

Answers

Given the roots of a quadratic equation, we can find the equation by using the fact that the product of the roots equals to the constant term (c) divided by the coefficient of the quadratic term (a) and the sum of the roots equals to the opposite of the coefficient of the linear term (b) divided by the coefficient of the quadratic term (a).

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable.

Given that the roots of the equation are -6 and 1, we can find the equation as follows:

The product of the roots is -6 * 1 = -6

The sum of the roots is -6 + 1 = -5

We know that:

c / a = product of roots and

-b / a = sum of roots

So we can form the equation as:

ax^2 + bx + c = 0

ax^2 + (-5)x + (-6) = 0

So the quadratic equation whose roots are -6 and 1 is

ax^2 - 5x - 6 = 0

We can also verify that the roots of this equation are -6 and 1 by factoring or using the quadratic formula.

Which statement is true

Answers

The correct option is A)The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

What  is rotation about origin?

The term "rotation" refers to an object moving in a circle around its centre. The centre point can be rotated at an angle to create various shapes. The rotation group of a particular space is the collective name for all rotations that revolve around a fixed point and form a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Since, By the definition of rotation about origin, When a figure is rotate 180° about the origin then we get a congruent figure to that figure.

Thus, when PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'. Then trapezoid P'Q'R'S' is congruent to trapezoid PQRS.

By the definition of congruence,

The corresponding sides and angle of trapezoid P'Q'R'S' are congruent to that of trapezoid PQRS.

=> ∠P' ≅ ∠P, ∠Q' ≅ ∠Q, ∠R' ≅ ∠R and  ∠S' ≅ ∠S

Option D) is correct.

=>P'Q'R'S' is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°

Option A) is incorrect.

=>Since, trapezoid P'Q'R'S' is congruent to trapezoid PQRS.

Option B) is incorrect.

We know that if two shapes are congruent then their area must be equal.

⇒ Area of trapezoid P'Q'R'S' = Area of trapezoid PQRS

Thus, Option C) is also incorrect.

Hence the correct option is A)The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid P'Q'R'S'.

To learn more about rotation about origin refer the below link

https://brainly.com/question/4077402

#SPJ1

On two​ examinations, you have grades of and . There is an optional final​ examination, which counts as one grade. You decide to take the final in order to get a course grade of​ A, meaning a final average of at least 90.
What must you get on the final to earn an A in the​ course?
b. By taking the​ final, if you do​ poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than​ 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

Answers

a. You 97 or more should be scored to get an A grade. b You should score less than 67 to lose B grade.

What is arithmetic mean?

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

a) Average of the three examinations should be greater than or equal to 90 to get an A grade

Let x represent the grade in the third exam

So, (82+91+x)/3=90

⇒ x= 270 - (82+91) = 270 - 173 = 97

Thus, 97 or more should be scored to get an A grade.

b) Let x represent the grade in the third exam

Then;

(x+82+91)/3 = 80

⇒ x = 240 - 173 = 67

Thus, you should score less than 67 to lose B grade.

Learn more about Arithmetic means here:

brainly.com/question/13000783

#SPJ1

The question seems incomplete, the complete question would be as:

On two​ examinations, you have grades of 81 and 92. There is an optional final​ examination, which counts as one grade. You decide to take the final in order to get a course grade of​ A, meaning a final average of at least 90. a. What must you get on the final to earn an A in the​ course?

Part B: By taking the​ final, if you do​ poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than​ 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

You have an infinite number of chocolate candies. Two‐fifths of them have a caramel center. You choose 3 candies. What is the probability that at least 2 of them have a caramel center?

Answers

We can use the complement rule to solve this problem, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

The event we're trying to find the probability of is "at least 2 of the candies have a caramel center." The complement event is "fewer than 2 of the candies have a caramel center."

To find the probability of the complement event, we need to find the probability that exactly 0 candies have a caramel center, plus the probability that exactly 1 candy has a caramel center.

The probability that exactly 0 candies have a caramel center is (2/5)^0 * (3/5)^3 = (3/5)^3

The probability that exactly 1 candy has a caramel center is 3 * (2/5) * (3/5)^2 = (18/125)

The probability of the complement event is (3/5)^3 + (18/125)

Therefore, the probability of at least 2 of the candies having a caramel center is 1 - (3/5)^3 - (18/125)

I hope this helps :)

what do u call equations like that? that are like ready to simplify or whatever

Answers

Answer:

x ≥ - 6

Step-by-step explanation:

- 4x ≤ 24

Step 1 : Multiply - 1 on both sides

4x ≥ - 24

Step 2 : Divide 4 on both sides

4x/4 ≥ - 24/4

x ≥ - 6

The final simplified answer is x ≥ - 6

Answer:

x ≥ -6

Step-by-step explanation:

Divide each term in -4x ≤ 24 by −4 and simplify

If ABCD is a parallelogram and x = 5, what is m∠D?

Answers

The measure of ∠D is equal to 120°.

What is a parallelogram?

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image attached.

We can write -

{8x}° + {4x}° + ∠B = 180°

∠B = 180° - {8x}° - {4x}°

∠B = 180 - 40 - 20

∠B = 120°.

∠B = ∠D = 120°      [Opposite angles of a ||gm are equal}

Therefore, the measure of ∠D is equal to 120°.

To solve more questions on triangles and parallelogram, visit the link below-

brainly.com/question/12413243

#SPJ1

Other Questions
For what value of k do the equations not have a unique solution? WHAT IS HAPPENING?SHEET 3Match each of the following seven scenarios with the most appropriate graph given. As youlook at each graph from left to right, remember that time is advancing.1. We rode the roller coaster steadily to the top, then went faster and faster as wewent down the other side. The speed of the roller coaster is the dependent vari-able of the graph, that is, the variable on the vertical axis.2. The kettle heats before the corn begins to pop. The corn starts to pop and contin-ues popping until almost all the corn had popped. The amount of unpopped cornin the kettle is the dependent variable.3. A balloon was blown up in class and then let go. It flew around the room. Theamount of air in the balloon is the dependent variable.4. At the beginning of spring, the grass grew slowly and I seldom had to mow thelawn. By midsummer it was really growing, so I mowed twice a week. In fall, Ionly mow once in a while. The number of lawn mowings to date is the dependentvariable.5. I turned the oven on. When it was hot, I put in the cake. The cake baked for aboutthirty minutes. I turned the oven off and removed the cake. The oven temperatureis the dependent variable.6. We bought a pair of rabbits last year. They have had several litters, and we have somany rabbits that the pens are full. If more are born, we will have to give some awayor find room for the new ones. The number of rabbits is the dependent variable.7. I put water in the ice-cube tray and placed it in the freezer. The temperature ofthe water in the ice-cube tray is the dependent variable.From the Mathematics Teacher, April 1999 1. for each of the environments below: (1) identify your system and surroundings and (2) predict whether it would be endothermic or exothermic. a. wood burning b. water freezing c. sweat evaporating d. chemical hand-warmer Whoever help me first on this I will reward you I promise Please help I cant think of anything to write-In a paragraph of 3-5 sentences, evaluate economic reforms passed during Woodrow Wilsons presidency. the nursing manager is preparing a schedule for delegating appropriate tasks to different | health care team members. which health care team member can be delegated the task of | administering oral medications? select all that apply. one, some, or all responses may be correct. How do you graph vertical and horizontal inequalities? the tier 3 investigation is designated for the following positions 21n/ 3nSimplify the algebraic fraction whose numerator is 21n and whos denominator is 3n Help me step by step Please thank you. 4. What does Von Petzinger say about writing specifically cuneiform and hieroglyphs? How do the graphics and pictographic representations relate to writing as we understand it today? a therapist interprets resistances and transferences to discover a person's underlying problems. a. psychoanalytic b. cognitive c. client-centered d. behavioral\ PLEASE HELP ASAP A SOON AS YOU CAN. The percentage of battery remaning y on a tablets battery after x hours can be represented by the the given graphA.After 40 hours the tablet will have 0 percent of battery leftB. The tablet will not have any battery remaining after 4 hours C. The tablet starts with 40 percent of battery remaining D. The tablet loses 4 percent of battery every hour The state of Wyoming is roughly rectangular in shape. It has an area of more than 96,000 square miles. Write some possible dimensions of the state's length and width Which of these was a technological innovation?A. Atomic BombB. Cluster BombC. Aerial WarfareD. Air to Air missiles A carpenter needs to cut a small triangular piece of wood for part of a jewelry box. He knows the height is 23 inches and the base is an unknown value a. The angle between the unknown base a and the hypotenuse is =29. What is the length of a to the nearest tenth of an inch? Do not include the units in your answer. The ________ learner learns better by hands-on activities and movement.A) kinesthetic B) auditory C) visual D) active Summarize the process of evolution. 4. Read the following excerpt from a treaty between France and Russia. Explain how treaties like this one helped lead to World War I. In your opinion, is this the most important cause of the war? Why or why not? Support your conclusions with well-organized historical evidence. (5 points)France and Russia, being animated by a common desire to preserve peace, and having no other object than to meet the necessities of a defensive war, provoked by an attack of the forces of the Triple Alliance against either of them, have agreed upon the following provisions:1. If France is attacked by Germany, or by Italy supported by Germany, Russia shall employ all her available forces to attack Germany.If Russia is attacked by Germany, or by Austria supported by Germany, France shall employ all her available forces to attack Germany....4. The General Staffs of the Armies of the two countries shall cooperate with each other at all times in the preparation and facilitation of the execution of the measures mentioned above.They shall communicate with each other, while there is still peace, all information relative to the armies of the Triple Alliance which is already in their possession or shall come into their possession.Ways and means of corresponding in time of war shall be studied and worked out in advance.5. France and Russia shall not conclude peace separately.- The Franco-Russian Alliance Military Convention - August 18, 18921i need this asap ill mark you brainliest Gather quotes and other examples from the text to use as evidence that provides insight into Thomas Jones. Then write a paragraph that describes and analyzes Thomas Jones, including relationships, traits, motivations, fears, and how (or if) they develop over the course of the text. (Chasing Lincolns Killer) what is the answer in history of world religions