The graph below shows two polynomial functions, f(x) and g(x): Graph of f of x equals x squared minus 2 x plus 1. Graph of g of x equals x cubed plus 1 Which of the following statements is true about the graph above? (4 points) f(x) is an even degree polynomial with a negative leading coefficient. g(x) is an even degree polynomial with a negative leading coefficient. f(x) is an odd degree polynomial with a positive leading coefficient. g(x) is an odd degree polynomial with a positive leading coefficient.

The value of the given expression; f(x) = 4 - 2x, for f(3r -1) as required in the task content is; f(3r-1) = 6 - 6r.

Since it follows from the task content that the given function is defined by the expression;

f(x) = 4 - 2x.

To evaluate the function f(x) = 4 - 2x, for f(3r -1); we must substitute 3r -1 for x in the equation as follows;

f(3r -1) = 4 - 2(3r-1)

f(3r-1) = 6 - 6r.

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The bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the square of the legs, that is, the two other sides.

If in a right triangle, c is the hypotenuse, and a and b are the two legs, then by the Pythagoras Theorem, we can write:

a² + b² = c².

In the question, we are informed that a building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.

We are asked to draw a diagram that represents the situation and find the height of the bottom edge of the window from the ground.

We assume the building to be DB, meeting the ground BC at a right angle. At point C, the ladder meets the ground and meets the bottom edge of the window at point A.

The diagram is attached.

Now, we get a right triangle ABC, right-angled at B.

By Pythagoras' Theorem, we know that:

AB² + BC² = AC²,

or, AB² + 6² = 10²,

or, AB² = 10² - 6² sq. inches,

or, AB² = 100 - 36 sq. inches,

or, AB = √64 inches,

or, AB = 8 inches.

Thus, the bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

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The provided question is incomplete. The complete question is:

"A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw a diagram that represents this situation. How far up from the ground is the bottom edge of the window?"

Answer:

answer is 121/9

Step-by-step explanation:

13.4444444444 (decimal form)

121/9 (improper fraction form)

13 4/9 (mixed fraction form)

Answer:

See below

Step-by-step explanation:

To pay the loan off more quickly.

To pay less overall interest.

Often get a lower interest rate for a shorter term loan.

The solution to the system of equations is (8, -4)

The system of equations is given as;

y = -1/4x - 2

y = 3/8x - 7

See attachment for the graph of the equations

From the attached graph, we have the point of intersection to be

(x, y) = (8, -4)

Hence, the solution to the system of equations is (8, -4)

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Answer:

  √5 is irrational

Step-by-step explanation:

A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.

Usually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.

The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.

__

Additional comment

A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.

Answer:

Step-by-step explanation:

B is the answer

Answer:

1.5, -1.5

Step-by-step explanation:

Using the quadratic formula, you should have a plus, and minus solution. These should be your answers.

The sum of the numbers is 7.69 * 10^6

The expression is given as:

(1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline)

Rewrite properly

(1.54 * 10^6) + (6.15 * 10^6)

Factor out 10^6

(1.54 + 6.15) * 10^6

Evaluate the sum

7.69 * 10^6

Hence, the sum of the numbers is 7.69 * 10^6

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Answer:

a

Step-by-step explanation:

Find the sum. Express the answer in scientific notation.

(1.54 times 10 Superscript 6 Baseline) + (6.15 times 10 Superscript 6 Baseline)

7.69 times 10 Superscript 6

9.471 times 10 Superscript 6

7.69 times 10 Superscript 12

9.471 times 10 Superscript 12

The cost of one gizmo is $18.

The cost of one thingamajigs is $9

3g + 6t = 102 equation 1

5g + 11t = 179  equation 2

Where:

Multiply equation 1 by 5 and equation 2 by 3

15g + 30t = 510 equation 3

15g + 33t = 537 equation 4

Subtract equation 3 from equation 4

3t = 27

t = 27 / 3

t = $9

Substitute for t in equation 1

3g + 6(9) = 102

3g + 54 = 102

3g = 102 - 54

3g = 48

g = 48 / 3

g = $18

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The correct option is D: G(x) = -5x².

The equation of G(x) will be -5x² after vertically stretching and flipping.

A function change called a stretch or compression makes a graph bigger or narrower without moving it horizontally or vertically.

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The complete question is -

The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x², which of the following could be the equation of G(x)?

A: G(x) = -1/5x²

B: G(x) = 5x²

C: G(x) = 1/5x²

D: G(x) = -5x²

The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].

Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].

We are required to find the solution of the differential equation when y(0)=1.

dy/dx=[tex]2xy/(x^{2} -1)[/tex]

Taking y to left side and dx to right side.

1/y dy=2x/[tex](x^{2} -1)[/tex] dx

Integrating both sides.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1

log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

Solving right side.

[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]

let [tex]x^{2} -1[/tex]=z

differentiating both sides with respect to x.

2x=dz/dx

2x dx=dz

Put 2x dx=dz in 1.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]

log y=log z+log c

Put z=[tex]x^{2} -1[/tex]

log y=log([tex]x^{2} -1[/tex])+log c

log y=log [{[tex]x^{2} -1[/tex])c]

y=([tex]x^{2} -1[/tex])c------------2

Put x=0 and y=1

1=(0-1)c

1=-c

c=-1

Put c=-1 in 2 to get the solution.

y=-1([tex]x^{2} -1[/tex])

y=[tex]-x^{2} +1[/tex]

Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is

y=[tex]-x^{2} +1[/tex].

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3a) The coordinate of R after dilation is; R' = (-6, 21)

3b) The coordinate of T after dilation is; T' = (1, 3)

5) A dilation by a scale factor of 2 followed by a translation right 1 up 3.

3a) We are given the coordinates of the rectangle as;

Q(-2, -1), R(-2, 7), S(4, 7), T(4, -1)

Now, we are told that R(-2, 7) is dilated about the origin with a scale factor of 3. Thus;

R' = (-2 *3), (3 * 7)

R' = (-6, 21)

3b) We are now told that T(4, -1) is dilated by a scale factor of 1/2 with R as center of origin. R has a coordinate of (-2, 7). Thus;

Coordinate of T' = (-2, 7) + ¹/₂((4, -1) - (-2, 7))

Coordinate of T' = (-2, 7) + ¹/₂(6, -8)

Coordinate of T' = (-2, 7) + (3, -4)

Coordinate of T' =  (1, 3)

5) We can see that LN is 2 units while L'N' is 4 units and so we can say scale factor in the transformation of ΔLMN to ΔL'M'N' is 2.

Now, if we apply scale factor of 2 to coordinates of N before transformation, we will have; 2(3, 1) = (6, 2)

Comparing to N' which is (5, 5) we can say that it was shifted up by 3 units and right by 1 unit.

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[tex]8 \: cars = 120 \: dollars \\ 1 \: car = \frac{120}{8} = 15 \: dollars[/tex]

[tex]m(c) = 15c[/tex]

Answer:

d: m=15c

Step-by-step explanation:

Usually (not always), variable y depends on variable x.

Since in this question, the amount of money Paul can earn changes based on the number of cars he washes, y is the amount of money, and x is the number of cars he washes.

This can be represented as: 120 = 8 times ___

___ is the amount of money Paul earns by cleaning 1 car.

___ is 120 divided by 8, which is 15.

--> Paul earns $15 by cleaning each car.

The new equation will be m = 15c

Answer:

  P = 160/A

Step-by-step explanation:

For P to vary inversely with A, we must have P be proportional to the reciprocal of A. The constant of proportionality is given.

Two quantities are directly proportional if there is a constant of proportionality (k) that multiplies one of them to give the value of the other:

  y = kx

They are inversely proportional if the inverse of one of them can be multiplied by a constant of proportionality to give the value of the other:

  y = k(1/x) = k/x

In this problem, the variables P and A are said to be inversely proportional. That means the equation that relates them will be of the form ...

  P = k/A

You are given such a form with k=160, which is an appropriate value for the relation given by the problem. All you need to do is fill in the variable:

  P = 160/A

Answer:

f(2) = 3

Step-by-step explanation:

Plug in 2 for x

Answer:we smoking fredoooooooooo

Answer:

Θ ≈ 37° , x ≈ 13 cm

Step-by-step explanation:

(a)

using the cosine ratio in the right triangle

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{10}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ([tex]\frac{8}{10}[/tex] ) ≈ 37° ( to the nearest whole number )

(b)

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{15}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 15[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 7.5[tex]\sqrt{3}[/tex] ≈ 13 cm ( to the nearest whole number )

Answer:

(D). 6.

Step-by-step explanation:

The number of parts = 1 + 10 = 11.

So 10/11 of the alloy is copper and 1/11 is aluminium.

So the answer is 1/11 * 66

= 66/11= 6 pound,s

The value of the probability P(A and B) is 0.12

The given parameters are

P(A) = 0.40

P(B) = 0.30

Given that the events are independent events;, we have:

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.40 * 0.30

Evaluate

P(A and B) = 0.12

Hence, the value of the probability P(A and B) is 0.12

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The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

Given a taxi charges $2.50 for the first mile and $0.40 for each mile

We are required to make an expression showing total cost and total cost of a 20 mile ride.

let the miles ride by tax be x.

Total cost of the product or service=Number of units*price of one units.

We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.

So,the expression showing looks like 2.50+0.40x.

Now to find the cost when taxi travels 20 miles, we have to put x=20,

Cost=2.50+0.40*20

=2.50+(40*20)/100

=2.50+800/100

=2.50+8

=$10.50

Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

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Solving a system of equations we can see that:

First, let's define the variables:

With the given information we can write 3 equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

Then we need to solve a system of equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

We can first replace the first equation into the third to get:

(3/4)*V + V + K = $386.4

And rewrite the second to get:

k = V + $18

And replace that in the other equation:

(3/4)*V + V + V + $18 = $386.4

Now we can solve this for V:

V*(1 + 1 + 3/4) = $386.4 - $18

V*(11/4) = $368.40

V = (4/11)*$368.40 = $133.96

Now that we know the value of V, we can replace it in:

K = V + $18 = $133.96 + $18 = $151.96

A = (3/4)*V = (3/4)*$133.96 = $100.47

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Using a proportional relationship, the scaled distances, in sheets of toilet paper, are given as follows:

The real distances are missing, and they are given in the table at the end of the answer.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

k is the constant of proportionality for both cases.

For this problem, the constant for the Scaled Distances as a function of the Real Distances is given as follows:

k = 5/149.6 = 7.6/227.9 = 0.03334795963.

Hence, the relationship for the Scaled Distances is given by:

S = 0.03334795963R

In which R is the real distance.

Then the scaled distances for the planets are given as follows:

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Answer:

edmentum/plato hope this can help someone :)

Step-by-step explanation:

Answer:

16. C

17. C

Step-by-step explanation:

16.

this is just a multiplication of the 2 functions.

that means we multiply the functional expressions, and the result is the new functional expression of the multiplied functions.

2(3x - 5) × (-2x + 1) = (6x - 10) × (-2x + 1) =

= 6x×-2x + 6x×1 + -10×-2x + -10×1 =

= -12x² + 6x + 20x - 10 = -12x² + 26x - 10

17.

the domain of a function is the interval or set of all valid x values (or input values).

the range is the interval or set of all valid y or functional result values.

so, for the domain we need to see what values x may have for a 4th root.

for this we can imagine that a 4th root is the square root of the square root of x.

this is directly related to x⁴ being the square of the square of x.

the valid input values for a square root are all positive numbers (incl. 0). the result will be again a positive number (incl. 0), which is again a valid input number for the second square root.

therefore, the valid values of x for a 4th root are also the valid values for a square root. and vice versa.

and that is

0 <= x < infinity

FYI : we can never say x = infinity, because infinity is not a number, just a generation concept. so, infinity can never be included in any interval, it can only be listed as an excluded limit concept.

The tiles to match the descriptions are;

Hull house - Neighbourhood assistance.

Muckrakers - Investigative journalists.

Protestants - Temperance movement.

Women's suffrage - Nineteenth amendment.

The Progressive Era, which encompassed the years between the 1890s and the 1920s in US history, was one of intense social and political reform with the goal of advancing the creation of a better society.

Case 1: The settlement home that welcomed newly arrived European immigrants to the United States in 1889 is known as Hull House. There were also social, educational, and artistic initiatives for immigrants in this building.

Case 2: Muckrakers A name used to describe a group of North American journalists in the early 20th century who made public criticisms of: government corruption, abuse of labor is destructive to society and is committed by influential people or institutions of the time.

Case 3: Third, the term "Protestantism" is used to describe a variety of 16th-century religious movements. Because the Catholic Church had a different understanding of the Bible's holy texts, this movement was distinguished by its break with it.

Case 4: The 19th Amendment to the United States Constitution, which was adopted in June 1919, guaranteed every American woman the right to vote.

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The complete question is-

Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the

descriptions                        

Tiles;

Hull House

Muckrakers

Protestants

Women's Suffrage

Pairs;

Investigative journalists

Temperance Movement

Neighbourhood assistance

Nineteenth Amendment

Answer:

Step-by-step explanation:

When the balloon, rising at 10 ft/sec, rises to 100 feet, the rate of change of the angle of elevation is 0.05 rad/sec

The rate at which the balloon rises = 10 ft/sec

Horizontal distance of the balloon from the observer, d = 100 feet

Therefore;

[tex] \frac{dy}{dt} = 10[/tex]

The angle of elevation can be presented as follows;

[tex] tan(\theta) = \frac{y}{100} [/tex]

[tex] y = 100 \times tan(\theta) [/tex]

Therefore;

[tex] \frac{dy}{dt} = \mathbf{ 100\cdot sec^2 \frac{d \theta}{dt}} [/tex]

Which gives;

[tex] \frac{d \theta}{dt}= \frac{ \frac{d y}{dt}}{100} \times cos^2 \theta [/tex]

[tex] \mathbf{ \frac{d \theta}{dt}} = \frac{ 10}{100} \times cos^2 \theta [/tex]

When the balloon is 100 ft. from the ground, we have;

Therefore;

[tex] \frac{d \theta}{dt}= \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 [/tex]

[tex] \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 = \frac{ 1}{20} [/tex]

Which gives;

[tex] \frac{d \theta}{dt}=\frac{ 1}{20} = 0.05 [/tex]

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Answer:

-2

Step-by-step explanation:

The slope of a line is rise/run

So, just see how much the line rises/how much the line runs

In this case, the line rises 2 units for every -1 unit it runs

So, the slope is -2

Answer:

y =  x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (0, - 2 )

m = [tex]\frac{-2-2}{0-4}[/tex] = [tex]\frac{-4}{-4}[/tex] = 1

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = x - 2 ← equation of line

Answer:

7

Step-by-step explanation:

given a polynomial divide by (x - a) then the remainder is f(a)

here f(x) is divided by (x - 5) , so remainder is

f(5) = 2(5)³ - 12(5)² + 11(5) + 2

     = 2(125) - 12(25) + 55 + 2

     = 250 - 300 + 57

     = - 50 + 57

    = 7