A piece of art is in the shape of a rectangular pyramid like the figure shown.

A rectangular pyramid with a base of dimensions 8 feet by 5 feet. The two large triangular faces have a height of 6.3 feet. The two small triangular faces have a height of 7 feet.

How much glass is needed to cover the entire pyramid?

250.8 ft2
167.6 ft2
125.4 ft2
62.7 ft2

The receiver should be positioned 3.0625 inches from the vertex.

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

Answer:

B. $52.50

Step-by-step explanation:

Just multiply the initial value by 1.05...

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, ∞)}

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:

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:

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

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

(ii) x−y=8,3x−3y=16

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

​

​

​

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).

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

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

Lucy owe $550 each month.

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

The value of each variable in the parallelogram:

u = 63° and g = 60°.

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

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 :)

To evaluate (gof)(-4), we first need to find the result of f(-4) and then plug that value into g(x),where (gof)(-4) = 29.

To learn more about function() refer:

brainly.com/question/17043948

#SPJ1

Answer:

6/8 is equivalent to 3/

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

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

The measure of ∠D is equal to 120°.

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

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

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

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

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.

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

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

⇒ y = kx

Where, k is constant of proportionality.

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

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]

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

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.

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.

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

Answer:  The answer should be 43

Step-by-step explanation:

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

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

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

Answer:

options d is the correct answer of this

The ratio for Tan A is 9/40.

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 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

Answer:

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.

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.

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.