The cross-sectional areas of a triangular prism and a right cylinder are congruent. The triangular prism has a height of 10 units, and the right cylinder has a height of 7 units. Which conclusion can be made from the given information?

Answer:

3.39

Step-by-step explanation:

Answer:

The height of the triangle could be found by the Pythagoras theorem, where the result is, with the data of the exercise:

And the area of the triangle is:

Step-by-step explanation:

When you have two measurements of a triangle, as the case in the picture, you can find the third with the Pythagoras theorem, which is:

As you can see in the picture, the measurement of the hypotenuse is 12, and the opposite leg could be 6, for this reason, we're gonna clear the adjacent leg of the formula above:

Now, we can replace the values in the formula obtained:

Now, as we just need the adjacent leg, we take the square root of both sides:

Now, with these data, we can find the area of the triangle with the next formula:

As the image does not contain units, it would be simply this number, however, you should know that the area units are usually given squared, for example: in^2 or ft^2.

The midpoints of a rectangle always form parallelogram.

Answer:

B) [tex]\frac{15}{4}[/tex]

Step-by-step explanation:

Area of a rectangle formula:

A = bh

Given:

b = [tex]2\frac{1}{2}[/tex]

h = [tex]1\frac{1}{2}[/tex]

Work:

A = bh

A = [tex](2\frac{1}{2} )(1\frac{1}{2} )[/tex]

A = [tex]\frac{15}{4}[/tex]

Answer: 143

Step-by-step explanation: hope this helps :)

Answer:

[tex]radius = \sqrt{ {15}^{2} + {36}^{2} } = 39 \\ area = 4 \times {39}^{2} \times \pi = 19103.76[/tex]

Answer:

x = 10

Step-by-step explanation:

First square both sides of the equation...

[tex]2\sqrt{x + 8} = 3\sqrt{x - 2} \\(2\sqrt{x + 8})^{2} = (3\sqrt{x - 2})^{2} \\ 4(x + 8) = 9(x - 2)\\4x + 32 = 9x - 18\\-5x = -50\\x = 10[/tex]

Answer:

Parallel: a and b, p and q, p and r, q and r

PErpendicular: p&a, p&b, q&a, q&b, r&a, r&b

Step-by-step explanation:

Parallel lines have the same slope so both of the lines would be going in the same direction and will never cross each other.

Perpendicular lines cross at a 90 degree angle.

Technically you do not know if q&a and q&b are perpendicular because you do not know if there is a 90 degree angle

Answer:

Parallel lines are equally spaced out in the same direction so it would be p,q, and r, Purpendicular Lines intersect at a 90 degee angle so it would be q and a, q and b, r and b, and r, and so on

Step-by-step explanation:

===============================================

Work Shown:

A = area of the rectangle

A = length*width

A = 16*17

A = 272 sq ft

B = area of triangle

B = base*height/2

B = 16*8/2    ..... note that 17-9 = 8

B = 16*4

B = 64 sq ft

C = area of shaded trapezoid

C = A - B

C = 272 - 64

C = 208 sq ft

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Alternative Method:

Apply the trapezoid area formula

b1 = 17 and b2 = 9 are the parallel bases

h = 16 is the height perpendicular to either base

A = h*(b1+b2)/2

A = 16*(17+9)/2

A = 16*(26)/2

A = 16*13

A = 208 sq ft

Answer:

54

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 4 ] , then

f(b) = f(4) = 81 ← value of y from table for x = 4

f(a) = f(3) = 27 ← value of y from table for x = 3

average rate of change = [tex]\frac{81-27}{4-3}[/tex] = 54

Answer:

----------------------

hope it helps...

have a great day!!

Answer:

x=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

on the dive boat deck :)

Answer:

answer is 6x^2+17x+12

Step-by-step explanation:

3x(2x+3)+4(2x+3)=6x^2+9x+8x+12=6x^2+17x+12

Answer:

0.11314

Step-by-step explanation:

The Long John Silver's restaurant parameters are;

The mean time spent at the window, μ = 59.3

The standard deviation, σ = 13.1

The time distribution is skewed right

The number of cars in the sample, n = 40 cars

The mean time spent at the window with the delivery system, [tex]\overline x[/tex] = 56.8 seconds

The Z-value for a mean time of 56.8 seconds is given as follows;

[tex]Z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}[/tex]

Therefore, we get;

[tex]Z=\dfrac{56.8-59.3 }{\dfrac{13.1 }{\sqrt{40}}} \approx -1.20697620617[/tex]

Therefore, the z-value ≈ -1.21

From the normal probability table, we have;

P([tex]\overline X[/tex] ≤ 56.8) = P(Z < -1.21) = 0.11314

The probability of obtaining a sample mean of 56.8 second or less, assuming that the population mean is 59.3 seconds P([tex]\overline X[/tex] ≤ 56.8) = 0.11314.

Zeros:

x = -2

x = 6

Smaller zero: -2

Answer:

he made a good choice, the width is: 4 inches

Step-by-step explanation:

12 x 8 x _4_ = 384

Answer: 9π/20 radians  

How to: Convert from degrees to radians using the ratio π/180 .

Have a great day !

Diagrammatic representation of the summarized box plot is attached below :

Answer:

Range = 20

Median = 8

Step-by-step explanation:

The median value of a box plot is obtained at the point where a vertical line divides the box into two parts. In the boxplot Given the median of the representation is 8. This is the point where the vertical line divides the box.

The range of the distribution is the difference between the maximum and minimum value :

Minimum (starting point of whisker) = 5

Maximum (end point of whisker) = 25

Range = 25 - 5 = 20

Answer:

The answers are A and D

Step-by-step explanation:

2/6 simplified is 1/3 and none of the other choices are equal to 1/3, so the answers are A and D.

Answer:

4a-3b+a-2b

5a-3b-2b

5a-3b-2b

5a-5b

solution: 5a-5b

Answer:

He is wrong because for the last part of foil he multiplies 3 times 3 and got 6 instead of 9.

Answer:

6/8??

Step-by-step explanation:

I am a little confused with the question but i believe its 6/8

Answer:

215 cm^2

Step-by-step explanation:

Area for triangles: 1/2(b)(h)

Area for parallelograms: (b)(h)

18 - 6 - 5 = 7

20 - 10 = 10

1/2(7)(10)

1/2(70)

35

18(10)

180

180 + 35 = 215

Thank you for the Points but please stop taking answers from people who need help... Its not very kind

Answer:

29

Step-by-step explanation:

5-(4*(6-12))=29

Answer:

La respuesta es 29, espero que esto ayude.

Answer:

24 meters

Step-by-step explanation:

First we need to show width and length as variables.

let width of garden 1 = W

let length of garden 1 = L

let width of garden 2 = w

let length of garden 2 = l

Now make equations that are explained in the question

L = 2W

l = L

w = W + 4

l × w = 120

Now with that we can find l and w.

Now by looking at the factors of 120, find the factors that work throughout the question.

That is 12 and 10.

l=12

w=10

This means that...

L=12

W=6

Now the answer is 24 meters

Answer:

12m

Step-by-step explanation:

just took the test

Answer:

The answer is 12

Hope it helps

Answer:

x = 12

Step-by-step explanation:

Since the 2 legs and base angles are congruent the triangle is isosceles.

The line from the vertex to the base is a perpendicular bisector dividing the triangle into  2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles with legs 3 and [tex]\frac{1}{2}[/tex] x , hypotenuse [tex]\sqrt{45}[/tex] , then

([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²

[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides ²)

[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Answer: 4,218,750

Step by explanation: