1 The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of the roof, to the nearest tenth of a foot, if the side lengths each measure 25 feet. In your final answer, include all necessary calculations. You may include a sketch as part of your work.

2 To determine the amount of roofing materials needed, the area of the roof's entire surface is calculated, including the ceiling of the garage. Considering the sketch of the roofing design, create a formula to model the area of the roof's entire surface. In your final answer, include all of your calculations.

3The contractor in charge of the roofing project is trying to make the job the most cost effective for the homeowners. In order to cut back on the cost of supplies, he decides that a ceiling in the garage is not necessary. In other words, there will not be a barrier built between the garage and the roof. In two or more complete sentences, explain how these changes affect the model for the area of the roof's entire surface.

4The contractor in charge of the roofing project is trying to make the job the most cost effective for the homeowners. In order to cut back on the cost of supplies, he decides that a ceiling in the garage is not necessary. In other words, there will not be a barrier built between the garage and the roof. Create a formula modeling the area of the roof’s surfaces that the contractor will be purchasing supplies for.

5 Use the formula you created in the previous question to calculate the area of the roof that the contractor will be purchasing supplies for, assuming that the side length of the triangular bases is 25 feet and the length of each rectangular face is twice its width.

try your best i really need help!!

Answer: I and III

Step-by-step explanation:

The graphs of f and g have the same axis of symmetry. The graph of f has a maximum point, and the graph of g has a minimum point. The graph is a result of a reflection of the graph pf g across the x-axis. The correct options are 1, 3, and 4.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

We can use the fact that the points (3,2) and (7,2) are on the graphs of both functions to find out which of the given statements are true.

Let's start by using the fact that the graphs of the functions f and g pass through the points (3,2) and (7,2).

Since the y-coordinate is the same for both points, we can set the equations of the functions equal to 2 and solve for the unknown coefficients.

For the downward-opening quadratic function f, the equation is of the form:

[tex]f(x) = a(x - h)^2 + k[/tex]

Where (h,k) is the vertex of the parabola. Since f opens downward, the coefficient a is negative.

Using the point (3,2), we get:

[tex]2 = a(3 - h)^2 + k[/tex]

Using the point (7,2), we get:

[tex]2 = a(7 - h)^2 + k[/tex]

Subtracting the second equation from the first, we get:

[tex]0 = a[(3 - h)^2 - (7 - h)^2][/tex]

Simplifying this expression, we get:

0 = a[(3 - h + 7 - h)(3 - h - (7 - h))]

0 = a[-4(h - 5)]

Since a is non-zero (otherwise the parabola is not quadratic), we get:

h = 5

Plugging in h = 5 and using one of the equations above, we can solve for k:

[tex]2 = a(3 - 5)^2 + k[/tex]

2 = 4a + k

k = 2 - 4a

Therefore, the equation of the quadratic function f is:

[tex]f(x) = a(x - 5)^2 + (2 - 4a)[/tex]

Using the same method for the upward-opening quadratic function g, we get:

[tex]g(x) = b(x - 5)^2 + (2 + 4b)[/tex]

Where b is positive.

Now, let's check which of the given statements are true:

The graphs of f and g have the same axis of symmetry.

Since the vertex of f is (5, 2 - 4a) and the vertex of g is (5, 2 + 4b), the x-coordinate of the axis of symmetry for both functions is 5. Therefore, statement 1 is true.

The graphs of f and g have the same x-intercepts.

The x-intercepts of f are given by:

[tex]0 = a(x - 5)^2 + (2 - 4a)\\4a = a(x - 5)^2[/tex]

x - 5 = ±√(4/a)

x = 5 ± 2√(a)

The x-intercepts of g are given by:

[tex]0 = b(x - 5)^2 + (2 + 4b)[/tex]

-4b = [tex]b(x - 5)^2[/tex]

x - 5 = ±√(-4/b)

x = 5 ± 2i√(b)

Thus, since a and b have opposite signs, the x-intercepts of f and g are different. Therefore, statement 2 is false.

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Answer:

D

Step-by-step explanation:

-7 cubed = -343

-3 squared = -9

-343 - (-9) = -334

Answer:

The volume is 196 cubic yards

Step-by-step explanation:

Given

[tex]Base\ Area = 7yd * 2yd[/tex]

[tex]Height = 14yd[/tex]

Required

The volume

The volume is given as:

[tex]Volume = Base\ Area * Height[/tex]

Where:

[tex]Base\ Area = 7yd * 2yd[/tex]

[tex]Height = 14yd[/tex]

So, the equation becomes

[tex]Volume = 7yd * 2yd * 14yd[/tex]

[tex]Volume = 196yd^3[/tex]

Answer:

Step-by-step explanation:

In mathematics, every integer is a rational number, hence a whole number 6 can be written as 6/1. 1/3 ÷ 6 = 1/18 in fraction form. 1/3 ÷ 6 = 0.0556 in decimal form.

Answer:

1/18 or 18 is your answer.

Step-by-step explanation:

Since 1/3 is already in fraction form, we will now turn 6 into fraction form.  Which is 1/6. Now we will put it into the equation 1/3 x 1/6 = 1/18.  The fraction 1/18 can also be 18.  Therefore, 18 or 1/18 is our answer.

Answer:

Step-by-step explanation:

Length of rectangle: s +1

Width of rectangle: S -6

Perimeter of rectangle:2(s+1+s-6)=2(2s-5)=4s-10

Answer:

The vertex is located on the x-axis between the second and third quadrants

Step-by-step explanation:

Whereby the function is f(x) = (x + 3)², we have;

f(x) = (x + 3)² = x² + 6·x + 9

The vertex, (h, k), of the quadratic function given in general form, a·x² + b·x + c is found as follows;

h = -b/(2·a) and k = f(h)

Therefore by comparison of the given quadratic function and the general form of a quadratic function, we have;

a = 1, b = 6, c = 9

h = -6/(2 × 1) = -3

k = f(-3) = (-3)² + 6 × (-3) + 9 = 0

The vertex (h, k) = (-3, 0)

Therefore, the location of the vertex is on the x-axis axis between the second and the third quadrant.

Answer:

B

Step-by-step explanation:

we are given a equation of a line

we want to figure out the equation of the perpendicular line passes through the (6,5) points

in order to do so

recall that,

[tex] \displaystyle m_{ \text{perpendicular}} = - \frac{1}{m} [/tex]

we got from our given equation that m=2

because equation of a line is y=mx+b

thus

[tex] \displaystyle m_{ \text{perpendicular}} = - \frac{1}{2} [/tex]

remember that, when we want to figure out perpendicular line or parallel line we should the formula given by

[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]

since we got our perpendicular m is -½, [tex]x_1=6[/tex] and [tex]y_1=5[/tex], substitute

[tex] \displaystyle y - 5 = - \frac{1}{2} (x - 6)[/tex]

to get the perpendicular equation you should simplify the above equation to y=mx+b form

distribute -½:

[tex] \displaystyle y - 5 = - \frac{1}{2} x + 3[/tex]

add 5 to both sides:

[tex] \displaystyle y = - \frac{1}{2} x + 8[/tex]

hence,

our answer choice is B

Answer:

x = 30

Step-by-step explanation:

2x + x + 90 = 180

3x + 90 = 180

3x = 90

x = 30

Answer:

It's called proportion.

Step-by-step explanation:

The equality of ratios are proportional because like for example 2:3 and 4:9 these two ratios are the same. If you break down 4:9 you will get 2:3. So That's how the term proportional is applied. If we apply these ratio on a triangle they would look the same but just one is small and one is large and we can get it bigger by increasing the ratios. But the difference bwtween the ratios would be same so they are all proportional

Answer:

The answer is "12 inches".

Step-by-step explanation:

Please find the image file of the graph.

We know [tex]AE = CF \ and \ EB = FB[/tex] so because the triangle is isosceles.

[tex]EB = 2x, FB = 2x,\ and \ CF = x[/tex] when [tex]AE[/tex] is called by [tex]x[/tex].

We know that [tex]AE = AD = x[/tex] since E and D are tangent points to a circle.

They have [tex]CD = CF = x[/tex] since D and F are tangent points only to circle.

Thus, if the perimeter is 32, the following is the result:

[tex]\to AE + EB + BF + FC + CD + DA = 32\\\\\to x + 2x + 2x + x + x + x = 32\\\\\to 8x = 32\\\\\to x = 4[/tex]

Therefore the length of [tex]BC = BF + FC = 2x + x = 3x = 12\ inches[/tex]

Answer:

Volume of left side cylinder will be less than the volume of right side cylinder.

Step-by-step explanation:

Volume of a cylinder is given by the formula,

Volume = πr²h

Here, r = radius of the circular base

h = Height of the cylinder

Volume of the left hand cylinder = π(b)²a

Volume of the right hand cylinder = π(a)²b

It's given in the question that a > b

Let the value of a = 3 and b = 2

Then the volume of left hand cylinder = π(2)²(3)

                                                               = 12π

Similarly, volume of right hand cylinder = π(3)²(2)

                                                                 = 18π

Therefore, volume of left side cylinder will be less than the volume of right side cylinder.  

Answer:

5066

Step-by-step explanation:

10 + 9 + 5047 = 5066

The answer is 5066

Answer:

5066

Step-by-step explanation:

(10 + 9) + 5047

Answer:

so take 354 and add 210 simple u will get 564

Answer:

The correct answer is 564

but a Estimate would be 561.

Your welcome.

Step-by-step explanation:

Answer:

6) yes

7) no

Step-by-step explanation:

Answer:

x = 9

z = 71

Hope this helps!

Answer:

Step-by-step explanation:

something like this  Gigi,

y = -5([tex]x^{2}[/tex])

The correct answer is A

A) [tex]8(-10)=10(-10)+20[/tex] becomes [tex]-80 = -80[/tex]

B) [tex]8(-35)=10(-35)+20[/tex] becomes [tex]-280 \neq -330[/tex]

C) [tex]8(-23)=10(-23)+20[/tex] becomes [tex]-184 \neq -210[/tex]

D) [tex]8(-40)=10(-40)+20[/tex] becomes [tex]-320\neq -380[/tex]

Answer:

9.0 - 15.0

Step-by-step explanation:

Give Brainllest

Answer:

Step-by-step explanation:

very sorry if I'm wrong

Answer:

A (I think because i cant tell what the answers are saying)

Step-by-step explanation:

1.5/5= 0.3

3/10=0.3

4.5/15=0.3

6/20=0.3

Next time take a screenshot because i can not really see what the answers are supposed to be. But A is the only one that should be correct

Answer: $0.44

Step-by-step explanation:

Since Marco has $1.31 in his coin bank and he spends 87c to buy a pen, the amount taht will be left with him after he buys the pen will be gotten by subtracting 87cents from $1.31.

Note that 100 cents = $1

Therefore, $1.31 will be = 100 × 1.31 = 131 cents.

Therefore, 131 cents - 87 cents = 44 cents or $0.44

He has $0.44 left

Answer:

robes were embroidered with strands of gold.

Step-by-step explanation:

based on archeological evidence

Answer:

4.23

Step-by-step explanation:

3.68 + 0.21 + 0.25 + 0.01 + 0.08 = 4.23

Answer:

No because one side would have to be 54 in order for it to work

Step-by-step explanation:

the area is 634 and the perimeter is 128 so that would mean that one side would need to be 54

Answer:

They most of the time used the ability to row ships to get to places

Step-by-step explanation:

They were more reliable to row ships to trade with other people because the Mediterranean Sea was critical to how they were able to trade.

the answer is 9 because

3x9=27

and 27-18=9

mark brainliest plz