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forsale [732]
4 years ago
9

Luke is building a storage building and needs to have a slab of concrete poured. He knows the contractor charges an initial cost

of $95 plus an additional $3.50 per square foot of concrete. Which function can be used to determine the cost, in dollars, to pour a concrete slab with an area of x square feet? A) f(x) = 3.5x + 95 B) f(x) = 9.5x + 3.5 C) f(x) = 95x + 3.5 D) f(x) = 98.5x
Mathematics
2 answers:
kherson [118]4 years ago
8 0
The answer is A.

 y is the total cost, than you would need to multiply x, the number additional number of square feet, which is 3.5x. you would then add 95 dollars to the equation to represent the initial fee. So the equation would look like Y=3.5x+95.

- beanz

ladessa [460]4 years ago
5 0
$3.50 each Square foot +$95
$3.5 times x+$95
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The ratio of the volumes of the similar solids is _____ 25:1 5:1 125:1
weqwewe [10]

Answer:

Part 1)

a) The ratio of the heights of the similar solids is 5/1

b) The ratio of the surface areas of the similar solids is (5/1)²=25/1

c)  The ratio of the volumes of the similar solids is (5/1)³=125/1

Part 2) Two spheres with different radii measurements are always similar

Part 3) The volume of the sphere is greater than the surface area of the sphere

Step-by-step explanation:

Part 1) we know that

The ratio of the corresponding heights of the similar solids is equal to the scale factor

The ratio of the surface areas of the similar solids is equal to the scale factor squared

The ratio of the volumes of the similar solids is equal to the scale factor elevated to the cube

In this problem

The scale factor is 5/1

therefore

a) The ratio of the heights of the similar solids is 5/1

b) The ratio of the surface areas of the similar solids is (5/1)²=25/1

c)  The ratio of the volumes of the similar solids is (5/1)³=125/1

Part 2)

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.  

In this problem to prove that two spheres  are similar, a translation and a scale factor (from a dilation) will be found to map one sphere onto another.

therefore

Two spheres with different radii measurements are always similar

Part 3) The length of the diameter of a sphere is 8 inches

<em>The volume of the sphere is equal to</em>

V=\frac{4}{3}\pi r^{3}

we have

r=8/2=4\ in -----> the radius is half the diameter

substitute

V=\frac{4}{3}\pi (4)^{3}

V=85.33\pi\ in^{3}

<em>The surface area of the sphere is equal to</em>

SA=4\pi r^{2}

substitute

SA=4\pi (4)^{2}

SA=64\pi\ in^{2}

therefore

The volume of the sphere is greater than the surface area of the sphere

3 0
3 years ago
A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round you
prisoha [69]

The volume of the prop is calculated to be 1,875.6 cubic inches.

Step-by-step explanation:

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying \frac{1}{3} with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 8 inches and the height is 12 inches.

The volume of the cone: \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.14) (8^{2}) (12)= 803.84 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying \frac{4}{3} with π and the cube of the radius (r³).

Here the radius is 8 inches. We take π as 3.14.

The volume of a full sphere= \frac{4}{3} \pi r^{3} = \frac{4}{3} (3.14) (8^{3} ) = 2,143.573 cubic inches.

The volume of the half-sphere= \frac{2,143.573}{2} = 1,071.7865 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume =  803.84+1,071.7865 = 1,875.6265 cubic inches.

Rounding this off, we get the volume of the prop as 1,875.6 cubic inches.

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Answer:

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Step-by-step explanation:

Also great pencil!

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