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3 years ago

Please help me with 8, 9, and 10 thanks! Show work too

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

In 8, 9, 10, all the triangles are similar, meaning corresponding sides have the same ratio.

8. hypotenuse / (short side) = 25/x = x/9
x² = 25*9 = 5²×3²
x = √(5²×3²) = 5*3 = 15

9. (long side) / (short side) = x/7 = 9/x
x² = 7*9
x = √(9*7) = 3√7

10. (short side) / (long side) = x/48 = 48/64
x = 48²/64 = 36

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A line is defined by the equation y = 2/3 x - 6 The line passes through a point whose y-coordinate is 0. What is the x-coordinat

Iteru [2.4K]

Answer:

x = 9

Step-by-step explanation:

Use the equation of the line, and let y = 0. Then solve for x.

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3 years ago

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2 years ago

What’s the equation.?

Stella [2.4K]

Answer:

See below

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You know that he spent 1/3 of his earnings, and then 1/4. After this, he has $28.90. You can write the equation like this:

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3 years ago

The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)

Misha Larkins [42]

ANSWER

The sphere is 10762 cubic centimeters bigger than the cube.

EXPLANATION

We want to find the difference in the volumes of the sphere and the cube.

To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.

The volume of a sphere is given as:

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

where r = radius

The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:

$\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}$

The volume of a cube is given as:

$V=s^3$

where s = length of the side

The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:

$\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}$

Therefore, the difference in the volumes of the sphere and cube is:

$\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}$

Therefore, the sphere is 10762 cubic centimeters bigger than the cube.

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1 year ago