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Alik [6]
3 years ago
14

Work out the equation of the line which has a gradient of 1/2 and passes through the point (4,-2) ❗️THIS IS DUE PRETTY SOON SO H

ELP IS APPRECIATED !!!❗️

Mathematics
1 answer:
boyakko [2]3 years ago
5 0

Answer:

When slope and 1 point are known:

m = (1/2) x = 4 and y = -2

We first calculate "b"

b = y -mx

b = -2 -.5 * 4

b = -2 -2

b = -4

Then, we enter the value of "b" and the slope into this equation:

y = mx + b

y = .5x -4

Source: https://1728.org/distance.htm

Step-by-step explanation:

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The parent function shifted right 2 units

Step-by-step explanation:

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The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol
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Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is \frac{7}{10}

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is \frac{343}{1,000}

Part c) The volume of the smaller pyramid is 4,116\ m^{3}

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

so

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid  

z=\frac{x}{y}

substitute the values

z=\frac{21}{30}

Simplify

z=\frac{7}{10} -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid  

z^{3}=\frac{x}{y}

we have

z=\frac{7}{10}

substitute

\frac{7}{10}^{3}=\frac{x}{y}

Rewrite

\frac{x}{y}=\frac{343}{1,000} -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

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we have

z=\frac{7}{10}

y=12,000\ m^{3}

substitute the values and solve for x

(\frac{7}{10})^{3}=\frac{x}{12,000}

x=\frac{343}{1,000}(12,000)=4,116\ m^{3}

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