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3 years ago

Solve each system by elimination

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

4 0

First equation 2(4X -5y = 4)
8X -10y = 8

Elimination 8x -10y =8
-8x + 9y =-8

-y =0
-1(-y =0)
y =0

8x -10(0) =8
8x =8
(8x =8)/8
x = 1

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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

Elina [12.6K]

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

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

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

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

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

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

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

8 0

3 years ago

Help find perimeter and area

klio [65]

Answer: perimeter = 96mm, Area = 564mm².

Step-by-step explanation:

From the diagram, it is a trapezium, it has a rectangle joined together by a right angled triangle. Now to find the perimeter, we add all the dimensions together. To get the other side of the rectangle, which is also the perpendicular height of the figure, we take the Pythagoras. Let the perpendicular height = x

Therefore,

25² = ×² + 7²

625 = x² + 49

x² = 625 - 49

x² = 576

x. = √576

= 24.

Now the perimeter

= 20 + 25 + 7 + 20 + 24

= 96mm.

Area of the figure will be

= 1/2( a + b )h

Where a = 20, b = 20 + 7 = 27 and h = 24, now substitute for the values

( 20 + 27) x 24

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

= 47 x 24/2

= 47 x 12

= 564mm²

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3 years ago