Need help with all questions.

Can someone please explain expanded form with this number 15,409

Anarel [89]

The expanded form of 15,409 would be 15,000 + 400 + 9.

Your 15 would alone be 15,000. The 409 is turned into zeros.
For 409, take the 9 off of the end and keep it by itself, and then add a zero in replace for the 9, which makes 400.
The 9 should come in at the last part as it is the last number.

Add them all together and you should get <span>15,000 + 400 + 9.</span>

3 0

3 years ago

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

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

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

Every day, Paula performs physical activity on her treadmill. For an hour, she runs 15,000 meters. Knowing that she spends an ho

natali 33 [55]

Answer: 105 kilometers

Step-by-step explanation:

1 kilometer=1,000 meters

15,000 (meters a day) x 7 (days a week) = 105,000 meters.

Convert the meters to kilometers:

105,000/1,000 = 105 kilometers

3 0

3 years ago

Which of the following is not a solution of 3x=5y-1 a.(3,3) b.(7,4) c.(-1/3,0) d.(-2,-1)

erik [133]

3x = 5y - 1

(3,3)...not a solution
(7,4)...not a solution
(-1/3,0)...is a solution
(-2,-1)...is a solution

8 0

3 years ago

Please help ASAP please

mihalych1998 [28]

do you some help ?, I can try my best to help

6 0

3 years ago

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