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2 years ago

Combine like terms to create an equivalent expression.

Mathematics

1 answer:

Lelu [443]2 years ago

5 0

Answer:

$\frac{1}{6}$ p - $\frac{4}{5}$

Step-by-step explanation:

collect like terms

- $\frac{2}{3}$ p + $\frac{5}{6}$ p + $\frac{1}{5}$ - 1

= - $\frac{2(2)}{2(3)}$ p + $\frac{5}{6}$ p + $\frac{1}{5}$ - $\frac{5}{5}$

= - $\frac{4}{6}$ p + $\frac{5}{6}$ p - $\frac{4}{5}$

= $\frac{1}{6}$ p - $\frac{4}{5}$

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66) Savings Account.Christine Chu borrowed $4500 from a bank at a simple interest rate of 2.5% for one year.

timurjin [86]

Answer:

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3 years ago

What is the probability of you picking a weekend day from the days of the week?

svet-max [94.6K]

Answer:

3/7

Step-by-step explanation:

its 3/7 because there are 3 weekend days and there are 7 days in total in one week, so out of the week there is 3 weekend days.

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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

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

33 points!!

Alika [10]

Answer:

the missing length would be 35 mm bc both of them are the same length

Step-by-step explanation: hope this helped

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3 years ago

3. Suppose U= {1,2,3,4,5,6,7,8,9,10} is the universal set and Q= {3,6,9}. What is Q'?

Readme [11.4K]

Answer:

3. Q' = {1 , 2 , 4 , 5 , 7 , 8 , 10} ⇒ answer C

4. A ⊂ B is False ⇒ answer B

Step-by-step explanation:

- The universal set U = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10}

- The set Q = {3 , 6 , 9}

- We need to find the complement of set Q (Q')

- The complement set of Q is the set of all elements belongs to the

universal set U but does not belong to the set Q

- That means take off all the elements belongs to set Q from the

universal set U

∵ U = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10}

∵ Q = {3 , 6 , 9}

- Cancel from set U the elements 3 , 6 , 9

∴ Q' = {1 , 2 , 4 , 5 , 7 , 8 , 10}

- The universal set U = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8}

- The set A= {1 , 3 , 5 , 7}

- The set B= {4 , 5 , 6}

- A ⊂ B means every element in set A belongs to set B

∵ A= {1 , 3 , 5 , 7}

∵ B= {4 , 5 , 6}

∵ The elements in set A ∉ in set B

∴ A ⊂ B is False

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3 years ago