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3 years ago

Please help with multiplying binomials! Show your work! (3n+2)(n+3)

1 answer:

7 0

To multiply binomials, use the FOIL method. You start by multiplying the first terms in each binomial, 3n * n. The F stands for first.

Then you multiply the outside terms, 3n * 3. The O stands for outsides.

Then you multiply the inside terms, 2 * n. The I stands for insides

Then you multiply the last terms, 2 * 3. The L stands for last

Now solve for each, place them in the same equation, and combine like terms.

3n * n = 3n²
3n * 3 = 9n
2 * n = 2n
2 * 3 = 6

Your equation becomes 3n² + 9n + 2n + 6.

The 9n and 2n can combine together because they are like terms. Your answer becomes:

3n² + 11n + 6

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Joseph bought some t-shirts and a pair of trousers. He bought 4 t-shirts that each cost the same amount of money and the cost of

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35-17= 18 so 18 divided by 4 is $4.50 each shirt

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3 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

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3 years ago

Find the value of . A. 8 B. 32 C. 192 D. 1,536

Tamiku [17]

Answer:

Step-by-step explanation:

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3 years ago

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If the price of an object dropped 75% down to $85.99 what was the original price?

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If the price of an object drastically dropped 75%, then the dropped price is equal to 25% of the original price. That means that to find the original price, we have to multiply by the reciprocal of 25% (4). The original price would be $85.99 * 4 which is $343.96.

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3 years ago

(-11r+14+9r^3) + (3-8r^5+14r^3)

murzikaleks [220]

-8r^5+23r^3-11r+17

Wasn’t Sure What It Was Asking So Hopefully That Works For You

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4 years ago