Is 5/12 or 8/10 larger?

A rectangle has a length of x + 5 and width of x - 3. What is the area of the rectangle? Write the answer as a polynomial in sta

goldfiish [28.3K]

Answer:

Step-by-step explanation:

Area = length * width

length: x + 3

width: x - 5

A = (x + 3)(x - 5)

Simplify (x + 3)(x - 5) using the FOIL method:

1. First numbers: multiply the first number of each binomial together--x*x = x%5E2

2. Outer numbers: multiply the outer number of each binomial (out of the entire expression, the number farthest to the left (x) and the number farthest to the right (-5))--x*-5 = -5x

3. Inner numbers: multiply the inner number of each binomial--3*x = 3x

4. Last numbers: multiply the last number of each binomial--3*-5 = -15

==> Now, add all of the results together and combine like terms: x%5E2+-+5x+%2B+3x+-+15 = x%5E2+-+2x+-+15

Therefore, A = x%5E2+-+2x+-+15

8 0

3 years ago

Sin (x/2)= √2- sin (x/2) solve for the exact solutions in the interval (0, 2π)

serg [7]

$sin\left( \frac{x}{2} \right)=\sqrt{2}-sin\left( \frac{x}{2} \right)\implies sin\left( \frac{x}{2} \right)+sin\left( \frac{x}{2} \right)=\sqrt{2}\implies 2sin\left( \frac{x}{2} \right)=\sqrt{2} \\\\\\ sin\left( \cfrac{x}{2} \right)=\cfrac{\sqrt{2}}{2}\implies sin^{-1}\left[ sin\left( \cfrac{x}{2} \right) \right]=sin^{-1}\left( \cfrac{\sqrt{2}}{2} \right) \implies \cfrac{x}{2}= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill$

$\cfrac{x}{2}=\cfrac{\pi }{4}\implies \boxed{x=\cfrac{\pi }{2}}~\hfill \cfrac{x}{2}=\cfrac{3\pi }{4}\implies \boxed{x=\cfrac{3\pi }{2}}$

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B8ux%5E%7B5%7D%20%7D%20%5Csqrt%7B2ux%7D" id="TexFormula1" title="\sqrt{8ux^{5} } \sqr

lozanna [386]

Answer:

4ux³

Step-by-step explanation:

√8ux⁵ √2ux

√8*2 u*u x⁵*x

√16u²x⁶

4ux³

3 0

3 years ago

TRUE OR FALSE: A translation maps each point to its image along a vector called the translation vector

Tomtit [17]

Answer:

True

Step-by-step explanation:

:) Hope this helps ! x

6 0

3 years ago

Suppose Aji and sunshine have to pay $11 in royalties for each Beatles song and $7 for each Donovan song. How many of each type

andrey2020 [161]

To minimize their royal costs to $200, the number of Donovan songs to include is <u>15</u> and the number of Beatles songs to include is <u>5</u>.

<h3>What are ratios?</h3>

Ratios are numerical relationships between variables that show how much each variable is contained in another.

Ratios are stated in fractions, percentages, or decimals.

<h3>Data and Calculations:</h3>

Total songs to include in the song = 20

The ratio of Donovan and Beatles = 5:1.5

The number of Donovan songs to include = 15 (20/6.5 x 5)

The number of Beatles songs to include = 5 (20/6.5 x 1.5)

Royalty cost per Donovan song = $11

Royalty cost per Beatles song = $7

Total royalty costs for Donovan and Beatles song = $200 ($11 x 15 + $7 x 5)

Thus, the number of Donovan songs to include is <u>15</u> and the number of Beatles songs to include is <u>5</u>.

Learn more about ratios at brainly.com/question/2914376

#SPJ1

<h3>Question Completion:</h3>

Aji and Sunshine want to make a CD of songs from the 1960s to donate to their school library to be broadcast during school picnics. Sunshine's parents were big fans of the 60s singer Donovan, and they named her after his song "Sunshine Superman." Aji's folks were devotees of the Beatles. Aji and Sunshine want their CD to consist entirely of songs by Donovan and the Beatles. Because Sunshine is named after a Donovan song, she wants to include at least as many Donovan songs as Beatles songs. Aji agrees. In return, Sunshine agrees to include at least five Beatles songs. 5 1.5 To provide enough variety to make the mix interesting, they decide to include at least 20 songs altogether.

3 0

1 year ago