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3 years ago

15

Simplify each ratio 1. $8 to 62 cents 2. 14 inches to 2 yards 3. 5 days to 40 hours 4. Ratio of dogs to cats at the kennel if th

ere are 68 animals and 21 are cats.

1 answer:

Vika [28.1K]3 years ago

4 0

Answer:9

Step-by-step explanation:

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Heather brought $7.14 to school. She then spent $1.08 to buy lunch. How much money does she have left?

Wewaii [24]

Answer:

6.06

Step-by-step explanation:

Simple subtraction.

5 0

4 years ago

Read 2 more answers

Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

$\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

5 0

3 years ago

Equation of elimination method<br> 4a+b=28<br> a+4b=-8

Vilka [71]

Download an app called Photomath then it will answer it for you with work and explaining

6 0

3 years ago

Divide 7/24 by 35/48 and reduce the quotient to the lowest fraction

Ahat [919]

Well, an easier way than to divide fractions is to multiply the fractions, but to do that, flip the numerator and denominator for the second fraction.
For example, it becomes: 7 48 2
-------- × -------- = --------- (top×top & bottom×bottom)
24 35 5

Answer is: 2/5

5 0

3 years ago

Factor -28x +20x show work

Shalnov [3]

Let's simplify step-by-step.<span><span>−<span>28x</span></span>+<span>20<span>x

</span></span></span>ombine Like Terms:<span>=<span><span>−<span>28x</span></span>+<span>20x</span></span></span><span>=<span>(<span><span>−<span>28x</span></span>+<span>20x</span></span>)</span></span><span>=<span>−<span>8<span>x

</span></span></span></span>Answer:<span>=<span>−<span>8<span>x</span></span></span></span>

8 0

3 years ago