Lily buys a sweater that is on sale for $42, which is 75% of the original price of the sweater. What was the original price of the sweater?

Answers

Answer 1

Answer: We have an equation: 42/? = 75/100

Cross multiply:
75*? = 42*100
⇒ ? = 42*100/75= 56

The original price of the sweater was $56.

Hope this helps~

Answer 2

Answer: 42 dollars is 75% so 25% is 14 and 100% is 56

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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 925 miles, for a total gas consumption of 35 gallons. How many gallons were consumed by each of the two cars that week?

Answers

The amount of gas consumed by first and second car were 20 gallons and 15 gallons respectively.

Explanation

Suppose, $x$ gallons of gas were consumed by the first car.

As the total gas consumption in one week is 35 gallons, so the amount of gas consumed by second car will be: $(35-x)$ gallons.

The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas.

So, the distance traveled by the first car in $x$ gallons of gas $=35x$ miles and the distance traveled by the second car in $(35-x)$ gallons of gas $=15(35-x)$ miles.

Given that, the two cars went a combined total of 925 miles. So, the equation will be.....

$35x+15(35-x)=925\n \n 35x+525-15x=925\n \n 20x=925-525=400\n \n x=(400)/(20)=20$

So, the amount of gas consumed by the first car is 20 gallons and the amount of gas consumed by the second car is: (35 - 20) = 15 gallons.

Find the dr/d(theta) for:
r = (theta)sin(theta) + cos(theta)

Answers

$r=\theta\sin\theta+\cos\theta$

$(\mathrm dr)/(\mathrm d\theta)=(\mathrm d(\theta\sin\theta))/(\mathrm d\theta)+(\mathrm d(\cos\theta))/(\mathrm d\theta)$

By the product rule,

$(\mathrm d(\theta\sin\theta))/(\mathrm d\theta)=(\mathrm d(\theta))/(\mathrm d\theta)\sin\theta+\theta(\mathrm d(\sin\theta))/(\mathrm d\theta)=\sin\theta+\theta\cos\theta$

and

$(\mathrm d(\cos\theta))/(\mathrm d\theta)=-\sin\theta$

So we have

$(\mathrm dr)/(\mathrm d\theta)=\sin\theta+\theta\cos\theta-\sin\theta$

$\implies(\mathrm dr)/(\mathrm d\theta)=\theta\cos\theta$

8+—3(6+—6a) help please

Answers

We know that:

$(+)+(-)=(-)$

and:

$(-)*(+)=(-)$

$8+(-3)[6+(-6a)]=8+(-3)*6+(-3)*(-6a)=8-18+18a$ $=(-10)+18a$

if you have solve for $a$ then:

$(-10)+18a=0$
$18a=10$
$a= (10)/(18)$
$a=(5)/(9)$

What is 11.48 divide by 3.28

Answers

11.48 divided by 3.28 is 3.5.

the answer to your question is 3.5

Cube root help please, I'm not quite sure I understand. What is 3^√56?
A. 7 3^√2
B. 3 3^√7
C. 2 3^√7
D. 7 3^√3

Answers

there is no square root button on my computer so i won't be adding one, sorry.
all of the options leave the 3 in its spot so you dont have to worry about that. To get the square root of 56 you just break 56 down until it is left with prim numbers:
56 / 2 =28
Now inside the square root: 2*28
28 / 4=7
Now inside the square root: 2*7*4
4 / 2=2
Now inside the square root: 2*7*2*2
you have two 2's so that comes out of th square root but the a 2 and 7 stays inside, you have to multiply the 2 and 7, giving you a 14.

2 3^ square root 14

PLEASE HELP ASAP!!! *problems attached

Answers

First one: A=5
Second one: no solution

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