Tickets to the movies cost $12 for adults and $8 for children. A group of 14 people went to the movies, and the tickets cost $136. The system of equations models this situation, where x is the number of adults and y is the number of children.x+y=14
12x+8y=136
How many adults and how many children were in the group?
A.
9 adults and 5 children

B.
6 adults and 8 children

C.
4 adults and 10 children

D.
8 adults and 6 children

Answers

Answer 1

Answer: -12*/x+y=14
12x+8y=136

-12x-12y=-168
12x+8y=136
+--------------------
-4y= -32

y=8

x+y=14

8+y=14,

y=6

This question answer is 6 adults and 8 children

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90% as a decimal rounded to the thousands place

What is the percent change of 92 to 69 first value to the second

Answers

The change is (92 - 69) = 23

The change as a fraction of the original value is 23/92

The fraction as a decimal is (23) divided by (92) = 0.25 .

To change a decimal to a percent, move
the decimal point two places that way ==> .

0.25 ==> 25%

The change is a loss of 25%. I guess you might say it's -25% .

7k^2-16k+100=0 using completing the square ?

Answers

$7k^2-16k+100=0$

$7k^2-16k=-100$

Add a squared constant to both sides:

$7k^2-16k+c^2=c^2-100$

On the left, we wish to condense the quadratic into a squared binomial,

$(\sqrt7\,k-c)^2$

Expanding this gives

$7k^2-2c\sqrt7\,k+c^2$

which tells us

$-2c\sqrt7=-16\implies c=\frac8{\sqrt7}$

Then $c^2=\frac{64}7$ , and

$\left(\sqrt7\,k-\frac8{\sqrt7}\right)^2=\frac{64}7-100$

$\left(\sqrt7\,k-\frac8{\sqrt7}\right)^2=-\frac{636}7$

If you're looking for real-valued solutions, there are none, since the square root of a negative number doesn't exist... but if you're allowing complex-valued solutions, we can take the square root of both sides to get

$\sqrt7\,k-\frac8{\sqrt7}=\pm 2i\sqrt{\frac{259}7}$

Multiply both sides by $\sqrt 7$ to eliminate denominators, then solve for $k$ :

$7k-8=\pm 2i√(259)$

$7k=8\pm 2i√(259)$

$\boxed{k=\frac{8\pm2i√(259)}7}$

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.

Mr. Carter is planning a special event for 98 guests. A catering company tells him that the cost of food for each guest will be $16. The cost for drinks for each guest will be another $5. Based on that, Mr. Carter works out that the total catering bill will be $20,580. Does that sound about right?

Answers

Answer: No, the correct answer is $2058.

Step-by-step explanation:

First, you should multiply 16 by 98. This will get you 1568. Then, you multiply 5 by 98, which will get you 490. Once you have these two numbers, you add them together, which gets you the total cost of $2058.

Hope this helped!

Snow fell at a rate of 3/4 an inch/hour. how much snow fell in a period of 6 hours

Answers

that implies a simple multiplication:
snow = (3/4)(6) = 4.5 inch
and note the units elimination in the operation as well:
= [inch/hour][hour] = inch

What the ratio of 72 to 126

Answers

1.75 is the answer because you divide 126 by 72 that is the answer if you do it the other way it comes out as 0.5754128 repeating

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