Solve the following:(2 points)

Question

ax+15=44
ax−44<15

Answer 1

1) For the equation ax + 15 = 44, we can solve for x by subtracting 15 from both sides and then dividing both sides by a:

ax + 15 - 15 = 44 - 15
ax = 29
x = 29/a

2) For the inequality ax - 44 < 15, we can solve for x by adding 44 to both sides and then dividing both sides by a:

ax - 44 + 44 < 15 + 44
ax < 59
x < 59/a

Answer 2

Write the ratio that compares 36 social media posts to 16 social media posts using fractional notation. Simplify the improper fraction to lowest terms.(1 point)

Answer 3

The ratio that compares 36 social media posts to 16 social media posts can be written as:

36/16

To simplify this improper fraction to its lowest terms, we can find the greatest common divisor (GCD) of 36 and 16, which is 4. Dividing both the numerator and denominator by 4, we get:

36/16 = 9/4

Therefore, the simplified ratio is 9/4.

Answer 4

Write the ratio 12:36 as an equivalent ratio of x:3.(1 point)

Answer 5

To find an equivalent ratio for 12:36 in the form of x:3, we need to find a value for x that can be multiplied by 3 to get 36.

We can do this by dividing both 12 and 36 by their greatest common divisor (GCD). The GCD of 12 and 36 is 12.

12 ÷ 12 = 1
36 ÷ 12 = 3

So, an equivalent ratio for 12:36 in the form of x:3 is 1:3.

Answer 6

How do you write 4 is to 16 as 12 is to 48 as a proportion in fractional notation? Do not simplify your answer.(1 point)

Answer 7

To write the proportion "4 is to 16 as 12 is to 48" in fractional notation, we express each ratio as a fraction:

4/16 = 12/48

Answer 8

A company pays their employees $20 per hour. Using fractional notation, write a proportion that represents how long an employee must work to make $80. Use x to represent the unknown number of hours.(1 point)

Answer 9

The proportion that represents how long an employee must work to make $80 can be written as:

$20/x = $80/1

This can be simplified to:

20/x = 80/1

Therefore, the proportion in fractional notation is 20/x = 80/1.

Answer 10

Describe three ways to write the ratio that compares 4 electronic devices for every 3 people.(1 point)

Answer 11

1) The ratio that compares 4 electronic devices for every 3 people can be written as 4:3. This is the most common way to express a ratio.

2) The ratio can also be written as a fraction. In this case, it would be 4/3.

3) Another way to represent the ratio is using words. It can be described as "4 electronic devices for every 3 people."

Answer 12

How do you write 5 is to 1 as 20 is to 4 as a proportion in fractional notation?(1 point)
Responses

Answer 13

To write the proportion "5 is to 1 as 20 is to 4" in fractional notation, we express each ratio as a fraction:

5/1 = 20/4

Therefore, the proportion in fractional notation is 5/1 = 20/4.

Answer 14

You fill your car with 15 gallons of gas at a cost of $45. Using fractional notation, how do you write a proportion that shows how much 5 gallons of gas will cost? Use x to represent the unknown cost.(1 point)

Answer 15

To write a proportion that shows how much 5 gallons of gas will cost, we can use the given information: 15 gallons of gas cost $45.

We can set up the proportion as follows:

15 gallons / $45 = 5 gallons / x dollars

In fractional notation, this proportion would be:

15/45 = 5/x

Therefore, the proportion in fractional notation is 15/45 = 5/x.