1) members at a yoga school pay $10 per class plus a one-time $100 membership fee. non-members pay$15 per class. how many classes would a member have to take to save money compared to taking classes as a non-member?

2) translate the statement into an equation. then solve the equation. the sum of 8 and 3 times a number is 23.

6) members at a yoga school pay $7 per class plus a one-time $120 membership fee. non-members pay $11 per class. how many classes would a member have to take to save money compared to taking classes as a non-member?

answer all questions , and if u can show u work,

3)a rental car costs $36 for one day plus an additional $0.42 per mile. what is the cost of renting a car for one day and driving it 78 miles?

4) alice earns 1.5 times her normal hourly rate for each hour she works after 40 hours in a week. she worked 50 hours this week and earned $660. what is her normal hourly rate?

5) cynthia orders 27 prints of a photograph she took. it costs her a total of $242.73. which equation can be used to find how much each print cost?

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3)

Part 4)

Part 5) The equation that can be used is  and the cost of one print is

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is

The y-intercept is

so

----> equation A

Non-Members

The slope is

so

----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

Solve for x

subtract 10 x both sides

Divide by 5 both sides

Rewrite

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

solve for x

subtract 8 both sides

Divide by 3 both sides

Part 3) we know that

The linear equation in slope intercept form is equal to

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is

The y-intercept is

so

For x=78 miles

substitute in the linear equation and solve for y

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

solve for x

Divide by 55 both sides

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

solve for x

Divide by 27 both sides

Part 6) we know that

The linear equation in slope intercept form is equal to

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is

The y-intercept is

so

----> equation A

Non-Members

The slope is

so

----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

Solve for x

subtract 7x both sides

Divide by 4 both sides

Rewrite

therefore

The number of classes must be greater than 30

its 4 because 2 times 2 is 4, if you double the number two you get four

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.