ANOTHER MATH QUESTION PLEASE!!!!

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 classe

Juli2301 [7.4K]

Answer:

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

Part 2) see the explanation

Part 3) $\$68.76$

Part 4) $\$12\ per\ hour$

Part 5) The equation that can be used is $27x=242.73$ and the cost of one print is $\$8.99$

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

$y=mx+b$

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 $m=\$10\ per\ class$

The y-intercept is $b=\$100$

so

$y=10x+100$ ----> equation A

Non-Members

The slope is $m=\$15\ per\ class$

so

$y=15x$ ----> 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

$10x+100 < 15x$

Solve for x

subtract 10 x both sides

$100 < 15x-10x$

$100 < 5x$

Divide by 5 both sides

$20 < x$

Rewrite

$x > 20$

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

$8+3x=23$

solve for x

subtract 8 both sides

$3x=23-8$

$3x=15$

Divide by 3 both sides

$x=5$

Part 3) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

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 $m=\$0.42\ per\ mile$

The y-intercept is $b=\$36$

so

$y=0.42x+36$

For x=78 miles

substitute in the linear equation and solve for y

$y=0.42(78)+36$

$y=\$68.76$

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

$40x+10(1.5x)=660$

solve for x

$40x+15x=660$

$55x=660$

Divide by 55 both sides

$x=\$12\ per\ hour$

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

$27x=242.73$

solve for x

Divide by 27 both sides

$x=\$8.99$

Part 6) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

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 $m=\$7\ per\ class$

The y-intercept is $b=\$120$

so

$y=7x+120$ ----> equation A

Non-Members

The slope is $m=\$11\ per\ class$

so

$y=11x$ ----> 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

$7x+120 < 11x$

Solve for x

subtract 7x both sides

$120 < 11x-7x$

$120 < 4x$

Divide by 4 both sides

$30 < x$

Rewrite

$x > 30$

therefore

The number of classes must be greater than 30

4 0

4 years ago

A parabola can be drawn given a focus of (−6,−1) and a directrix of y=1. Write the equation of the parabola in any form.

kkurt [141]

Answer:

y = -(x + 6)²/4

Step-by-step explanation:

Since the equation of a parabola is given as the distance of a point to a given point(focus) being equal to the distance of the point fro a given line (directrix),

and our focus is at (-6,-1) and our directrix is y = 1, then by the distance equation, the distance from each point to the point (x, y) is

√[(x - x)² + (y - 1)²] = √[(x - (-6))² + (y - (-1))²]

√[0² + (y - 1)²] = √[(x + 6)² + (y + 1)²]

√(y² -2y + 1) = √[(x² + 12x + 36) + (y² + 2y + 1)]

squaring both sides, we have

y² - 2y + 1 = x² + 12x + 36 + y² + 2y + 1

collecting like terms, we have

y² - 2y - y² - 2y = x² + 12x + 36 + 1 - 1

simplifying, we have

- 4y = x² + 12x + 36

factorizing the expression in x, we have

-4y = (x + 6)²

y = -(x + 6)²/4

3 0

3 years ago

A square patio has an area of 168 square feet how long is each side of the patio to the nearest 0.05

omeli [17]

Answer:

12.96

Step-by-step explanation:

since it is a square, both sides are equal. to find the area of any square, it is the side squares. since you are given what the area is, simply square root 168.

which is about 12.96

8 0

3 years ago

Can someone answer this for me ill give brainliest asap

Valentin [98]

The answer is non linear

6 0

3 years ago

Can this be simplified?

liraira [26]

No Nothing Further Can Be Done

6 0

3 years ago

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