The local fitness center is running two different monthly payment options to attract new customers. The options are shown below.

What is the rate of change for the plans and at what number of visits would the plans cost the same amount?

Answer:

925.04cm²

Step-by-step explanation:  

Curved surface area of a cylinder = 2πrh

If the sum of the radius of the base and height of the cylinder is 21 cm, then;

r + h = 21

r = 21-h..... 1

The curved surface area is expressed according to the formula

CSA =  2πrh

Substitute the value of CSA given into the formula

616 = 2πrh ....2

Substitute equation 1 into 2;

]616 = 2π(21-h)h

616 = 2π(21h-h²)

Note that π = 3.14

616 = 42(3.14)h - 2(3.14)h²

616 = 131.88h - 6.28h²

98.09 = 21h - h²

h²-21h+98.09 = 0

h = 21±√21²-4(98.09)/2

h = 21±√441-392.36/2

h = 21±√48.64/2

h = 21±6/97/2

h = 21+6.97/2 and 21-6.97/2

h = 27.97/2 and 14.03/2

h = 13.985 and 7.015

Recall that r = 21-h

r = 21 - 13.985

Substitute r = 7.015  into the total surface area of the cylinder

The total surface area = 2πrh + 2πr²

The total surface area = 616 + 2(3.14)7.015²

The total surface area = 616 + 309.04

The total surface area = 925.04

Hence the total surface area of the cylinder is 925.04cm²

Answer: Yes

Step-by-step explanation: The answer of 1400 is correct.

What I did is I found the area of the figure assuming it was a rectangle, then I subtracted the corners that were removed.

1800 - 150 - 100 - 150 = 1400

Answer:

Yup Its Correct

Step-by-step explanation:

The Calculated Area Al adds up to 1400

Answer:

D. 8x³ + 4x⁷ - 3x³ + 3x² - 2x + 9

Step-by-step explanation:

(8x⁸ - 9x³ + 3x² + 9) + (4x⁷ + 6x³ - 2x)

Apply distributive property to eliminate parentheses

8x⁸ - 9x³ + 3x² + 9 + 4x⁷ + 6x³ - 2x

Collect like terms

8x⁸ + 4x⁷ - 9x³ + 6x³ + 3x² - 2x + 9

8x³ + 4x⁷ - 3x³ + 3x² - 2x + 9

Answer: -0.25 and 5

Step-by-step explanation:

Khan

Answer:

(5,-1)

x=5

y= -1

Step-by-step explanation:

To solve this we're going to solve for one variable in either equation

so we have

x+y=4

We can subtract y and 4 from both sides to get

x-4= -y

Then divide by -1 so that y will be a positive number

-x+4=y

We can plug this in for y in the other equation

2x -2(-x+4)=12

Distribute the -2 and get

2x+2x-8=12

Combine like terms and add 8 to get

4x=20

divide and get x=5

Plug in x=5 into the first equation to get

5+y=4

subtract 5 to get y= -1

Our answer is (5,-1) or x=5 y= -1

I checked this on desmos and the math is correct

Answer:

The solution to the system of equations will be:

x = 5, y = -1

Step-by-step explanation:

Given the system of equations

x + y = 4

2x - 2y = 12

Isolate x for x + y = 4:    x = 4 - y

substitute x = 4 - y in the equation 2x - 2y = 12

2(4-y) - 2y = 12

8 - 2y - 2y = 12

8 - 4y = 12

4y = 8 - 12

4y = -4

divide both sides by 4

4y/4 = -4/4

y = -1

substitute y = -1 in x + y = 4

x + y = 4

x + (-1) = 4

x - 1 = 4

x = 5

so

(x, y) = (5, -1)

Therefore, the solution to the system of equations will be:

x = 5, y = -1

Answer:

$125

Step-by-step explanation:

To solve this, we need to find 2.5% of 5,000. To do this, we multiply 5,000 by .025. This gets us 125. That means you earn $125 worth of interest in one year.

Answer:

 = 2

Step-by-step explanation:

3  +  6  =  1 2

subtract 6 from both sides of the equation

3  +  6  −  6  =  1 2  −  6

3  =  1 2  −  6

3y/3 = 6/3

y = 6/3

y = 2

i'm taking the same thing :)

Answer:

6

Step-by-step explanation:

there are six outcomes:

waffle cone apricot

waffle cone chocolate

waffle cone blackberry

sundae apricot

sundae chocolate

sundae blackberry

Answer:

Step-by-step explanation:

1) slope = 3 ; y-intercept = 1

y = mx + b

y = 3x + 1

0 = 3x + 1 -y

-1 = 3x - y

ANS: 3x - y = -1

2)   Passing through (0,2), slope = -4

y - y₁ = m(x -x₁)

y - 2 = -4(x - 0)

y - 2 = -4x

4x + y - 2 = 0

Ans: 4x + y = 2

3)Passing through (-1,3) and (1,1)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]= \frac{1-3}{1-[-1]}\\\\= \frac{-2}{1+1}\\\\= \frac{-2}{2}\\\\= - 1[/tex]

m= -1 ; (-1 , 3)

y - y₁ = m(x -x₁)

y - 3 = (-1)(x - [-1] )

y -3 = (-1)(x +1 )

y - 3 = -x - 1

x +  y -3 = -1

x +y = -1 + 3

Ans: x + y = 2

4) Passing through (1,3), slope = 1/2

y - y₁ = m(x -x₁)

[tex]y - 3 = \frac{1}{2}(x - 1)\\\\y - 3 = \frac{1}{2}x - \frac{1}{2}\\\\[/tex]

Multiply the equation by 2

[tex]2*y - 2*3 = 2*\frac{1}{2}x - 2*\frac{1}{2}\\\\2y - 6 = x - 1\\[/tex]

2y - 6 +1 = x

2y - 5 = x

    -5 = x - 2y

Ans: x - 2y = -5

5)  Passing through (1/2,1) and (4,2)

Slope = [tex]\frac{2-1}{4-\frac{1}{2}}[/tex]

         [tex]= \frac{1}{\frac{7}{2}}\\\\= \frac{2}{7}[/tex]

m = 2/7 ; (4 , 2)

y - y₁ = m(x -x₁)

[tex]y - 2 = \frac{2}{7}(x - 4)\\\\7y - 7*2 = 7*\frac{2}{7}(x - 4)\\\\7y - 14 = 2(x -4)\\\\7y - 14 = 2x - 8\\\\[/tex]

7y - 14 + 8 = 2x

7y - 6 = 2x

Ans:  2x - 7y = -6

Answer:

Let's go step-by-step ⇒

[tex]\frac{10x + 4}{7} = 8[/tex]

= [tex](\frac{7}{1})\frac{10x+4}{7} = \frac{8}{1}(\frac{7}{1})[/tex]

= [tex]10x+4=56[/tex]

= [tex]10x = 52[/tex]

= [tex]x = 5.2[/tex]

Your answer is x = 5.2

I hope this helps!

- sincerelynini

Answer:

y=1.125×8 or y=1.125×24

Answer:

Step-by-step explanation:

Hahahhhh Lol

Answer:

66 and 52?

Step-by-step explanation:

Answer:

The first number line is correct.

Step-by-step explanation:

To find the number which best represents Eva's stock, we look into the text, and find the changes:

Monday: Stock bought at $42.

Tuesday: Change of -$15, so now it is worth $42 - $15 = $27

Wednesday: Change of +$15, so now it is worth $27 + $15 = $42

The number line which represents the decrease, and then the increase, is the first one.

Answer:

it would cost £15

Step-by-step explanation:

12 ÷ 4 = 3

3 × 5 = 15

Answer: 900 times

Step-by-step explanation:

1 kilometer = 1000 meters

1.8 kilometers = 1000 × 1.8

1.8 kilometers = 1800 meters

2 meters = 1 click

1800 meters = 1800 ÷ 2

1800 meters = 900 clicks

The wheel will click 900 times when Ty walks 1.8 kilometers.

Hope this helped!

Answer:

It will click 900 times

Step-by-step explanation:

We know that there are 1000 meter in 1 km.

So 1.8 km is basically

1.8*1000=1800

So 1800 meters

And every 2 meters it clicks once

So 1800/2=900

So 900 times in 1.8 km

Answer:

[tex]z = x + y \\ \huge \boxed{x = z - y}[/tex]

Answer:

4x+20

Step-by-step explanation:

Using the distributive property you multiply the terms outside by the terms inside. So the expression will be like this

4(x)+4(5)

When simplified the answer is

4x+20

Answer:

Step-by-step explanation:

Here you go mate

Step 1

4(x + 5)  equation

Step 2

4(x + 5)  simplify the expression

(x+5)4

(x+5)(4)

answer

20+4x

Answer:

r = 16.5

Step-by-step explanation:

Move the subtraction over to the over side first

0.1r - 1 = 0.65

It becomes addition on the right side

0.1r = 0.65 + 1

Move the multiplication over to the over side first

0.1r = 1.65

It becomes division on the right side

r = 1.65 / 0.1

r = 16.5

Answer:0.1r-1=0.65  (85% sure this is the answer

Answer:

20

Step-by-step explanation:

Answer:

LM = 20

Step-by-step explanation:

To find LM we have. to subtract MN from LN

So 23 - 3 = 20

Answer:

D. [tex] x = \frac{5*\sqrt{2}}{2} [/tex]

Step-by-step explanation:

Reference angle = 45°

Length of Opposite side = x

Hypotenuse length = 5

Applying trigonometric ratio, we have:

[tex] sin(45) = \frac{x}{5} [/tex]

Multiply both sides by 5

[tex] 5*sin(45) = \frac{x}{5}*5 [/tex]

[tex] 5*sin(45) = x [/tex]

[tex] 5*\frac{1}{\sqrt{2}} = x [/tex] (sin 45 = 1/√2)

[tex] \frac{5}{\sqrt{2}} = x [/tex]

Rationalize

[tex] \frac{5*\sqrt{2}}{\sqrt{2}*\sqrt{2}} = x [/tex]

[tex] x = \frac{5*\sqrt{2}}{2} [/tex]

Answer:

Let x be the discounting price of a surfing lessons per person

Let y be the discounted price of a surfing lessons per person

The cost of taking a surfing lesson and go parasailing is $130

x + y = 130--------------(i)

25 people take

Surfing lessons, and 30 people go parasailing and a total of $3,650 is collected

25x + 30y = 3650--------------(ii)

We solve for y using equ (i):

y = 130 - x ------------(iii)

Substitute equ (iii) to equ (ii) and solve for x

25x + 30(130 - x) = 3650

25x + 390 - 30x = 3650

-5x = -250

-x = 50

We solve for y using equ (iii):

y = 130 - x

y = 130 - 50

y = 80

So, the discounted price to take a surfing lesson is $50 and the discounted price to go parasailing is $80

Answer:

-189

Step-by-step explanation:

[tex]\int^9_0 \ |6x-6| \ dx[/tex]

⇒ 6x - 6 = 0

6x = 6

x = 1

[tex]\int^9_0 \ (6x- 6 ) \ dx = \int^9_0 \ -(6x - 6) \ dx[/tex]

[tex]= - \Big[ \dfrac{6x^2}{2}- 6x \Big]^9_0[/tex]

[tex]= - \Big[ \dfrac{6(9)^2}{2}- 6(9) - 0 \Big][/tex]

[tex]= -(243 - 54 - 0 )[/tex]

= -189