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zloy xaker [14]
3 years ago
8

Community Gym charges a $50 membership fee and a $70 monthly fee. Workout Gym charges a $170 membership fee and a $60 monthly fe

e. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?

Mathematics
1 answer:
Greeley [361]3 years ago
3 0
The answer to the question is 12 months.

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HELP!!! PLEASE!!!!
Makovka662 [10]

Answer:

  • y = 2x² - 5x + 7

Step-by-step explanation:

For this problem, imagine the standard form, which is:

f(x) = ax² + bx + c = y

Using the table, and adding that y at the end, we can plug in and write out the following equations. (<em>Writing it out is important</em>):

f(-1) = a(-1)² + b(-1) + c = 14

f(0) = a(0)² + b(0) + c = 7

f(1) = a(1)² + b(1) + c = 4

f(2) = a(2)² + b(2) + c = 5

Now if this doesn't look familiar, it's actually a <u>systems of equations</u> using the a, b, and c elements as your three variables! If you simplify the equations:

f(-1) = a - b + c = 14

f(0) = c = 7

f(1) = a + b + c = 4

f(2) = 4a + 2b + c = 5

Something unique just happened. We have already defined what ' c ' is!

<u><em>c = 7</em></u>

Setting that aside, if you remove the f(x) portion of the equations, you're left with:

a - b + c = 14

a + b + c = 4

4a + 2b + c = 5

Using the two upper equations, if we add them together (you can do that as it doesn't change the values of the variables) you get:

2a + 2c = 18

Note: the ' b ' variables cancelled out in the addition [ b +  (-b) ]

If you further simplify the equation:

a + c = 9

Awesome. Now we already know that <u>c = 7</u>, so if you plug that into the equation:

a + 7 = 9

Solve for a. So then a = 2

Now that we know the following:

a = 2

c = 7

We can then use the equation:

a + b + c = 4

And solve for b!

2 + b + 7 = 4

Simplify.

b + 9 = 4

Simplify.

b = -5

Now at this point, since you know what a, b and c are, you can write the equation!

f(x) = 2x² - 5x + 7

You can confirm your work by putting any of the x values in the table through!

4 0
3 years ago
Read 2 more answers
Is the relation a function? Explain<br><br><br> Set-builder notation?<br><br><br> Domain/range?
saveliy_v [14]

Answer:

doamin = set builder nation

4 0
3 years ago
Read 2 more answers
Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her h
wolverine [178]

Answer:

 f = 0.84 or 84%

Step-by-step explanation:

Given:

- Original constant velocity of water v_o = 3.5 m/s

- The original diameter of the hose opening d_o = 1.5 cm

- The total vertical distance y(f) = 1.0 m

- The total range x(f) = 10.0 m

Find:

What fraction of the original area does Isabella has to reduce or pinch so the water can cover the entire range.

Solution:

- We will assume the flow of water as a stream of particles that follow a path of single point.

- Using second kinematic equation in the vertical direction and compute the time it takes the water to reach the ground:

                                  y(t) = y(0) + v_y*t + 0.5*gt^2

Where, y(0) = v_y = 0,

                                  1.0 = 0.5*g*t^2

                                  t = sqrt ( 2*1 / 9.81 )

                                  t = 0.4515 s

- Now we will use the second equation of motion for the x- direction motion:

                                 x(t) = x(0) + v_x*t

Where, x(0) = 0,

                                 10 = 0 + v_x*(0.4515)

                                 v_x = 10 / 0.4515 = 22.1 m/s

- We have calculated the minimum velocity required to reach the range from isabella and ferdinand.

- We will use the continuity equation to compute the area required for the velocity calculated v_x = 22.1 m/s:

                                A_f*v_x = A_o*v_o

                                A_f = A_o*v_o / v_x

                                A_f = pi*0.015^2*3.5 / 4*22.1

                                A_f = 1.12 * 10^-4 m^2

- The fraction f of the reduction of area is:

                                f = (A_o - A_f) / A_o

                                f = (7.068*10^-8 - 1.12*10^-4) / (7.068*10^-8)

                               f = 0.84 or 84%

4 0
2 years ago
Figures A and B at right are similar. Assuming that figure A is the original figure, find the scale factor and find the lengths
AnnZ [28]

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

<h3>How to find Scale Factor?</h3>

Scale factor = dimension of new figure / dimension of original figure

The polygons given are shown in the diagram attached below.

Figure A is the original figure

Figure B is the new figure.

x, y, and z has been used to mark the missing sides of figure B.

One dimension of original figure = 15

Corresponding dimension of the new figure = 3

Scale factor = new/original = 3/15

Scale factor = 1/5

To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:

x = 12 × 1/5 = 2.4

y = 18 × 1/5 = 3.6

z = 20 × 1/5 = 4

In summary:

The scale factor is: 1/5.

The missing sides of figure B are: 2.4, 3.6, and 4.

Learn more about scale factor on:

brainly.com/question/2826496

3 0
2 years ago
Zack is designing wheels for aconcept car. The diameter of the wheel is18 inches. Zack wants to make spokes inthe wheel that run
Ket [755]

Answer:

The spokes are 9 inches because the radius is half the diameter.

Comment if this is right.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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