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MrMuchimi
3 years ago
5

Gym membership costs $100 per year in a $2 fee per visit another gem charges $12 fee per visit with no yearly membership find th

e number of visits for which the charges for both gyms will be
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
3 0

Answer:

<em>For 10 visits, both gyms charge the same</em>

Step-by-step explanation:

<u>Equations</u>

Gym memberships' costs are:

G1 = 100 + 2x

G2 = 12x

Where x is the number of visits to the gym.

We need to find the number of visits for which the charges for both gyms are the same. Thus equating the costs:

12x = 100 + 2x

Subtracting 2x:

10x = 100

Dividing by 10:

x =10

For 10 visits, both gyms charge the same

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Y - 1  =  4y - 2/3.      Move the ys over to one side,  +4y crosses over to become -4y,
                                  and -1 crosses over the right side to become +1.
y -4y  = -2/3  + 1
-3y  =    1 - 2/3
-3y =  1/3          Divide both sides by -3.

-3y/-3  = (1/3) / -3.
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y =  - 1/9

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Step-by-step explanation:

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A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)
LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

  • You must have 3 points lie on the parabola
  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
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∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

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Then divide -1 on both sides.

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I'm pretty sure when you divide a negative number when solving inequalities, you switch the sign.

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Answer:

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