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miskamm [114]
3 years ago
11

Please help! Final grade of my semester!

Mathematics
1 answer:
Irina-Kira [14]3 years ago
5 0

Answer:

12 visits is the BREAK EVEN POINT of two fitness plans.

Step-by-step explanation:

BREAK EVEN: A point is said to be break even in which, there is NO GAIN and NO LOSS.

Let us assume after m visits, he break even point is achieved.

Now, here at Fitness plan 1:

The charge per visit = $ 4

So, the total charge for m visit  = m x ( Cost per visit) = m ( $4)  = 4 m

So, Fitness plan 1 costs (4 m) for m visits.

Now, here at Fitness plan 2:

The charge per visit = $ 2

Member ship fee = $24

So,  charge for m visit  = m x ( Cost per visit) = m ( $2)  = 2 m

Now,the total = Member ship fee + Fees for m visit  = $24 +  2 m

So, Fitness plan 2 costs (24 + 2 m) for m visits.

Now, for break even, For m visits, BOTH PLAN COSTS SAME:

⇒4  m = 24  +  2 m

or, 2 m = 24

or, m= 24/2  = 12

or, m = 12

or, after 12 visits, the both Plan will cost same amount,

Hence, 12 visits is the BREAK EVEN POINT of two fitness plans.

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3 years ago
The table includes points on a quadratic function used to model the shape of a hole for one support beam at a new building site.
erastovalidia [21]

The hole is 8 feet deep at ground level ⇒ 3rd answer

Step-by-step explanation:

The form of the quadratic function is y = ax² + bx + c, where

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the y-intercept (at x = 0)

The vertex point of the quadratic is (h , k), where h=\frac{-b}{2a}

and k is the value of y when x = h

The table:

→  x  :  -2   ,  0  ,  2

→  y  :  -6   , -8  ,  -6

∵ x represents distance from hole's center in feet

∵ y represents the depth from level ground

∴ The quadratic function is y = ax² + bx + c

∵ c is the value of y at x = 0 ⇒ y-intercept

- From the table at x = 0 ⇒ y = -8

∴ c = -8

- Substitute its value in the function model

∴ y = ax² + bx - 8

- To find the values of a and b substitute x and y in the model by

   the coordinates of the point in the table

∵ x = -2 and y = -6

∴ -6 = a(-2)² + b(-2) - 8

∴ -6 = 4a - 2b - 8

- Add 8 to both sides

∴ 2 = 4a - 2b

- Switch the two sides

∴ 4a - 2b = 2 ⇒ (1)

∵ x = 2 and y = -6

∴ -6 = a(2)² + b(2) - 8

∴ -6 = 4a + 2b - 8

- Add 8 to both sides

∴ 2 = 4a + 2b

- Switch the two sides

∴ 4a + 2b = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equations(1) and (2) to eliminate b

∵ 8a = 4

- Divide both sides by 8

∴ a = 0.5

- Substitute value of a in equation (1) or to to find b

∵ 4(0.5) + 2b = 2

∴ 2 + 2b = 2

- Subtract 2 from both sides

∴ 2b = 0

- Divide both sides by 2

∴ b = 0

Substitute the values of a and b in the function model

∴ y = 0.5x² + (0)x - 8

∴ y = 0.5x² - 8

∵ y represents the depth from level ground

∵ The vertex of the function model is (h , k)

∴ The deep of the hole at ground level is the value of k

∵ h=\frac{-b}{2a}

∴ h=\frac{-(0)}{2(0.5)}

∴ h = 0

∵ k is the value of y when x = h

- From the table at x = 0 ⇒ y = -8

∴ k = -8

- Ignore the sign (-) because the k represents the depth of the

  hole in feet

∴ The deep of the hole at ground level is 8 feet

The hole is 8 feet deep at ground level

Learn more:

You can learn more about the quadratic function in brainly.com/question/1332667

#LearnwithBrainly

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There's no need to get into an ethical morass over math homework.


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When we know <em>a, </em>the average, and <em>n, </em>how many numbers there are, we know the sum <em>s</em>, because <em>a=s/n </em>so <em>s=na.</em>


So the sum of our six numbers is 6(3.5)=21 so the sum of the seven numbers is 21+4.2=25.2 so the average is 25.2/7 = 3.6


Answer: 3.6


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Answer: -3



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3 years ago
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Set the proportions up and solve for b

b. 3

---- = ------

10. 5

3 0
3 years ago
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