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igomit [66]
3 years ago
14

The function f(x) = –x2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is th

e number of windshields repaired, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Mathematics
1 answer:
Fynjy0 [20]3 years ago
4 0
The function is: f ( x ) = - x² + 60 x - 116 is in the form: f ( x ) = a x² + b x + c
Part A:
x = -b / 2 a = - 60 / ( - 2 ) = 30
Then we will charge it into the function:
f ( 30 ) = - 30² + 60 · 30 - 116 = - 900 +1,800 - 116 = 784
The vertex is ( 30, 784 ).
It means that the maximum profit is $784, when 30 windshields are repaired.
Part B:
x 1/2 = ( -60 +/- √(3600 - 464 )/ (- 2 ) = ( -60 +/- 56 ) / ( - 2 )
x 1 = 2, x 2 = 58
It means that a shop has to repair at least 2 windshields and not more than 58 windshields for making a profit.
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Maria just got a raise at work. She was making $9 per hour, but now she makes 150% of that amount.
Stolb23 [73]

Answer:

13.50

Step-by-step explanation:

150. x

___ ___ x = $13.50 per hour

100. 9

5 0
3 years ago
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7(2x-5)=21<br><br> What is x?
Over [174]

Answer:

x = 4

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define Equation</u>

7(2x - 5) = 21

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute 7:                   2x - 5 = 3
  2. Isolate <em>x</em> term:                2x = 8
  3. Isolate <em>x</em>:                         x = 4

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                  7(2(4) - 5) = 21
  2. Multiply:                             7(8 - 5) = 21
  3. Subtract:                            7(3) = 21
  4. Multiply:                             21 = 21

Here we see that 21 does indeed equal 21.

∴ x = 4 is the solution to the equation.

6 0
2 years ago
PLEASE HELP!!!
Paladinen [302]

Answer:

d (w) = 0.1w² – w+ 5

Step-by-step explanation:

d(w) = c(w) - a(w)

= -0.3w²+2w+13 -(-0.4w²+3w+8)

= -0.3w²+0.4w²+2w-3w+13-8

= 0.1w²-w+5

4 0
3 years ago
Find the 6th term of a geometric sequence with t1=5 and r = -1/2
Hoochie [10]
In this item, we are to calculated for the 6th term of the geometric sequence given the initial value and the common ratio. This can be calculated through the equation,
   
                 An = (A₀)(r)ⁿ ⁻ ¹ 
where An is the nth term, A₀ is the first term (in this item is referred to as t₀), r is the common ratio, and n is the number of terms. 

Substitute the known values to the equation,

                   An = (5)(-1/2)⁶ ⁻ ¹
                   An = -5/32

Hence, the answer to this item is the third choice, -5/32. 
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3 years ago
A space vehicle deploys its re-entry parachute when it's traveling at a vertical velocity of -150 meters/second (negative becaus
Arlecino [84]
The initial velocity is -150m/s.
Remember that:
V(t) = Vi + at, where v(t) is velocity at time t, Vi is initial velocity, and a is acceleration.
We know that the vehicle stopped after 30 seconds, so V(30) = 0.
Let's plug the useful info into our function and solve for a:
0 = -150 + a*30     Add 150 to both sides
150 = 30a             Divide both sides by 30
a = 5 m/s²
The average acceleration is 5 meters per second squared. 
8 0
3 years ago
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