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kirill115 [55]
2 years ago
8

A retired math teacher takes his shopping. he tells nephew that they can spend x dollars and 14x=931 . What operation does the n

ephew need to use to find how much money they can​ spend?
Mathematics
1 answer:
navik [9.2K]2 years ago
8 0
The nephew would need to use division to isolate x giving him $66.50 to spend
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4x2+2x+4 I gotcha(:

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two positive numbers x and y, with the maximum value 4, add up to 5. what is the difference between the maximum and minimum valu
Svetach [21]

Answer:

  92

Step-by-step explanation:

Since the sum of the two numbers is 5, we can represent one of them by x and the other by 5-x. Then the desired product is ...

  x²(5-x)³

A graphing calculator can show the extreme values of this on the interval 1 ≤ x ≤ 4. The maximum is 108 at x=2; the minimum is 16 at x=4.

The difference between the maximum and minimum is 108-16 = 92.

_____

If you like, you can take the derivative and set it to zero.

  f(x) = x²(5 -x)³

  f'(x) = 2x(5 -x)³ +x²(-3)(5-x)² = x(5 -x)²(2(5-x) -3x)

  f'(x) = 5x(5-x)²(2-x)

This will be zero for x=0, x=5, and x=2. The points at x=0 and x=5 represent minima in the product. The values x=0 and x=5 are not in the domain of interest. The point at x=2 represents a maximum.

To find the function extremes on an interval, we need to evaluate the function where the derivative is zero, and also at the ends of the interval. So, the function values of interest are ...

  f(1) = 1²·4³ = 64

  f(2) = 2²·3³ = 108 . . . . product maximum

  f(4) = 4²·1³ = 16 . . . . . . product minimum

The difference between the maximum and minimum is 92.

5 0
3 years ago
What is the solution to the system of equations below? y= -4/5 x + and y = –30
Naya [18.7K]

Answer:

x=37.5

Step-by-step explanation:

We need to find the solution to the following system of equations:

y = -\frac{4}{5} x and y=-30

By plugging the value of 'y' into the first equation we have that:

-30 = -\frac{4}{5} x ⇒ 30=\frac{4}{5} x

Solving for 'x' we have:

x=37.5

So, the solution to the system of equation is: (37.5, -30)

8 0
3 years ago
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