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3 years ago

5 more than 3 times a variable, x, is 23

Mathematics

1 answer:

Monica [59]3 years ago

5 0

3x + 5 = 23

5 more than(addition) 3 times(multiplication) a variable(x) is(equals) 23

(you add 5 to 3x)

If you need to solve for "x", you need to isolate/get the variable "x" by itself in the equation:

3x + 5 = 23 Subtract 5 on both sides

3x + 5 - 5 = 23 - 5

3x = 18 Divide 3 on both sides to get "x" by itself

$\frac{3x}{3} =\frac{18}{3}$

x = 6

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Step-by-step explanation:

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3 years ago

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Answer:

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3 years ago

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A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the

d1i1m1o1n [39]

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

$Trees = 24$

$Yield = 104$

$x \to additional\ trees$

So, we have:

$Trees = 24 + x$

$Yield = 104 - 2x$

Required

The additional trees to be planted for maximum yield

The function is:

$f(x) = Trees * Yield$

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Open bracket

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$f(x) = 2796 + 56x - 2x^2$

Rewrite as:

$f(x) = - 2x^2 + 56x + 2796$

Differentiate

$f'(x) = -4x + 56$

Equate $f'(x) = -4x + 56$ to 0 and solve for x to get the maximum of x

$-4x + 56 = 0$

$-4x =- 56$

Divide by -4

$x =14$

The farmer should plant 14 additional trees, for maximum yield.

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