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3 years ago

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A university has raised $8,000 for a new scholarship fund. A university trustee offers to match the donation up to 60% if the un

iversity can raise $1,500 more for the fund. If the university is able to raise the extra amount, how much money will be in the fund after the trustee's donation?

2 answers:

inysia [295]3 years ago

7 0

$8,000 + $1,500 = 9,500

So 9,500 x .6 = 5,700 dollars donated by trustee.

$9,500 + $5,700 = $15,200 dollars tota

kherson [118]3 years ago

6 0

Answer:

15200

Step-by-step explanation:

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2p=kx-t how do you solve for x

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Isolate x on one side of the equation. divide by k.
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3 years ago

A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum val

Taya2010 [7]

Answer:

The local maximum and minimum values are:

Local maximum

$g(0) = 0$

Local minima

$g(5.118) = -350.90$

$g(-1.368) = -9.90$

Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

$g(x) = x^{2}\cdot (x^{2}-5\cdot x -14)$

Then, first and second derivatives of the function are, respectively:

First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

$g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}$

$g'(x) = 4\cdot x^{3}-15\cdot x^{2}-28\cdot x$

$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:

$x\cdot (x-5.118)\cdot (x+1.368) = 0$

The critical points are 0, 5.118 and -1.368.

Each critical point is evaluated at the second derivative expression:

x = 0

$g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28$

$g''(0) = -28$

This value leads to a local maximum.

x = 5.118

$g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28$

$g''(5.118) = 132.787$

This value leads to a local minimum.

x = -1.368

$g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28$

$g''(-1.368) = 35.497$

This value leads to a local minimum.

Therefore, the local maximum and minimum values are:

Local maximum

$g(0) = (0)^{4}-5\cdot (0)^{3}-14\cdot (0)^{2}$

$g(0) = 0$

Local minima

$g(5.118) = (5.118)^{4}-5\cdot (5.118)^{3}-14\cdot (5.118)^{2}$

$g(5.118) = -350.90$

$g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}$

$g(-1.368) = -9.90$

7 0

3 years ago

Bill’s car gets 30 miles to the gallon. For every gallon of gas it consumes, his car runs 30 miles. Use this information to dete

pshichka [43]

this relation is a function, y=30x

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3 years ago

Which expression is equivalent to 36 ÷ 4? 4 ÷ 36 36 ÷ x 36 x

denis23 [38]

Answer:

36 x 1/4

Step-by-step explanation:

divide sign can be written in the form 1/x. so by the above equation it means that 36 ÷ 4 = 36 x 1/4

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3 years ago

To make coffee for 4 people, Mrs. Smith needs 1 cup of milk. How many cups of milk does she need to make coffee for 10 people?

disa [49]

Use the proportion, 4/1 = 10/x

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2 years ago

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