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Anastasy [175]
2 years ago
9

Given the function h(a) = -x^2+ 7x + 14, determine the average rate of change

Mathematics
1 answer:
Yakvenalex [24]2 years ago
6 0

Answer:

- 2

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [a, b ] is

\frac{f(b)-f(a)}{b-a}

Here [a, b ] = [1, 8 ], thus

f(b) = f(8) = - 8² + 7(8) + 14 = - 64 + 56 + 14 = 6

f(a) = f(1) = - 1² + 7(1) + 14 = - 1 + 7 + 14 = 20

average rate of change = \frac{6-20}{8-1} = \frac{-14}{7} = - 2

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How do humans interact with the geosphere? Explain
tresset_1 [31]

Answer:

there are many ways

Step-by-step explanation: we walk on the crust of our earth interact with rocks, and some glasses are made of molten lava. which is also from a specific layer of earth (sorry, dont remember which) and some people drill in the mines and maybe even get lower than the crust. i hope this helps :/

8 0
2 years ago
5. 3x + 5y + 5z =1<br> x - 2y = 5<br> 2x + 4y = 11
lilavasa [31]

Answer:

see explanation

Step-by-step explanation:

Given the 3 equations

3x + 5y + 5z = 1 → (1)

x - 2y = 5 → (2)

2x + 4y = 11 → (3)

Use (2) and (3) to solve for x and y

Multiply (2) by 2

2x - 4y = 10 → (4)

Add (3) and (4) term by term

4x = 21 ( divide both sides by 4 )

x = \frac{21}{4\\}

Substitute this value of x into (3)

2 × \frac{21}{4\\} + 4y = 11

\frac{21}{2\\} + 4y = 11 ( subtract \frac{21}{2\\} from both sides )

4y = \frac{1}{2} ( divide both sides by 4 )

y = \frac{1}{8\\}

Substitute the values of x and y into (1) and solve for z

3 × \frac{21}{4\\} + 5 × \frac{1}{8\\} + 5z = 1

\frac{63}{4} + \frac{5}{8} + 5z = 1

\frac{131}{8} + 5z = 1 ( subtract \frac{131}{8} from both sides )

5z = - \frac{123}{8} ( divide both sides by 5 )

z = - \frac{123}{40}

Solution is

x = \frac{21}{4\\}, y = \frac{1}{8\\}, z = - \frac{123}{40}

3 0
2 years ago
Which number line represents the solution to the inequality x - 3 &gt; 2
Ivahew [28]

Answer: x > 5

Step-by-step explanation: To solve for <em>x</em> in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.

Since 3 is being subtracted from x, we add 3 to

both sides of the inequality to get x > 5.

When graphing x > 5, we have an open circle on 5 and the

open circle tells us that 5 is not part of our answer.

Then we draw an arrow going to the right to represent

all possible solutions to this inequality, any number greater than 5.

6 0
3 years ago
If one letter is chosen at random from the word assists, what is the probability that the letter chosen will be an "s"?
OLEGan [10]

Answer:

4/7 or 57%

There are 7 letters in the word "assists" and 4 of them are "s"

4 divided by 7 will give you the percentage

7 0
3 years ago
Which of the following describes similarity in general
sweet [91]
Similarity is the comparison between two things in a fashion that shows what is similar or shared between those two things. Similar qualities, similar behaviors, etc are all categorized as a similarity comparison.
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3 years ago
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