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grin007 [14]
3 years ago
9

Which scenario best matches the linear relationship expressed in the equation y = 32x + 80?

Mathematics
2 answers:
Llana [10]3 years ago
5 0
He has 80 in the bank account and earns 32 each day....where x represents the number of days and y represents the total in the account
FrozenT [24]3 years ago
4 0

Answer:

Option (2) best matches the given the linear relationship y = 32x + 80

Step-by-step explanation:

Given linear relationship as  y = 32x + 80

We have to find the best match from the given options to the given the linear relationship.

1) Joseph has $80 in his bank account and spends $32 each day.

Let the money Joseph spend each day be $x

Since, the amount one spend gets deducted from the money one have.

So, given statement is represented as y = 80 - 32x .

2) Joseph has $80 in his bank account and earns $32 each day.

Let the money Joseph earns each day be $x

Since, the amount one earns gets added to the money one have.

So, given statement is represented as y = 80 + 32x .

3) Joseph had $32 in his bank account and deposited another $80.

Since, he is depositing money in account so it gets add up

So, given statement is represented as  y = 32 + 80 = 112

4) Joseph has $32 in his bank account and earns $80 each day.

Let the money Joseph earns each day be $x

Since, the amount one earns gets added to the money one have.

So, given statement is represented as y = 32 + 80x .

Out of all four option, option (2) best matches the given the linear relationship y = 32x + 80

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Using linear and composite functions, it is found that the x-intercept of g(h(x)) is x = -\frac{5}{6}, given by option B.

-------------------------------

The equation of a line is:

y = mx + b

In which:

  • m is the slope.
  • b is the y-intercept.

Function g:

  • Two of the points are (-6,16) and (-4,10).
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m = \frac{10 - 16}{-4 - (-6)} = -3

Thus:

g(x) = -3x + b

Point (-4,10) means that when x = -4, g(x) = 10, and we use this to find b, so:

10 = -3(-4) + b

12 + b = 10

b = -2

Then

g(x) = -3x - 2

Function h:

  • Two of the points are (-6,-11) and (-4,-7).
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m = \frac{-7 - (-11)}{-4 - (-6)} = \frac{4}{2} = 2

Thus:

h(x) = 2x + b

Point (-4,-7) means that when x = -4, h(x) = -7, and we use this to find b, so:

-7 = 2(-4) + b

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b = 1

Then

h(x) = 2x + 1

The composite function is:

g(h(x)) = g(2x + 1) = -3(2x + 1) - 2 = -6x - 3 - 2 = -6x - 5

The x-intercept it the zero of the function, thus:

-6x - 5 = 0

6x = -5

x = -\frac{5}{6}

Which is option B.

A similar problem is given at brainly.com/question/21010520

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