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3 years ago

8) Which equation has a vertex of (−6, 3)? A) y = 2(x + 6)2 + 3 B) y = 2(x − 6)2 + 3 C) y = 2(x + 6)2 − 3 D) y = 2(x − 6)2 − 3

Mathematics

1 answer:

Allisa [31]3 years ago

4 0

Answer:

Step-by-step explanation:

hello :

y = 2(x + 6)2 + 3 .....(vertex form)

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(help!) Without graphing or solving either system of equations explain how you know what the solution to the system is.

Pavel [41]

Answer:

For A, both equations have the same slope, but different y-intercepts. This means that they are parallel, and will never cross, meaning there is no solution.

For B, it's the same equation, meaning that they are always crossing (it's the same line!), so there are infinite solutions.

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3 years ago

Angelique is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for t

marusya05 [52]

Answer:

A) both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.

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Answer:

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Step-by-step explanation:

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