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kenny6666 [7]
4 years ago
9

Hunter and Brian are creating a poster for a project and they need to combine two different size boards to create their project.

If the total area cannot exceed 7x to the second power -6x+2 square inches and one board Is 2x to the second power -9x+8 square inches, then what must be the maximum area of the second board?
Mathematics
2 answers:
Jet001 [13]4 years ago
8 0

Answer:

5x² + 3x - 6

Step-by-step explanation:

Data:

  • Total area: 7x² - 6x + 2
  • Area of one board: 2x² - 9x + 8
  • Area of the other board: f(x)

The addition of the area of the two boards cannot exceed the total area. Then:

f(x) + 2x² - 9x + 8 ≤ 7x² - 6x + 2

f(x) ≤ 7x² - 6x + 2 - 2x² + 9x - 8

f(x) ≤ (7x² - 2x²) + (-6x + 9x) + (2 - 8)

f(x) ≤ 5x² + 3x - 6 in square inches

shepuryov [24]4 years ago
7 0

Answer:

<em>The maximum area of the second board must be (5x^2+3x-6) square inches.</em>

Step-by-step explanation:

The total area of two different size boards cannot exceed (7x^2-6x+2) square inches.

The area of one board is  (2x^2-9x+8) square inches.

Suppose, the area of the second board is  y square inches.

That means......

y+(2x^2-9x+8)\leq 7x^2-6x+2\\ \\ y\leq (7x^2-6x+2)-(2x^2-9x+8)\\ \\y \leq 7x^2-6x+2-2x^2+9x-8\\ \\ y\leq 5x^2+3x-6

So, the maximum area of the second board must be (5x^2+3x-6) square inches.

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Answer:

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Step-by-step explanation:

The minimum point on the graph is also the <u>vertex</u>.

The quadratic function equation is given in <u>vertex form</u>, which is f(x) = a(x - h)^{2} + k

Using this equation, the vertex is (-h, k).

Whatever number you see for "h", find its opposite negative/positive. That will be the x-coordinate of the vertex. The y-coordinate for the vertex is the same as "k", keeping the negative and positive.

In f(x) = (x - 1)² - 3 using (-h, k) is:

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