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3 years ago

Hi. Please I need help with these questions.

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

3 0

9514 1404 393

Answer:

8. 4 +2q²/p² -4r/p +r²/p²

9. (x, y) = (3/4, -17/8)

Step-by-step explanation:

All of these questions are asking you to make use of the fact that ...

α + β = -q/p

αβ = r/p

8. (2 +α²)(2 +β²) = 4 + 2(α² +β²) +α²β²

= 4 +2((α+β)² -2αβ) +(αβ)²

Substituting the above for the sum and product, you have ...

= 4 + 2((-q/p)² -2(r/p)) +(r/p)²

= 4 +2q²/p² -4r/p +r²/p²

9. This is asking for the vertex of the parabola. The x-coordinate is ...

x=-b/(2a) = -(-3)/(2(2) = 3/4

Then the y-coordinate is ...

y = (2(3/4) -3)(3/4) -1 = (-3/2)(3/4) -1 = -9/8 -1 = -17/8

The (x, y) values of interest are (3/4, -17/8).

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Solve the equation <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B8%7Dx%20-%2017%20%3D%2010" id="TexFormula1" titl

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x = 72

Step-by-step explanation:

To solve for 'x', isolate it. This means to keep 'x' on one side of the equal sign, while moving the other numbers to the other side. The numbers on the other side will tell you what 'x' equals to.

When 'moving' a number to the other side, you cancel it out where it originally is by doing reverse operations. (Reverse operation pairs are addition/subtraction and division/multiplication). To keep an equation balanced, what you do to one side you have to do to the other.

$\frac{3}{8}x-17=10$ Keep 'x' on the left and move everything over.