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lukranit [14]
3 years ago
6

Determine the points of intersection of the line y = -2x + 7 and the parabola y = 2x2 + 3x - 5.

Mathematics
1 answer:
Nata [24]3 years ago
8 0

Answer:


Step-by-step explanation:

The x-values of those points can be found by equating the expressions for y, then solving for x.

... -2x +7 = 2x² +3x -5

... 2x² +5x -12 = 0 . . . . . . . . subtract the left side to put into standard form

This can be factored by looking fro two factors of 2·(-12) = -24 that add to give 5, the x-coefficient. Those factors are 8, -3.

... 2x² +8x -3x -12 = 0 . . . . rewrite the middle term

... 2x(x +4) -3(x +4) = 0 . . . factor by pairs

... (x +4)(2x -3) = 0 . . . . . . . complete factorization

... x = -4, x = 3/2 . . . . . . . . values of x that make the factors be zero

The corresponding y-values are ...

... for x = -4, y = -2(-4) +7 = 15

... for x = 3/2, y = -2(3/2) +7 = 4

The points of intersection are (-4, 15) and (3/2, 4).

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Find the measurement of both complementary angles, if:
aniked [119]

We are given one angle is 3 times less than other.

Let us assume one angle measure is x degrees and another is 4x.

Because x is 3x less than 4x.            ( We can check 4x-x= 3x)

Sum of complementary angles is 90 degrees.

So, we can setup an equation

First angle measure + first angle = 90 degrees.

x+4x = 90.

Adding x and 4x, we get 5x.

So, 5x = 90.

Dividing both sides by 5, we get

5x/5 = 90.

x= 18.

So, one angle is of 18 degrees.

Another angle = 4x = 4 times 18 = 72 degrees.

So, required angles are of 18 degree and 72 degree.



8 0
3 years ago
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Irina-Kira [14]

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8/7x^3 + x^4 + 6x +1

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The answer is B.

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