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gladu [14]
3 years ago
11

Find the points of Intersection of these graphs

Mathematics
1 answer:
geniusboy [140]3 years ago
8 0

Answer:

the line crosses the parabola at (-2,4) and (3,9)

Step-by-step explanation:

y=x^2

y=x+6

set them equal to each other

x^2=x+6, now set it equal to zero

x^2-x-6=0, now find the root

(x+2)(x-3)=0, the x=-2, and x=3; now substitute into any of the equation to find the points where graphs intercept

at x= -2, y=(-2)^2=4, so one point is (-2,4)

at x=3, y=(3)^2=9, so other point is (3,9)

the line crosses the parabola at (-2,4) and (3,9)

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In one day, a book store earned $199 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. On the
Marina86 [1]

Answer:

The cookbook costs $36 per copy while the science fiction costs $11 per copy

Step-by-step explanation:

Here in this question, we are interested in calculating the price of the cookbook and the price of the science fiction novel.

Since we do not know the price of each, we start by assigning variables to stand in for these unknown prices.

Let the price of the cookbook be $x , while the price of the science fiction be $y

Now, on the first day, 4 copies of the cookbook and 5 copies of the fiction;

mathematically that would be 4 * x and 5 * y

We add both and sum to be $199

Thus we have;

4x + 5y = 199 ••••••••••(i)

On the second day;

3 copies of cookbook 3 * x = 3x with 4 copies of science fiction 4 * y

Adding both yielded 152;

Thus, we have ;

3x + 4y = 152••••••••••(ii)

So we need to solve both equations simultaneously to get the values of x and y

4x + 5y = 199

3x + 4y = 152

Multiply equation i by 3 and equation ii by 4

3 * 4x + 5y = 199

4 * 3x + 4y = 152

12x + 15y = 597

12x + 16y = 608

Now, subtract multiplied equation ii from multiplied equation i

(12x-12x) + (15y-16y) = (597-608)

-y = -11

y = 11

To get x, simply substitute in any of the equations;

let’s use equation 1

4x + 5y = 199

4x + 5(11) = 199

4x + 55 = 199

4x = 199-55

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x = 144/4

x = 36

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3 years ago
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1/9
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If the slope is 3 and one ordered pair on the line is (2,9), what is the equation?
Ksenya-84 [330]

Answer:

y = 3x+3

Step-by-step explanation:

we can find the equation of the line with this formula:

y-y1 = m(x-x1) where y1 and x1 indicate the coordinates of the given point and m the slope

so we have

y-9 = 3(x-2)

y = 3x-6+9

y = 3x + 3

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3 years ago
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