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grigory [225]
3 years ago
11

How to solve the problem

Mathematics
1 answer:
777dan777 [17]3 years ago
4 0
Hope this helps.....

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Graph the line and the parabola and find the points of intersection: y= 3-x ; y=x(squared)+x-12
melomori [17]

Answer:

Step-by-step explanation:

We have to graph a line y = 3 - x which has the slope = -1 and y intercept 3.

We will select two points where line intersects at x = 0 and y = 0

The given line will intersect x-axis at (3, 0) and at y- axis (0, 3).

Joining these two points we can draw a straight line showing y = -x + 3

Now we will draw the parabola given by equation y = x² + x - 12

We will convert this equation in vertex form first to get the vertex and line of symmetry.

Standard equation of a parabola in vertex form is

y = (x - h)² + k

Where (h, k) is the vertex and x = h is the line of symmetry.

y = x² + x - 12

y = x² + 2(0.5)x + (0.5)²- (0.5)²-12

y = (x + 0.5)² - 12.25

Therefore, vertex will be (-0.5, -12.25) and line of symmetry will be x = 0.5

For x intercept,

0 = (x + 0.5)² - 12.25

x + 0.5 = ±√12.25

x = -0.5 ± 3.5

x = -4, 3

For y- intercept,

y = (0+0.5)² - 12.25

 = 0.25 - 12.25

y = -12

So the parabola has vertex (-0.5, - 12.25), line of symmetry x = 0.5, x intercept (4, 0), (and y-intercept (0, -12).

Now we have to find the points of intersection of the given line and parabola.

For this we will replace the values of y

3 - x = x² + x - 12

x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x(x + 5) - 3(x + 5) = 0

(x - 3)(x + 5) = 0

x = 3, -5

For x = 3

y = 3- 3 = 0

For x = -5

y = 3 + 5 = 8

Therefore, points of intersection will be (3, 0) and (-5, 8)

 

4 0
2 years ago
HELP PLZ I WILL GIVE BRAINLIEST!!! Write the prime factorization of 675 using exponents.
Viktor [21]

Answer:

Step-by-step explanation:

The prime factorization of 675 is 3 × 3 × 3 × 5 × 5. The factors of a number, x, are the numbers that multiply together to...

5 0
2 years ago
Order from greatest to least 10.9, 10 2/5, 10 1/4
Ede4ka [16]

Answer:10.9,,,,,10 2/5,,,,,10 1/4

Step-by-step explanation:

3 0
2 years ago
Kathleen makes bracelets to sell in a booth at a local store. She spent $62.30 on supplies to make bracelets for the next month.
vodomira [7]

Answer:

$105.20

Step-by-step explanation:

Given that :

Cost of materials = $62.30

Cost of booth = $25 / month

Price per bracelet = $5.50

Profit of 35 bracelet is sold next month =?

Profit = Revenue - Expenses

Revenue = $5.50 * 35 = $192.50

Expenses = $25 + $62.30 = $87.30

Profit = $192.50 - $87.30

= $105.20

4 0
2 years ago
3 3/8 - 1 1/2 how do you solve e this
ser-zykov [4K]
In exact form it would be 15/8
5 0
3 years ago
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