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MA_775_DIABLO [31]
3 years ago
13

Consider the function f(x) = x2 + 2x – 15. What are the x-intercepts of the function?

Mathematics
1 answer:
Rus_ich [418]3 years ago
4 0

Answer:

The x-intercepts of the function are x = 3 and x = -5.

Step-by-step explanation:

We are given the function \displaystyle f(x) = x^2 + 2x - 15.

In order to find the x-intercepts of the equation, we need to solve this quadratic. We can use factoring methods to solve it.

The parent function for a quadratic is f(x) = ax^2 + bx + c = 0.

We can use this information to determine what factoring technique we want to use.

There are several different methods, including using the quadratic formula, but because this is easily factorable, we can avoid using it.

We see that our <em>a</em> is equal to 1 (there is no coefficient in front of x²), so we can use the easier of the techniques:

  • Find what factors of c add up to give you b.
  • Add to x if positive or subtract from x if negative and set it equal to zero.
  • Solve for x - these are your x-intercepts.

Therefore, let's determine what our c is: 15.

Now, let's label the factors for 15.

  • 15 cannot be divided by 2 evenly.
  • 15 can be divided by 3 evenly: 15/3 = 5
  • 15 cannot be divided by 4 evenly.
  • 15 can be divided by 5 evenly: 15/5 = 3

Therefore, our two factors are 3 and 5 since they cannot be broken down any further (they are prime numbers - we just performed prime factorization).

Now, we need to pay attention to the sign for c. It's negative, so one of our factors needs to be negative. Therefore, we can test this out:

  • 5 + -3 = 2
  • -5 + 3 = -2

Now, we check for which one matches the sign for b. This is positive 2, so our two factors are 5 and -3.

Finally, to factor, we add or subtract the factors from x depending on the sign. If the factor is positive, we add it. If the factor is negative, we subtract it. Therefore, we can set up our equations.

x + 5 = 0\\\\x = -5

x - 3 = 0\\\\x = 3

Therefore, for when x = 3 or x = -5, the line crosses the x-axis. These are the x-intercepts of the function.

Our answers are x = -5 and x = 3.

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4 pencils and 3 crayons are 20.9 inches. 5 pencils and 4 crayons are 26.5 inches. Each pencil is the same length as the other pe
erastova [34]

Answer:

The length of the pencils is 4.1 inches and for the crayons 1.5 inches

Step-by-step explanation:

We can solve by means of a 2x2 system of equations, we have to:

let "x" be the length of the pencils

let "y" be the length of the crayons

4 * x + 3 * y = 20.9

5 * x + 4 * y = 26.5 => x = (26.5 - 4 * y) / 5

Replacing:

4 * (26.5 - 4 * y) / 5 + 3 * y = 20.9

21.2 - 3.2 * y + 3 * y = 20.9

-0.2 * y = 20.9 - 21.2

y = -0.3 / -0.2

y = 1.5

now for x:

x = (26.5 - 4 * 1.5) / 5

x = 4.1

This means that the length of the pencils is 4.1 inches and for the crayons 1.5 inches

5 0
3 years ago
Solve the following quadratic equation for all values of x in simplest form.
NNADVOKAT [17]

Answer:

x = ± 1

Step-by-step explanation:

Given

3(x² - 4) + 7 = - 2 ( subtract 7 from both sides )

3(x² - 4) = - 9 ( divide both sides by 3 )

x² - 4 = - 3 ( add 4 to both sides )

x² = 1 ( take the square root of both sides )

x² = ± \sqrt{1} = ± 1

Thus

x = - 1, x = 1

8 0
3 years ago
If somebody answered my question i will give them thanks and brill and vote
kykrilka [37]

Answer:

which out of those you want answer for? happy to help

Step-by-step explanation:

5 0
2 years ago
What is the solution to the system of equations?<br><br> y=1<br> y=-5x+3
In-s [12.5K]

Answer:

y=1

x=2/5

Step-by-step explanation:

1=-5x+3

-2=-5x

x=2/5

7 0
3 years ago
Read 2 more answers
I don't know how to solve this. How would I solve this? Thanks!!!!
Afina-wow [57]

Answer:

x = 11 units

Step-by-step explanation:

Area of triangle = (base + base 2) * h *1/2

so (7 + x )* 7 * 1/2 = 63

63 x 2 = 126

126 / 7 = 18

18-7 = x

x = 11

Check

(7+11)* 7 * 1/2

18* 7 = 126

126 x 0.5 = 63

CORRECT!

(p.s., tell me if wrong :P)

6 0
3 years ago
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