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3 years ago

Find the x and y intercepts of the following function. g(x)=x^2-5x-84

Mathematics

1 answer:

Ahat [919]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

To find the y- intercept let x = 0 in the function

g(0) = 0 - 0 - 84 = - 84 ← y- intercept

To find the x- intercepts let y = 0, that is

x² - 5x - 84 = 0

To factor the quadratic

Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term

The factors are - 12 and + 7, since

- 12 × 7 = - 84 and - 12 + 7 = - 5, thus

(x - 12)(x + 7) = 0

Equate each factor to zero and solve for x

x - 12 = 0 ⇒ x = 12

x + 7 = 0 ⇒ x = - 7

x- intercepts are x = - 7 and x = 12

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Simplify negative 9 over 6 divided by 3 over negative 2. . (5 points) a 3 b 1 c −1 d −3

vladimir2022 [97]

Answer:

b) 1

Step-by-step explanation:

$\frac{9}{6} \times \frac{2}{3} = \frac{18}{18}$

$\frac{18}{18} = 1$

6 0

3 years ago

Someone please help me with this

Sedbober [7]

Answer:

The area of the shaded figure is:

20 units^2

Step-by-step explanation:

To obtain the area of the shaded figure, first, you must calculate this as a rectangle, with the measurements: wide (4 units), and long (6 units):

Area of a rectangle = long * wide
Area of a rectangle = 6 * 4
Area of a rectangle = 24 units^2

How the figure isn't a rectangle, you must subtract the triangle on the top, so, now we calculate the area of that triangle with measurements: wide (4 units), and height (2 units):

Area of a triangle = $\frac{wide*height}{2}$
Area of a triangle = $\frac{4*2}{2}$
Area of a triangle = $\frac{8}{2}$
Area of a triangle = 4 units^2

In the end, you subtract the area of the triangle to the area of the rectangle, to obtain the area of the shaded figure:

Area of the shaded figure = Area of the rectangle - Area of the triangle
Area of the shaded figure = 24 units^2 - 4 units^2
Area of the shaded figure = 20 units^2

I use the name "units" because the exercise doesn't say if they are feet, inches, or another, but you can replace this in case you need it.

5 0

3 years ago

Factor the expression completely.

Ksju [112]

Answer:

Step-by-step explanation:

-9.75 + 3.25x

3.25(-3 + x)

-3.25(3 - x)

8 0

3 years ago

What is 9/4 divided by 3/8?

Contact [7]

The answer would be 6

7 0

3 years ago

Read 2 more answers

- Write a recursive formula to represent the sequence below. (3,7, 11, 15, 19,23,27,31,35, ...)

NemiM [27]

The recursive formula to find nth term of sequence is:

$a_n = 4n - 1 \text{ where } n \geq 1$ and n = 1, 2, 3, ....

Solution:

Given a sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35

Let us find the difference between terms

7 - 3 = 4

11 - 7 = 4

15 - 11 = 4

19 - 15 = 4

23 - 19 = 4

27 - 23 = 4

31 - 27 = 4

35 - 31 = 4

Thus the difference between terms is constant

Thus the given sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

The nth term of arithmetic sequence is given by:

$a_n =a_1+(n-1)d$

$a_n$ = the nᵗʰ term in the sequence

$a_1$ = the first term in the sequence

d = the common difference between terms

Here in the given sequence

d = 4

$a_1=3$

Substitute in above formula,

$a_n = 3 + (n-1)(4)\\\\a_n = 3 + 4n - 4\\\\a_n = 4n - 1$

Thus the recursive formula to find nth term of sequence is:

$a_n = 4n - 1 \text{ where } n \geq 1$ and n = 1, 2, 3, ......

8 0

3 years ago