Mathematics: 1. a set of equations is given below: equation s: y = x + 9 equation t: y = 2x + 1 which of the following steps can be used to find the solution to the set of equations? (4 points) x = 2x + 1 x + 9 = 2x x + 1 = 2x + 9 x + 9 = 2x + 1 2. a system of equations is given below: y = –2x + 1 6x + 2y = 22 which of the following steps could be used to solve by substitution? (4 points) 6x + 2(–2x + 1) = 22 –2x + 1 = 6x + 2y 6(–2x + 1) + 2y = 22 6(y = –2x + 1) 3. solve the system of equations and choose the

1. a set of equations is given below: equation

Wolfgirl2032

17.03.2023

The x-intercepts are:

(1, 0)(2, 0)(6, 0)

The y-intercept is (-12, 0)

Step-by-step explanation:

Given the function

$f\left(x\right)=x^3-9x^2+\:20x\:-12$

Determining the x-intercepts and the y-intercept of the graph of f(x)

Finding x-intercept

We can determine the x-intercept by setting y = 0 and determining the corresponding value of x.

$y=x^3-9x^2+\:20x\:-12$

plug in x = 0

x^3-9x^2+20x-12=0

$(x-1) (x-2) (x-6) = x^3-9x^2+\:20x\:-12$

$\left(x-1\right)\left(x-2\right)\left(x-6\right)=0$

Using the zero factor principle

if ab = 0 then a=0 or b=0 (or both a=0 and b=0)

Thus,

$x-1=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-6=0$

$x=1,\:x=2,\:x=6$

Thus, the x-intercepts are:

(1, 0)(2, 0)(6, 0)

Finding y-intercept

We can determine the y-intercept by setting x = 0 and determining the corresponding value of y.

$y=x^3-9x^2+\:20x\:-12$

plug in y = 0

$y=\left(0\right)^3-9\left(0\right)^2+\:20\left(0\right)\:-12$

y=0-0+0-12

y=-12

Therefore, the y-intercept is (-12, 0)

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