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3 years ago

14

What is the slope-intercept form of a line that contains the point (0,3) and a slope =-2?

1 answer:

rosijanka [135]3 years ago

5 0

Answer:

C.

Step-by-step explanation:

-2 is in front of x so thats gonna be the slope

and +3 is the y-intercept

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

<u>Given function</u>:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find <em>a</em>, compare the coefficients of x³:

$\implies a=3$

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find <em>c</em>, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

<u>Zero Product Property</u>

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

Find the Volume: 3.2 cm<br> 7 cm<br> 4.8 cm

REY [17]

V = 0.5*b*h*l
v = 0.5*4.8*3.2*7
v = 0.5*107.52
v = 53.76cm3

7 0

3 years ago

Number of seconds equal to 1/5 hour

kirill115 [55]

1/5 of an hour is 12 minutes. 60 seconds x 12 minutes= 720 seconds

8 0

3 years ago

Read 2 more answers

A gym has soccer balls and basketballs. The ratio of soccer balls to basketballs is 3 : 2. The number of soccer balls at the gym

lutik1710 [3]

How many soccer balls are in the gym?

3 0

3 years ago

Read 2 more answers

Which pairs of points would result in a line with a rate of change of 2:1? Select all that apply.

Helen [10]

Answer:

Options A, C, D are true.

Step-by-step explanation:

We have to choose the pair of points from that given in the attached file which will result in a line with a rate of change i.e. slope of 2:1 i.e. 2.

A. The points are (-4,-11) and (-2,-7).

Then the slope of the joining line is $\frac{-7-(-11)}{-2-(-4)} =2$

B. The points are (5,6) and (-5,12).

Then the slope of the joining line is $\frac{12-6}{-5-5} =-\frac{3}{5}$

C. The points are (0,-3) and (-4,-11).

Then the slope of the joining line is $\frac{-11-(-3)}{-4-0} =2$

D. The points are (0,-3) and (5,7).

Then the slope of the joining line is $\frac{7-(-3)}{5-0} =2$

Therefore, options A, C, D are true. (Answer)

7 0

3 years ago