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SVETLANKA909090 [29]

3 years ago

11

What is the slope and y intercept of 6x + 24 =0

1 answer:

yuradex [85]3 years ago

6 0

X = -4 is your answer

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The graph of a quadratic function passes through the points (-1,0), (-2,0), and (0,2). Write the quadratic function in general f

ddd [48]

Answer:

$f(x)=x^2+3x+2$

Step-by-step explanation:

step 1

we have the points

(-1,0), (-2,0), and (0,2)

Plot the points

using a graphing tool

see the attached figure

The graph of a quadratic function must be a vertical parabola open upward

The vertex is a minimum

The quadratic function in general form is equal to

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

Substitute the value of x and the value of y of each given ordered pair in the general equation and solve for a,b and c

(0,2)

For x=0, y=2

substitute

$2=a(0)^2+b(0)+c$

$c=2$

(-1,0)

For x=-1, y=0

substitute

$0=a(-1)^2+b(-1)+2$

$0=a-b+2$ ----> $a=b-2$ ----> equation A

(-2,0)

For x=-2, y=0

substitute

$0=a(-2)^2+b(-2)+2$

$0=4a-2b+2$ ----> equation B

we have the system

$a=b-2$ ----> equation A

$0=4a-2b+2$ ----> equation B

substitute equation A in equation B

$0=4(b-2)-2b+2$

solve for b

$0=4b-8-2b+2$

$2b=6$

$b=3$

Find the value of a

$a=3-2=1$

therefore

The quadratic function in general form is equal to

$f(x)=x^2+3x+2$

see the attached figure N 2 to better understand the problem

7 0

3 years ago

WILL GIVE BRAINLIEST <3

Lynna [10]

Answer:

I cant solve number 1 but I can for number 2

Calculate GCF for each

You can learn how to use the prime factorization method to do this

GCF(12, 18, 40, 45) = 1

So I dont get what the problem is because there are no numbers for #2. So either I dont understand the problem or it is a trick question whereas the answer is UNDEFINED/IMPOSSIBLE.

5 0

3 years ago

Rewrite all three fractions with the lowest common denominator.

anastassius [24]

Answer:

$- \frac{2}{4 } = - \frac{16}{32}$

$- \frac{6}{8} = - \frac{24}{32}$

$- \frac{13}{32} =$

remains the same

5 0

2 years ago

Read 2 more answers

3/25% in decimal form

Elis [28]

I will try my best to assist you with your question!

3/25 = .12 or 12%

12% can also be written as .12

3/25% in decimal form is .12

Hope I helped!

Good Luck!

7 0

3 years ago

Use the denition of the derivative to find f 0 (3), where f (x) = 3x+5 / 2x−1

Crazy boy [7]

Answer:

$f'(3)= -\frac{13}{25}$

Step-by-step explanation:

We are asked to find $f'(3)$ of function $f(x)=\frac{3x+5}{2x-1}$ using definition of derivatives.

Limit definition of derivatives:

$f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Let us find $f(3+h)$ and $f(3)$ .

$f(3+h)=\frac{3(3+h)+5}{2(3+h)-1}$

$f(3+h)=\frac{9+3h+5}{6+2h-1}\\\\f(3+h)=\frac{3h+14}{2h+5}$

$f(3)=\frac{3(3)+5}{2(3)-1}$

$f(3)=\frac{9+5}{6-1}\\\\f(3)=\frac{14}{5}$

Substituting these values in limit definition of derivatives, we will get:

$f'(3)= \lim_{h \to 0} \frac{f(3+h)-f(3)}{h}$

$f'(3)= \lim_{h \to 0} \frac{\frac{3h+14}{2h+5}-\frac{14}{5}}{h}$

Make a common denominator:

$f'(3)= \lim_{h \to 0} \frac{\frac{(3h+14)*5}{(2h+5)*5}-\frac{14(2h+5)}{5(2h+5)}}{h}$

$f'(3)= \lim_{h \to 0} \frac{\frac{5(3h+14)-14(2h+5)}{5(2h+5)}}{h}$

$f'(3)= \lim_{h \to 0} \frac{5(3h+14)-14(2h+5)}{5h(2h+5)}$

$f'(3)= \lim_{h \to 0} \frac{15h+70-28h-70}{5h(2h+5)}$

$f'(3)= \lim_{h \to 0} \frac{-13h}{5h(2h+5)}$

Cancel out h:

$f'(3)= \lim_{h \to 0} \frac{-13}{5(2h+5)}$

$f'(3)= \frac{-13}{5(2(0)+5)}$

$f'(3)= \frac{-13}{5(5)}$

$f'(3)= -\frac{13}{25}$

Therefore, $f'(3)= -\frac{13}{25}$ .

8 0

3 years ago