Given the points (2, k) and (0, -6), for which values of k would the distance between the points be square root of 5?

Answers:

Roots of g(x) are: -1, -6, 1, -4

Y intercept of g(x) is:  24

==============================================

Explanation:

Part 1) Finding the roots of g(x)

To do this, we need the roots of f(x). Plug in f(x) = 0 and solve for x using the zero product property.

f(x) = (x-2)(x+3)(x-4)(x+1)

0 = (x-2)(x+3)(x-4)(x+1)

(x-2)(x+3)(x-4)(x+1) = 0

x-2 = 0  or  x+3 = 0  or  x-4 = 0   or  x+1 = 0

x = 2  or  x = -3   or   x = 4   or   x = -1

Those four x values are the roots of f(x). Plugging any of those values into f(x) leads to f(x) = 0.

Now onto g(x). We see that g(x) = -f(x+3). The x+3 indicates the xy axis has been shifted by 3 units to the right. This gives the illusion the f(x) curve is shifted 3 units to the left. This will move each root 3 units to the left as well.

The four roots of g(x) are:  -1, -6, 1, -4

------------------------------------------------

Part 2) The y intercept of g(x)

Let's plug x = 0 into g(x) to see what happens

g(x) = -f(x+3)

g(0) = -f(0+3) ... replace every x with 0

g(0) = -f(3)

We don't know f(3) yet, but we can plug x = 3 into f(x) to find out

f(x) = (x-2)(x+3)(x-4)(x+1)

f(3) = (3-2)(3+3)(3-4)(3+1)

f(3) = (1)(6)(-1)(4)

f(3) = -24

Therefore,

g(0) = -f(3)

g(0) = -(-24)

g(0) = 24

The y intercept of g(x) is 24.

Answer:

its A

Step-by-step explanation:

Answer:

yes because 422+ 562= 70

Answer: -3/4*x=-27

x=36

Step-by-step explanation:

-3/4*x=-27

Divide on -3/4 on both sides:

-3/4/-3/4*x=-27/-3/4

x=36

Step-by-step explanation:

Melissa have about 90$

7. subtract 3

x=(-2)

x=2

8. 8c-4=20

add 4

8c=24

divide 8

c=3

9.[tex]\frac{h+9}{5} =\frac{h-1}{3} \\[/tex]

Answer:

Part A: Brianna made a error on step 2. Because it has to be + 31 not + 41 cause it is a -5+36

Part B: x= -1

Step-by-step explanation:

This is how it should have been done.

Step 1: -5+6(6x+6)= 1+6x

Step 2: -5+36x= 36=1+6x

Step 3: 36x+31= 1+6x

Step 4: 36x= 6x-30

Step 5: 30x= -30

Step 6: x= -1

Answer:8 ounces more

Step-by-step explanation:Toppings cost 50 cents, 50 cents times 8 = $3.50

Answer: 8 ounces more

Step-by-step explanation: Toppings cost 50 cents, 50 cents times 8 = $3.50

=============================================

Work Shown:

Isolate y in the first equation

2x+y = 5

y = 5-2x .... subtract 2x from both sides

y = -2x+5

Then plug this into the other equation

-3x - 5y = 3

-3x - 5( y ) = 3

-3x - 5( -2x+5 ) = 3 .... replace y with -2x+5

-3x + 10x - 25 = 3 .... distribute

7x-25 = 3

7x = 3+25 .... adding 25 to both sides

7x = 28

x = 28/7 .... divide both sides by 7

x = 4  is the answer

-------------------------------------

Optional Section:

Use this value of x to find y

y = -2x+5

y = -2(4)+5

y = -8+5

y = -3

Then we can check our answers by plugging them into the original equations

2x + y = 5

2(4) - 3 = 5

8 - 3 = 5

5 = 5

That confirms the first equation. Repeat for the second equation

-3x - 5y = 3

-3(4) - 5(-3) = 3

-12 + 15 = 3

3 = 3

We've confirmed both equations, so (x,y) = (4, -3) is the solution to this system. This system is considered independent and consistent.

Graphing the two original equations will show that they intersect at (4, -3).

Answer:

9

Step-by-step explanation:

9/2= 4.5

Answer:

hehhehhe what the other guy said lol 10+9=21

Answer:

Marrisa plans on studying for 5 hours today!

Step-by-step explanation:

1.5 hours =  (3/10) of X    ...... where X is the "number of hours she plans on studying today" and OF means to multiply....

so..... 1.5 = (3/10)X

then you will solve for X!  

Multiply by 10 on both sides and you get:   15= 3X

then divide by 3 on both sides and you get your answer!   5 = X

Answer:

4.5

Step-by-step explanation:

2x=9

x=9/2

 =4.5

Answer:

x = 4.5

Step-by-step explanation:

[tex]2x=9\\\\\text{Divide both sides by 2.}\\\\\frac{2x=9}{2}\\\\\boxed{x=4.5}[/tex]

Hope this helps.

Answer:

The equation would be:

Y=-3/4 + 9

Step-by-step explanation:

Hope it helps.

Answer:

The answer is similar, AA similar.

Step-by-step explanation:

The triangles are obviously similar; but we only know that because of the two identical angles. (AA)

Please mark Brainliest!

Answer:

5(2+8)+(12-6/3)2

5(10)+(12/1-6/3)2

50+(36/3-6/3)2

50+(30/3)2

50+60/3

50+20

70

Step-by-step explanation:

Answer: 70

If the equation is  [tex]5(2+8)+(12-\frac{6}{3} )2[/tex]

[tex]5*10+(12-2)*2[/tex]

[tex]5*10+10*2[/tex]

[tex]10(5+2)[/tex]

[tex]10*7[/tex]

Answer: 70

Please mark brainliest if correct :)

Answer:

Slope of line 1 = 3

Slope of line 2 = -3

Slope of line 3 = -1/3

Line 1 and 2 = perpendicular

Line 1 and 3 = perpendicular

Line 2 and 3 = perpendicular

Step-by-step explanation:

trust me its correct

pls mark me as brainliest

Answer:

3.7a/10+3b

Step-by-step explanation:

Answer:

CS M=2/3 , KP M=2/3

Step-by-step explanation:

Neither because, they have the same slope but CS is negative so, the slopes are in a line.

Answer:

true

Step-by-step explanation:

Answer:

35 years

Step-by-step explanation:

A= P(1 + r)^n

A= $8400

r= 3%

n= ?

P= $3000

8400 = 3000(1 + 0.03)^n

8400/3000 = (1 + 0.03)^n

log2.8 = log (1.03)^n

log 2.8 = nlog 1.03

n=log 2.8/log 1.03

n= 35 years

Answer:

y=56.9933034497, x=.00561680186

Step-by-step explanation:

Answer:

I found this : graph the inequality by finding the boundry line, then shading the appropriate area

8 > 10p^2h-8c/5   (draw a line under the >)

Step-by-step explanation:

Answer:

(6,2)

Step-by-step explanation:

because math

Answer:y=-4/5x+4

Step-by-step explanation:

Answer:

y = -4/5 + 4

Step-by-step explanation: