Convert the following function to vertex form by completing the square.

y = x²+6x+15

A. y=(x + 3)² + 15

B. y=(x+6)² + 24

C. y= (x+ 3)²+ 24

D. y=(x+3)²+6

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Answer:

y = -2x + 12

Step-by-step explanation:

Step 1: find the slope

y = 1/2x + 5

The equation of the line is

y = mx + c

m - slope

m = 1/2

Note : if two lines are perpendicular to the other, both lines are negative reciprocal of each other

m = -2

Step 2 : using a point slope form

y - y1 = m( x - x1)

( 2 , 5)

x1 = 2

y1 = 5

y - 2 = -2( x - 5)

y - 2 = -2x + 10

y = -2x + 10 + 2

y = -2x + 12

The equation of the line is

y = -2x + 12

I dunno the answer so I just found another answer I found in here for this question:P

Sorry- it’s useless

Answer:

7.28011

Step-by-step explanation:

a² + b² = c²

7² = 49

2² = 4

49 + 4 = 53

√53 = 7.28011

Answer:

Step-by-step explanation:

2^2+b^2=7^2

4+b^2=49

b^2=45

b= 6.708

Answer:

0.083

163.20

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Answer:

a= 4

b= -1

c= 10

Step-by-step explanation:

First we start by multiplying both sides of 1/2c = 5 by 2.

c = 10

Add b to both sides of the last equation to make it a=b+5

knowing these two things, we can plug them into the first equation like this:

2(b+5) + b + 10 = 17

then you solve for b:

distribute the 2

2b + 10 + b + 10 = 17

combine like terms

3b + 20 = 17

subtract 20 from each side

3b = -3

divide by 3

b = -1

then you can plug that into the last equation again so a - (-1) =5

Subtracting a negative is the same as adding so its a + 1 = 5 or a = 4

Answer:

The average rate of change is -75

Step-by-step explanation:

The Average Rate of Change (ARC)

It's a measure of how much the function changed per unit, over a given interval.

Given a function F(x) and an interval between x=a and x=b, the average rate of change is:

[tex]\displaystyle A=\frac{F(b)-F(a)}{b-a}[/tex]

The function is:

[tex]F(x)=-x^3+24x^2-179x+495[/tex]

and it's required to find the ARC between x=2 and x=5.

Calculate F(2) and F(5):

[tex]F(2)=-2^3+24*2^2-179*2+495=225[/tex]

[tex]F(5)=-5^3+24*5^2-179*5+495=75[/tex]

The ARC is:

[tex]\displaystyle A=\frac{75-225}{5-3}=\frac{-150}{2}=-75[/tex]

The average rate of change is -75

Answer:[tex]P=\frac{2}{5}[/tex]

Step-by-step explanation:

Given

A movie theater has 7 seats in the front row  

12 seats in the middle row

11 seats in the back row

Probability first person who enters the theater will be in the middle row

[tex]P=\frac{\text{No. of middle seats}}{\text{total seats}}[/tex]

[tex]P=\frac{12}{7+12+11}=\frac{12}{30}[/tex]

[tex]P=\frac{2}{5}[/tex]

Answer:

B. 21

Step-by-step explanation:

The fractions are there to just make the problem seem complicated, but just rewrite it without the fractions.

"What is a common multiple for 7 and 3?"

In this problem it's easy, all you have to do is guess and check.

A: A doesn't work. 7 is not a factor of 18.

B: B works! Both 3 and 7 are factors of 21.

C: C doesn't work. 7 is not a factor of 3.

D: D doesn't work. Neither are a factor of 4.

They only leave us with one solution, B.

Answer:

c² = 34

Explanation:

Pythagorean Theorem: a² + b² = c²

3² + 5² = c²

3² = 9

5² = 25

9 + 25 = 34

34 = c²

- PNW

______________________________

 - When finding c, it doesn't matter what you put for a or b. So if you want to make a = 5, and b = 3, it wouldn't make any difference.

______________________________

Answer:

[tex]16\ \text{miles}[/tex]

Step-by-step explanation:

In a parallelogram the diagnols bisect each other. So,

[tex]DE=EB\\\Rightarrow y+2=3y-4\\\Rightarrow 4+2=3y-y\\\Rightarrow 6=2y\\\Rightarrow y=\dfrac{6}{2}\\\Rightarrow y=3[/tex]

[tex]DE=y+2\\\Rightarrow DE=3+2\\\Rightarrow DE=5[/tex]

[tex]BD=2DE\\\Rightarrow BD=2\times 5\\\Rightarrow BD=10[/tex]

[tex]EC=2y-3\\\Rightarrow EC=2\times 3-3\\\Rightarrow EC=3[/tex]

[tex]AC=2EC\\\Rightarrow AC=2\times 3\\\Rightarrow AC=6[/tex]

The sum of the diagonals is [tex]BD+AC=10+6=16\ \text{miles}[/tex]

The sum of the lengths of the two trails is [tex]16\ \text{miles}[/tex].

Answer:

16  Miles

Step-by-step explanation:

Just took the quiz and got it right

Answer:

Part A; 15x

Step-by-step explanation:

Part A; 15(67)

= $1005

Part B; ??

The number of tickets to be sold if, The cost of the banquet hall is $500, The cost per ticket is $15, the Total money to be raised is $1000, is 67, and the equation is given by 1000 = 15x.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

In other terms, it is a mathematical statement stating that "this is equivalent to that."

Given:

The cost of the banquet hall = $500,

The cost per ticket = $15,

Total money to be raised = $1000

Write the equation of the number of tickets as shown below,

1000 = 15x

Here, x is the number of tickets,

x = 1000 / 15

x = 66.67 or 67

To know more about equation:

https://brainly.com/question/12788590

#SPJ2

Answer:

2+2=4

Step-by-step explanation:

Answer:

A,   x(x-4)

Step-by-step explanation:

None of them will give you the vertex you want but the x intercepts are only correct for A

Answer:

Its The Bottom Right one I think D

Step-by-step explanation:

Answer:

1190

Step-by-step explanation:

We have the ratio: 8:340 which means that 340 copies are printed in 8 minutes

We want to find out how many color copies are printed in 1 minute so we divide by 8

so our new ratio is now 1:42.5

We now multiply this ratio by 28 to find out how many are printed in 28 minutes

28:1190

our answer is 1190 copies

Answer:

y=1+1/3x

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Given the triangle AEC - trianhle BED the 4th equation, ED/EC = AC/BD is true.

Answer:

D. x>-3

Step-by-step explanation:

Since the dot on -3 is not shaded in we know it is not ≤ or ≥ so option A and C are eliminated.

Remember if the arrow is pointing to the left (<-----) Then it is Less-than which is <.

If the arrow is pointing to the right (----->) Then it is Greater-than which is >.

Since the arrow is pointing right the answer will be x>-3 which is D

Answer:

x=7

Step-by-step explanation:

11+3=14, x+x=2x, divided by two, x=7

Answer:

y=1, x=2

Step-by-step explanation:

so first solve for y. plus x=3y-1 into the other equation.  

so 3(3y-1)+4y=10.  

Simplify

9y-3+4y=10           Add 3 to both sides

9y+4y=13               Add

13y=13 .                  Divide 13 from both sides

y=1

Plug 1 into the first equation.  

x=3(1)-1

x=3-1

x=2 and y=1

Answer:

d. 50%

Step-by-step explanation:

Answer:

how we go answer it

Step-by-step explanation:

Answer:

No solution, D

Step-by-step explanation:

If you rewrite the second one to be the y=mx+b form then you get

8x-14= -2y

Divide by -2 and get

-4x+7=y

Because the slopes are the same the lines will never intersect which means there is no solution

Answer:

$75

Step-by-step explanation:

Cost = $500

Sam has to pay a 15% tax

To compute his tax, we use the step outlined bellow

tax= 15/100*500

tax= 0.15*500

tax=$75

Hence his tax is $75

Answer:

$90.98

Step-by-step explanation: