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abruzzese [7]
3 years ago
7

the vertex of the parabola represented by f(x)=x^2-2x+6 has coordinates (1,5). Find the coordinates of the vertex of the parabol

a defined by g(x)=f(x+3). Explain how you arrived at your answer
Mathematics
1 answer:
Sever21 [200]3 years ago
5 0
Plug \ in \ x+3 \ into \ f(x) \ to \ get \ g(x)
\\\ g(x) = (x+3)^2-2(x+3)+6
\\\ g(x)= x^2+6x+9 -2x-6+6
\\\ g(x) = x^2+4x+9
\\\ -\frac{b}{2a} --\ \textgreater \  vertex
\\\ \frac {-4}{2}
\\\ x \ coordinate = -2, plug \ it \ back \ into \ g(x)
\\\ (-2)^2+4(-2)+9
\\\ 4-8 + 9
\\\ y \ coordinate = 5
\\\ \boxed{(-2,5)}
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sesenic [268]

Answer:

$195.00

Step-by-step explanation:

perimeter is 54 feet

area is 152  ft^{2}

54' * $1.50 = $81.00

152/8 = 19 bags of mulch needed

19*$6.00= $114.00

$195.00    you get away from the store for under 200 :P

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8 0
3 years ago
Which graph shows the solution to the system of linear inequalities?
Brilliant_brown [7]

Answer:

this is answer

Step-by-step explanation:

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line. If the inequality is strict ( < or > ), graph a dashed line.

4 0
2 years ago
please help me The question involves multiplying two complex numbers, then turning it into an a+bi equation (pictures included)
Sloan [31]

Answer:

  (a, b) = (0, -15)

Step-by-step explanation:

In "cis" form the product of two complex numbers is the product of their magnitudes at the angle that is the sum of their angles. I find this the easiest way to multiply complex numbers.

  z1 × z2 = (3 cis π)(5 cis π/2)

  = (3·5) cis (π +π/2)

  = 15 cis 3π/2

Of course, "cis" is short for "cosine + i·sine", so you have ...

  z1 × z2 = 15 cis 3π/2 = 15(cos(3π/2) +i·sin(3π/2))

  = 15(0 +i·(-1))

  = 0 -15i

(a, b) = (0, -15)

8 0
4 years ago
Which mixed number is greater 5 7/24 or 5 5/16
Sauron [17]
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3 0
3 years ago
Read 2 more answers
Use slopes and y-intercepts to determine if the lines 6x+y=−1 and −2x−5y=1 are parallel.
kobusy [5.1K]

Answer:

The two lines are not parallel.

Step-by-step explanation:

Every linear equation follows this structure:

y = mx + b

y is the y value

x is the x value

m is the gradient/slope of the line

b (or sometimes c) is the y-intercept of the line

Firstly, we have to get the y term on one side by itself.

6x + y = -1

-6x        -6x

y = -6x - 1

-2x -5y = 1

+2x         +2x

-5y = 2x + 1

Secondly, we make it so the y term is just the y value.

The first equation is already like this, so we don't need to do anything to that.

-5y = 2x + 1

÷ -5  ÷ -5

y = (2x + 1) / -5

This can be expanded and simplified to:

y = -2/5x - 1/5

Thirdly, we have to compare the slopes and y-intercepts.

y = -6x - 1

y = 2/5x - 1/5

If the slopes are the same and the y-intercepts are different, they are parallel. However, the slopes are different, therefore they are not parallel.

7 0
3 years ago
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