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Ann [662]
2 years ago
10

Find the values of a and b such that x^2-2x+2=(x-a)^2+b

Mathematics
1 answer:
vekshin12 years ago
6 0

Answer:

a = 1, b = 1

Step-by-step explanation:

Expand the right side and compare the coefficients of like terms on both sides, that is

right side

(x - a)² + b ← expand factor using FOIL

= x² - 2ax + a² + b

Compare to left side x² - 2x + 2

Compare the coefficients of the x- term

- 2a = - 2 ( divide both sides by - 2 )

a = 1

Compare the constant terms

a² + b = 2 ( substitute a = 1 )

1² + b = 2

1 + b = 2 ( subtract 1 from both sides )

b = 1

Thus a = 1, b = 1

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Estimate and classify the critical points for the graph of the function<br> Please show work
ikadub [295]

The critical points of the function graphed are given as follows:

  • x = -1.5: Local maximum.
  • x = -1: Local minimum.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In a graph, they are turning points, and are classified as follows:

  • Local maximum, if the functions changes from increasing to decreasing.
  • Local minimum, if the functions changes from decreasing to increasing.

Looking at the graph, the turning points are approximately:

  • x = -1.5: Local maximum.
  • x = -1: Local minimum.

More can be learned about critical points at brainly.com/question/2256078

#SPJ1

5 0
1 year ago
two friends have a conversation mario tells roberto "the money i have is twice that you have" roberto answer "if you give me 6 d
crimeas [40]

Answer:

Before anyone gives anyone money, Mario has 24 dollars and Roberto has 12 dollars. After they give each other money, both of them have 18 dollars.

Step-by-step explanation:

Mario has twice as much as Roberto, BUT if Mario gives Roberto 6 dollars, then they have the same amount.

M = 2R

M - 6 = R + 6

To isolate M, you need to add 6 on both sides.

M - 6 + 6 = R + 6 + 6

M = R + 12

M = 2R

Substitute M for the value above that we found.

R + 12 = 2R

Now we subtract R on both sides, so that only one side has the variable R.

R - R + 12 = 2R - R

12 = R

M = 2R

Substitute for the value of R.

M = 2 x 12

M = 24

3 0
2 years ago
sal makes a 10% commission on the first $5000 of sales and 15% on any sales over $5000. find his total graduated commission on $
Helga [31]
0.10(5000) = 500
0.15(10,000) = 1500

total commission on 15,000 = (150 + 500) = 2,000
5 0
3 years ago
This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Show
Soloha48 [4]

Answer:

area of the figure: 29.92 m²

formula's:

  • area of rectangle: length * width
  • area of sector: ∅/360 * πr²

solving steps:

area of rectangle + area of sector

5.5 * 4 + 30/360 * π(5.5)²

22 + 7.919

29.92 m²

8 0
2 years ago
Read 2 more answers
Please please please help me
Montano1993 [528]

the answer is c i used a algebra calculator

7 0
3 years ago
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