In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the
function with its graph

In Exercises 4548, Let F(x) = (x - 2)2 + 1. Match Thefunction With Its Graph

Answers

Answer 1

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

[tex]f(x)=(x-2)^{2}+1[/tex]

45)

The function g(x) is given by:

[tex]g(x)=f(x-1)[/tex]

using f(x) we can find f(x-1)

[tex]g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1[/tex]

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

[tex]g(x)'=2(x-3)[/tex]

[tex]2(x-3)=0[/tex]

[tex]x=3[/tex]

Puting it on g(x) we will get y value.

[tex]y=g(3)=(3-3)^{2}+1[/tex]

[tex]y=g(3)=1[/tex]

Then, the minimum point of this function is (3,1) and it corresponds to (A)

46)

Let's use the same method here.

[tex]g(x)=f(x+2)[/tex]

[tex]g(x)=((x+2)-2)^{2}+1[/tex]

[tex]g(x)=(x)^{2}+1[/tex]

Let's find the first derivative and equal to zero to find x and y minimum value.

[tex]g'(x)=2x[/tex]

[tex]0=2x[/tex]

[tex]x=0[/tex]

Evaluatinf g(x) at this value of x we have:

[tex]g(0)=(x)^{2}+1[/tex]

[tex]g(0)=1[/tex]

Then, the minimum point of this function is (0,1) and it corresponds to (C)

47)

Let's use the same method here.

[tex]g(x)=f(x)+2[/tex]

[tex]g(x)=(x-2)^{2}+1+2[/tex]

[tex]g(x)=(x-2)^{2}+3[/tex]

Let's find the first derivative and equal to zero to find x and y minimum value.

[tex]g'(x)=2(x-2)[/tex]

[tex]0=2(x-2)[/tex]

[tex]x=2[/tex]

Evaluatinf g(x) at this value of x we have:

[tex]g(2)=(2-2)^{2}+3[/tex]

[tex]g(2)=3[/tex]

Then, the minimum point of this function is (2,3) and it corresponds to (B)

48)

Let's use the same method here.

[tex]g(x)=f(x)-3[/tex]

[tex]g(x)=(x-2)^{2}+1-3[/tex]

[tex]g(x)=(x-2)^{2}-2[/tex]

Let's find the first derivative and equal to zero to find x and y minimum value.

[tex]g'(x)=2(x-2)[/tex]

[tex]0=2(x-2)[/tex]

[tex]x=2[/tex]

Evaluatinf g(x) at this value of x we have:

[tex]g(2)=(2-2)^{2}-2[/tex]

[tex]g(2)=-2[/tex]

Then, the minimum point of this function is (2,-2) and it corresponds to (D)

I hope it helps you!


Related Questions

1) Heather writes a number that shows 30 parts of 100. Select all that could be Heather's number. 0 0.30 3/100 30/10 0.3 30/100 ! This is a required question​

Answers

Answer:

im guessing .30, .3, and 30/100

Step-by-step explanation:

im not sure how to explain it but fractions. yes.

Please answer <3 thanks

Answers

Answer:

The slope of the line would be 3/6 or 1/2

Step-by-step explanation:

To get from point (1,2) to point (7,5) you have to rise 3 places and run (move to the right) 6 times. Rise/run=3/6

hope this helps. ; )

A photographer has a print that is 3.5 inches wide and 2.5 inches tall. If the photographer enlarges the print so that it is 7 inches wide, how tall will it be?
5 inches
6 inches
8 inches
12 inches

Answers

b. if it is 7 inches wide it will be 6 inches tall

Answer:

5 inches

Step-by-step explanation:

Hope I helped

r+6<10 what’s the answer?

Answers

Answer:

r < 4

Step-by-step explanation:

r+6<10

r < 4

The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

Answers

Answer:

a) 0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.

b) 0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.

c) The distribution of the population is normal, which means that the sample size does not need to exceed 30.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm.

This means that [tex]\mu = 200, \sigma = 8.3[/tex]

a. Find the probability that an individual distance is greater than 210.00 cm.

This is 1 subtracted by the pvalue of Z when X = 210. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{210 - 200}{8.3}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

1 - 0.8849 = 0.1151

0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.

b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm

Now [tex]n = 20, s = \frac{8.3}{\sqrt{20}} = 1.8559[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 197.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{197.8 - 200}{1.8559}[/tex]

[tex]Z = -1.19[/tex]

[tex]Z = -1.19[/tex] has a pvalue of 0.117

1 - 0.117 = 0.883

0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The distribution of the population is normal, which means that the sample size does not need to exceed 30.

PLEASEEEE HELP THIS IS DUE TODAY!!!

Answers

Answer: $200

Step-by-step explanation:

On the X axis, it shows the kilograms. Since the problem asks for how much money she makes for 60 kg, go to the point on the X axis that represents 60 kg and then go up to the corresponding y or dollar value, which is 200.

s + 10.7 = 7.2



s = ?
how do i solve

Answers

10.7 - 7.2 = 3.5
So -3.5 + 10.7 = 7.2

6t/9-22;t=60
please help me

Answers

Answer:

if t=60, then 6(60)/9-23. (360-198)/9

=18

please help helppppppp

Answers

it a quadrilateral, square, and parallelogram.

PLEASE ANSWER THIS QUESTION
Show that 4x – 7 is equivalent to 4(x - 1) – 3 when x = 3.​

Answers

Answer:

4(3) - 7 = 4(3 - 1) - 3

12 - 7 = 4(2) - 3

5 = 8 - 3

= 5

They are equivalent because when they are both simplified they have the same answer 5

Work out the size of angle x.

Answers

Answer:

First: 105

Second: 65

Third: 133

Fourth: 129

Fifth: 60

I will venmo if someone can please help me

Answers

Answer: 14.967

Step-by-step explanation:

Use Pythagorean Theorem to find the missing length.  

a² + b² = c²        

x² + 10² = 18²      

x² + 100 = 324         [Subtract 100 from both side]  

          x²= 224        

      √x² = √224     [solve the square root from both sides]

        x   ≈  14.967

Circumference = 69.1yd​

Answers

Answer:

What do you want us to find?

Step-by-step explanation:

Pls help this is due today! Find the value of x, then the value of each angle:

Answers

The top angle is 56 degrees

The bottom angle is 34 degrees

X=29

Answer:

x = 29

angles are 90 degrees, 56 degrees, and 34 degrees

Step-by-step explanation:

90 + (2X-2) + (X+5) = 180

3X + 93 = 180

3X = 87

X = 29

Francine can ride 16 miles on her bicycle in 45 minutes. At this speed, how many minutes would it take Francine to ride 60 miles?

Answers

Answer:

2000 minutes on 16 miles

Answer:

168.75 minutes

Step-by-step explanation:

Francine's speed (the unit rate) is (16 miles) / (45 minutes), or 16/45 miles/min.

Recalling that distance = speed times time, we recognize that

time = distance / speed

which here is  

(60 miles) / (16/45) miles/min = 168.75 minutes, or 168 min 45 sec

All the prizes for the contest were won by Josh. Rewrite in an active voice.

Answers

Answer:

Josh won all the prizes for the contest

Step-by-step explanation:

PLEASE HELP THIS ASSIGNMENT IS OVER DUE

Answers

Answer:

91m + 13n + 52

Step-by-step explanation:

13(n + 4 + 7m)

= (13) (n+4+7m)

= (13) (n) + (13) (4) + (13) (7m)

= 13n + 52 + 91m

= 91m + 13n + 52

hope this helps and is right :)

p.s. i really need brainliest

Answer:

13n + 52 +91m

Step-by-step explanation:

As far as I can tell, all you are doing is distributing the 13 into the numbers. You multiply 13* 1n, 13*4, and 13*7m to give you 13n +52+91m.

I need some gosh darn help because I will fail my math test. Suppose two angles in a coordinate plane, one measuring 80 and the other measuring 160, were both rotated 180 about the origin and then translated 40 units down. which of these would be a measure of one of the resulting angles? Select 2 answers

Answers

Answer:

120 and 40

Step-by-step explanation:

Because when we subtract 80 and 40 is equal 40 or 160 and 40 is 120.

Please help I don't get this

Answers

Answer:

18n+9

Step-by-step explanation:

9(2n+1)

multiply the 9 with the numbers in the parenthesis

18n+9

C/2 - 3 + 6/d when c=14 d=3

Answers

Answer:

6

Step-by-step explanation:

14/2 - 3 + 6/3

Divide 14 by 2 to get 7.

7−3+6/3

Subtract 3 from 7 to get 4.

4+6/3

Divide 6 by 3 to get 2.

4+2

Add 4 and 2 to get 6.

6

Solve the system by substitution.
2x + 3y = 32
y = x + 9

Answers

Answer:

x=1 and y=10 (1,10)

Step-by-step explanation:

2+30=32

10=1+9

Dexter deposited 6,300 into a saving account that earns 2.60% simple interest per year. How much interest will she earn in 4 years

Answers

Answer:

2

Step-by-step explanation:

HELP PLEASE PLEASE HELP, also show work!

Answers

Answer:

1 6 3b 0ny 5i bhk

Step-by-step explanation:

The original cost is $25. The item has a discount of 20% off. What is the discount amount?

Answers

Answer:20 dollars.

not sure

Step-by-step explanation:

19. Frank and Jenny want to cut a plank for a sandbox they are making. If the plank is
12 inches long, and they want four pieces of equal size, how long will each piece measure?
A. 44 inches
44 in
B. 3 inches
C. 8 inches
0.3 inches

Answers

Answer:

it is 3 inches

3 x 4 = 12

Need answers for 1 and 2. Please

Answers

Answer:soultion

Step-by-step explanation:      solution

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches
What is the greatest possible whole-number length of the unknown side?

Answers

Answer:

Step-by-step explanation:

If you add the lengths of two sides, 12 and 14, you will get 28. Using the above theorem, the third side cannot be greater than or equal to 28. Therefore, the greatest possible whole-number length of the unknown side is 27.

Answer:

Step-by-step explanation:

7 or C

Which one of these grids is shaded red and blue in the ratio 0.5: 1?
A
B
D
E
F

Answers

Answer:

B

Step-by-step explanation:

Answer:

Its E

Step-by-step explanation:

Helpppppp please i need help on this question

Answers

Step-by-step explanation:

K=12 if you want explanation i will

Explanation:
k + 6 = 18
k = 18 - 6
k = 12

What is the initial value of the equation shown? (1 point) y = −7x − 6 −13 −7 −6 −1

Answers

Answer:

-6

Step-by-step explanation:

The equation is y = -7x - 6.

The initial value is found when x = 0.

y = -7(0) - 6

y = 0 - 6

y = -6

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