Functions f(x) and g(x) are shown: f(x) = x2 g(x) = x2 − 8x + 16 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 4 units Right by 4 units Left by 8 units Right by 8 units

Answers

Answer 1

Answer:

Shift right by 4

Step-by-step explanation:

Given f(x)=x^2

g(x)= x^2-8x+16

Using

Horizontal Shift theorem dealing with the question

If the graph were to be move to to the right, we must use of graph f (x-L)

Where L= 4 and

NOTE:

POSITIVE L MAKES GRAPH SHIFT RIGHT

2) NEGATIVE MAKES GRAPH SHIFT LEFT

g(x)= x^2-8x+16

If we factorize this we have

(x-4)(x-4)

Since the two terms are the same we have (x-4)^2

Then it can move by factor of 4 to the right since constant 4 can be substracted from the parents function

Answer 2

Answer:

Left by 4

Step-by-step explanation:

graph x^2 and x^2 − 8x + 16 on Desmos . com

you start at f(x) and end at g(x)


Related Questions

Please solve these questions on the topic of exponents

Answers

Answer/Step-by-step explanation:

Recall: [tex] x^{-a} = \frac{1}{x^a} [/tex]

a. [tex] 4^{-3} = \frac{1}{4^3} = \frac{1}{64} [/tex]

b. [tex] 13^{-2} = \frac{1}{13^2} = \frac{1}{169} [/tex]

c. [tex] (-3)^{-2} = \frac{1}{-3^2} = \frac{1}{9} [/tex]

PLEASE ANSWER QUICKLY ASAP
COMPLETE QUESTION B​

Answers

Answer:

Sector

Step-by-step explanation:

A sector of a circle is the portion of circle enclosed by two radii and arc


The table below shows the number of cars Jing sold each month last year.
What is the median of the data in the table.
13
16
19
20.5
23.5
Other:

Answers

Answer:

The median of the data in the table is 19.

Step-by-step explanation:

We are given the following data that shows the number of cars Jing sold each month last year below;

Number of cars Jing sold: 13, 16, 19, 20.5, 23.5

For calculating the median, firstly we have to observe that the number of observations (n) in our data is even or odd because;

If n is odd, then the formula for calculating median is given by;

                           Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

If n is even, then the formula for calculating median is given by;

                           Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs.} + (\frac{n}{2}+1 )^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations in our data is odd, i.e. n = 5.

So, Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

                   = [tex](\frac{5+1}{2} )^{th} \text{ obs.}[/tex]

                   = [tex](\frac{6}{2} )^{th} \text{ obs.}[/tex]

                   = 3rd obs. = 19

Hence, the median of the data in the table is 19.

At the end of the day, a bakery gives everything that is unsold to food banks for the needy. If it has 12 apple pies left at the end of a given day, in how many different ways can it distribute these pies among 6 food banks for the needy?

Answers

Answer:

462 ways

Step-by-step explanation:

The formula to use in solving this problem is given as the Combination formula

The Combination formula is given as

C(n , r) = nCr = n!/r! (n - r)!

We are told that a food bakery has 12 pies unsold at the end of the day which they intend to share to 6 food banks

n = 12, r = 6

In order to ensure that at least 1 food bank gets 1 pie, we have:

n - 1 = 12 - 1 = 11

r - 1 = 6 - 1 = 5

Hence,

C(11, 5) = 11C5

= 11!/ 5! ×(11 - 5)!

= 11!/5! × 6!

= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/ (5 × 4 × 3 × 2 × 1) ×( 6 × 5 × 4 × 3 × 2 × 1)

= 462 ways

What are all the numbers of Pi? I need this now please

Thank you!! ♥︎

Answers

Answer:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...

Step-by-step explanation:

If two angles are complements of each other then each angle is

Answers

Answer:

each angle is less than 90 degrees. angle 1+angle2=90 degrees

Step-by-step explanation:

We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?

Answers

Answer:

1.18 dollar.

Step-by-step explanation:

E = 17/20D

E => The amount in euros.

D => The amount in dollars.

From the question given,

E = 1

D =?

E = 17/20D

1 = 17/20D

Cross multiply

20 x 1 = 17D

20 = 17D

Divide both side by 17

D = 20/17

D = 1.18

Therefore, 1.18 dollar is equivalent to 1 euro.

Answer:

How many Euros have the same value as 1 U.S. dollar?

17/20 euros

How many U.S. dollars have the same value as 1 euro?

59/50 dollars

(or 0.85 either one is correct)

Step-by-step explanation:

Khan Academy

Hope this helps! ;)

Which is greater than 4? (a) 5, (b) -5, ...

Answers

It must be 5 (a) because it’s 4

Answer:

(a) 5

Step-by-step explanation:

5 is geater than 4

4 is greater than -5

There are 4 colas, 1 ginger, 7 root beers, and 6 cherry sodas in a cooler. What are the odds of choosing a ginger ale? Give your answer in a proportion in lower terms.

Answers

Answer:

Step-by-step explanation:

the odds of choosing a ginger ale is 1/21

The odds of choosing a ginger ale is 1/18.

To find the proportion, add all the numbers together, and put that as the denominator. Put the number that you are trying to find the proportion of as the numerator

Last week, 17 employees exceeded their sales quota, 13 employees met their sales quota, and 3 employees didn't meet their sales quota. Express the number of employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota. Question 11 options: A) 3:13 B) 16:17 C) 17:16 D) 17:33

Answers

Answer:

17:16

Step-by-step explanation:

Number of employees exceeded their sales quota = 17

Number of employees met their sales quota = 13

Number of employees didn't exceed their sales quota = 3

Now, we need to find the ratio of the number employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota.

 

Which polynomial is a factor of both expressions? x – 8 x + 7 x – 2 (x – 2)2

Answers

Answer:

C. x-2

Step-by-step explanation:

edge

Answer: the 3rd the answer c

x-2

Step-by-step explanation:

Fachorise completely
x^2y^2-1​

Answers

Answer:

[tex](xy+1)(xy-1)[/tex]

Step-by-step explanation:

x²y²-1

=(xy)²-(1)²

=(xy+1)(xy-1)

multiple choice
a. 12 pie cm
b. 21 pie cm
c. 35 pie cm

Answers

Answer:

The correct option is;

a. 12 pie cm

Step-by-step explanation:

Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;

Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same

The volume of the square based prism = 452 cm³

Therefore, the volume of the cylinder (of equal base area) = 452 cm³

The formula for the volume of square based prism = Area of base × Height

∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm

Which gives;

Area of the base of the square based prism  = 452/4 = 113 cm²

The area of the base of the cylinder [tex]A_c[/tex]  = The area of the base of the square based prism = 113 cm²

The area of the base of the cylinder,[tex]A_c[/tex]  is given by the following equation;

[tex]A_c[/tex] = π×r² = 113 cm²

r = √(113/π) = √35.97 ≈ √36  = 6 cm

The circumference of the base of the cylinder,[tex]C_c[/tex]  is given by the following equation

[tex]C_c[/tex] = 2×π×r ≈ 2×π×6 = 12×π cm

The correct option is 12 pie cm.

Find the term of each sequence.

32, 80, 200, ...5th term

Answers

Answer:

t5 = 1250

Step-by-step explanation:

Each term is derived by multiplying the previous term by 2.5

t2 = t1 * 2.5

t2 = 32 * 2.5

t2 = 80

===========

tn = a*b^(n - 1)

t3 = 32*2.5^2

t3 = 200

That's just to test the formula. It does work.

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

t5 = 32*2.5^(5 -1)

t5 = 32*2.5^4

t5 = 1250

how many terms are there in the expressions 1 + 2k - j

Answers

Answer:

3 terms

Step-by-step explanation:

A term in mathematics, especially in Algebra, could be a number, a variable, variable together with a number or variables multiplied together as a single whole. Terms are usually separated with either negative or positive sign in an expression.

In the expression, [tex] 1 + 2k - j [/tex] , there are 3 terms here spared by either the negative sign or the positive.

The 3 terms are: [tex] 1, 2k, j [/tex].

Answer the questions when examining the data.
What is the domain?
What is the range?

I got (-infin.,infin) for domain but I’m not sure because there can’t be less that 0 days so I was wondering if it would be (3,infin), (3,192), (-infin,infin) or another coordinate. Please answer the range too

Answers

Greetings from Brasil...

In this case, we can say:

Domain = [0; 6]

Image = [3; 192]

see attachment

8(4k - 4) = -5k - 32

Answers

Answer:

k=0

Step-by-step explanation:

8(4k-4)=5k-32

32k-32=-5k-32

32k-32+32=-5k-32+32

32k=-5k

32k+5k=-5k+5k

37k=0

37k/37=0/37

k=0

Answer:

k=0

Step-by-step explanation:

To solve for k, we need to first distribute the 8 through the parenthesis.

32k-32=-5k-32

Lets add 5k to both sides.

37k-32=-32

add 32 to both sides

37k=0

divide 37 from both sides

k=0


Rita bought 4 CDs that were each the same price. Including sales tax, she paid a total of $ 61.60. Of that total,$ 2.80 was tax. What was the price of each CD before tax

Answers

Answer:

The price of each CD is:

$14.70

Step-by-step explanation:

(61.6 - 2.8) /4

=  58.8/4

= $14.7

Answer:

$14.70

Step-by-step explanation:

We want to find the price of each CD before tax. Therefore, we must first subtract the tax from the total.

total -tax

The total cost was $61.60 and the tax was $2.80

$61.60 - $2.80

$58.80

The price for the 4 CDs (without tax) was $58.50.

We know that each CD costs the same price and Rita bought four CDs. Therefore, we can divide the cost without tax by 4.

cost without tax / 4

The cost without tax is $58.80

$58.80 /4

$14.70

Each CD before tax costs $14.70

I forgot how to do this. I will give brainliest!

Answers

Answer:

A = 2, B = 3 and C = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y = 2 ( subtract 2x from both sides )

3y = - 2x + 2 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

Parallel lines have equal slopes, thus

y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

To find c substitute (2, 0) into the partial equation

0 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{4}{3}[/tex]

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form

Multiply through by 3

3y = - 2x + 4 ( add 2x to both sides )

2x + 3y = 4 ← in standard form

with A = 2, B = 3 and C = 4

Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 4x+4\leq9x+84x+4≤9x+8

Answers

Answer:

  x ≥ -4/5

Step-by-step explanation:

Maybe you want to solve ...

  4x+4 ≤ 9x +8

  0 ≤ 5x +4 . . . . . subtract 4x+4

  0 ≤ x +4/5 . . . . . divide by 5

  -4/5 ≤ x . . . . . . . subtract 4/5

Answer:

x ≥−4/5

Step-by-step explanation:

Convert 25 feet per second to miles per hour.​

Answers

1 mile = 5,280 feet

1 hour = 3600 seconds

3600/5280 = 0.681818 feet per second

25 ft per second x 0.681818 = 17.045 miles per hour

Round the answer as needed.

Answer:

The correct answer is 17.045 miles per hour.

1 1/3 minus 5/6 please help me out

Answers

Answer:

17/6

So this is the answer. If you want to convert to decimal... The answer will be 2.83..hope it is right

The mean amount purchased by a typical customer at Churchill's Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions.
(a) What is the likelihood the sample mean is at least $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
(c) Within what limits will 90 percent of the sample means occur? (Round your answers to 2 decimal places.)

Answers

Answer:

a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex]     ( to four decimal places)

b. [tex]P(22.5<X<25) = 0.9043[/tex]   ( to four decimal places )

c. The limits will be between the interval of   ( 22.33,24.67 )

Step-by-step explanation:

Given that :

mean = 23.50

standard deviation = 5.00

sample size = 50

The objective is to calculate the following:

(a)  What is the likelihood the sample mean is at least $25.00?

Let X be the random variable, the probability that the sample mean is at least 25.00 is:

[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]

[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]

[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]

[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]

[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex]   to two decimal places

From the normal tables :

[tex]P(X \geq 25) = 1 - 0.9830[/tex]

[tex]\mathtt{P(X \geq 25) =0.0170}[/tex]     ( to four decimal places)

(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]

[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]

[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]

[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]

[tex]P(22.5<X<25) = 0.9043[/tex]  to four decimal places

(c) Within what limits will 90 percent of the sample means occur?

At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10

The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65

Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

Standard Error =  [tex]\dfrac{5}{\sqrt{50}}[/tex]

Standard Error = 0.7071

Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]

Lower limit =  ( 23.5 - (1.65×0.707) )

Lower limit =  ( 23.5 - 1.16655 )

Lower limit = 22.33345

Lower limit = 22.33    (to two decimal places).

Upper Limit = ( 23.5 + (1.65*0.707) )

Upper Limit = ( 23.5 + 1.16655 )

Upper Limit = 24.66655

Upper Limit = 24.67

The limits will be between the interval of   ( 22.33,24.67 )

The height of the rectangular prism is 2 m. If its volume is 72 cubic meters, what is the area of the base, in square meters?

Answers

Answer:

Base area is 36 square meters

Step-by-step explanation:

The volume of a rectangular prism is V = (height)(length)(width).  We know all of these dimensions except for the area of the base, which is (length)(width).

Solving this equation for (length)(width), we get:

                                                       volume        72 m^3

(length)(width) = (area of base) = -------------- = -------------  = 36 m^2

                                                         height          2 m

A VERTICAL POLE OF CAST A SHADOW OF 4.5m LONG AT THE SAME TIME A TREE OF HEIGHT 24m LONG CAST A SHADOW OF 6m LONG. FIND THE HEIGHT OF THE POLE.​

Answers

Answer:

18 metres

Step-by-step explanation:

4.5/6 = x/24

¾= x/24

x = 18 m

Betsy's high school is putting on a production of a play as a fundraiser for the school's music programs. A local bank has agreed to allow the school to use a line of credit from which they can withdraw money to pay for the play. Then, any deposits they make at the bank will be applied to the negative balance of the credit account. The play cost $3,200.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 1,007 people attend the play's opening night, what will the balance of the bank account be?

Answers

Answer:

Hey there!

If 1007 people attend, they will make a profit of 10070 dollars.

The play costed 3200 dollars to produce, so we have -3200+10070=7500 dollars as the final balance of the bank account.

Let me know if this helps :)

Answer:

Step-by-step explanation:

the correct answer is 6,870 it was d for me it might be different :)

-

On a number line if point A lies -3 and point B lies on 4, what is the length of AB

Answers

Answer:

7

Step-by-step explanation:

4-(-3)=

4+3=

7

Answer:

7

Step-by-step explanation: take the absolute value of both numbers and add them together so -3 becomes 3 and 4 stays the same they add up to 7.

the first four terms of the sequence an=2n+3are
answer
5,8,11,14
3,5,7,9
1,3,5,7
5,7,9,11​

Answers

Step-by-step explanation:

Hey, there!!!

Your required answer is optionD.

checking,

The 1st sequences are,

5,8,11,14

here,

now, use formula,

(an = 2n+3) in the sequences,

a1 = 2×1+3=5 = matching

a2= 2×2+3=7 = not matched

a3= 2×3+3= 9 = not matched

a4= 2×4+3=11 = not matched.

For 2nd sequences

3,5,7,9

Use the formula of an term,

a1 = 2×1+3=5 = not matched

a2 =2×2+3=7not matched

a3 = 2×3+3=9= not matched.

For 3rd sequences,

1,3,5,7

a1=2×1+3=5= not matched

a2=2×2+3=7= not matched

a3=2×3+3=9= not matched

a4=2×4+3=11= not matched

Now, for 4th sequences,

5,79,11

a1=2×1+3=5= matching

a2=2×2+3=7= matching

a3= 2×3+3=9= matching

a4=2×4+4=11= matching

Therefore, the answer is option D.

Hope it helps..

On Thursday, 40 trains left the station. Eight left late. On Saturday 50 trains left the station. Nine left late. What percentage of trains were not late on each day?

Answers

Answer:

Thursday=80%

Saturday=82 %

Step-by-step explanation:

Thursday trains not late=40-8=32

% trains not late=32/40×100=80

Saturday trains not late=50-9=41

% trains not late on Saturday=41/50×100=82

Represents the solution to the inequality -9=2/3x-7<5

Answers

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

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They wondered what was below the water, and at last Beavers Grandchild, the little Water-beetle, offered to go and see if he could learn. He darted in every direction over the surface of the water, but could find no firm place to rest. Then he dived to the bottom and came up with some soft mud, which began to grow and spread on every side until it became the island that we call Earth. It was afterward fastened to the sky with four cords, but no one remembers who did this. At first Earth was flat and very soft and wet. The animals were anxious to get down, and set out different birds to see if it was yet dry, but they found no place to alight and came back again to Gallati. At last it seemed to be time, and they sent out the Buzzard and told him to go and make ready for them When Earth was dry and the animals came down, it was still dark, so they got the sun and set it in a track to go every day across the island from east to west, just overhead This story contains elements of which two types of creation stories? 73Ge32hasneutrons. About thirteen different species of finches inhabit the Galpagos Islands today, all descendants of a common ancestor from the South American mainland that arrived a few million years ago. Genetically, there are four distinct lineages, but the thirteen species are currently classified among three genera. The first lineage to diverge from the ancestral lineage was the warbler finch (genus Certhidea). Next to diverge was the vegetarian finch (genus Camarhynchus), followed by five tree finch species (also in genus Camarhynchus) and six ground finch species (genus Geospiza). 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One of the companys products is grilled salmon with new potatoes and mixed vegetables. During the most recent week, the company prepared 4,800 of these meals using 2,350 direct labor-hours. The company paid its direct labor workers a total of $23,500 for this work, or $10.00 per hour. According to the standard cost card for this meal, it should require 0.50 direct labor-hours at a cost of $9.40 per hour. Required: 1. What is the standard labor-hours allowed (SH) to prepare 4,800 meals? 2. What is the standard labor cost allowed (SH SR) to prepare 4,800 meals? 3. What is the labor spending variance? 4. What is the labor rate variance and the labor efficiency variance?