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)?

A. Left by 4 units

B. Right by 4 units

C. Left by 8 units

D. Right by 8 units

**Answer:**

Option A, Left by 4 units

**Step-by-step explanation:**

Step 1: Convert g(x) to a function square

We currently have g(x) in this order: [tex]ax^2 + bx + c[/tex]

However, we want g(x) to be in this order: [tex](ax + c)^{2}[/tex]

The first thing we have to do is to** factor it out:**

[tex]g(x)=x^{2}+8x+16[/tex]

[tex]g(x) = (x + 4)(x + 4)[/tex]

[tex]g(x) = (x+4)^{2}[/tex]

Step 2: Now we can see which way we need to move it

The original form is: [tex]f(x) = (ax - b)^{2}[/tex]

Since the - has changed to a +, that means that we moved -4 spaces down the x-axis. This means that we move left by 4 units.

**Answer: **Option A, Left by 4 units

*Look at the graphs below to make sure:*

**Answer:**

*A.) Left By 4 Units*

**Step-by-step explanation:**

Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 + 8x + 16

The direction in which and by how many units the f(x) should be shifted to obtain the g(x) is given by as follows.

Given,

f(x) = x²

g(x) = x² + 8x + 16

we have to consider, the dependent term while selecting the direction.

Therefore, except x², only x term is dependent term.

In g(x), the x term is given by 8.

Therefore, we need to shift the f(x) left by 4 units.

*
*

*Therefore, option A is correct.*

Pierre found a new store where he hopes to save

money on his supplies. He bought 4 brushes and 7

tubes of paint for $32. He has another order for 6

brushes and 8 tubes of paint that will cost $43.

What is the cost of one brush? What is the cost of

one tube of paint?

Your first equation is 4x + 7y= 32, the x’s representing the brushes and the y’s the tubes of paint. Our second equation is 6x+8y=43. What I did is I multiplied the first equation by 1.5 so that it turns into 6x+10.5y=48. Then I subtracted the second equation from the first, canceling out the x’s and leaving us with 2.5y=5. Then divided and got y=2. We then go back to any of the original equations and plug it in to get the x’s.

6x+8(2)=43. We get 6x+16=43. We subtract and are left with 6x=27 and then x=4.5. Then plug both of them in to a different equation to double check. You could also use substitution by isolating one of the variables in one equation and then plugging it in to the other one.

6x+8(2)=43. We get 6x+16=43. We subtract and are left with 6x=27 and then x=4.5. Then plug both of them in to a different equation to double check. You could also use substitution by isolating one of the variables in one equation and then plugging it in to the other one.

Pythagorean theorem

**Answer:**

a^2 + b^2 = c^2

**Step-by-step explanation:**

**Answer:**

a^2 + b^2 = c^2

**Step-by-step explanation:**

Used to find side lengths of right triangles, a and b represent sides, while c represents the hypotenuse.

I NEED HELP WORTH THIS there is one more option of 6,6 also

**Answer:**

C. (2,4)

**Step-by-step explanation:**

which is the least -1 1/4 or -3/2

**Answer:**

-3/2

**Step-by-step explanation:**

2 1/3 x 3 5/6 please answer

**Answer:**

8 17/18

**Step-by-step explanation:**

I used an online calculator (calculator soup)

**Answer:**

8 17/18

**Step-by-step explanation:**

7/3 * 23/6

7*23

3*6

161/18

8 17/18

The equation x = 1 is an example of linear but not function. Why?

Because there is more than two y values for x = 1

more on fraction

21×5

**Answer:**

105.

**Step-by-step explanation:**

21+21+21+21+21=105.

Answer these correctly I’ll give brainalist + 10 points

first one is choice 1 second one is choice 3

the picture is the question

**Answer:**

Swap the direction of the inequality

**Step-by-step explanation:**

Anytime you multiply or divide by a negative number in an inequality, you flip the symbol so > turns into <

If you buy 4 turkey subs that in total costs 26 dollars how much would 5 turkey subs cost.

**Answer:**

33/32.5

**Step-by-step explanation: **

**26** divided by 4 equals 6.5

then 6.5 times 5 equals 32.5

Jimmy ate 1/3 of his sandwich at lunch. He ate another 2/3 of the sandwich. How much of the sandwich did Jimmy eat in all?

A.1/3

B.2/3

C.3/3

D.5/3

The answer is c (this needs too be 20 characters long)

Regina read his novel three nights in a row. Each night, he read for 3/4 of an hour. How many hours did regina read his novel altogether?

**Answer:**

Regina read for 2 1/4 hours or 2 hours and 15 minutes

**Step-by-step explanation:**

He read for 2 hours and 15 minutes

Can someone write down the answers pls!!!!!!!!!!

**Step-by-step explanation:**

6b x>=1

6c y>7

7a x>3

7b -2<=2x<6

-1<=x<3

answer:-1,0,1,2,3

The Gable Construction Corporation has placed bids for installing electronic message boards on two different highways.

Because of competition from other companies, Gable Construction Corporation officials estimate that the probability that

they will be awarded the Macon Expressway contract is 0.65 and the probability that they will be awarded the Seaview

Expressway contract is 0.43. Furthermore, the probability that they will be awarded both contracts is 0.22. What is the

probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

**Answer:**

0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

**Step-by-step explanation:**

We solve this question using these events as** Venn sets.**

**I am going to say that:**

Event A: Awarded the Macon Expressway.

Event B: Awarded the Seaview Expressway.

**Probability that they will be awarded the Macon Expressway contract is 0.65**

This means that [tex]P(A) = 0.65[/tex]

**The probability that they will be awarded the Seaview Expressway contract is 0.43. **

This means that [tex]P(B) = 0.43[/tex]

**Furthermore, the probability that they will be awarded both contracts is 0.22.**

This means that [tex]P(A \cap B) = 0.22[/tex]

What is the

**Probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway?**

Only A:

[tex]P(A) - P(A \cap B) = 0.65 - 0.22 = 0.43[/tex]

Only B:

[tex]P(B) - P(A \cap B) = 0.43 - 0.22 = 0.21[/tex]

**Either**

0.43 + 0.21 = 0.64

0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway

I just need help cause if I don’t I don’t know what imma do

**Answer:**

[tex]P(32) = \frac{1}{90}[/tex]

[tex]P(Odd) = \frac{1}{2}[/tex]

[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]

**Step-by-step explanation:**

**Given**

**Sample Space = 10 to 99**

**First, we calculate the sample size (n)**

[tex]n = 99 - 10 + 1[/tex]

[tex]n = 90[/tex]

**Solving (a): P(32)**

**In 10 to 99, there is only 1 32.**

**So,**

[tex]P(32) = \frac{n(32)}{n}[/tex]

[tex]P(32) = \frac{1}{90}[/tex]

**Solving (b): P(Odd)**

**There are 45 odd numbers between 10 and 99**

**i.e.**

[tex]n(Odd) = 45[/tex]

**So:**

[tex]P(Odd) = \frac{n(Odd)}{n}[/tex]

[tex]P(Odd) = \frac{45}{90}[/tex]

[tex]P(Odd) = \frac{1}{2}[/tex]

**Solving (c): P(Multiple of 5)**

There are 18 multiples of 5 between 10 and 99

i.e

[tex]P(Multiples\ 5) = \frac{18}{90}[/tex]

[tex]P(Multiples\ 5) = \frac{1}{5}[/tex]

heyy i need help on me hw

**Answer:**

the answer is b

**Step-by-step explanation:**

brainliest pleasee?

Pls answer this for me

**Answer:**

A) 216in squared

**Step-by-step explanation:**

6 / 2 = 3

4 * 3 = 12

12 * 2 = **24**

5 * 12 = 60

60 * 2 = **120**

6 * 12 = **72**

**24 + 72 + 120 = 216in^2**

**Hope this helped! Have a nice day! Plz mark as brainliest!!! :D**

**-XxDeathshotxX**

Simplify the expression: 5(-5 + 2y) =

The answer is-25+ 10y

6+x=23 what is x in the equation

the correct answer is x=17

What is the median of data set 32 25 25 32 32 10 -10 25

**Answer:**

-10, 10, 25, 25, 25, 32, 32, 32

Its 25

**Step-by-step explanation:**

The median is the middle number if there are an even amount of numbers you would have two medians add them the divide by two

the median is 25. you can put the numbers in order from least to greatest values and cross out one by one to make it easier! hope this helps :D

I need some help

I will give you brainliest and heart!

**Answer:**

Correct!

**Step-by-step explanation:**

First, I'll try to solve it myself.

2(2a-1)+3a=7a-2

7a-2

4a-2=7a-2

His is very correct!

i need help with everything please if you help you are a legend please.

2. Closer to 0. Because it is always getting smaller. The smaller it gets, the closer it get to 0.

3.

a. Closest to 1.

b. Closest to 0.

c. (1/12)

4.

a. Closest to 1.

b. Closest to (1/2)

c. (14/16)-(10/16)=(4/16)

Does anyone know the answer??????

Answer:

i think its the 2nd choice but im not 100% sure

Determine the length of the diagonals of the isosceles trapezoid below when KL= h+7 and UE= 4h-25

**Answer:**

KL= 17.67 unit

UE = 17.67 unit

**Step-by-step explanation:**

**Given:**

Diagonals

KL= h+7

UE = 4h-25

**Find:**

Length of diagonals KL and UE

**Computation:**

We know that in isosceles trapezoid the length of diagonals are equal

So,

KL = UE

h+7 = 4h-25

3h = 32

h = 10.67

So,

KL= h+7

KL= 10.67+7

**KL= 17.67 unit**

UE = 4h-25

UE = 4(10.67)-25

**UE = 17.67 unit**

100 - 50 + 4

HELP PLS PLS PLSSSSS

**Answer:**

54

**Step-by-step explanation:**

100-50+4=50+4

=54

.....

Please this will determine if I pass

The answer is B through ASA (Angle-Side-Angle) similarity criterion.

calculate the GPA of a student with the following grades: B (3 hours), D (8 hours), C (18 hours). Note that an A is equivalent to 4.0, a B is equivalent to a 3.0, a C is equivalent to a 2.0, a D is equivalent to a 1.0, and an F is equivalent to a 0. Round your answer to two decimal places.

**Answer:**

The GPA of the student is 1.83.

**Step-by-step explanation:**

We use a **weighted average** to solve this question.

**We have the following grades:**

B, which is equivalent to 3, with weight 3.

D, which is equivalent to 1, with weight 8.

C, which is equivalent to 2, with weight 18.

So

[tex]M = \frac{3*3 + 1*8 + 2*18}{3 + 8 + 18} = \frac{53}{29} = 1.83[/tex]

The GPA of the student is 1.83.

-2y + 4 > 10

solve the inequality

**Step-by-step explanation:**

-2y+4>10

subtract 4 from both sides

-2y+4-4>10-4

-2y>6

divide both sides by two

-2/2y>6/2

-1y>3

if negative y is greater than three than you have to multiply both sides of the equation by -1

y>-3 if you put that back into the earlier equation it is impossible.

so we have to switch the signs to < or less than

y<-3

Hope that helps:)

A student must leave for campus in 10 minutes or he will be late for class. Unfortunately, he is snowed in. He can shovel the driveway in 18 minutes, and his brother claims to be able to do it in 12 minutes. If they shovel together, how long will it take to clear the driveway? Will this give enough time for the student to get to the campus?

**Answer:**

I believe if they did it together they would finish in 6 minutes

**Step-by-step explanation:**

How many quarts are in two gallons?

2 gallons = 8 quarts

hope it's help ;3

Please help me!! ill mark you brainliest. please actually answer all of em.
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