Evaluate the function for f(x) = x + 3 and g(x) = x2 – 2.
(f + g)(t – 5)

Evaluate The Function For F(x) = X + 3 And G(x) = X2 2.(f + G)(t 5)

Answers

Answer 1

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[tex]f(x) = x + 3[/tex]

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

_________________________________

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

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

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

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

_________________________________

[tex](f + g)(t - 5) = ({t - 5})^{2} + (t - 5) + 1 \\ [/tex]

[tex](f + g)(t - 5) = {t}^{2} - 10t + 25 + t - 5 + 1 \\ [/tex]

Collect like terms

[tex](f + g)(t - 5) = {t}^{2} - 9t + 21 \\ [/tex]

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Related Questions

There are 35 female performers in a dance recital. The ratio of men to women in the recital is 2 : 7 How many men are in the recital?

Answers

There are 32 female performers in a dance recital the ratio of men to women is 3/8 How many men are in the dance recital

But we have 32 female performers in the dance recital. Hence there are 3×4=12 men in the dance recital.

Could anyone help me find the missing value of W,X,Z, and Y ?

Answers

Answer:

x= 50°

w= 130°

y°= 110°

z°=30°

Step-by-step explanation:

x°= 180° - 60°- 70° ( angle sum of triangle)

= 50°

w°= 180° - 50° ( adjacent angles on a straight line)

= 130°

y°= 180° - 70° ( adjacent angles on a straight line)

= 110°

z°= 180 - 40° - 110° ( angle sum of triangle)

= 30°

False regarding Earnest money

Answers

Answer:

?

Step-by-step explanation:

Answer:

Earnest money is typically in the form of a check.

Step-by-step explanation:

Not everyone writes checks. Can be paid in any form.

What is the solution to the system of equations?
O (-8,-4)
O(-4,-8)
O (44)
0 (4-4)

Answers

Answer:

C.

(2,4)

Step-by-step explanation:

i did it on edge

happy holidays :)

Answer: It's B (-4, -8)

Step-by-step explanation:

what does it mean to be a function how can you determine functionality of a relation or eqaution graph

Answers

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function.

610 divided by 20 without a decimal

Answers

Answer:

30 remainder 1 or 30.5

Step-by-step explanation:

please make me brainliest

expand form 16(2x - 1)​

Answers

Answer:

32x - 16

Step-by-step explanation:

16(2x - 1)​

16 • 2x - 16

32x - 16

Answer:

32x - 16

Step-by-step explanation:

distrubutive property: 16 times 2x plus 16 times -1

please help will give brianliest

Answers

Answer:

I helped

Step-by-step explanation:

you okay do can I get some points cuh

Answer:

with what?? >_>

ed
A running track has two straight sides with length 130 m and two semicircle
ends with radius 40 m. It takes Kat 20 seconds to jog 80 m. How long would
it take her to jog around the track 42 times? Give your answer in hours and
minutes, to the nearest minute.
40 m
130 m

Answers

Answer:

1 hour 29 minutes and 29 seconds

Step-by-step explanation:

We need to find the circumference of the two semicircles of the track (which forms a full circle of radius 40m):

pi×40×2 = 80pi

The total length of the track to be travelled would be:

(80pi+130+130) × 42 = (80pi+260) ×42

                       = 21 476m (Rounded to 5 s.f.)

80m/20s

1s = 80÷20

   = 4m

For every 1 second, Kat travels 4m.

Total Time taken:

21 476÷4 = 5369 seconds

               = 1 hour 29 minutes and 29 seconds

A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is 2584 square inches, find the width of the frame

Answers

Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

(x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0  

→ Add 4 to both sides to find x

x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

The width of the is 4 inches

The mean of birth weights for individual babies in the population is 3,500 grams. What is the mean birth weight for the sampling distribution for samples of 100 babies?

Answers

Answer:

The mean birth weight for the sampling distribution is

3,500 grams.

Step-by-step explanation:

The sample mean is the average of the sample values collected divided by the number of the samples, while the population mean is the average or mean of all the values in the population.  If the sample is random and the sample size is large enough, then the sample mean would be a good estimator of the population mean.  This implies that with a randomly distributed and unbiased sample size, the sample mean and population mean will be equal, according to the central limit theorem. Therefore, the mean of the sample means will always approximate the population mean.

Yvette invests $300 each quarter in a fixed-interest mutual fund paying annual
interest of 7% compounded quarterly. How much will her account have in it at
the end of 11 years?

Answers

Answer:

Step-by-step explanation:

The formula for  calculating the amount after t years is expressed as;

A = P(1+r/n)*nt

P is the Principal (amount invested) = $300

r is the rate = 7% = 0.07

t is the time used to save = 11 years

n is time of compounding = 1/4 (quarterly)

Substitute;

A = 300 (1+0.07/(1/4))^(1/4)(11)

A = 300(1+4(0.07))^2.75

A = 300(1+0.28)^2.75

A = 300(1.28)^2.75

A = 300(1.9716)

A = 591.49

Hence the amount that will be in her account after 11 years is $591.49

Can someone help me with this? am i supposed to graph

Answers

Answer:

Step-by-step explanation:

1). a(x) = -4x + 7  If x > 1

   a(8) = -4(8) + 7

          = -32 + 7

          = -25

2). a(x) = 2x - x² If -6 < x ≤ 1

    a(1) = 2(1) - 1²

           = 2 - 1

           = 1

3). a(x) = |x - 8| If x ≤ -6

   a(-7) = |- 7 - 8|

           = |-15|

           = 15

4). a(x) =  2x - x² If -6 < x ≤ 1

   a(-3) = 2(-3) - (-3)²

           = -6 - 9

           = -15

5). a(x) =  2x - x² If -6 < x ≤ 1

    [tex]a(-\frac{1}{2})=2(-\frac{1}{2})-(-\frac{1}{2})^{2}[/tex]

               = - 1 - [tex]\frac{1}{4}[/tex]

               = [tex]-\frac{5}{4}[/tex]

6). a(x) = -4x + 7 If x > 1

    [tex]a(\frac{9}{4})=-4(\frac{9}{4})+7[/tex]

            = -9 + 7

            = -2

Helppp please I need help ASAP!!!!!

Answers

Answer:

D

Step-by-step explanation:

The answer is D because the 45 would represent his songs, and 180 would represent the total.

Match the following Match the items in the left column to the items in the right column
1 fish to Starfish
2. total to fish
3. Starfish to total
4. Starfish to fish

Answers

Answer:

Sorry, you didn't send the picture with it. But, I have the picture that you forgot to send, here is the picture.

Step-by-step explanation:

That is the image down there! Thanks. Sorry, I can't answer though.

A firm producing poultry feeds finds that the total cost C(x) in dollars of producing and selling x units is given by

C(x) - 20x+100. Management plans to charge $24 per unit for the feed. How many units must be sold for the firm to break even?

Answers

Answer:

Break-even point in units= 25

Step-by-step explanation:

Giving the following information:

Fixed cost= $100

Unitary variable cost= $20

Selling price per unit= $24

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 100 / (24 - 20)

Break-even point in units= 25

the picture is the answer​

Answers

Answer:

4. 3

The answer is the last option, all you do is reduce

Step-by-step explanation:

rise over run = rise/run = 6/2

reduce,

6/2

3/1

3x

How many filled sandwich cookies would you need to reach of 1700 mm if you only had one top of the cookie, the stuffing and one bottom of the cookie? Height of top of cookie 3.5 mm height of stuffing 2 mm and height of bottom of cookie 3.5 mm

Answers

Answer:

??

Step-by-step explanation:

What is the volume of the figure? Enter the answer in the box.


Answers

Answer:

217,600

Step-by-step explanation:

Multiply all the sides


You earned a 90% on a science test. You answered 18 questions
correctly. How many questions were on the test?

Answers

Answer:

20 questions

Step-by-step explanation:

10 divided by 20 is 0.9 which would be 90%

Please help. This is a solve for x problem!

Answers

Answer:

3/10 = x or 0.3 = x

Step-by-step explanation:

2.1 /  x + 1 4/5 = 3 / 10x

1. first cross multiply and solve it normally:

3 (x + 1 4/5) = (2.1) 10x

3x + 5 2/5 = 21x

-3x               -3x

5 2/5 = 18x

3/10 = x or 0.3 = x

these questions are kind annoying to solve because of the fractions, so if you can, use a calculator to solve them! its much easier!

hope this helps!

Answer:

x = 3/10 = 0.3

Step-by-step explanation:

{(2.1)/(x+1 4/5)} = 3/10x

x + 1 4/5 = x + 5/5 + 4/5 = x + 9/5

then:

(2.1)/(x+9/5) = 3/10x

10x*2.1 = 3(x+9/5)

21x = 3x+ 27/5

21x - 3x = 27/5

18x = 27/5

90x/5 = 27/5

90x = 27

x = 27/90

x = 3/10 = 0.3

16\1024 cuánto es 16 dividido por 1024

Answers

Answer:

64

Step-by-step explanation:

1024÷16=64

hope this helps

Why it said he used partial products to write 7 × 870 = 5600 + 49 explain why its error in use math to justify your explanation

Answers

The equation doesn’t equal each other
6090=5649

The person is wrong because instead of writing the product as 5600 + 49 he must write 5600 + 490.

The given equation is 7 × 870 = 5600 + 49.

What is multiplication?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Now, product of two numbers 7 and 870 is

7 × 870=6090

⇒ 7 × 870 = 5600 + 490

Hence, the person is wrong because instead of writing the product as 5600 + 49 he must write 5600 + 490.

Learn more about the multiplication here:

https://brainly.com/question/1562995.

#SPJ2

Consider a coin that a head is twice more likely to occur than a tail. Find the variance of number of heads when the coin is tossed three times.

Answers

Answer:

0.667

Step-by-step explanation:

Given that :

Head is twice more likely to occur than a tail.

P(head) = p(H) = 2/3

P(tail) = p(T) = 1/3

If coin is tossed 3 times :

P(H = 0) :

1st toss = tail ;2nd toss = tail ; 3rd toss =. Tail

(1/3) * (1/3) * (1/3) = 1 / 27

P(H= 1)

HTT, THT, TTH

(2/3 * 1/3 * 1/3) + (1/3 * 2/3 * 1/3) + (1/3 * 1/3 *2/3)

= 2/27 + 2 /27 + 2/27

= 6/27 = 2/9

P(H=2)

HHT, HTH, THH

(2/3 * 2/3 * 1/3) + (2/3 * 1/3 * 2/3) + (1/3 * 2/3 * 2/3)

= 4/27 + 4/27 + 4/27

= 12 / 27

= 4 /9

P(H = 3)

HHH

(2/3 * 2/3 * 2/3)

= 8 / 27

X ___ 0 ___ 1 ____ 2 ____ 3

P(x) _ 1/27 _ 2/9 __ 4/9 __ 8/27

E(X) = (0 * (1/27)) + (1 * (2/9)) + (2 * (4/9)) + (3 * (8/27)) = 2

E(X) = 2

Var(X) = Σx²p(x) - E(X)²

= (0^2 * (1/27)) + (1^2 * (2/9)) + (2^2 * (4/9)) + (3^2 * (8/27)) - 2^2

= 4.667 - 4

= 0.667

Hence, Var(x) = 0.667

Addison has a balance of $3,450 on her credit card that has an APR of 18%. She currently pays the minimum monthly payment of $86.25. If Addison wants to pay off her balance in 24 months, determine the monthly payments she would need to make. Choose the following modification with the least cuts to her current expenses that will allow Addison to pay off her balance in 24 months.

Income
WAgES
$2,278.00
EXPENSES
Rent
$950.00

Utilities
$232.45

Food/Clothes
$445.00

Entertainment
$270.00

Car
$200.00

Credit Card
$86.25

Cell Phone
$77.89
Net Income $16.41

a.
Addison can eliminate $73 from Food/Clothes and $100 from Entertainment.
b.
Addison can eliminate $45 from Food/Clothes and $41 from Entertainment.
c.
Addison can eliminate $25 from Food/Clothes and $22 from Entertainment.
d.
The minimum payment is enough to pay off the balance within 24 months.

ANSWER IS B)Addison can eliminate $45 from Food/Clothes and $41 from Entertainment.

Answers

Answer: (B) Addison can eliminate $45 from Food/Clothes and $41 from Entertainment.

Based on the information given, Addison should eliminate $45 from the money budget for Food/Clothes ($445.00) and $41 from Entertainment ($270.00).

Given the following data:

Balance = $3,450.APR = 18%.Monthly payment = $86.25.Time = 24 months (2 years).

How to calculate monthly payment.

Mathematically, the monthly payment for a credit card can be calculated by using this formula:

[tex]M=P(\frac{r}{1-(1+r)^{-nt}} )[/tex]

Where:

P is the principal.r is the interest rate.M is the monthly payment.t is the time.n is the number of times it's compounded.

In this scenario, Addison should eliminate $45 from the money budget for Food/Clothes ($445.00) and $41 from Entertainment ($270.00) because they are the least cuts to her current expenses and they would avail her an opportunity to pay off her balance in 24 months (2 years).

Read more on monthly payment here: https://brainly.com/question/2151013

Michael pays $30 to enter a state fair, plus $4 for each ride. Which of the following
equations represents his total cost?

A. y = 30x + 4
B. y = 34x
C. y = 4x + 30
D. y = 4x + 34

PLEASE HELPP!!!

Answers

Answer:

The required equation is:

[tex]y=4x+30[/tex]

So, Option C is correct option.

Step-by-step explanation:

Entry fee for fair = $30

Cost of one ride = $4

Cost of x rides = $4x

If y represents the total cost the equation will be sum, of entree fee and cost of x rides i.e

[tex]y=4x+30[/tex]

The required equation is:

[tex]y=4x+30[/tex]

So, Option C is correct option.

Just the image below.

Answers

Answer:

Step-by-step explanation:

I'm answering this silly thing only because it seems to have an expected answer

B: is about the only answer you cannot give.

C and D are Both open ended at 15 which doesn't allow you to say that the first acceptable answer is 16

The only answer you can pick is A. The amount starts at 15 and you keep going until you hit 70. That doesn't mean you have to stop. It just means that it represents what he desires to make.

Can someone please help me and tell me if this is correct or no I’ll give brainliest
Please be honest

Answers

Answer: B

Step-by-step explanation: i googled it

i need help on 23 !!

Answers

Answer:

Step-by-step explanation:

1/4 * 2/3 = 2 / 12 = 1/6

Find the difference
5/5 - 2/10

Answers

Answer:

0.8

Step-by-step explanation:

Answer:

8/10

Step-by-step explanation:

5/5 is equivalent to 1 whole or one.

So all your suppose to do is 1 minus 2/10 which is 8/10.

Hope that helps

↖(^ω^)↗

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