Answers
[tex](f \circ g)(x) = x+12[/tex]
Domain = [-3, infinity)
==================================================
Work Shown:
[tex]f(x) = x^2 + 9\\\\f(g(x)) = (g(x))^2 + 9\\\\f(g(x)) = (\sqrt{x+3})^2 + 9\\\\f(g(x)) = x+3 + 9\\\\f(g(x)) = x+12\\\\(f \circ g)(x) = x+12\\\\[/tex]
In step 2, we replaced every x with g(x)
In step 3, we plugged in g(x) = sqrt(x+3)
The domain of g(x) is [-3, infinity), so this is the domain of [tex](f \circ g)(x)[/tex] as well since the composite function depends entirely on g(x). Put another way: the input of f(x) depends on the output of g(x), so that's why the domains match up.
Related Questions
Original price $80 Rate of discount 4% what is the Discount and Sale price
Answers
Answer:Price after discount: $76.80
You saved: $3.20
Step-by-step explanation:
Nathan ran 2.35 miles on Tuesday and 3.15 on Thursday. What total distance did he run?
Answers
Answer:
5.5 miles
Step-by-step explanation:
2.35 + 3.15 =5.5
Solve for k.
k + 4 over 2 = 3
Answers
Answer:
K = 1
Step-by-step explanation:
K + 2 = 3
K = 3 -2
K = 1
Answer:
K=2
Step-by-step explanation:
K+4 / 2 = 3
If you input 2 into the equation you get 3.
2+4=6
6/2 = 3
April invested $7500 into a continuously compounded account with an interest rate of 2.7% for 2 years. How much money was in the account after that time?
Round your answer to the nearest dollar.
Answers
Answer:
The final balance is $7,913 and the total compound interest is $413.27
To calculate compound intrest, you need to multiply the initial principal amount ($7500) by one , plus the annual intrest rate (2.7%) raised to the number of compound periods minus one. The total initial amount of the loan is the subtracted from the resulting value.
After two years, the balance on the account will be $7916 if April invested $7500 into a continuously compounded account with an interest rate of 2.7% for 2 years.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
It is given that:
April invested $7500 into a continuously compounded account with an interest rate of 2.7% for 2 years.
The formula to find the money is:
[tex]\rm A = Pe^{rt}[/tex]
Here P = $7500
r = 2.7% = 0.027
t = 2 years
[tex]\rm A = 7500e^{0.027\times2}[/tex]
After solving:
A = 7916.13 ≈ 7916
Thus, after two years, the balance on the account will be $7916 if April invested $7500 into a continuously compounded account with an interest rate of 2.7% for 2 years.
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18 red marbles; 6 to 9
Answers
Answer:
Im not sure what the question is
Step-by-step explanation:
Rewrite using distributive property and GCF.
16 + 24
Answers
determine whether or not the two triangles below could lie on the same graphed line
Answers
Answer:
I think they could because they are both right trigangles and have a flat bottom
Step-by-step explanation:
I’m not sure if I’m right but can someone help.!
Answers
Answer:
4/9
Step-by-step explanation:
because it is 0.44444444 repeating :)
Answer:
I think this is right. I checked with my mom, a math wiz, and she says its 11/25. But that can't be simplified, and its not an option. Try simplifying the fraction 11/25.. Hope it helps
Step-by-step explanation:
Is -2.75 greater than -3.25? HURRY!
Answers
sergio must ride 7.5 miles in 1/4 hour to achieve this target speed, so he needs to ride an additional ____ mile per 1/4 hour
Answers
Answer: 7.0
Step-by-step explanation:
sergio must ride 7.5 miles in 1/4 hour to achieve this target speed so he needs to ride an addititonal 9.8 mile per1/4 hour
Answer:
30 mph
Step-by-step explanation:
since it is 1/4 you would multply 7.5 times 4, which adds up to 30.
in the diagram below ,segment A'B' is the image of segment AB after a rotation by 103 degrees counterclockkwise about point C. Which segments below, when drawn, would not have to be the same length
Answers
Answer:
2
Step-by-step explanation:
7n + 5 =68.... how to solve this problem and show my work
Answers
Answer:
n = 9
Step-by-step explanation:
7n + 5 = 68
7n + 5 - 5 = 68 - 5
7n = 63
7n / 7 = 63 / 7
n = 9
If |14 -2x = 20, x could equal which of the following?
Answers
Answer:
x would equal -3
Step-by-step explanation:
want to get rid of 14 from each side so 14 - 14 would get rid of that 20 - 14 = 6 now you still have a negative 2x
-2x / -2x gives you X to be alone now divide 6 with -2 which gives you -3
The value of x is -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
14 -2x = 20
Now, solving for x
Subtract 14 both side
14- 2x - 14= 20- 14
-2x = 6
Divide by (-2)
-2x/(-2)= 6/ (-2)
x= -3
Hence, the value of x is -3.
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What is 956.3 written in scientific notation?
Answers
9.563 * 10^2
The decimal number that is multiplied by 10 must be less than a two-digit number.
We move the decimal point to the left for this problem and stop where the decimal is less than a two-digit number.
So, 956.3 becomes 9.56 after moving two places to the left. Moving to the left makes the exponent of 10 positive. Moving to the right, makes the exponent of 10 negative.
We want our answer in the form
(decimal number) x 10^(n).
Answer: 9.56 x 10^2
Understand???
In my town, gas prices are always listed to the thousandths place. Since the smallest coin we have is
the penny, we have to round them to the hundredths place. If the price of gas is $5.897, what will the
price be when we round it to the hundredths place?
Answers
Answer:
It would be rounded to $5.90 per gallon. As if something is 5 or above you round up and if it is 4 or less you round down.
Help please (screenshot)
Answers
Answer:
Step-by-step explanation:
Adam, Barry, and Charles visited a small farmers market last Saturday. Adam purchased 3 dozen eggs, 1 wheel of cheese, and 5 pounds of potatoes. Barry bought 1 dozen eggs and 10 pounds of potatoes, while Charles purchased 2 dozen eggs and 2 pounds of potatoes. If Adam’s bill was $38.25, Barry’s $36.50 and Charles’ $17.20, how much did a dozen eggs, a wheel of cheese and a pound of potatoes cost?
Answers
Answer:
Dozen eggs = $5.5
Wheel of cheese = $6.25
Pound of potatoes = $3.1
Step-by-step explanation:
Let the cost
Dozen of egg = x
Wheel of cheese = y
Pound of potato = z
We will form linear equations using the information given in the question
Adam purchased 3 dozen eggs, 1 wheel of cheese, and 5 pounds of potatoes
3x + y + 5z = 38.25 ................(1)
Barry bought 1 dozen eggs and 10 pounds of potatoes
x + 10z = 36.50 ............(2)
Charles purchased 2 dozen eggs and 2 pounds of potatoes
2x + 2z = 17.20 .................(3)
solving 2 and 3
x = $5.5 and z = $3.1
substitute these values in equation 1
we get
y = $6.25
The cost
Dozen eggs = $5.5
Wheel of cheese = $6.25
Pound of potatoes = $3.1
The total bill for dinner, including tax, was $65.81. In Indiana there is a 7% sales tax. What was the price of the meal before taxes?
Answers
Answer:
$56.41
Step-by-step explanation:
You have to divide the total bill by the sales tax and the multiply that number by 100. Then subtract that number from the total bill and that's how you get your answer.
Find the midpoint of the segment whose endpoints are (8,6) and (10.4)
Answers
Answer:
the midpoint is (9,5). hope this helps
if the number of different schedules is represented by three consecutive even integers, what is the expression for that total number of schedules they have to choose from?
Answers
Answer:
s
Step-by-step explanation:
s
Apply the distributive property x+( x+2)+(x+4)
Arrange like terms = x+x+2+x+4
Simplify =x+x+x+2+4
=3x+6
How many 7/8-teaspoon servings are in 1/4 of a teaspoon of sugar? Yor anwer needs to be in farction in simplest form.
Answers
Plz mark brainliest
4/9 as a ratio? please answer ASAP!!!
Answers
Answer: 49
Step-by-step explanation:
If I run 2 1/2 miles in 19 1/5 minutes what is my average time per mile
Answers
Answer:
7:41
Step-by-step explanation:
19 1/5 as a decimal is 19.2, and the mileage would be 2.5. to find the time per mile, you divide the finish time by the number of miles you ran:
19.2 / 2.5 = 7.68
now you're prolly wondering, "why isn't the answer 7.68?" that's a good question, and the reason that 7.68 isn't the answer is bc time is all in factions of 60, not 100 like most things, so there are 60 seconds in a minute, instead of 100 seconds in a minute.
so, you have to find out how many seconds are in 0.68 of a minute. to do this, you multiply 60 by 0.68:
60 x 0.68 = 40.8
so 0.68 of a minute is 40.8 seconds, so your average pace was 7:40.8. i would just round up to 7:41, but your teacher may want exact numbers.
hopefully that helps and isn't too confusing! if you need any other help, let me know! :)
QUESTION 1 of 10: You purchased 100 shares of stock valued at $55 per share. The stock value increases to $85 per share.
What was the rate of increase?
a. 48%
b. 55%
c. 64%
d. 85%
Answers
Answer:
55%
Step-by-step explanation:
The stock value has increased at rate of B) 55%
Calculation of percentage rate of increase
Percentage rate of Increase or decrease is calculated by dividing the change (increase or decrease) by the initial before change value
Formula = ( Change / Initial Value ) x 100
Given : Initial value = $55 , New Value = $85
So, change = New - Initial Value = 85 - 55 = 35
Percentage rate = (30 / 55) x 100
= 54.54% ≈ 55%
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Pleaseee answer I will give brainiest if it helps me
Answers
Answer:
3+(-4)= -1
Step-by-step explanation:
Originally on 3 and goes to -4, and for addition add (-4) to positive 3 and you'll get -1
A triangle has a base of 3 2/5 inches and an area of 5 1/10 square inches. Find the height of the triangle.
Answers
Answer:
3.33 is the answer
Binary of 18 and 168
Answers
Answer:
18=10010
168=00110001 00110110 00111000
Step-by-step explanation:
18=10010
168=00110001 00110110 00111000
A machine cuts 25 circuit boards every 5 minutes. What is the unit rate of production for the machine?
Answers
Answer:
25 divided by 5 = 5, so the unit rate is 5 circuit boards every minute.
The unit rate of production for the machine would be 5 circuit boards per minute.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
We have been given that a machine cuts 25 circuit boards every 5 minutes.
To determine the unit rate of production for the machine.
Here the number of circuit boards = 25
And time = 5 minutes
We have to calculate the ratio of the number of circuit boards to time.
So the unit rate of production for the machine :
= number of circuit boards/time
⇒ 25/5 = 5
Therefore, the unit rate of production for the machine would be 5 circuit boards per minute.
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The sum of two binomials is 7x 2 - 15. If one of the binomials is 4x 2-8. what is the other binomial?
0 33²-7
o 11x².7
O 3x2-23
O 11x 2 + 23
Previous
Answers
Answer:
c
Step-by-step explanation:
You dont have to help but it would be nice if you would :)
Ethan invested $25,000 in an account that earns 4.25% simple interest. If Ethan doesn't make any additional deposits or withdrawals, how much interest will he have earned after 9 years?
Answers
Answer:
I think it might be $36,360.06
Step-by-step explanation:
