Answer:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2[/tex]
And we want to find:
[tex]\displaystyle (f\circ g)(-1)[/tex]
Recall that this is equivalent to:
[tex]\displaystyle (f\circ g)(-1) = f(g(-1))[/tex]
Hence, find g(-1):
[tex]\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}[/tex]
Substitute:
[tex]\displaystyle f(g(-1)) = f(1)[/tex]
Find f(1):
[tex]\displaystyle \begin{aligned} f(x) & = 2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]
10.6 m 9.1 m 6.8 m find volume
Answer:
218.36 m^3
Step-by-step explanation:
volume = 1/3 * base area * height
volume = 1/3 * (9.1*6.8) * 10.6
volume = 1/3 * (61.8) * 10.6
colume = 20.6 * 10.6
volume = 218.36
Answer:
109.3 m³
Step-by-step explanation:
Volume of a pyramid
1/3BhBase Area
1/2 x 9.1 x 6.83.4 x 9.130.94 m²Solving
V = 1/3 x 30.94 x 10.6V = 327.964/3V = 109.321333V = 109.3 m³ (approximately)A geometric sequence can be used to describe the population of rabbits on a
farm. The first spring, the farmer purchased 8 rabbits. Five years later, there are
648 rabbits at the farm. Assuming that none of the rabbits leave the farm, how
many rabbits were on the farm in year 3?
Answer:
step 1
Find the average growth per year of the populations of rabbits farm A
Over the first 2 years
for t=0
numbers of rabbits=5 (is not exact)
for t=2
numbers of rabbits=40
average=[40-5]/2---------> 17.5
step 2
Find the average growth per year of the populations of rabbits farm B
Over the first 2 years
for t=0
numbers of rabbits=5 (is not exact)
for t=2
numbers of rabbits=30
average=[30-5]/2---------> 12.5
step 3
Compare the average growth per year of the populations of rabbits on both farms
farm A=17.5
farm B=12.5
the average rate of population growth of rabbits in farm A is greater than average rate of population growth of rabbits in farm B by about 5 rabbits per year.
therefore
the answer is the option C)
the average rate of population growth of rabbits in farm A is greater than average rate of population growth of rabbits in farm B by about 6 rabbits per year.
Step-by-step explanation:
Identify the statement as true or false.
As the size of the random sample increases, the sample distribution more closely represents the population distribution.
HELP PLEASE ASAP 30 POINTS
Write the equation of the graph.
ANSWERS;
A. y+3=-1/2(x-1)
B. y-3=-1/2(x+1)
C. y=1/2x+5
D. y-3=1/2(x+1)
What is the total number of unique triangles that can be formed with side lengths of 6.5 centimeters, 6 centimeters, and 2.5 centimeters?
Enter your answer in the answer box below.
Answer:
One
Step-by-step explanation:
For unique triangles with 3 sides, the sum of the two shorter sides must be greater than the third side.
Shorter sides: 6 cm and 2.5 cm
Longer side: 6.5 cm
6 + 2.5 = 8.5
As 8.5 > 6.5 this is a unique triangle
As the side lengths are fixed, only one unique triangle can be formed.
A classroom board is 24 inches wide and 18 inches tall, Koda
is putting ribbon along the outside edge of the board. How
many inches of ribbon will he need?
18 inches
24 inches
Answer:
84 inches
Step-by-step explanation:
It is the perimeter.
Koda needs 84 inches of ribbon to put it around the edge of the board.
A classroom board is 24 inches wide and 18 inches tall, Koda s putting ribbon along the outside edge of the board.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
length = 24 inch
width = 18 inch
The perimeter of the board, = 2 {length + width]
= 2 [24 + 18]
= 84
Thus, Koda needs 84 inches of ribbon to put it around the edge of the board.
Learn more about perimeter here:
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What is the length of the missing leg? If necessary, round to the nearest tenth
Answer:
80m
Step-by-step explanation:
Pythageoreum Theorum since it is a right triangle.
a^2 + b^2 = c^2
60^2 + b^2 = 100^2
3600 + b^2 = 10,000
-3600 -3,600
b^2 = 6,400
Square root both sides of the equation
b = [tex]\sqrt{6400}[/tex]
[tex]\sqrt{6400}[/tex] = 80
The length of side a is 80 m
Please help
What is 94*106 as a difference of two squares
What is 94*106 as a product of a sum and a difference (factored form)
Answer:
Hi, I am going to help you! ➡ 94 * 106Formula: ( a+b) (a-b)
a=100
b=6
100+6=106
100+6=106100-6= 94
➡ 2. 100² - 6²
= (100 - 6) ( 100 + 6)
= 94 * 106
( THE BOLD IS THE FINAL ANSWER FOR BOTH QUESTIONS)
If instead of randomly selecting two people there were five, what is the probability that all five are right-handed
Answer:
1/32
Step-by-step explanation:
We can break this question down. If we had 1 person and they are right-handed, the probability is 1/2 because they are either left-handed or right-handed. Knowing that, we can multiply the probability of having 1 person being right-handed 5 times because there are 5 people in the question.
1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/(2⁵) = 1/32
Therefore, the probability of randomly selecting 5 people who are right-handed is 1/32.
I hope this helps and please mark me as brainliest!
In rectangle EFGH, the length of EF is 12 units and the length of FG is 5 units. The rectangle is translated 6 units to the right and 4 units down to produce rectangle WXYZ. What is the length of YZ ?
Answer: 12
Step-by-step explanation:
Because a translation is a rigid motion, we know that YZ corresponds to GH (and they will have the same length).
Now, we can the fact that EFGH is a rectangle to obtain that EF=GH=12 (since opposite sides of a rectangle are congruent)
Hence, YZ=12.
What is a "closing balance?"
a.
The amount of
money you have at the end of the statement period
b.
C.
The amount of money you have when you close your account
d.
The amount of money you owe at the end of the statement period
The amount O1 money waiting
to be transferred out of your account
Please select the best answer from
the choices provided
Answer:
A. The amount of money you have at the end of the statement period
Step-by-step explanation:
A "closing balance" is the The amount of money you have at the end of the statement period
A factory inspector found flaws in 4 out of 22 wooden boxes. Considering this data, how many flawed boxes would you expect the inspector to find in a batch of 44 boxes
Answer:
8
Step-by-step explanation:
We can form a simple ratio to solve this problem.
Flaws:Total Box
Plug in current values
4:22
44/22 = 2
Multiply the ratio by 2
8:44
8 boxes would be flawed.
Answer:
8
Step-by-step explanation:
There are 2 ways to do this I have seen.
1. 4/22 will get you .18, you can then multiply that by 44 and get 8
2. 22*2 is 44 so you can assume the number of flaws will also be the same amount multiplied (a multiple of 2) and you will get 8
ANSWER THIS PLEASE !!!!!!
Answer:
C
Step-by-step explanation:
Becuase 68 is closer to c than b
If f(1) = 1 and f(n) = 2f(n − 1) then find the value of f(4).
Answer:
[tex]f(4)=8[/tex]
Step-by-step explanation:
Given:
[tex]f(1)=1[/tex][tex]f(n)=2f(n-1)[/tex][tex]\implies f(2)=2f(1)=2(1)=2[/tex]
[tex]\implies f(3)=2f(2)=2(2)=4[/tex]
[tex]\implies f(4)=2f(3)=2(4)=8[/tex]
An employee is starting a job with an annnual salary of $40,000. The employee's annual salary will increase by 3% at the end of each year with the company.
What will the employee's annual salary, in dollar, be at the end of the second year with the company?
Answer:
$ 42 436
Step-by-step explanation:
3% = .03
40 000 ( 1 + .03)^2 = 42436
Choose the correct item from each drop-down menu to factor the trinomial 3x² + 13x – 10 by grouping.
3x2+ 13x - 10 = 3x2 -
Choose.
x +
Choose.
X-10
Choose.
V (3x-2) +
Choose.
(3x - 2)
=
Choose.
Choose.
D(x - 2)
The trinomial, 3x² + 13x – 10, when factored will give you: (3x + 10)(x - 1).
How to Factor a Trinomial?To factor a trinomial, we need to find two factors that would give us the exact trinomial when expanded.
Given, 3x² + 13x – 10:
3x² -3x + 10x - 10
(3x² - 3x) + (10x - 10 )
3x(x - 1) +10(x - 1)
(3x + 10)(x - 1)
Learn more about factoring trinomial on:
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Round 987 to 2 significant figure
987
to find:2 sf of 987
solution:( to find 2sf just round of if the previous digit is 5 or more)
2 sf= 990
Answer:
990
Step-by-step explanation:
х
y
1
4
2
16
3
64
4
256
5
1,024
The table above represents what type of function?
A. linear
B. linear and nonlinear
c. neither linear nor nonlinear
D. nonlinear
Reset
Submit
Answer:
B
Step-by-step explanation:
When the x goes up 1, the y multiplies by 4. This graph would be a curve.
Hope that helps
What are the values of a1 and r of the geometric series?
2 – 2 + 2 – 2 + 2
a1 = 2 and r = –2
a1 = –2 and r = 2
a1 = –1 and r = 2
a1 = 2 and r = –1
Answer:
a1=2 and r=-1
Step-by-step explanation:
"A geometric series is a series with a constant ratio between successive terms".
Here, we can observe that the first term 'a' is '2'.
And the common ratio 'r' =
Therefore, the first term 'a' is 2 and common ratio 'r' is '-1'.
First term, a, is 2. Next term, -2, is the product of 2 and -1 and is -2. Next term, 2, is the product of -2 and -1. Thus, the first term, a, is 2 and the common ratio, r, is -1
Answer:
a1 = 2 and r = –1
Step-by-step explanation:
The answer above is correct.
what number should be added to both sides in order to solve x^2 -8x=0
Answer:
16
Step-by-step explanation:
x^2 -8x=0
rewrite in this form and add 16 to both sides:
x² + 2(- 4)x + 16 = 0 + 16
(x - 4)² = 16 ( take square root of both sides )
x - 4 = ± 4
x = 4 ± 4
x=8 , x= 0
Can somebody help me please?
Answer:
it's a that's the answer
Solve for x
4x-16 2x+16
Answer:
The value of x is equal to 30.
Step-by-step explanation:
Let's define what are 2 equations are:
Since we are dealing with a straight line, the line's angle will always equal 180°.
Since the 2 angles must add up to 180°, then they must be supplementary angles.
We can set up our equation to solve for x:
4x - 16 + 2x + 16 = 180This equation states that the 2 angles, given in formulas, must be equal to the angle of the line.
We can now solve this equation and get a value of x:
Define:∴ we have found the value of x to be equal to 30.
Hope this helps!
Given:
Universal Set U = {3, 7, 8, 10, 11}
Subset B = {7}
What is B' ?
Answer:
B' = {3, 8, 10, 11}
Step-by-step explanation:
B' is the complement of B. It is a set that contains all elements of the universal set that are not elements of set B.
B' = {3, 8, 10, 11}
Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y-2 =3(x+3)
What is the answer to x-5y=30 so I can graph it?
Answer:
x + 5y = 30
x + 5(0) = 30
x1 = 30 y1 = 0
x + 5y = 30
1(0) + 5y = 30
y2 = 6 x2 = 0
(x1,y1) and (x2,y2)
(30,0) and (0,6)
Step-by-step explanation:
Hello I need Help with this question ASAP PLS.
Question: The cost of 6 Apples is $1.20. What is the cost of 4 apples? State units of your answer.
Pls Help me, I'm stuck :(
-- Biruh
Answer:
$0.80
Step-by-step explanation:
Find the unit rate
1 apple costs ?
1.20/6 = cost of 1 apple
1 apple = $0.20
4 apples = $0.20 * 4
4 apples = $0.80
Darnell collected data from two different sales teams in his department, each with four employees.
The results of the study, based on each worker's age and sales, are listed in the tables below.
Team 1
Team 2
Worker's Age
Sales
Worker's Age
Sales
25
30,000
29,000
27
32,000
35,500
28
35,000
37,000
33
38,000
65,000
Which of the following is a true statement?
225
28
29
31
Answer:
The answer is C The sales range for team 2 is greater than the sales range for team 1.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Find the answers to the picture
(triangle) ASAP
Answer:
measure of angle C = 18°
c = 2.47
a = 7.61
Step-by-step explanation:
Make sure your calculator is in degree mode.
Angle A measures 72°, so angle C measures 18° (Angles A and C are complementary angles, so their sum is 90°).
[tex] \sin(18) = \frac{c}{8} [/tex]
[tex]c = 8 \sin(18) = 2.47[/tex]
[tex]a = 8 \cos(18) = 7.61[/tex]
Lily is going to invest $750 and leave it in an account for 18 years. Assuming the
interest is compounded daily, what interest rate, to the nearest tenth of a percent,
would be required in order for Lily to end up with $1,180?
Please help!! I need helppppp ASAP
Answer:
The interest rate would be 2.5%
I need this answered please
Answer:
Step-by-step explanation: