Answers
Question 1
Answer: Choice A) -7-----------------
Explanation:
To compute f(g(2)), we'll first need to find g(2).
Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4
This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) = -9
Overall, we can say f(g(2)) = -9
We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2
Lastly, we subtract the results we got:
f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7
==============================================
Question 2
Answer: Choice B) 0-----------------
Explanation:
If you were to graph each equation, you should get what you see below.
The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.
==============================================
Question 3
Answer: Choice B[tex]-2x^2+250x-2000[/tex]-----------------
Explanation:
x = number of scooters made and sold
Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression [tex]150x+2000[/tex]
The cost function is [tex]C(x) = 150x+2000[/tex]. We'll subtract this from the revenue function R(x) to get the profit P(x)
[tex]\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\[/tex]
==============================================
Question 4
Answer: Choice B[tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]
-----------------
Explanation:
[tex]g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\[/tex]
I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.
So we start off with the real number line, and poke holes at x = -2 and x = 1.
The notation [tex]x \in \mathbb{R}[/tex] means x is a real number. Then we tack on [tex]x \ne -2, x \ne 1[/tex]
Overall, the domain is [tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]
Let's see what happens if we tried plugging x = -1 into this composite function:
[tex](g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\[/tex]
We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.
Related Questions
Simplify. x+y -x²-y²/x-y
Answers
Help help help math math help
Answers
Answer:
63°
Step-by-step explanation:
Angle 2 is congruent in angle that has 63°
Refer to the attached pic
this is long division… please help
Answers
Which graph represents a function?
Answers
Answer:
just the first on. upper left corner
it goes through the center (0,0) and it’s a straight line.
Which of the following is an example of a ratio variable?
A-Martha is the same gender as Ruth
B-Mary's IQ is 115 and Janet's is a 90, which means Mary's IQ is slightly higher than Janet's
C-Sam is twice the age of his son
D-George and Harry attend religious services about the same amount
Answers
On a human, what is the ratio of arms to fingers?
Answers
Ratio:-
[tex]\\ \sf\longmapsto \dfrac{2}{20}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{10}[/tex]
[tex]\\ \sf\longmapsto 1:10[/tex]
The cost C to produce x number of tennis rackets is C = 190 + 18. The tennis rackets are sold wholesale for $23
each, so revenue R is given by R = 23x. Find how many tennis rackets the manufacturer needs to produce and
sell to break even.
38 tennis rackets or
43 tennis rackets or
19 tennis rackets or
33 tennis rackets
Answers
Answer:
19 tennis rackets
Step-by-step explanation:
What’s the 16th term for 32,27,22,17
Answers
Answer:
-43
Step-by-step explanation:
By staring at it for a while you can tell that you're losing 5 every step. You can write the succession as [tex]a_n = 32-5n[/tex] (please notice the first terms starts when [tex]n=0[/tex], not 1!). The 16th term happens at [tex]n=15[/tex]:
[tex]a_1_5=32-5(15) = -43[/tex]
Which is a composite number? A.97 B.89 C.95 D.13
PLEASE I REALLY NEED THE CORRECT ANSWER RIGHT NOW!!!!
Answers
Answer: C. 95 is a composite number.
Step-by-step explanation:
You can look at the ones place of each number to see if any end in 0, 2, 5, or any other digit that indicates that the number is not prime. Since 95 ends in a 5, it can be divided by 5, making it have more factors than 1 and itself. Therefore, 95 is the composite number of the list of numbers.
Answer:95
Step-by-step explanation:composite numbers are numbers that have more factors than 1 and itself, factors are numbers you can multiply to get a number. 95 is a composite number since 1,95, AND 5 are all factors of 95 making it a composite number
Identify the parent function. 5 -5 5 -5 A. Cube root
Answers
A.) Square Root
s.p. is 4000, profit is 25% than find c.p.please explain itt
Answers
[tex] \sf= \frac{100}{100 + 25} \times 4000 \\ = \frac{100}{125} \times 4000 \\ = \frac{4}{5} \times 4000 \\ = 4 \times 800 \\ = 3200[/tex]
[tex] \huge \sf \: Answer[/tex]
The cost price is 3200.
Hope you could get an idea from here
Doubt clarification- use comment section.
In a computer tape library there are two racks with 50 tapes per rack. On Monday there are 35 tapes in use, on Tuesday 60, and on Wednesday 25. What fraction on the average is in use for the 3 days
Answers
Based on the number of tapes used on those days and the number of tapes in the rack, the fraction on the average used was 2/5
The average tapes used in those 3 days was:
= (35 + 60 + 25) / 3
= 120 / 3
= 40 tapes
The total number of tapes that can be used are:
= 50 + 50 per rack
= 100 tapes
The fraction of the average is:
= 40 / 100
In the lowest term this is:
= 2 / 5
In conclusion, the fraction is 2/5
Find out more about fractions at https://brainly.com/question/233783.
A researcher testing a hypothesis that the population mean is 25 takes a sample of size 36 and obtains a sample mean of 23 with an estimated standard error of 4. What is the observed value of the test statistic
Answers
Answer:
The test statistic is 23
Step-by-step explanation:
Best way to understand this is to think of a sample and it's purpose;
You take a sample to get information that can be extrapolated to apply to the whole population;
So, for example, you have a factory making light bulbs, and you want to find out how long they last;
You would take a number of light bulbs from the production line, i.e. a sample, and test these;
It would be impossible to test every light bulb as this would take too long and there would be none left unused to sell, i.e. it would not be feasible or viable to do;
You would then find a mean of these times from the sample, and then extrapolate and assume it to be the duration of any light bulb coming off the production line;
The sample is the handful of light bulbs chosen to test;
The test statistic refers to the quantity or value, calculated from the sample data, this would be the mean light bulb duration in the light bulbs example;
Similar and yet different to a test statistic, a population parameter refers to a quantity or value calculated from population data;
A population refers to all members of a particular group of objects/items, so in the example, it would be all the light bulbs produced;
The population parameter would refer to the mean calculated based on data from the population (i.e. all the light bulbs produced);
Realistically, it is impossible to determine a population since it would be unviable in the practically all cases, as we can see in the example;
This value is almost always theoretical and would be assumed from a test statistic in any real scenario.
PLEASE HELP:
Check for understanding:
Answers
Answer:
P = 106
A = 330
Step-by-step explanation:
= 2(l+w) (perimeter of rectangle)
= 2·(18+15)
= 66
picture below of perimeter of right angle triangle
Add both values
P= 66 + 40
P = 106
= w*l (Area of rectangle)
=15·18
= 270
= ab/2 ( Area of triangle )
= 8·15/2
=60
Add both values
A = 60 + 270
A = 330
I hope it helps
If
x
=
4
and
y
=
5
, evaluate the following expression:
2
(
y
−
x
)
Answers
Answer:
2 because if y is 5 and x is 4 and we subtract them and get one and then multiply it by two to get two using pemdas
The answer is 2
I need help with problem.
Answers
Answer:
Reflection across the x-axis
Step-by-step explanation:
Rule of thumb: If the figure is diagonal, it is x-axis, but if it is horizontal, it is the y-axis.
please someone help me this is the third time i have had to post this question bc of bots
Answers
Answer: It,ll increase
Step-by-step explanation:
Answer:
Add all of the numbers together then multipy them by 25
Step-by-step explanation:
35X25=875
-6
Which graph represents function g if g(x)= f(2x)
Answers
Answer:
2
Step-by-step explanation:
a forrest covers an area of 2400 km^2. if each year the area decreases by 8.5%, what will the area be after 14 years? round answer to nearest square kilometer. (please explain how you get the answer so i can do future questions myself! thank you :) )
Answers
Answer:
1581.62810745 square km
Step-by-step explanation:
P = Initial Area = 2500 square km.
r = rate of decreasing = 8.75%
n = number of years = 5 years
A = 2500 ( 1 - 8.75/100)^5
A = 2500 {(100–8.75)/100}^5
A = 2500 (91.25/100)^5
A = 2500 (0.9125)^5
A = 2500 * 0.63265124298
A = 1581.62810745
) The price of broccoli is $1.25 per pound. Let y be the total cost in dollars of buying a pounds
of broccoli
.) Which equation represents this situation?
y = 1.252
• Which graph represents the situation?
Broccoli Prices
Broccoli Prices
Broccoli Prices
(4,5)
.
(3.4.5)
15
15
(5.
(3.3.75
(2,3)
(3.75,3)
(2.2.5)
3
5 25
8 2
(2.5.2
1.5 (1.1.25)
(1.1.5)
(0.5, 0.75)
(1.25.1)
0.5
0.5
0 05 1 1.5 2 25 3 3.5 4 US 5
Amount of Broccoli (b)
0 0.5 1 1.5 2 2.5 3 3.5 4 155
Amount of Broccoli (b)
0 05 1 15 2 2.5 3 3.5 5 5
Amount of Broccoli (b)
DONE
Answers
Answer:
The graph that represents the situation is A
Step-by-step explanation:
PLEASE HELP ME NOW!!! I WILL MARK U AS BRAINLIEST
Answers
[tex]\huge \bf •Answer •\\ [/tex]
1188 g
[tex]\huge \bf •Solution •\\ [/tex]
We know,
[tex]\sf \dfrac{mass \: \: of \: \: solute}{mass \: \: of \: \: solution} \times 100= concentration \: \: of \: \: solution \\ = > \sf \dfrac{mass \: \: of \: \: solute}{mass \: \: of \: \: solute + mass \: \: of \: \: solvent} \times 100= concentration \: \: of \: \: solution[/tex]
Given, concentration of solution = 1%
Mass of sugar (solute) = 12 g
Let the mass of water (solvent) be x.
Therefore,
[tex]\sf \dfrac{12g}{12g + x} \times 100= 1 \\ \sf = > 1200g= 12g + x \\ \sf= > (1200 - 12)g = x \\ \sf = > x = 1188g[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
1. Which of the following is the remainder when the polynomial x^2-5x+3 is divided by (x -8)?
(1) 107
(3) 3
(2) 27
(4) 9
Answers
Answer:
27
Step-by-step explanation:
Use synthetic division:
8 | 1 -5 3
__8_24
1 3 | 27
Therefore, (x²-5x+3)/(x-8) = x+3 R27
y<-2/3 x-1 graphing the inequality
Answers
Answer:
y < − 2/3x − 1
Step-by-step explanation:
Which is an example of incompatible goals?
A. Your parents want to take family photos, but you already have
plans with friends that day.
B. Your teacher gives you an assignment you did not expect.
C. A friend does not agree with your opinion on a topic.
D. Your uncle enjoys fishing, but you do not believe in killing animals.
Answers
A board is 81.28 centimeters long. How long is the board in inches? Use the following conversion: 1 inch is 2.54 centimeters
Answers
Find the quotient.
32 ÷ 0.08
Answers
Answer:
The quotient of the equation is 400
Answer:
hi
Step-by-step explanation:
the correct answer is 400
A square plywood platform has a perimeter which is 11 times the length of a side,
decreased by 42. Find the length of a side. (P = 4L)
Answers
Answer:
Step-by-step explanation:
The Suarez family paid $16.00 for 4 movie tickets. How much would they have paid for 12 tickets?
Answers
Answer:
$48
Step-by-step explanation:
Each ticket costs 4 dollars.
1/2 x 1 1/3 x 2=?
please help on this
Answers
Henry jumped up 6 steps. Each step was 3/10 feet high. How high did he jump all together (in simplest form)
Answers
Answer:
1.8 or 14/5
Step-by-step explanation:
HENry MuST Be A KaNGaRoO
Answer:
Step-by-step explanation:
Multiply "3/10 ft high per step" by "6 steps." This works out to:
18/10 ft was the highest that this young man jumped.
This reduces to 9/5 ft, or 1.8 ft
