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
what are the values? f(3)
Answers
Answer:
it's simply what we follow and respect like we value our culture
Step-by-step explanation:
hope this will help
Evaluate.
16÷(2+1/2)2
(the 2 at the end is a 1 half to the 2 power)
Answers
PEMDAS, notice Parentheses is first, then Exponents 2nd
[tex]16\div\left(2 + \left( \frac{1}{2} \right)^2 \right)\implies 16\div\left(2 + \left( \frac{1^2}{2^2} \right) \right)\implies 16\div\left(2+\frac{1}{4} \right)[/tex]
now that the exponent got done, let's keep in the parentheses
[tex]16\div\left(\frac{2}{1}+\frac{1}{4} \right)\implies 16\div\left(\cfrac{8+1}{\underset{\textit{using this LCD}}{4}} \right)\implies 16\div \left( \cfrac{9}{4} \right)[/tex]
PEMDAS, after all that we'll do D, Division next
[tex]16\div \left( \cfrac{9}{4} \right)\implies \cfrac{16}{1}\div \cfrac{9}{4}\implies \cfrac{16}{1}\cdot \cfrac{4}{9}\implies \cfrac{64}{9}\implies 7\frac{1}{9}[/tex]
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this just some addition to your previous posting, since you kinda got spammed some
[tex]\stackrel{\stackrel{\textit{E first}}{\downarrow }}{2^3}+4\cdot 2-7\implies 8+4\cdot 2-7\implies 8+\stackrel{\stackrel{\textit{M second}}{\downarrow }}{8}-7\implies \stackrel{\textit{AS last from left to right}}{16-7\implies 9}[/tex]
notice, PEMDAS, P first and so on, AS are last, from left to right.
we laid out strands of lights to decorate the school each strand was 12 feet long how many strands did we need if we needed at least 70 feet of lights
Answers
70/12=5.83
Because you can’t have .8 of a strand, you would need to round up to the next whole number (6)
help i dont know how to do the rest of this homework
Answers
Answer:
Step-by-step explanation:108 divided by 12 equals 9 so nine feet next to 108 inches.
and nine divided by 3 is 3 so nine yards in the row with 108 inches.
360 divided by 12 which is 30 so 30 feet in the row with 360 inches.
90 feet divided by three so 30 so 30 yards in the row with 360 inches.
24 inches equals 2 feet
double this length is 48 inches or 4 feet
so in all he cut 6 yards and since he only had three yards you will still have 3 yards left over.
Determine whether f(x) = 5x^2-20x+ 3 has a maximum or a minimum value and find that value.
PLEASE HELP I’ll mark brainliest
Answers
Answer:
Answer in the attachment, as it wasn't letting me answer it, saying rude words.
If16 = x/20, then x=
Answers
Answer:
320
Step-by-step explanation:
16 × 20 = 320
To double check it, we insert 320 into the equation:
320 ÷ 20 = 16
I’m not sure how to solve this, anyone know?
Answers
Answer:
A' = (-4, 7)
B' = (3, 5)
C' = (1, 2)
Step-by-step explanation:
The question is asking you to translate the function by adding 4 to the x-value of each point and 2 to the y-value of each point.
I didn't double-check my math, but since the question is asking for an ordered pair, this should be correct.
An average 1-year-old baby boy weighs around 9.6 kilograms. Convert this
weight into ounces.
Answers
Answer:
338.63 ounces
Step-by-step explanation:
1=35.274
35.274 times 9.6 is 338.6304
At a soccer game, a vendor sold a combined a total of 220 sodas and hotdogs. The number of sodas was sold was 46 more than the number of hotdogs sold. Find the number of sodas sold and the number of hotdogs sold.
Answers
Answer:
133 sodas and 87 hotdogs were sold.
Step-by-step explanation:
math
Answer:
number of sodas: x+46 (46 more than hotdogs)
number of hotdogs: x
x+x+46=220
2x+46=220
2x=174
x=87
87+46=133
number of sodas: 133
number of hotdogs: 87
PLEASE HURRY! WILL MARK BRAINLIEST IF CORRECT (Screenshot)
Answers
Answer:
The length of XY is 22.5
Step-by-step explanation:
Since you need to hurry I will not write an explanation
Hope this helps! :)
૮ ・ﻌ・ა
You are on level ground in the late afternoon. The Sun is at angle of elevation of 17 degrees. A tree casts a 206-foot long shadow feet. What is the height of the tree in the nearest foot
Answers
[tex]\\ \sf\longmapsto tanC=\dfrac{AB}{BC}[/tex]
[tex]\\ \sf\longmapsto tan17=\dfrac{AB}{206}[/tex]
[tex]\\ \sf\longmapsto AB=0.3(206)[/tex]
[tex]\\ \sf\longmapsto AB=61.8ft[/tex]
Breakfast eaten and the slim camp-outfit lashed to the sled, the men turned their backs on the cheery fire and launched out into the darkness. At once began to rise the cries that were fiercely sad—cries that called through the darkness and cold to one another and answered back. Conversation ceased. Daylight came at nine o'clock. At midday the sky to the south warmed to rose-colour, and marked where the bulge of the earth intervened between the meridian sun and the northern world. But the rose-colour swiftly faded. The grey light of day that remained lasted until three o'clock, when it, too, faded, and the pall of the Arctic night descended upon the lone and silent land.
As darkness came on, the hunting-cries to right and left and rear drew closer—so close that more than once they sent surges of fear through the toiling dogs, throwing them into short-lived panics.
At the conclusion of one such panic, when he and Henry had got the dogs back in the traces, Bill said:
"I wisht they'd strike game somewheres, an' go away an' leave us alone."
"They do get on the nerves horrible," Henry sympathized.
They spoke no more until camp was made.
Read this line from the story:
As darkness came on, the hunting-cries to right and left and rear drew closer, ...
What is the purpose of this sentence in the story? (5 points)
It implies a mood of utter despair.
It implies a near tragic event.
It creates a feeling of being trapped.
It creates a sense of action. I AM GIVING 50 POINTS!!!!!!!!!!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
The problem with this kind of question is that the author tells you what you should see in that sentence. The dogs experienced fear. Any other answer you suggest is not what the author means. So you are guessing. It is adding to the notion that the arctic is not a friendly place and you cannot go sunbathing in and be comfortable in the middle of winter.
A is as good an answer as you are likely to get, but I don't think it's right.
Twenty young men got a quote for the cost of a car insurance policy. The policy cost and ages of the men are shown in the scatter plot. The
equation for the line of best fit for the data is y=-315.67x + 8986.5 and the correlation coefficient is-0.951.
Select all the statements that are true based on the scatter plot and line of best-fit equation
4,000
3,500
...
3,000
2.500
,,
2,000
1,500
1,000
18
19 20
21 22 23 24 25
D. The line of best fit indicates that, in general, the cost of a car insurance policy for a 21-year-old should be on average, about $315
less than the cost of a car insurance policy for a 20-year-old.
06 The y-intercept from the line of best fit indicates that, if the linear trend holds, a car insurance policy would be 50 for a person who
is about 8,987 years old.
OcEvery 19-year-old in this group has a lower cost of car insurance than the 18-year olds
Od
The value of the correlation coefficient is very close to -1, so there is no association between age and car insurance policy cost.
Car insurance policy cost tends to decrease as the age of the driver increases.
e
Answers
The statements that are true based on the scatter plot and the given equation of line of best-fit are:
In general, the line of best fit indicates that, the cost of a car insurance policy for a 21-year-old should be on average of about $315 less than the cost of a car insurance policy for a 20-yr-old.Car insurance policy cost tends to decrease as age of driver increases.Given that the correlation coefficient of -0.951, it suggests that the policy cost and ages of the men as shown in the scatter plot are strongly negatively correlated.
This means that, the lower the higher the age of the men, the lesser the cost of a car insurance policy.
The slope value in the equation, y = -315.67x + 8986.5, is -315.67, which is the average cost of a car insurance policy per year.
Therefore, the statements that are true based on the scatter plot and the given equation of line of best-fit are:
In general, the line of best fit indicates that, the cost of a car insurance policy for a 21-year-old should be on average of about $315 less than the cost of a car insurance policy for a 20-yr-old.Car insurance policy cost tends to decrease as age of driver increases.Learn more about line of best fit on:
https://brainly.com/question/17261411
A line with a slope of 8 goes through the point (2, 27). It also goes through the point (-2,p). What is the value of p?.
Answers
Answer:
The value of p is -5.
Step-by-step explanation:
Given the slope and a known point, you have 3 of the 4 variables and you can use them to solve for the y-intercept of the line.
[tex]y=mx+b\\(27)=(8)(2)+b\\27=16+b\\11=b\\b=11[/tex]
Now, with the slope and the y-intercept, you can write the equation of the line:
[tex]y=8x+11[/tex]
Finally, you can use that equation to solve for y at x = -2:
[tex]y=8(-2)+11\\y=-16+11\\y=-5[/tex]
The value of p is -5.
You can also see that on a graph.
Suppose that 26% of people own cats. If you pick two people at random
Answers
Answer:13 percent would have cats and the other 13 percent wouldn’t
Step-by-step explanation:plz mark for brainlist
Thank you
Probability of a person owning a dog is 0.28
Choose two persons at random, find probability that both are dog-owners.
Solution:
probability of dog-ownership for one person chosen at random = 0.28
probability of dog-ownership for two persons chosen at random = 0.28%5E2+=+0.0784
Answer: probability of two dog-owners out of two randomly chosen persons is 0.0784.
most of the mathematical symbols were not invented until 16th century, before that how equations were written?
Answers
Answer:
During the 16th and early 17th Century, the equals, multiplication, division, radical (root), decimal and inequality symbols were gradually introduced and standardized. ... In the Renaissance Italy of the early 16th Century, Bologna University in particular was famed for its intense public mathematics
Prior to the invention of the Mathematical Symbols, mathematical equations were written in words.
For example, Y + 10 = 4.5 would be written as
The thing plus ten equal to eight.
It is true that MOST, that is, the majority of the mathematical symbols we have today were invented in the 16th century. Examples of such symbols are:
Multiplication Sign × (1618)Plus/Minus Sign ± (1628)Inequality Signs > and < (1631)Percentage Sign % (1650)Infinity Sign ∞ (1655)Division Sign ÷ (1659) to mention a few.Prior to the 16th century, some mathematical signs were already in use. They are:
Plus Sign + (1360)Minus Sign - (1489)Square Root Sign (1525)Equals Sign = (1557) to mention a few.See the link below for more about Mathematical Signs:
https://brainly.com/question/11855662
Find the slope.
y = 3x – 11
m =[?]
Answers
you know that y=mx +c then in the place of m is 3 then answe is also three.
please help ill mark brainliestl
Answers
Answer:
A) Yes...ABC and GFC are similar using AA.
Step-by-step explanation:
It takes 4/5 of an hour to fill 1/2 tank.how many tanks can she fill in an hour
Answers
Answer:
5/8 of a tank
Step-by-step explanation:
Divide 1/2 by 4 to get how much of a tank you would be able to fill in 1/5 of an hour. 1/2 ⁒ 4 is 1/8 so she can fill 1/2+1/8 of a tank or 5/8 of a tank.
I Was Not That Day On College, I Don't Have The Formulas To Study
Answers
Answer:
check online for more information
Can someone help please
Answers
=========================================================
Explanation:
If you know the cost function C(x), to find the marginal cost, we apply the derivative.
Marginal cost = derivative of cost function
Marginal cost = C ' (x)
Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.
[tex]\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\[/tex]
[tex]C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]
D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).
To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.
Therefore, we go from this
[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]
to this
[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\[/tex]
which is the final answer.
HELP!!!! If you help me with this you’ll be my favorite person ever
Answers
Pls look at the picture for the question.
Answers
Answer:
10
Step-by-step explanation:
each tick mark is worth 5
there is the -10, then one to the right is -5, next is 0, next is 5, next one (the one where the x is) 10, next 15, next 20.
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week. About how many gallons of milk does the class drink in 10 weeks? Round your answer to the nearest tenth of a gallon if needed.
Answers
262.5 gallons of milk does the class drink in 10 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.
as, we know that
1 pint= 0.125 Galloon
So, 210 pints milk = 210 x 0.125 = 26.25 Galloon
Then, In 10 weeks amount of milk drink
= 26.25 x 10
= 262.5 Gallon
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
is 5.243 greater, equal to ,or less than 5.4?
Answers
Answer:
5.243 is less than 5.4....
Driving at a constant rate, Dan traveled 310 miles in 5 hours. If he drives at the same speed, how far will Dan travel in 8 hours?
Answers
According to the amount he drove in 5 hours, he drove an average of 62 MPH. If he continued to drive at this speed for 8 hours, he would travel 496 miles.
Find the area and the circumference of a circle with radius 4 yd
Answers
First, let's find the area! The formula to find the area of a circle is πr²
πr²
3.14 · 4²
50.24 yds²
Now let's find the circumference. The formula for this is 2πr
2πr
2 · 3.14 · 4
25.12 yds
Hope this helps!
can anyone please help? I'm stuck on this problem
Answers
Answer:
I think 38.7 if you do<j it would be 38.7
The solution is -1/2.
Which multiplication equation has the given solution?
Answers
Answer:
5x=-(5/2) ~~ first choice
Step-by-step explanation:
divide both sides by 5
-> x=(5/2)/5
simplify the above
-> x = - (5/2x5)
simplify
-> x = -(5/10)
simplify and solve
=> x = - 1/2
(basically trial and error)
what is 2 equivalent fractions of this 2/5=_=_
Answers
Answer:
4/10, 6/15, 120/300, etc.
Equivalent fractions can be anything, as long as they divide to .4 (2/5).
Basically any equivalent fraction
[tex]\frac{2*n}{5*n}[/tex]
with n as any integer, is an equivalent fraction to 2/5 since
[tex]\frac{2*n}{5*n}=\frac{2}{5}*\frac{n}{n}=\frac{2}{5}*1=\frac{2}{5}[/tex]