Given the piecewise function shown below, select all of the statements that are true.
Answers
So b is correct
The statements f(1) = 0 and f(-1) = 2 are true based on the piecewise function.
Options B and C are the correct answer.
We have,
The piecewise function:
f(x) = -x + 1, x < 0
f(x) = -2, x = 0
f(x) = x² - 1. x > 0
Now,
f(-2) = 0
False.
When x = -2, we are in the first condition, so f(-2) = -(-2) + 1 = 3, not 0.
f(1) = 0
True
When x = 1, we are in the third condition, so f(1) = (1)² - 1 = 0.
f(-1) = 2
True
When x = -1, we are in the first condition, so f(-1) = -(-1) + 1 = 2.
f(4) = 7
False.
When x = 4, we are in the third condition, so f(4) = (4)² - 1 = 15, not 7.
Therefore,
The statements f(1) = 0 and f(-1) = 2 are true.
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Related Questions
Is y=2x-8 and 2x-y=8 a dependent independent or inconsistent
Answers
Answer:
dependent
Step-by-step explanation:
[tex]y=2x-8[/tex] and [tex]2x-y=8[/tex]
First equation is already solve for y
LEts solve the second equation for y
[tex]2x-y=8[/tex]
Subtract 2x on both sides
[tex]-y=-2x+8[/tex]
Divide the whole equation by -1
[tex]y=2x-8[/tex]
After solving for y, both equation are same
When both the system of equation are same then it has infinite solutions.
They are said to be dependent.
michael wittry has been investing inhis roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origional value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?
Answers
a = 215,658
ok... so.. he first lost 1/3 of that
[tex]\bf \textit{\underline{lost} }\frac{1}{3}a\qquad \qquad a-\cfrac{1}{3}a\implies a-\cfrac{a}{3}\implies \cfrac{3a-a}{3}\implies \cfrac{2a}{3} \\\\\\ \textit{then he \underline{gained} }\frac{1}{2}\textit{ of }\frac{2a}{3}\qquad \qquad \cfrac{2a}{3}+\cfrac{\frac{2a}{3}}{2}\implies \cfrac{\frac{2a}{3}}{\frac{2}{1}} \\\\\\ \cfrac{2a}{3}+\cfrac{2a}{3}\cdot \cfrac{1}{2}\implies \cfrac{2a}{3}+\cfrac{2a}{6}\implies \cfrac{4a+2a}{6} \\\\\\ \cfrac{6a}{6}\implies \boxed{a}\implies 215,658[/tex]
so, his nickname might just be even steven, because, he ended up with the same original amount after the 1/2 bump.
His current value is 215658 dollars.
How to calculate a fraction of amount of a total amount ?To calculate a fraction of amount of a total amount just multiply the given fraction to the total amount.
According to the given question
Michael wittry has been investing in his roth IRA retirement account for 20 years.
Two years ago his account was worth $215,658.
1/3rd of it's original value is
= (1/3) × 215658
= 71886 dollars.
∴ Remaining value is
=(215658 - 71886)
=143772 dollars.
After some time it gained half of it's new value back
∴ Half of this new value is
(1/2) × 143772
= 71886 dollars.
So , the current value is
(143772 + 71886)
=215658 dollars.
Actually his currect value of roth IRA is same as it was two years ago.
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solve for x −1/2(x+2)+11/2x=3
Answers
A machine produces 240 bolts in 25 minutes. At the same rate how many bolts would be produced in 45 minutes
Answers
And in 45 minutes = 45 x 9.6 = 432 bolts
Hope that helped. :^)
386-123= estimate then find the difference
Answers
Round 386 to 390 and 123 to 125
400-100=300
The 1998 team payroll of the Baltimore orioles was $68,988,134
Answers
Suppose a line has slope 4 and passes through the point (-2, 5). Which other point must also be on the graph?
A) (2, 6) B) (-1, 9) C) (-1, 1) D) (-6, 4)
Answers
so the rise is 4 units and the run is 1 unit, ok.
now, from point -2, 5, if we move 4/1, that is, "1 unit over the x-axis, and 4 units over the y-axis", we'll find another point, now, a fraction can be positive so long both top and bottom are the same sign, so -4/-1 is the same as 4/1 and therefore, if we move +4 and +1 over the axes we get a point, or if we move -4 and -1 we also get another point, and any other subsequent points from there on.
so, hmm let's check [tex]\bf (\stackrel{x+1}{-2}~,~\stackrel{y+4}{5})\implies (-1~,~9)[/tex]
50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~
Refer to the graph.
The function is increasing on the interval(s):
The function is decreasing on the interval(s):
The function is constant on the interval(s):
Please explain the steps you used.
Answers
round 2,412 to the nearest thousands
Answers
Which of the following statements is true? 0.74 < 0.80 0.61 > 0.93 0.83 < 0.94 1.548 < 0.698
Answers
0.83 < 0.94
Among the given statements, the only true statements are
0.74 < 0.80 and 0.83 < 0.94.
How is this so?In both cases, the number on the left is less than the one on the right. Which makes the expression and or use of the less than symbol correct.
The greater than symbol (>) and the less than symbol (<) are used to compare two numbers or expressions to determine their relationship.
The greater than symbol (>) represents "greater than" and indicates that the number on the left side is larger than the number on the right side.
The less than symbol (<) represents "less than" and indicates that the number on the left side is smaller than the number on the right side.
For example, 5 > 3 means "5 is greater than 3," and 2 < 7 means "2 is less than 7."
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3a/(a+1)^2
Give the equivalent numerator if the denominator is (a + 1)³.
Answers
To make the denominator a cube, you would have to multiply by 1 or (a+1)/(a+1)
yielding 3a(a+1)/(a+1)^3
(3a^2 + 3a) is the equivalent numerator
Answer:
3a(a+1)
Step-by-step explanation: for those who were confused on the other asnwer he gave a different veriation of this answer. however it is correct.
Brainliest plsss
An important part of customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first 5 troubles reported on a given day, what is the probability that fewer than 2 troubles will be repaired on the same day?
Answers
D. .2373
Hope this helps
Answer:
The probability that fewer than 2 troubles will be repaired on the same day is:
0.015576
Step-by-step explanation:
We have to use the Binomial function is n=order to calculate the probability of r successes out of the n-events.
We know that the probability of r success out of the n-events is given by:
[tex]P(X=r\ successes)=n_C_r\cdot p^r\cdot (1-p)^{n-r}[/tex]
where p is the probability of an success.
Here we have:
n=5 and r=0,1.
since we are asked to find the probability that fewer than 2 troubles will be repaired on the same day.
i.e we have to find:
[tex]P(X<2)=P(X=0)+P(X=1)[/tex]
Also p=0.75 ( since, likelihood is 0.75 that troubles in a residential service can be repaired on the same day )
Hence,
[tex]P(X=0)=5_C_0\cdot (0.75)^{0}\cdot (1-0.75)^{5-0}\\\\P(X=0)=1\cdot 1\cdot (0.25)^5\\\\P(X=0)=0.000976[/tex]
and
[tex]P(X=1)=5_C_1\cdot (0.75)^{1}\cdot (0.25)^{5-1}\\\\P(X=1)=5\cdot (0.75)\cdot (0.25)^4\\\\P(X=1)=0.0146[/tex]
Hence,
[tex]P(X<2)=0.000976+0.0146\\\\P(X<2)=0.015576[/tex]
Hence, the probability that fewer than 2 troubles will be repaired on the same day is:
0.015576
A segment has endpoints ar (-2,3) and (7,9) how long is the segment
Answers
Is m=1/2 a solution of the equation 6m-8= -5
Answers
Add 8 to both sides
(6m = -5 + 8)
Simplify -5 + 8 to 3
(6m = 3)
divide both sides by 6
(m = 3/6)
simplify 3/6 to 1/2
Answer: m = 1/2
Which of the following is the inverse of the statement "If I like math, then I like science"? A. If I do not like science, then I do not like math. B. If I do not like math, then I like science. C. If I do not like math, then I do not like science. D. If I like science, then I like math
Answers
Inverse: If not P, then not Q
Using that template, the inverse would be "If I do not like math, then I do not like science" (simply insert those two "not" words keeping the order the same)
so the answer is choice C
Answer:
Option C If I do not like math, then I do not like science
Step-by-step explanation:
we know that
To find the inverse of a conditional, negating both the hypothesis and conclusion of a conditional statement
In this problem we have
"If I like math, then I like science"
therefore
the inverse is
If I do not like math, then I do not like science
Order pairs (x,y) that is the solution to the equation.
5x-y=4
(x,y) =
Answers
x=1 results in y=1. Thus, (1,1) is a solution.
x=-3 results in -15-y=4, or -y=19, or y=-19. Thus, (-3,-19) is a solution.
x=0 results in -y=4, so that y=-4. Thus, (0,-4) is a solution.
If you drive for 2 hours, at 60 miles per hour, you will have traveled 120 miles. this is a very common type of calculation, involving three quantities: distance, rate and time. if you know just two of these three quantities, you can always calculate the third. thus, if you want to know how much time it is going to take you to get somewhere, and you know that the distance is 120 miles and you will drive at a rate of 60 miles per hour, you can divide the 120 miles by the 60 miles per hour and obtain a time of 2 hours.
Answers
The sum of three numbers is 99. The first number is 9 more than the third. The second number is 4 times the third. What are the numbers?
Answers
second number=4x
third number=x
4x+x+x+9=99
6x=90
x=15
first number=24
second number=60
third number=15
The first number is 24, the second number is 60, and the third number is 15.
Explanation:Let's assign variables to represent the three numbers. Let x represent the third number. Since the first number is 9 more than the third, we can write the equation:
First number = x + 9
Since the second number is 4 times the third, we can write the equation:
Second number = 4x
Now, we can add the three numbers together, according to the given information:
(x + 9) + 4x + x = 99
Simplifying this equation, we get:
6x + 9 = 99
Subtracting 9 from both sides, we have:
6x = 90
Dividing both sides by 6, we find:
x = 15
So the third number is 15. Plugging this value back into the two other equations, we find that the first number is 24 and the second number is 60. Therefore, the three numbers are 24, 60, and 15.
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Using place value how to increase 2384598 by six million
Answers
2,384,598 + 6,000,000 = 8,384,598
your answer is 8,384,598
hope this helps
Banks pay interest on savings accounts because
A. they can get more customers that way.
B. they want to encourage you to save.
C. they invest your money.
D. they're just very nice.
Answers
Banks aren't in the business of being nice and actually get most of their revenue from their relentless overdraft fees. While it may seem like they're doing something nice or encouraging you to save your money, they're really just encouraging you to become a customer. They don't invest your money, since it needs to be present for you if you want to withdraw it.
Interest on your savings is simply a method for getting new customers.
Hope this helped you out! :-)
12 tenths plus 9 tenths =21 tenths = ____ ones _____ tenths
Answers
The arctic lion's Mane Jellyfish is one of the largest known animals. Its tentacles can be as long as 120 feet. Find how this length compares to your height. Round your height to the nearest foot. 120 feet is time as long as feet.
Answers
To solve this problem, we must first know your height. So assuming that your height is 5 feet. Therefore we can divide:
120 feet / 5 feet = 24
So that the answers in the blanks are:
120 feet is 24 times as long as 5 feet
A rectangular plot of land has an area of 1/8 square mile. Its width is 3/20 mile.What is the length of the plot of land?
Answers
A = 1/8
W = 3/20
1/8 = 3/20L
(1/8) / (3/20) = L
1/8 * 20/3 = L
20/24 reduces to 5/6 miles = L <===
Nia is three years older than half Jordans age , if Jordan is eight years old , how old is Nia?
Answers
If Nia is three years older than half of Jordan's age, we must divide Jordan's age by 2 (to find half of his age).
Jordan is eight years old:
8 divided by 2 equals 4
4 years old is half of Jordan's age. Now, to find Nia's age, we must add 3 to half of Jordan's age (4).
4+3= 7
Nia is 7 years old.
I hope this helps answer your question! Have a great day!
Answer:
7
Step-by-step explanation:
kim has 3/4 pound servings of grapes. how many 1/8 pound servings can Kim make from his grapes
Answers
3/4 * 8/1 =
24/4 =
6 <=== there are 6 one-eighth pound servings
A book had a length of 5 inches and a width of 8 inches. What is the perimeter of the book
Answers
The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter?
Answers
thus
[tex]\bf 5\frac{7}{32}-\cfrac{5}{32}\implies \cfrac{5\cdot 32+7}{32}-\cfrac{5}{32}\implies \cfrac{167}{32}-\cfrac{5}{32}\implies \cfrac{162}{32} \\\\\\ \cfrac{81}{16}\implies 5\frac{1}{16}''[/tex]
The length of a rectangle is 11 m greater than the width. The area is 42 m^2. Find the length and width.
Answers
What is 10000 times 20000000
Answers
Hope this helps you!
Have a nice day!
solve (6-5x)/10-(2x+1)/5+x/3=2x/15
Answers
multiply both sides by 30 which is the LCM of 10, 5, 3, and 15
expand it
simplify 18 - 15x - 12x - 6 + 10x to 12 - 17x
add 17x to both sides
add 4x + 17x to = 21x
divide both sides by 21
simplify 12/21 to 4/7
now simplify
Answer: x = 4/7.