Which of the following accurately shows the range of the function defined below?
a. [3, 00)
b. [2,00)
c. [3,6]
d. (-00,00)
(00 is infinite
Answers
Given:
A piecewise function
[tex]f(x)=\begin{cases}3 &,x<0 \\ x^2+2 &,0\leq x<2 \\ \dfrac{1}{2}x+5 &,x\geq 2 \end{cases}[/tex]
To find:
The range of the function.
Solution:
Range is the set of output values.
For [tex]x<0[/tex], the function is [tex]f(x)=3[/tex] ...(i)
For [tex]0\leq x<2[/tex], the function is [tex]f(x)=x^2+2[/tex].
[tex]0\leq x<2[/tex]
Squaring each side.
[tex]0^2\leq x^2<2^2[/tex]
Adding 2 on each side.
[tex]0+2\leq x^2+2<4+2[/tex]
[tex]2\leq f(x)<6[/tex] ...(ii)
For [tex]x\geq 2[/tex], the function is [tex]f(x)=\dfrac{1}{2}x+5[/tex].
[tex]x\geq 2[/tex]
Divide both sides by 2.
[tex]\dfrac{1}{2}x\geq 1[/tex]
Adding 5 on each side.
[tex]\dfrac{1}{2}x+5\geq 1+5[/tex]
[tex]f(x)\geq 6[/tex] ...(iii)
From (i), (ii) and (iii), it is clear that the values of f(x) lies in the interval [2,∞).
So, the range of the given function is [2,∞).
Therefore, the correct option is b.
correct answer is B
Life is a high way i wan to drive it all night long.
Related Questions
Woman .......Kam hir
Answers
GIVING BRAINLIEST
In the coordinate plane, the points A (7, 5), B(-10, -9), and C(4, - 11) are reflected over the x-axis to the points A, B', and C', respectively. What are
the coordinates of A', B', and C'?
Answers
Answer:
A (-7,5) . B (10,9) . C (-4,-11
Step-by-step explanation:
What is the ordered pair for A’ if A(2,-3) is reflected over the x-axis?
Answers
Answer:
A´= (2, 3)
Step-by-step explanation:
Chuck is taking his kids to the store to buy new converse shoes. he is given a choice of high tops or low tops. They may also choose from the colors red, gray, black, or pink.
What is the probability that his kids will choose a low top shoe that is gray or pink?
A. 1/4
B. 1/2
C. 1/3
D. 3/4
Answers
Answer:
B. 1/2
Step-by-step explanation:
The kids are given 4 options (grey, pink, red, black)
pink and grey are 2 options out of the 4 so 2/4
or 1/2 probability that they will choose the grey or pink shoes
plz mark me brainliest
find the sum of 0.48 and 0.6
Answers
Answer: the sum is 1.08
integers between -1and -5
Answers
an integer is a number that isn't a fraction. so literally any natural number like 1, 0, or -1. all integers.
Help! I think this is correct but im unsure
Answers
Shiloh needs to randomly select one of the six days between Sunday and Friday. Which simulation tools could she use in this situation?
((( MULTIPLE ANSWERS))
A-a spinner divided evenly into 12 sections, with each section a different color
B-two coins
C-a six-sided number cube
D-a bag containing 12 chips in two different colors, with six of each color
E-two full suits from a standard deck of cards
Answers
Answer:
The correct answer is C. She could use a six-sided number cube.
Step-by-step explanation:
Since Shiloh has 6 options from which to choose a unique alternative, it can be stated that her eligibility ratio is 1/6. Thus, since the dice has 6 numbers and only 1 will come up face up, the option of the dice is the most appropriate to make her decision.
On the other hand, the other options do not contemplate 6 possibilities but 12, 2, 12 and 13 possibilities respectively, with different possible alternatives, which does not give an equitable distribution of possibilities between each option.
Answer:
Behold!
Step-by-step explanation:
I Need help pls!
What is 75% of 800?
A; 9 3/8
B; 10.66
Answers
Answer:
it's 600
Step-by-step explanation:
that's not an option there but...
10% of 800 is 80
5% of 800 is 40
80 × 7 = 560
560 + 40 = 600
the ratio of strawberries to grapes in the fruit salad is 3:9. the ratios of strawberries to honey dew is 6:14. if there 36 grapes. how many strawberries?
Answers
Answer:
12 strawberries
Step-by-step explanation:
Represent strawberry with S, grape with G and honeydew with H
Given
[tex]S : G = 3 : 9[/tex]
S : H = 6 : 14
Required
Solve for S when G = 36
To do this, we make use of the first ratio
[tex]S : G = 3 : 9[/tex]
Substitute 36 for G
[tex]S : 36 = 3 : 9[/tex]
Convert to fractions
[tex]\frac{S}{36} = \frac{3}{9}[/tex]
[tex]\frac{S}{36} = \frac{1}{3}[/tex]
Multiply both sides by 36
[tex]36 * \frac{S}{36} = \frac{1}{3} * 36[/tex]
[tex]S = \frac{1}{3} * 36[/tex]
[tex]S = \frac{36}{3}[/tex]
[tex]S = 12[/tex]
Hence, there are 12 strawberries
the mean of 31,29,33,37,43,38,33,40
Answers
Answer:
37 is the mean of this question
Answer:
35.5
Step-by-step explanation:
31+29+33+37+43+28+33+40=284
284/8 (the amount amount numbers in question)
284/8=35.5
Lesson 4 problem solving practice
Answers
Answer:
what is your question?
Step-by-step explanation:
Find the value for x and y for the triangle. Show work.
Answers
Answer:
tan60=p/b
tan60=12/x
x=37.5
now taking sin
sin60=p/h
sin60=12/y
y=(-40) but as length can be negative so
y=40
Find the area of the parallelogram shown below.
3
6
square units
Stuc. TAI
Answers
Answer: 18
Step-by-step explanation:
Area of parallelogram: b × h
3 × 6 = 18
Hope this helped! :3
1.
Ginger works at the local putt-putt golf course. Her
weekly wages, y, are $7.25 per hour, x, she works.
Which equation best represents this relationship?
Answers
Answer: The equation that best represent this relationship is y=7.25x
Step-by-step explanation:
translate into mathematical phrase.the weight (w) is more than 2kg
Answers
Answer:
w>2kg
Step-by-step explanation:
the weight is greater than 2kg.
what is the gradient?
Answers
Answer:
[tex] \frac{3}{2} [/tex]Step-by-step explanation:
hi thereas we know gradient of Graf=[tex] \frac{∆y}{∆x} [/tex]
[tex] \frac{3}{2} [/tex]Find the distance between the points (1.0) and (0.2)
Answers
YEH ITS WRONG SORRY DON'T REPORT ME!
4/5 + 1/2 = ?
A 1 3/10
B 15/10
C 2 4/10
D 5/7
Answers
Answer:
13/10
Step-by-step explanation:
Steps to Solve:
-(2³)p + (-6p) = -112
Answers
Answer: p=8
Step-by-step explanation:(−23)(p)−6p=−112
−8p+−6p=−112
(−8p+−6p)=−112(Combine Like Terms)
−14p=−112
−14p=−112
−14p/−14 = −112/−14
p=8
What is 9 square foot in square feet ?
Answers
HURRY PLEASE On a coordinate plane, point A is 2 units to the left and 5 units up. Point B is 5 units to the right and 5 units up. What is the distance between the points? Point A is located at the point . Point B is located at the point . The distance between the points is units.
Answers
Answer:
point A is located at (-2,5) and point B is located at point (5,5), the distance between the points is 7 units. hope this helps!
The distance between the points will be 7 units. Point A is located at the point (-2, 5). Point B is located at the point (5, 5).
What is distance between points?The formula of distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: [tex](A,B) = \sqrt{( x_{2} - x_{1} )^2 + ( y_{2} - y_{1})^2}[/tex]
We have,
Point A (-2, 5) and Point B (5, 5).
i.e.
x₁ = -2, x₂ = 5 and
y₁ = 5, y₂ = 5
Now,
Using the above mentioned formula of distance,
i.e.
Distance [tex](A,B) = \sqrt{( x_{2} - x_{1} )^2 + ( y_{2} - y_{1})^2}[/tex]
So,
Substituting values,
Distance [tex](A,B) = \sqrt{(5-(-2) )^2 + ( 5-5)^2}[/tex]
Now, simplify,
Distance [tex](A,B) = \sqrt{(7)^2 + 0}[/tex]
We get,
Distance [tex](A,B) = 7[/tex]
So, the distance between AB is 7 units.
Hence, we can say that the distance between the points will be 7 units. Point A is located at the point (-2, 5). Point B is located at the point (5, 5).
To know more about distance between the points click here
https://brainly.com/question/15958176
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I don't know if I'm right or not. I think it's C, but I'm not too sure.
Answers
Answer:
its c
Step-by-step explanation:
Answer:
Ya its c
Step-by-step explanation:
It's correct u can cliuck or do it without any fear best of luck
Which is the correct answer?
(Note): (if you give me a silly or absurd answer I will report you)
Answers
Step-by-step explanation:
Since N ≡ 0 (mod 2) and N ≡ 0 (mod 3),
N ≡ 0 (mod (2*3)) ≡ 0 (mod 6).
Hence when N is divided by 6,
the remainder is 0. (A)
83, 694 ,357 expanded notation using descending order
Answers
Answer:
Step-by-step explanation:
eighty three, three hundred and fifty seven,six hundred and ninty four
80+3=83,300+50+7=357,600+90+4=694
This is the order.
Hope this helps!
the ratio of dogs to cats is 5 to 3, if there are 14 more dogs than cats, how many animals are there altogether?
Answers
Answer:
35
Step-by-step explanation:
3D=5C, 14+C=D
D=(5/3)C
14+C=(5/3)C
14=(2/3)C
C=21
21+14=D=35
So there are 21 cats and 35 dogs, or 56 total animals.
Sienna decides to buy a car. She has enough money saved up for the down payment on the car. The total cost of the car including taxes is $4800. She pays $500 down and then agrees to pay the balance over the next two years in 24 equal payments. Sienna works part time at a bookstore and is paid $12 for each hour she works. Her employer has agreed to let her work extra hours each month over the next two years to earn the additional money she will need for her car payment each month. What is the approximate number of additional hours per month Sienna will have to work over the next two years in order to earn enough extra money to cover her monthly car payment?
Answers
Answer:
4 hours
Step-by-step explanation:
For Pham to maximize her income, she must consider the jobs with the highest per-hour earnings first. She has 15 hours to work. Her priorities should be as below.
Work at the cafe for 6 hours for $15 per hour
Work at the garage for 5 hours for $13 per hour
Work at the books store for 4 hours for $12 per hour
A total of 15 hours. Pham can work at the book store for 4 hours per week to maximize her income.
might be wrong srry
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Louis and Ricardo took a timed a reading test, and the results below show the number of words each student can read per minute which student reads at a faster rate ?
Answers
Answer:
Louis reads faster
Step-by-step explanation:
See attachment for complete question.
The table represents Louis data while the graph represents Ricardo's data.
To solve this question, we simply calculate the slope of the table/graph,
The slope (m) is calculated by:
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Louis:
From the table, we pick any corresponding x and y values
[tex](x_1,y_1) = (2,436)[/tex]
[tex](x_2,y_2) = (6,1308)[/tex]
[tex]m_1 = \frac{1308 - 436}{6-2}[/tex]
[tex]m_1 = \frac{872}{4}[/tex]
[tex]m_1 = 218[/tex]
For Ricardo:
From the graph, we pick any corresponding x and y values
[tex](x_1,y_1) = (2,300)[/tex]
[tex](x_2,y_2) = (6,900)[/tex]
[tex]m_2 = \frac{900- 300}{6-2}[/tex]
[tex]m_2 = \frac{600}{4}[/tex]
[tex]m_2 = 150[/tex]
So, we have:
Louis: [tex]m_1 = 218[/tex]
Which means 218 words per minutes
Ricardo: [tex]m_2 = 150[/tex]
Which means 150 words per minutes
PLEASE ANSWER ASAP!!!!!!!!!!!!!!!
Authors set a TONE or MOOD in literature by conveying an emotion or emotions through ________.
Answers
Answer:
Author's craft
Step-by-step explanation:
f dcsdfsxadszcdxsfaczdsadzxsaddesdxxedrdrdsqxd
Please help me due today?
Answers
3x = 9
x = 9
ABD
7(3) - 1
21 - 1
20
DBC
4x + 8
4(3) + 8
12 + 8
20
3x - 17 + x + 40 + 2x - 5 = 180
6x + 18 = 180
6x = 198
x = 33
3(33) - 17
99 - 17
82
33 + 40
73
2(33) - 5
66 - 5
61