Find the range of the following piecewise function.
[0,11)
(-4,6]
(0,11]
[-4,6)
](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/JERoLzmWssEPrxOTiM6LvoL8Ut6SEbAD.png)
Answers
Given:
The piecewise function is
[tex]f(x)=\begin{cases}x+4 & \text{ if } -4\leq x<3 \\ 2x-1 & \text{ if } 3\leq x<6 \end{cases}[/tex]
To find:
The range of given piecewise function.
Solution:
Range is the set of output values.
Both functions [tex]f(x)=x+4[/tex] and [tex]f(x)=2x-1[/tex] as linear functions.
Starting value of [tex]f(x)=x+4[/tex] is at x=-4 and end value is at x=3.
Starting value: [tex]f(-4)=-4+4=0[/tex]
End value: [tex]f(3)=3+4=7[/tex]
Starting value of [tex]f(x)=2x-1[/tex] is at x=3 and end value is at x=6.
Starting value: [tex]f(3)=2(3)-1=5[/tex]
End value: [tex]f(6)=2(6)-1=11[/tex]
Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.
Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.
So, the range of the given piecewise function is [0,11).
Therefore, the correct option is A.
Related Questions
what is the step-by-step answer to
-3(X + 2)=-18
Answers
-3x - 6 = -18
-3x = -12
-x = -4
x = 4
Answer:
x = 4Step-by-step explanation:
Simplify both sides of the equation:−3 (x+2) = −18
(−3) (x) + (−3) (2) = −18 (Distribute)
−3x + −6 = −18
−3x −6 = −18
Add 6 to both sides:−3x −6 +6 = −18 + 6
−3x= −12
Divide both sides by -3:−3x/−3 = −12/−3
x = 4
Work out the difference between 88.1 and 2.81
Answers
Arika and Savroop have 19 ½ cups of flour. They want to make loaves of banana
bread for a bake sale. Arika had a recipe for banana bread that calls for 1 ⅞
cups of flour. Savroop has a recipe that calls for 1 ½ cups of flour. Select all the
statements that are true about the recipes.
O Arika's recipe will make 10 whole loaves of banana bread.
O Savroop's recipe will make 14 whole loaves of banana bread.
O There will be less flour leftover if Savroop's recipe is used.
( There will be less flour leftover if Arika's recipe is used.
D More loaves of bread can be made using Arika's recipe than using Savroop's recipe.
Answers
Statements A and C are correct.
Here, we are given that Arika and Savroop have 19 ½ cups of flour. Arika had a recipe for banana bread that calls for 1 ⅞ cups of flour. Savroop has a recipe that calls for 1 ½ cups of flour.
Let us evaluate each option one by one-
A. Arika's recipe will make 10 whole loaves of banana bread.
Arika's recipe requires 1 ⅞ cups of flour = (8 + 7)/8
= 15/8
Total flour they have = 19 ½ = (19 × 2 + 1)/2
= 39/2
Thus, Arika's recipe will make = 39/2 ÷ 15/8
= 39/2 × 8/15
= 13 × 4/ 5
= 52/5
= 10.4
Thus, the given statement is correct.
B. Savroop's recipe requires 1 ½ cups of flour = (2+ 1)/2
= 3/2
Thus, Savroop's recipe will make = 39/2 ÷ 3/2
= 39/2 × 2/3
= 13
Thus, the given statement is incorrect. Savroop's recipe will make only 13 whole loaves.
C. As we can see above, Arika's recipe will make 10.4 loaves and thus 0.4 cups of flour will be left over. Whereas, in case of Savroop, no flour will be left over. Thus, the given statement is true.
D. By the same reasoning given above, the given statement is false as there will be less flour leftover if Savroop's recipe is used.
E. The given statement is again false as Arika's recipe will make only 10 loaves whereas Savroop's recipe will make 13.
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Calculate the distance between the points P= (-7, 8) and J =(-3, 1) in the coordinate plane.
Give an exact answer (not a decimal approximation).
Distance:
Answers
The distance between the given points P(-7,8) and J(-3,1) is √65 = 8.06225775
Given that, The points are P=(-7,8) and J = (-3,1).
A coordinate plane is a surface formed by two dimensional lines .
The distance between the points is calculated using the distance formula that is, distance between A(x1,y1) and B(x2,y2) is,
√[(x2-x1)²+(y2-y1)²], by using this formula you can find the distance between any two points on the plane.
Therefore the distance between the given points P and J is ,
PJ = √[(-3+7)²+(1-8)²]
= √[(4)²+(-7)²]
= √[(16) + (49)]
= √[16+49]
= √[65]
= 8.06225775
PJ = 8.06225775
Therefore the distance between the given points P(-7,8) and J(-3,1) is 8.06225775
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Find the value of f(-2)
Answers
Answer:
y= -3 or just -3
Step-by-step explanation:
Please help it’s argent!!
5 employees are working on Saturday and get their base pay $125 per day plus an additional $40. How much will the company pay their employees to work on Saturday?
Answers
Answer:
=($25×5)+($125×5)
=$125+$625
=$750
50,500-35,675 and work for it
Answers
Answer: 14,825 is the answer
Step-by-step explanation:
Answer: 14,825
Step-by-step explanation:
its easy.
Some friends are going to be driving to a city 900 miles away from home. They are planning to stay the night in a city 420 miles away, then drive the rest of the distance the following day. If they plan to drive on average 60 miles per hour, how long will they be driving the second day?
Answers
The total time they will be driving the second day is 8 hours
The total distance they are planning to go = 900 miles
Distance travelled on first day = 420 miles
Distance yet to be travelled on second day = Total distance - distance covered = 900 miles- 420 miles= 480 miles
The speed of the car = 60 miles per hour
60 miles of distance covered in time = 1 hour
1 mile of distance covered in time = 1 hour /60 miles = 1 minute
This is solved using Unitary Method
1 hour = 60 minutes
480 miles can be covered in time = 1 minute × 480 miles
= 480 minute
=8 hours
Hence, The total time they will be driving the second day is 8 hours
Distance and displacement are two quantities that appear to mean the same thing but have very different meanings and definitions. Distance is defined as "how much ground an object has covered during its motion," whereas displacement is defined as "how far out of place an object is."
Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.
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The area of the parallelogram is 4 times the area of the triangle.
The perpendicular height of the parallelogram is h cm.
Find the value of h.
*HOMEWORK QUESTION*
Answers
Answer:
13
Step-by-step explanation:
Area of triangle = 0.5 × base × height
= 0.5 × 6 × 13
= 39
Area of parallelogram = 4 × Area of triangle
Note - Area of parallelogram = base × perpendicular height
Hence,
Base × perpendicular height = 4 × 39
12 × H = 156
H = 156 ÷ 12
= 13
Answer = 13
Answer:
h = 13 cm
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 6 and h = 13 , then
A = [tex]\frac{1}{2}[/tex] × 6 × 13 = 3 × 13 = 39 cm²
Then the area (A) of the parallelogram = 4 × 39 = 156 cm²
the area (A) of the parallelogram is calculated as
A = bh ( b is the base and h the height )
here b = 12 , then
12h = 156 ( divide both sides by 12 )
h = 13
Manny took home a couple of his friends after soccer practice. he originally had 4 gallons of gas in his car. he used 1.05 gallons of gas to take one friend home and three tenths gallon to take the other friend home. how much gas did he have left in his car after taking both friends home? 1.04 gallons 2.95 gallons 3.70 gallons 2.65 gallons
Answers
Answer:
2.65 gallons
Step-by-step explanation:
He originally had 4 gallons and he used 1.05 gallons.
4 - 1.05 = 2.95
He then used another three-tenths to take another friend home.
Three-tenths is equal to 3/10 or 30/100 or 0.30
2.95 - 0.30 = 2.65 gallons
PLEASE HELP ASAP! WILL GIVE BRAINLIEST!
Describe the pattern.
1, 2, 3, 4, 10, 19, 36, 69, 134, 258, 497, ...
Answers
Answer: the front of the four numbers is always the total
Step-by-step explanation: like 258 + 134 + 69 + 36= 497
Please helpp
−5(−2/3)
Answers
Answer:
[tex]\frac{10}{3}[/tex] or 3.3333.....
Hope this helps.
Step-by-step explanation:
( negative ) * ( negative ) = ( positive )
5 * [tex]\frac{2}{3}[/tex] = [tex]\frac{5*2}{3}[/tex] = [tex]\frac{10}{3}[/tex]
The length of a rectangle is twice the width. The area of the rectangle is 90 square units. Note that you can divide the rectangle into squares. A. Which irrational number represents the length of each side of the square? B. Estimate the length and width of the triangle
Answers
Answer: A. [tex]3\sqrt{5}[/tex]
B. l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]
Step-by-step explanation:
A. A=l*w
l=2w
A=2w*w
90=2w*w
w*w=45
w=[tex]\sqrt{45}[/tex]
w=[tex]\sqrt{9*5}[/tex]
w=[tex]3\sqrt{5}[/tex] ==> Square length and the rectangle width
B. 90=l*w
90=l*[tex]3\sqrt{5}[/tex]
30=l[tex]\sqrt{5}[/tex]
l=[tex]\frac{30}{\sqrt{5} }[/tex]
l=[tex]\frac{30\sqrt{5} }{5}[/tex]
l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]
Help with math problems
Answers
In the given picture there is a graph and we have to find out is that graph is one to one or not.
It is a one to one graph.
In the graph there is line.
To know is the line is one to one or not we have to check 1st that the line is a function or not.
To check the line is function or not we have to do by vertical line test.
Graphically, the vertical line test is a way to determine if a line is a function or not.
To perform the vertical line test, we pass the vertical lines arrows the graph and if it does not intersect the graph more then one point it passes the vertical line then it can say as a function.
In the given figure1 we can see the vertical lines does not touch the line in the graph more then one point so it is a function.
Now, we know the line is a function so now we have to check if the line is one to one or not.
To check the line is one to one or not we have to do by horizontal line test.
Graphically, the horizontal line test is a way to determine if a line is a one to one or not.
To perform the horizontal line test, we pass the horizontal lines arrows the graph and if it does not intersect the graph more then one point it passes the horizontal line then it can say as a one to one function.
In the given figure2 we can see the horizontal lines does not touch the line in the graph more then one point so it is a one to one function.
Therefore, The graph is a one to one function.
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10 QUESTIONS IM ON 3
Answers
Answer:
x = 9
m<H = 38 degrees
Step-by-step explanation:
Answer: 9
Step-by-step explanation: sub in 9 for x in 5x-7. we get 38. add 38 and 89 and then subtract that sum from 180, which is 53. now add 53 to 14x+1 and make it equal to 180. To solve for x, subtract 54 from both sides, which gives us 14x=126. Divide both sides by 14 and we get x =9. Now that we know that 9 works for x in both equations, the answer is 9.
Factor: x^2 - 169
please and thank you
Answers
Answer:
13,-13 are the factors
The steps are
x²-13²=(x+13)*(x-13)
so the factors are 13,-13
The graph shows the relationship between pounds of grapes, g, and their cost, c.
A graph on a coordinate plane shows cost of grapes on the horizontal axis (c), numbered 2 to 6, and pounds of grapes on the vertical axis (g), numbered 1 to 4. Solid circles are at points (0, 0), (2, 1), (4, 2), (6, 3), and are connected by a solid line.
Use the graph to complete the statements.
For every dollar you spend, you can get
pounds of grapes.
For each pound of grapes, you would need $
.
Answers
For the two given statements are:
"For every dollar you spend, you can get pounds of grapes."
If one pound costs $2, then for each dollar you will get half a pound.
"For each pound of grapes, you would need"
For each pound of grapes you will need 2 dollars.
How to complete the given statements?
Here we know that the graph shows the relationship between the pounds of grapes (g) and the cost (c). Such that the cost is on the horizontal axis, and the weight on the vertical axis.
We have the points:
(0, 0) For 0 dollars you buy 0 pounds.(2, 1) for 2 dollars you buy one pound.(4, 2) for 4 dollars you buy 2 pounds.(6, 3) for 6 dollars you buy 3 pounds.Then this is a proportional relationship, and we can see that each pound of grapes costs $2
Then the statements are:
1) "For every dollar you spend, you can get pounds of grapes."
If one pound costs $2, then for each dollar you will get half a pound.
2) "For each pound of grapes, you would need"
For each pound of grapes you will need 2 dollars.
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. f(x) = 2x-5; Find f(-8)
Answers
f(-8)=2x-5. then you solve it if x is -8 you do this next.
f(-8)=2(-8)-5, then you solve the two step equation.
f(-8)= -16-5
f(-8)= -21
Before the break at swim-team practice, Nicole swam 1,200 yards. After the break, she swam 1,600 yards. What is the percent of increase in the number of yards Nicole swam? Round to the nearest tenth if necessary.
Answers
The percent of the increase in the number of yards Nicole swam will be 33.33%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Nicole swam 1,200 yards during the swim rookie minicamp before the break. She swam 1,600 yards after the break.
Then the percent of the increase in the number of yards Nicole swam will be
P = [(1600 - 1200) / 1200] x 100
P = (400 / 1200) x 100
P = 0.3333 x 100
P = 33.33%
The percent of the increase in the number of yards Nicole swam will be 33.33%.
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A road is 8/9 of a mile long. A crew needs to replace 4/5 of the road how long is the section that needs to be repaved
Answers
Answer:
4/45
Step-by-step explanation:
8 - 4
9 5
= 8 × 5 - 4 × 9
9 × 5 5 × 9
= 40 - 36
45 45
= 40 – 36
45
= 4
45
8/9 - 4/5
= 4/45
what is the value of arccos(-sqrt3/2)
the answer is 5pi/6
Answers
5. YOU BE THE TEACHER Your friend identifies
the terms and like terms in the expression
3x-5-2x + 9x. Is your friend correct?
Explain your reasoning.
SIMPLIFYING ALGEBRAIC EXPRESSIONS Simplify the
16. 12g + 9g
17. 11x 9-7
O
Answers
The correct form of the expression is 5(2x - 2)
How to solve the expression?It should be noted that the expression that is given is illustrated as:
3x-5-2x + 9x.
To solve this, collect the like terms
3x - 2x + 9x - 5
= 10x - 5
= 5(2x - 1)
The correct form of the expression is 5(2x - 1)
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Write in standard form y=2(x-3)^2+2
Answers
what is it called when you make predictions about data that is not recorded, but falls between the data collected?
Answers
when you make predictions about data that is not recorded, but falls between the data collected it is called Predictive analytic.
What is Predictive analytics?Data mining, predictive modeling, and machine learning are only a few of the statistical methods included in predictive analytics, which examine current and past data to anticipate future or otherwise unknowable occurrences.
Predictive models are used in business to detect risks and opportunities by making use of trends observed in historical and transactional data. In order to estimate the risk or potential associated with a certain set of variables and guide decision-making for possible transactions, models contain interactions among many different elements.
When we make a prediction about data is called predictive analytic.
But when it's not recorded it's called extrapolation.
But if it falls between data collected it called Predictive analytic.
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" .
8x + 4 = -28
solve for x
Answers
Answer:
x=-4
Step-by-step explanation:
8x+4=-28
8x=-28-4
8x=-32
x=-4
SOMEONE PLEASE HELP ME I REALLY NEED HELP ON THIS
Answers
The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.
How to determine the volume of the Washington Monument
In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:
V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)
V' = 1018791.667 ft³
V'' = (1 / 3) · (34.5)² · 55.5
V'' = 22019.625 ft³
Second, calculate the volume of the obelisc:
V = V' + V''
V = 1018791.667 ft³ + 22019.625 ft³
V = 1040811.292 ft³
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Find the difference in altitude between a mountain that has an altitude of 2593feet and a desert valley that is 394feet below sea level.
Answers
The difference in altitude between a mountain that has an altitude of 2593feet and a desert valley that is 394feet below sea level is
dA=2987feet
What is the difference in altitude?
Generally, the equation for the difference is mathematically given as
dA= mountain altitude - desert valley
Therefore
dA=2593-(-394)
dA=2593+394
dA=2987feet
In conclusion, The height of a mountain that is located at an elevation of 2593 feet compared to the elevation of a valley in the desert that is 394 feet below sea level is the difference in altitude.
dA=2987feet
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A bank Teller's annual salary will increase by 12% next year to an annual salary of
$48,000. What is the teller's annual salary now?
Answers
Answer:
$42,857.14
Step-by-step explanation:
12% = 12/100 = 0.12
If the teller's current salary is D and it increases by 12% in one year, the salary next year would be
X(1+0.12) = 1.12X
We know that salary next year is 48000
Using this fact,
1.12X = 48000
Dividing by 1.12 on both sides,
X = 48000/1.12 = 42,857.14
Bella and her friends have a half-day at school, so they plan to spend the afternoon
paddleboarding at Lake Evergreen. They want to spend the rest of the day on the water, but
it starts to rain after paddleboarding for only of an hour! Bella is disappointed when she
of a
realizes the sun doesn't go down for another 4
hours.
Use an equation to find the amount of time Bella planned to spend paddleboarding.
Answers
Jen planned to spend 19/4 hours paddleboarding
Bella and her friends spent 3/4 hour at the Lake paddleboarding
Proportions: A proportion is an equation that can be solved and is made up of two ratios that have been set equal to one another.
When I state that a proportion is the product of two ratios that are equal to one another, I mean that two fractions must also be equal to one another.
Also, the sun doesn't go down for another 4 hours
So, 4 + 3/4 = 4.75 hours = 475/100 = 19/4 hours
Hence, Jen planned to spend 19/4 hours paddleboarding
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Simplify this expression.
2d + 1 + d-5
[?]d + []
Answers
Answer:
3d-4
Step-by-step Explanation:
2d+1+d-5 Combine like terms 2d and d together which is 3d. That leaves you with 1-5 which is -4. so then you end up with 3d-4 as your answer.