Consider the function given by the graph. What are
these values?
fl-2) =
10) =
f(4) =
Answers
Answer:
f(-2) = 2
f(0) = 4
f(4) = -1
Step-by-step explanation:
Given the graph of a piecewise function:
[tex]\displaystyle\mathsf{f(x) = \left \{ {{x\:+\:4\quad if\:\:x\leq \:0} \atop {-\frac{1}{2}x\:+\:1\quad if\:\:x\: >\:0}} \right.}\\[/tex]
Side note:
I used the method of finding the linear equations in slope-intercept form to establish the piecewise function. First, I solved for the slope by choosing two points in each defined interval. Then, I plugged in the y-intercepts of each interval, for f(x) = x + 4: the y-intercept is (0, 4) where b = 4; for f(x) = -½x + 1, the y-intercept is (0, 1) where b = 1.
Explanation:There are two methods for determining the range values of the given domain values.
Method 1: The first method is using the graph to find the corresponding range values of the given domain {-2, 0, 4}.
Method 2: Alternatively, we could use the rules provided by the piecewise function in evaluating the following domain values. This post will use the second method (using the piecewise function) to evaluate the input values.
Regardless of the method used, the results will remain the same.
f(-2)Since the input value is x = -2, then we must use the function, f(x) = x + 4:
f(x) = x + 4
f(-2) = -2 + 4
f(-2) = 2
Therefore, the range value given the domain, x = -2 is 2, or simply: f(-2) = 2.
f(0)
Given the input value is x = 0, then we must also use the function, f(x) = x + 4:
f(x) = x + 4
f(0) = 0 + 4
f(0) = 4
Therefore, the range value given the domain, x = 0 is 4, or f(0) = 4.
f(4)
Since the input value is x = 4, then we must use the function, f(x) = -½x + 1:
f(x) = -½x + 1
f(4) = -½(4) + 1
f(4) = -2 + 1
f(4) = -1
Therefore, the range value given the domain, x = 4 is -1, or f(4) = -1.
Related Questions
Each big square below represents one whole.
Answers
Answer:
103%
Step-by-step explanation:
each little box is 1%
plz help will mark as brainliest
Answers
Answer:
the three sides are 8, 12 and 16
Step-by-step explanation:
since the ratio is in 2:3:4, we need to work out each side individually so add them=2+3+4=9
9n=36, n=4
2:3:4
2 × 4 = 8
3 × 4 = 12
4 × 4 = 16
To go to school in the morning. I first walk to the garden shed at 6 km/h to collect my bicycle. I then cycle to school at 15 km/h. The total journey normally takes 18.5 minutes, One day, I am lote and I run to the shed at 18 km/h and cycle at 27 km/h. The journey takes me 10 min 10 s. How far is it from my house to the garden shed?
Answers
Answer:
1
Step-by-step explanation:
Answer:
Trip A from House to Shed is 0.062 km
Trip B from Shed to School is 4.47 km
Step-by-step explanation:
Set up a table (attached) that summarizes and organizes the data. Let A be the distance from the hosue (I assume) to the shed, and B the distance from the shed to the school. We know that distance = (speed)*(time).
The total time for a trip is the sum of the two segments, A and B, divided by the speed for each segment.
TRIPS
1 2
House/Shed A 6 18 km/hr
Shed/School B 15 27 km/hr
18'30" 10'10" min
18.5 10.16 min
0.308 0.169 hr [Convert the minutes into hours]
[The distance divided by the speed will give the time required for each segment, A and B].
Trip 1: 1) A/6 + B/15 = 0.308
Trip 2: 2) A/18 + B/27 = 0.169
Trip 1: A/6 + B/15 = 0.308
A + (6/15)B = 1.85 [Multiply each side by 6]
A = 1.85 - (6/15)B [Rearrange]
A = 1.85 - (0.4)B [This will be the defination of A we'll use in the second equation]
Trip2: A/18 + B/27 = 0.169
(1.85 - (0.4)B)/18 + B/27 = 0.169 [Use A= 1.85 - (0.4)B from above]
27(1.85 - 0.4B)/18 + B = 27*(0.169) [Multiply each side by 27]
1.5*(1.85-0.4B) + B = 4.58
2.78 - 0.6B + B = 4.58
0.4B = 1.85
B = 4.47 km
Now use B = 4.47 km in either original equation to find A.
A/18 + B/27 = 0.169
A + (18/27)B = 18*(0.169) {Multiply both sides by 18]
A + (0.67)B = 3.042
A + (0.67)(4.47) = 3.042
A + (2.98) = 3.042
A = 0.062 km
Trip A from House to Shed is 0.062 km
Trip B from Shed to School is 4.47 km
Sales tax in a certain community is 7%. If the sales tax on a new car was $1,400, what was the selling price of the car
Answers
Answer:
20,000
Step-by-step explanation:
Answer:
%7 1400
100 x
7x=140000
x=20000$
You are going on vacation. You have $105 to take with you. You expect to spend $15 each day. You want to have $30 remaining at the end of the vacation. Write an explicit formula to represent this scenario. For how many days can you spend $15 a day?
Answers
Answer:
105-15x=30
5 days
You can spend the amount of $15 a day for 5 days if you have $105 to take with you.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
You're going on vacation. You have $105 with you. You plan to spend $15 per day. You want to have $30 left at the end of your trip.
Let the number of days would be x
According to the given information, the required solution would be as
105 - 15x = 30
The above explicit formula represents the given scenario.
105 - 15x = 30
Rearrange the terms in the above equation,
15x = 105 - 30
Apply the subtraction operation,
15x = 75
x = 75/5
Apply the division operation,
x = 5
Therefore, you can spend the amount of $15 a day for 5 days.
To learn more about numerical expression click here :
https://brainly.com/question/6037813
#SPJ2
What type of angle is 19 degrees
Answers
Answer:
Obtuse Angle
Step-by-step explanation:
Answer:
Acute
Step-by-step explanation:
Nestle Crunches cost 30 cents and Snickers cost 50 cents. Jessica and Tori
treated the class and they spent $6.80. How many students had Snickers if these
numbered 4 less than those who had Nestle Crunches?
Answers
Answer:
7 students had SnickersStep-by-step explanation:
Nestle Crunches - nSnickers - sSystem of equations according to given:
30n + 50s = 680 (converted $6.80 into 680¢)n = s + 4Substitute n into first equation and solve for s:
30(s + 4) + 50s = 68030s + 120 + 50s = 68080s = 680 - 12080s = 560s = 560/80s = 7Equations are
0.30x+0.50y=6.80=>30x+50y=680--(1)x=4+y=>x-y=4-(2)[/tex]EQUATION(2)× 30
[tex]\\ \sf\longmapsto 30x-30y=120--(3)[/tex]
Subtracting (1) and (3)
[tex]\\ \sf\longmapsto 80y=560[/tex]
[tex]\\ \sf\longmapsto y=7[/tex]
what multiples to -36 but adds to 16
Answers
Answer:
answer in the link below
mathhelp.mhlp
Step-by-step explanation:
Anybody know the answer and how did you get it
Answers
Answer:
so I'm guessing you're solving for x
because angle 2 is the vertical angle to angle 3 so this means that they are congruent
4x-26=3x+4
4x-3x=4+26
x=30
Answer 5 and 6 please
Answers
Answer: 5) F:(1,-1)
6) W:(-3,-2)
Step-by-step explanation:
GIVING BRAINLIEST!!!!!!!!
Answers
[tex]\red{\bold{Answer:}}[/tex]
The Inverse variation of the total stopping distance and the force of the pavement to determine the speed the car travelling.
#BrainlyFast
#CarryOnLearning
(≡^∇^≡)
Please help me this is due tomorrow.
Answers
Answer:
C
Step-by-step explanation:
The domain of a function is a set of values that make the function real and defined. No matter what number you substitute as x, the result is always real. Hence, the domain would be from negative infinity to positive infinity.
Answer: I think it’s D
Step-by-step explanation:
There were m balloons at the beginning of a party. By the end of the party, 4 of them had popped. Using m, write an expression for the number of balloons that were left. Please help! <3
Answers
Answer:
m - 4
Step-by-step explanation:
So, m amount of balloons at the beginning.
When 4 pop, that means there are 4 less than the beginning.
m - 4
A weightlifter's maximum amount he can lift is 300 pounds. Write and solve an equality to find the number of 50 pound weights he can possibly lift.
Answers
50w/50 = 300/50
----------- -----------
1w (or) w = 60
w = # of weights
The weightlifter can lift a maximum of 60 weights if each weight weighed 50 pounds.
193 / 240
what will be the percentage for this
Answers
Answer:
84%
Step-by-step explanation:
To find a percentage, just divide the first number by the second.
[tex]\frac{193}{240}=0.80417[/tex]
So 193 is about 80% of 240.
If you were to do it in the other order:
[tex]\frac{240}{193} =1.24352[/tex]
240 is 124% of 193.
193 / 240 = 0.80416666 x 100 = 80.4
0.9 is the result of finding the product of 2 and 34 minus a number.
Answers
Answer:
The answer is 3/10
Step-by-step explanation:
I took the test using K-12
Sorry if it is late.
Solve for X:
6(4X - 6) + 5 = 8X + 4X - 28 + 12X + 5 - 8
Answers
Answer:
I think it's infinantly many solutions
Step-by-step explanation:
6•4x= 24x.
6•-6=-36. 8x+4x+12x=24x 24x-36+5 -28+5-8=-31
24x-31 24x-31
sorry that's it's set up so wierdly
Answer:
Any value of X makes the equation true.
Step-by-step explanation:
8.3g of sugar is needed for every cake made. How much sugar is needed for 5 cakes?
Answers
Answer:
41.5g of sugar
Step-by-step explanation:
8.3 x 5
Plzzzzzz help one more time
Answers
Non linear means not a straight line
Write an equation in slope-intercept form of the line shown. (-6, 4) (-2, 2)
Answers
5 (m - 3) = 40
What do 5m and m represent?
(Quick Question I NEED REAL QUICK!)
(Thanks)
Answers
[tex]5(m -3 ) = 40 \\ = > 5m - 15 = 40 \\ = > 5m = 40 + 15 \\ = > 5m = 55 \\ = > m = 11[/tex]
Therefore, m = 11
5m = 5 × 11 = 55
Answers5m is 55, m is 11.
Hope it helps.
Do comment if you have any query.
Answer:
m=11
5m=55
Step-by-step explanation:
To find the answer to this question, isolate m. Do this by using the properties of equality.
First, distribute the 5 to the terms within the parentheses
5m-15=40Then, add 15 to both sides
5m=55Next, divide both sides by 5
m=11This gives you the solution to both questions. If you want to check the answer, simply plug the variable back in. This gives you, 5(11-3)=40. Once solved this equals 40=40. Therefore, 11 is correct.
what is 5 minutes to four and how?
Answers
Answer:
4 minutes to 4 is actually 3 56 am or pm
Step-by-step explanation:
it simply means you are left with 1 2 3 4 minutes only till is 4 o'clock
four w plus ten equals negative w
Answers
Answer:
4w+10=-w
w=-2
Step-by-step explanation:
First, write out the equation in the algebraic form to make it easier to solve. This equation written out is 4w+10=-w. Then, isolate the variable and solve. Do this by subtracting 4w from both sides. Then, divide both sides by -5.
4w+10=-w10=-5w-2=wWhat is the image of the point. (6, – 7) after a rotation of 180° counterclockwise
about the origin?
Answers
Answer:
(-6,7)
Step-by-step explanation:
The rotation is 180 degrees, so its means that the direction (clockwise vs counterclockwise) doesn't actually matter. With a rotation of 180 degrees, the preimage is switched to the opposite side of both the y and x-axis. This means that the rule for rotation around 180 is (-h,-k). Therefore, the answer will have the opposite signs. Thus. the image of (6,-7) is (-6,7).
Answer:
(-6, 7)
Step-by-step explanation:
the original and new points are both six units above/below the x-axis and 7 units to the right/left of the y-axis
Find the value by using the suitable identities 84 2 The 2 is square so the question is 84 square Pls i need the ans fastt
Answers
84²
it is like saying 84×84
so
84×84=7,056
so our answer is
= 7,056
How to find Y intercept of the line passing through the points
Answers
Answer:
Y-intercept: (0, -3)
Step-by-step explanation:
Given the two points, (6, 5) and (3, 1):
We can find the y-intercept by using the slope-intercept form, y = mx + b. However, the first step that we must do is to solve for the slope.
SlopeWe must first solve for the slope of the line using the following formula:
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
Let (x₁, y₁) = (3, 1)
(x₂, y₂) = (6, 5)
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{5 - 1}{6 - 3}\:=\:\frac{4}{3}}[/tex]
Hence, the slope of the line is: [tex]\sf{m\:=\frac{4}{3}}[/tex] .
Y-intercept:Next, we must determine the y-intercept, which is the point on the graph where it crosses the y-axis, with coordinates of (0, b ).
In order to find the y-intercept, use one of the given points, (6, 5), and the slope, [tex]\sf{m\:=\frac{4}{3}}[/tex], and substitute these values into the slope-intercept form and solve for the value of b:
y = mx + b
[tex]\displaystyle\mathsf{5\:=\:\frac{4}{3}(6)\:+\:b }[/tex]
5 = 8 + b
Subtract 8 from both sides to isolate b:
5 - 8 = 8 - 8 + b
-3 = b
Therefore, the y-intercept is (0, -3), where b = -3.
A jar contains 35 coins made up of 20c and 50c coins only. Then total value of the coins is
$13.90.
(I) If there were x 20c coins, write an equation in x for the number of 50c coins.
(ii) Using the given information, write an equation in terms of x for the total sum of money
the jar holds.
(iii) Solve the equation to find the number of each type of coin in the jar.
Answers
There are 12 coins which are 20 cent each and 23 coins which are 50 cent each.
Let x represent the number of 20 cent ($0.2) coins
i) Since there are 35 coins in total:
Number of 50 cent coins = 35 - x
ii) The total value of the coins is $13.90. Hence:
0.2x + 0.5(35 - x) = 13.90
iii) 0.2x + 17.5 - 0.5x = 13.90
0.3x = 3.6
x = 12
Number of 50 cent coin = 35 - x = 35 - 12 = 23
Therefore there are 12 coins which are 20 cent each and 23 coins which are 50 cent each.
Find out more at: https://brainly.com/question/21105092
At GameStop, there is a 30% off discount sale for a PS 5 originally priced at $600. After the sale, the discounted price of the PS5 was increased by 30%. What is the final price of the PS5 after the increase?
Answers
Answer:600-30 precent is $420 so is you increase it by 30 precent it would be
420 + (30% × 420) =
420 + 30% × 420 =
(1 + 30%) × 420 =
(100% + 30%) × 420 =
130% × 420 =
130 ÷ 100 × 420 =
130 × 420 ÷ 100 =
54,600 ÷ 100 =
546
Step-by-step explanation:
so 546 if wrong i am sorry
Help please! If a bot answers pls ignore!
Answers
Answer:
3.70
Step-by-step explanation:
Answer:
a. $58.75
b. 3.75p +5.00d
Step-by-step explanation:
As with any sort of purchase, the cost for a number of items of the same kind is the product of the number of items and the cost of each. For several different items, the total cost is the sum of the costs of each of the kinds of items. If you do any shopping, you know this.
a.5 popcorn and 8 drinks cost 5($3.75) +8($5.00) = $18.75 +40.00 = $58.75
__
b.p popcorn and d drinks cost p($3.75) +d($5.00) = 3.75p +5.00d . . . . dollars
Please help me ASAP!! And please don’t just answer randomly for points..thanks
Answers
Answer:
46
Step-by-step explanation:
3x3=9
5x7=35
9+35=46
Answer:
44 inches
Step-by-step explanation:
Cut off the pertruding bit of the shape
3inches × 3 inches = 9 inches
5 inches × 7 inches = 35 inches
9 inches + 35 inches = 44 inches