3.3 Practice - Piecewise Functions
Find the value of the given function at the indicated domain value.
-X2 - 5x + 2, x < 1
2x2 - 2x + 1,
xs-6
g(x) = x3 - 5x, 1 < x < 11
h) =
3x – x3 -3
3x - 16,
X > 11
(2x - (x - 100
x > 1
1. g(1) =
2. g(11) =
3. h(5) =
4 h(-10) =
5. g(-1) =
6. h(0) =
7. g(20) =
8. h(-4)=
Answers
Answer:
Step-by-step explanation:
1. g(1) = (1)³ - 5(1) = - 4
2. At x = 11 function g(x) is not defined,
3. h(5) = 2(5) - | 5 - 10 | = 5
4 h( - 10) = 2( - 10)² - 2(- 10) + 1 = 221
5. g(- 1) = - (- 1)² - 5(- 1) + 2 = - 1 + 5 + 2 = 6
6. h(0) = 3(0) - (0)³ = 0
7. g(20) = - √[3(20) - 16] = - 2√11
8. h(- 4) = not defined
The value of each function is shown below.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
From the given function we can find the values as:
g(1) = x³ - 5x
g(1) = 1³ -5 = -4
2. For x= 11 the function g(x) is not defined.
3. h(5) = 2x - |x -10|
h(5) = 4
4. h(-10) = 2x² - 2x + 1
h(-10) = 221
5. g(-1) = -x² -5x + 2
g(-1) = 6
6. h(0) = 3(0) - (0)³
h(0) = 0
7. g(20) = - √[3(20) - 16]
g(20) = - 2√11
8. h(- 4) is not defined for the function h(x).
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Answer:
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Step-by-step explanation:
fdsfa
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ANSWER = -1
hi, take x = -1
[tex]-1\leq -1 \ so \ x\leq -1 \\ \\\text{ BUT } x^3=-1 < -1 \text{ is wrong}[/tex]
Thanks
Answer:
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Find two positive integers such that their sum is 10, and minimize and maximize the sum of their squares.
Answers
Two numbers whose sum is 10 is required.
The answer is
Minimum: 5, 5
Maximum: 9, 1
Let [tex]x[/tex] and [tex]y[/tex] be two numbers
[tex]x+y=10\\\Rightarrow y=10-x[/tex]
The sum of the squares would be
[tex]x^2+y^2=x^2+(10-x)^2\\ =2x^2-20x+100[/tex]
[tex]f(x)=2x^2-20x+100[/tex]
Differentiating with respect with x
[tex]f'(x)=4x-20[/tex]
Equating with zero
[tex]4x-20=0\\\Rightarrow x=\dfrac{20}{4}\\\Rightarrow x=5[/tex]
Double derivative of f(x)
[tex]f''(x)=4[/tex]
[tex]f''(x)>0[/tex]
So, at [tex]x = 5[/tex] the value of the function is minimum.
Therefore, at [tex]x=5[/tex] and [tex]y=10-5=5[/tex] the function has minimum value of [tex]5^2+5^2=50[/tex]
For the finding the maximum values of [tex]x[/tex] and [tex]y[/tex] we have to use trial and error method
[tex]9^2+1^2=82[/tex]
[tex]8^2+2^2=68[/tex]
[tex]7^2+3^2=58[/tex]
[tex]6^2+4^2=52[/tex]
0 and 10 will not be considered as 0 is neither positive nor negative.
So, the maximum value of the numbers is 9 and 1 and the maximum value of the function is 82.
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What is the standard form of y –7 = – 23 (x + 1)
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Answer:
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Step-by-step explanation:
PLEASE HELP ME! WILL MARK BRAINLIST!!!!
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Answer:
Yes, {9,−1,−2,−4},{9,−1,−5,5}
Step-by-step explanation:
Since there is one value of y for every value of x in ((9,9),(−1,−1),(−2,−5),(−4,5)), this relation is a function. The relation is a function.
The domain is the set of all the values of . The range is the set of all the values of
y.Domain:{9,−1,−2,−4}Range:{9,−1,−5,5}
<3
What did philosophical pig say?
(Geometry Version)
Answers
Answer:
A: m<BOD = 95°
O: m<AOC = 75°
R: m<AOD = 113°
T: m<GUH = 61°
M: m<GUI = 92°
E: m<EUF = 37°
F: m<EUI = 160°
K: m<MAN = 30°
I: m<LAM = 40°
S: m<KAM = 80°
H: m<JAN = 140°
N: m<KAN = 110°
✅I STINK THEREFORE I HAM
Step-by-step explanation:
A: m<BOD = 57° + 38° = 95°
O: m<AOC = 18° + 57° = 75°
R: m<AOD = 18° + 57° + 38° = 113°
T: m<FUG = 31°, since, FUG ≅ HUI, therefore, m<HUI = 31°
m<FUI = 123°
m<GUH = m<FUI - (m<FUG + m<HUI)
m<GUH = 123° - (31° + 31°)
m<GUH = 61°
M: m<GUI = m<GUH + HUI
m<GUI = 61° + 31°
m<GUI = 92°
E: m<EUH = 129° (given)
m<EUF = m<EUH - (m<FUG + m<GUH)
m<EUF = 129° - (31° + 61°)
m<EUF = 37°
F: m<EUI = m<EUF + m<FUG + m<GUH + m<HUI
m<EUI = 37° + 31° + 61° + 31°
m<EUI = 160°
K: since <JAK ≅ <MAN, and m<JAK is given as 30°, therefore,
m<MAN = 30°
I: m<JAM = 110° (given), m<JAK = 30° (given)
Since <KAL ≅ <LAM, therefore,
m<LAM = ½(m<JAM - m<JAK)
m<LAM = ½(110° - 30°)
m<LAM = 40°
S: m<KAM = m<KAL + m<LAM
Since <KAL ≅ <LAM, therefore,
m<KAM = 40° + 40°
m<KAM = 80°
H: m<JAN = m<JAK + m<KAL + m<LAM + m<MAN
m<JAN = 30° + 40° + 40° + 30°
m<JAN = 140°
N: m<KAN = m<KAL + m<LAM + m<MAN
m<KAN = 40° + 40° + 30
m<KAN = 110°
Place the letters on the appropriate lines given to match the angle measure we've cakcukated, to figure out the joke.
✅We would have:
I STINK THEREFORE I HAM
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a
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b
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c
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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
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solve 7x -2 + 10x + x + 6x
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Let's simplify step-by-step.
7x−2+10x+x+6x
=7x+−2+10x+x+6x
Combine Like Terms:
=7x+−2+10x+x+6x
=(7x+10x+x+6x)+(−2)
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Step-by-step explanation:
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Answer:
D. 680
Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Answer:
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b.$10
c. 2x
d. $3
e. $9
f. 2y
g. $22
h. $21.5
i. 2x + 1.5y
2)
a. 2x + 1.5y = 22
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Stefan sells Jin a bicycle for $163 and a helmet for $17. The total cost for Jin is 150% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin? Stefan originally spent $
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Answer:
44$
Step-by-step explanation:
Answer:
Answer
5.0/5
7
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Ace
5K answers
22.1M people helped
The selling cost for Stefan bicycle = $114 and
the selling cost of a helmet = $18.
The total cost for Jin is 120% of the money spent.
Let us assume purchasing cost of a bicycle = $x.
Purchasing cost of a halmet = $y.
For bicycle
120% of x is $114
=> 1.20 × x = 114
Dividing both sides by 1.20, we get
x=$95.
For helmet.
120% of y is $18.
=> 1.20 × y = 18.
Dividing both sides by 1.20, we get
y = $15.
Therefore, Stefan spent originally to buy a bike $95 and $15 to buy a helmet.
$114 - 95 = $19
$18 - 15 = $3.
Therefore, he made $19 by selling the bicycle and $3 by selling the helmet to Jin.
Step-by-step explanation:
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Super Sitters charges a flat rate of $20 an hour per child.
For ________hours of service, both babysitting services would cost the same.
Answers
Answer:
After 5 hours of service, both babysitting services would cost the same.
Step-by-step explanation:
Babysitter's Block: y = 15x + 25
Super Sitters: y = 20x
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x = 5
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Answer:
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Answer:
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Part B:
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Answer:
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Answer:
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Answers
Answer:
50 miles per hour
Step-by-step explanation:
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