Answers
Answer:
f(0) = 0
f(-2) = 0
f(5) = 15
f(-10) = 16
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases} \begin{aligned}-2x-4 & \;\;\textsf {if }\;x < 0\\3x & \;\;\textsf {if }\;x\geq 0\\\end{aligned}\end{cases}[/tex]
Therefore, the function has two definitions:
[tex]\textsf{$f(x)=-2x-4$ when $x$ is less than zero}.[/tex][tex]\textsf{$f(x)=3x$ when $x$ is more than or equal to zero}.[/tex]When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of the function
Substitute zero into the first function:
[tex]\implies f(0)=-2(0)-4=-4[/tex]
Place an open circle at point (0, -4).
To help graph the line, find another point on the line by inputting another value of x that is less than zero into the same function:
[tex]\implies f(-2)=-2(-2)-4=0[/tex]
Place point (-2, 0) and draw a straight line from the open circle at (0, -4) through (-2, 0). Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of the function
Substitute zero into the second function:
[tex]\implies f(0)=3(0)=0[/tex]
Place an closed circle at point (0, 0).
Again, to help graph the line, find another point on the line by inputting another value of x that is more than zero into the same function:
[tex]\implies f(2)=3(2)=6[/tex]
Place point (2, 6) and draw a straight line from the closed circle at (0, 0) through (2, 6). Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
To find the given functions, decide which function to use based on the given value of x, then solve.
f(0) means to find the value of the function when x = 0.
Therefore, input x = 0 into the second function as x ≥ 0.
[tex]\implies f(0)=3(0)=0[/tex]
f(-2) means to find the value of the function when x = -2.
Therefore, input x = -2 into the first function as x < 0.
[tex]\implies f(-2)=-2(-2)-4=0[/tex]
f(5) means to find the value of the function when x = 5.
Therefore, input x = 5 into the second function as x ≥ 0.
[tex]\implies f(5)=3(5)=15[/tex]
f(-10) means to find the value of the function when x = -10.
Therefore, input x = -10 into the first function as x < 0.
[tex]\implies f(-10)=-2(-10)-4=16[/tex]
Related Questions
What is the value of (-2) • (7) • (5) • (-4)= Enter your answer as a number, like this: 42
Answers
Answer:
280
Step-by-step explanation:
-2 x 7 = -14
-14 x 5 = -70
-70 x -4 = 280
Answer:
280
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)According to the order of operations (PEMDAS), when multiplying, work from left to right:
Given expression:
(-2) · (7) · (5) · (-4)
Multiply -2 by 7:
⇒ (-14) · (5) · (-4)
Multiply -14 by 5:
⇒ (-70) · (-4)
Finally, multiply -70 by -4, remembering that if both numbers are negative, the answer is positive:
⇒ 280
Given the line y = -1, write the equation
of the line that is parallel to that line and
passes through (-3,5).
Answers
Answer:
Y+5=0
Step-by-step explanation:
Here,given eqn of line is 0.X+Y+1=0_____(i)
since required eqn is parallel to eqn (i)
0.X+Y+K=0____(ii)
passing point (-3,5)
putting the value of Y
5+K=0
.-.K=(-5)
r required eqn is Y-5=0
Find the 6th term of the arithmetic sequence x+2, -6x-3, -13x-8,...
Answers
Ming says that 0.24>1/4 because 0.24=2/4 which best explains Ming’s error
Answers
19yd.28in.-16yd.31in.
Answers
Answer:
2yds 33 in
Step-by-step explanation:
Convert everything to the lowest unit(inches) perform the operation and convert back
1 yard = 3 feet
1 foot = 12 in
1 yard = 3feet x 12in = 36 in
19yd, 28in = 19 x 36 + 28 = 684 + 28 = 712 in
16yd, 31 in= 16 x 36 + 31 = 576 + 31 = 607 inches
19yd, 28in - 16yd, 31 in = 712 - 607 = 105 inches
Divide by 36 to get the whole number of yards as quotient
105/36 with remainder of 33
∴ 19yd, 28in - 16yd, 31 in = 105 inches = 2yds 33 inches
We can verify this by converting 2yds 11inches to inches and seeing the values agree
2 yds 33 in = 2 x 36 + 33 = 105
Find the unit rate for each store. Then decide which offers the better buy.
Store A
5 bottles of juice for $10
Store B
9 bottles of juice for $21
Answers
Store B = 2.3$ a bottle
Store A is better
Write the following statement in the "if-then" form.
A side of a square measures 3 decimeters if the side's measure is 30 centimeters.
Choose the correct answer below.
OA. If the side of a square measures 3 decimeters, then the side's measure is 30 centimeters.
OB. If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.
Answers
If the side's measure is 30 centimeters, then the side of a square measures 3 decimeters, is the "if-then" form of A side of a square measures 3 decimeters if the side's measure is 30 centimeters.
A statement with an assumption and a conclusion is known as a conditional statement (also known as an if-then statement). The hypothesis is the initial clause, or "if," part of a conditional statement which is followed by the second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.
Thus, option B is correct which is, if the side's measure is 30 centimeters, then the side of a square measures 3 decimeters.
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What numbers are a distance of 1/2 unit from 3/5 on a number line?
Select the locations on the number line to plot the points.
info(i rather you draw on the image where the dot goes, if you can)-
picture-------------------------------------------------------
Answers
Step-by-step explanation:
hey try out the questions urself some tips would be to make the 1/2 and 3/5 have the same denominator as those shown in the diagram denominator means the number below
so1/2 x5 would give u 5/10 and 3/5 would give you 6/10
The tree in Naomi's backyard lost 120 leaves in 12 days.
Which expression below models the change in the number of
eaves per day?
a. 120 ÷ 12
D. -120 ÷ 12
c. 120
-12
d. -120
-12
Answers
The tree in Naomi's backyard lost 120 leaves in 12 days. Therefore, the required expression is A. 120÷12
Hope this helps :)
Write 2 decimals that are equivalent to the decimal 9.50?
Please help
Answers
Answer: 9.5 and 9.500
Answer:
One would be 9/5 and another could be 1.8
. f(x) = 2x-5; Find f(-8)
Answers
Answer:
D.
Theres no need for a explanation :)
determine the gradient of the line through (-1;2)and (0;-4)
Answers
Step-by-step explanation:
gradient = slope. or similar names.
it expresses the "steepness" of the line. how strongly is it going up or down or ... at all ?
it is represented by the ratio
(y coordinate difference / x coordinate difference)
when going from one point on the line to another.
for these 2 points we see (when going from the first to the second)
x changes by +1 (from -1 to 0).
y changes by -6 (from 2 to -4).
so the slope or gradient is
-6/+1 = -6
The midpoint of \overline{\text{AB}} AB is M(-5, 0)M(−5,0). If the coordinates of AA are (-3, 3)(−3,3), what are the coordinates of BB?
Answers
The coordinate of B is (13, -3).
What is Midpoint of line?
Measure of Distance between the two points and then divide by two is known as midpoint of line.
Given that;
The midpoint of the line AB is M (-5, 0).
The coordinate of A is (-3, 3).
Now, Let the coordinate of the point B is (x, y )
Then, By definition of midpoint of two point,
(-3 + x / 2 , 3 + y / 2 ) = (-5, 0)
By compare we get;
-3+ x / 2 = -5
- 3 + x = 2 * 5
- 3 + x = 10
x = 10 + 3
x = 13
And, 3 + y / 2 = 0
3 + y = 0
y = -3
Hence, The coordinate of B (x, y) = (13, -3).
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Answer: (−7,−3)
Step-by-step explanation: I had the question
Help please
An airline charges an extra fee for a checked bag that weighs more than 50 pounds.
Your bag weighs 44.9 pounds.
You have a 2.5 pound hair dryer, a 1.3 pound souvenir, and a 3.6 pound pair of boots.
Which items can you add to the bag without paying the extra fee?
Answers
you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb
Which items can you add to the bag without paying the extra fee?
The maximum weight that your bag can have is 50 pounds.
The actual weight of your bag is 44.9 pounds, so if we define x as the weight you can add, then we can write the inequality:
44.9 lb + x ≤ 50lb
Solving the inequality for x, we get:
x ≤ 50lb - 44.9 lb
x ≤ 5.1 lb
Now, the weight of the items are:
hair dryer = 2.5 lb
souvenir = 1.3 lb
boots = 3.6 lb
So you can choose any of the 3 items, or any combination of two of the items unless the hair dryer and the boots, because the combined weight is 3.6lb + 2.5lb = 6.1 lb
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What are the minimum and maximum temperatures recorded in this table?
Temperature (°C) 11 0 24.2 -32.4 -0.6 0.5
Answers
The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.
What is comparison of values?The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.
Now, given values :11.0, 24.2, -32.4, -0.6, 0.5
Arranging them in ascending order: -32.4, -0.6, 0.5, 11.0, 24.2Thus, The minimum temperature recorded is -32.4°C and the maximum temperature is 24.2°C, as seen by basic comparison of values.
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1. There are 2 floors in the initial building.
The workers can build 3 floors each week.
When will the building have 15 more floors
than the INITIAL building?
week #
2
5
0 1
8
2
?
Answers
The number of weeks it would take the workers to build 15 more floors is 5 weeks.
How many weeks would it take to build 15 more floors?
The number of weeks it would take to build 15 more floors can be determined by dividing the number of additional floors by the number of floors the workers can build in one week.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient.
Number of weeks = additional floors ÷ number of floors that can be built in a week
15 ÷ 3 = 5 weeks
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2x + 6y = -3
12y = 4x + 20
Answers
Answer: x=-3.25
y=7/12
Step-by-step explanation:
2x + 6y = -3
12y = 4x + 20
6y = -3-2x
6y=20-(-3)+4x-(-2x)
6y=20+3+4x+2x
6y=23+6x
23+6x=-3-2x
23=-3-8x
-8x=26
x=-13/4
x=-3.25
12y = 4(-3.25) + 20
12y=-13+20
12y=7
y=7/12
To the citizens of the country of Merka, there is no meal
better than a hot dog nestled securely in a hot dog bun. Relish is optional, mustard is not. The hypothetical market for hot dogs in Merka is graphed. Suppose that the price of hot dog buns decreases. Illustrate the impact of this change on the
market by manipulating the appropriate curve or curves.
The equilibrium price it hot dogs:
a) decreases
b) increases
c) remains the same
The equilibrium quantity of hot dogs:
a) increases
b) decreases
c) remains the same
The supply curve shifts:
a) left
b) right
The demand curve shifts:
a) left
b) right
Answers
Based on the price of hot dog buns decreasing, the impact on the market would be the equilibrium price of hot dogs decreases.
The equilibrium quantity of hot dogs decreases.
The supply curve shifts left. The demand curve shifts right.
What happens to the supply curve when prices drop?When the price of a good like the hot dog duns decreases, supplier will have less incentive to keep making it and so will reduce the quantity supplied to the market. This would mean that the supply curve would shift left.
The demand curve on the other hand would shift right because more people would demand the cheaper hotdogs. The equilibrium price which had fallen would then have to rise.
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help like rn, like rn rn rn rn , thanks
Answers
Answer: 13π/6 √45
Step-by-step explanation:
[tex]\displaystyle\\\sqrt{11} +3\approx6.32\\\\\pi +3,8\approx6.94\\\\Hence,\\\\6.32 < x,6.94\\\\\frac{61}{10}=6.1 \notin\\\\\frac{13\pi }{6}\approx6.81\in\\\\\sqrt{45}\approx6.71\in \\\\6\frac{1}{9}\approx6.11\notin\\\\\sqrt{83}-3\approx6.11\notin[/tex]
4. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
Answers
The additional information required to prove the SSS Triangle Congruence Postulate is TR = JL
How to state the additional information required?The congruence postulate is given as:
SSS Triangle Congruence Postulate
The above means that the three sides of the triangles are congruent.
From the figure, the following side lengths are said to be congruent
ST and KL
SR and KJ
For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent
This is represented as:
TR = JL
Hence, the additional information required to prove the SSS Triangle Congruence Postulate is TR = JL
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Give an angle which has the same sine as 300
Answers
I might me wrong, but i believe that its -36.
Have a nice day <3
which operation should be used to solve x-5=12
Answers
First you add 5 to both sides (inverse operation)
X-5=12
+5 +5
The 5 cancels out and 12+5 =17
X=17
The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
x - 5 = 12
Now,
Adding 5 on both sides,
x = 17
Thus, The required solution of the given expression is x = 17, this is been evaluated by the association of alike terms.
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The point P(–5,–5) is translated 1 unit left and 1 unit up. What are the coordinates of the resulting point, P'?
Answers
WILL CHOOSE THE BRAINLIEST ANSWER!!!
Answers
The difference between the area of the square and the area of the circle is C. 9x²(4 - π).
How to calculate the area?The area of the square will be:
= Side ×Side
= 6x × 6x
= 36x²
The area of the circle will be:
= πr²
= 3.14 × (3x)²
= π × 9x²
= 9πx²
The difference will be:
= 36x² - 9πx²
= 9x²(4 - π)
Therefore, the correct option is C.
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Tell whether the figure has line symmetry. If so how many lines of symmetry are there?
Answers
) consider the following sets s with binary operation ∗. which pairs (s,∗) form a group? if (s,∗) is not a group, which axioms fail? (a) let s be the set of integers z and let a ∗ b
Answers
The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.
The following subsets of Z (with ordinary addition and multiplication) satisfy all but one of the
axioms for a ring. In each case, which axiom fails?
(a) The set S of odd integers.
• The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.
Hence, Axiom 1 is violated.
(b) The set of nonnegative integers.
• If a is a positive integer, then there is no solution of a + x = 0 that is also positive. Hence, Axiom
5 is violated.
In general, to show that a subset S of a ring R, is a subring of R, it is sufficient to show that
(i) S is closed under addition in R
(ii) S is closed under multiplication in R;
(iii) 0R ∈ S;
(iv) when a ∈ S, the equation a + x = 0R has a solution in S.
Let a, b, c ∈ S ⊂ Z with a = rk, b = sk, c = tk.
(i) a + b = rk + sk = (r + s)k ∈ S
(ii) ab = (rk)(sk) = (rsk)k ∈ S
(iii) 0Z = 0 = 0 · k ∈ S
(iv) a = rs ∈ S ⇒ x = −rs ∈ S is a solution ofa + x = 0S
Thus, S is a subring of Z.
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Find the volume of this object.
Use 3 for π.
Volume of a Cylinder
V= πr²h
6 in
10 in
8 in
12 in V≈ [?]in³
Answers
The volume of the object which is made up of two different cylinders will be 383 cubic inches.
What is the volume of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be given as,
V = π r²h cubic units
The object is made up of two cylinders. Then the volume of the object will be
V = π x (3)² x 8 + π x (5)² x 2
V = π(72 + 50)
V = 3.14 x 122
V = 383.08 ≈ 383 cubic inches
The volume of the object which is made up of two different cylinders will be 383 cubic inches.
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I am offering 50 points to answer this and i will do it again and again
Answers
Answer: Between 2 and 7
Answer:
2 to 5
Step-by-step explanation:
i don't know because of i don't this transmission may not have the completed Questionnaire
help pls i hslsjdnkxkdjdjdj
Answers
Answer:
(a)20π
(b)74π
Step-by-step explanation:
(a) 2π(5) + (2π(10) × 1/2) = 2π(5) + 2π(5)
= 2π(10)
= 20π
(b) π(5)^2 + (π(10)^2 × 1/2) = 25π + 50π
=75π
Answer: P=20 cm S=75 cm²
Step-by-step explanation:
We have 2 semicircles with diameter d=10 cm and 1 semicircle with diameter D=20 cm
[tex]\displaystyle\\The\ length \ of \ the\ circle\ is\ \pi D\\The\ length\ of \ the\ semicircle \ is\ \frac{\pi D}{2}[/tex]
[tex]\displaystyle\\a)\\P=2*\frac{\pi d }{2} +\frac{\pi D}{2} \\\\P=\pi d+\frac{\pi D}{2} \\\\P=\pi *(d+\frac{D}{2} )\\P=\pi *(10+\frac{20}{3} )\\\\P=\pi *(10+10)\\\\P=20\pi \ cm\\\\[/tex]
[tex]b)\\\displaystyle\\The\ area \ of \ the\ circle\ is\ \frac{\pi D^2}{4} \\The\ area\ of \ the\ semicircle \ is\ \frac{\pi D^2}{8}\\\\S=2*\frac{\pi d^2}{8} +\frac{\pi D^2}{8} \\\\S=\frac{2*\pi *10^2}8} +\frac{\pi *20^2}{8} \\\\S=\frac{2*\pi*100 }{8} +\frac{\pi *400}{8} \\\\S=\frac{200\pi }{8}+\frac{400\pi }{8} \\\\S=\frac{600\pi }{8} \\\\S=75\pi \ cm^2[/tex]
2x+3y-4;where x=1 and y=-1 answer
Answers
Answer:
-5
Step-by-step explanation:
2x+3y-4
Evaluate for x=1,y=−1
(2)(1)+(3)(−1)−4
(2)(1)+(3)(−1)−4
=−5