Answers
Answer:
The range is:
{-4, 1, 2, 5, 8}
Step-by-step explanation:
Given the function
[tex]f(x)=3x+2[/tex]
We know that the domain of a function is the set of input or argument values for which the function is real and defined.As the domain interval -2 ≤ x ≤ 2
i.e. the values in the domain = {-2, -1, 0, 1, 2}
We also know that the range of a function is the set of values of the dependent variable for which a function is defined.As the domain interval -2 ≤ x ≤ 2
Putting all the x-values in the domain interval in the function
so
putting x=-2 in the function
[tex]f(x)=3x+2[/tex]
[tex]f(-2)=3(-2)+2=-6+2=-4[/tex]
putting x=-1 in the function
[tex]f(x)=3x+2[/tex]
[tex]f(-1)=3(-1)+2=-3+2=1[/tex]
putting x=0 in the function
[tex]f(x)=3x+2[/tex]
[tex]f(0)=3(0)+2=0+2=2[/tex]
putting x=1 in the function
[tex]f(x)=3x+2[/tex]
[tex]f(1)=3(1)+2=3+2=5[/tex]
putting x=2 in the function
[tex]f(x)=3x+2[/tex]
[tex]f(2)=3(2)+2=6+2=8[/tex]
Thus, when we put the domain values, the corresponding range values are:
x y
-2 -4
-1 1
0 2
1 5
2 8
Therefore, the range is:
{-4, 1, 2, 5, 8}
Related Questions
HELP PLEASE ITS MY LAST QUESTION!!
Jonathan and his band want to record and sell CDs. The recording studio charges an initial set-up fee of $250, and it charges $6.00 to burn each CD.
a) Define the variables:
Let n = _______
Let C = _______
Answers
Answer:
N=CD C=2-3 sentance
Step-by-step explanation:
If 3 pens cost $2, then how many can can you buy with $20
Answers
Answer:
30
Step-by-step explanation:
Ian's monthly allowance is $21. In January he starts saving for a birthday gift in June. Each month he saves of his allowance. The gift he wants to buy costs $110. Will Ian have enough money? Explain.
Answers
Answer:
Ian will have enough money to buy the giftStep-by-step explanation:
Step one:
given
monthly allowance= $21
from January to June= 6 months
total savings = 21*6= $126
cost of gift = $110
Step two:
Ian will have enough money to buy the gift
since he saved $126 which is greater than the cost of the gift of $110
he would have a balance of $16
Clue #1: The sum of the digits of a 3 digit number is 20. Clue #2: The tens digit is 2 less than the hundreds digit. Clue #3: The units digit is 12 less than the sum of the other two digits What is the 3 digit number, show or explain how you solved the problem. Help me! Please show work
Answers
Answer: The number is 974
Step-by-step explanation:
First, any 3 digit number can be written as:
N = a*100 + b*10 + c
Where a, b, and c are single-digit numbers.
a is the hundreds digit
b is the tens digit
c is the unit digit
We can write the clues as:
#1: a + b + c = 20
#2: b = a - 2
#3: c = a + b - 12
Then we have a system of equations:
a + b + c = 20
b = a - 2
c = a + b - 12
To solve this, we need to isolate one of the variables in one equation and then replace this in the other equations, we can see that b is already isolated in the second equation, then we can replace that in the first and third equations:
a + (a - 2) + c = 20
c = a + (a - 2) - 12
Now we can see that c is isolated in the second equation, then we can replace that in the first one to get:
a + (a - 2) + (a + (a - 2) - 12) = 20
Now we can solve this for a:
a + a - 2 + a + a -2 - 12 = 20
4*a - 16 = 20
4*a = 20 + 16
4*a = 36
a = 36/4 = 9
With this, we can find the values of b and c.
b = a - 2 = 9 - 2 = 7
c = a + b - 12 = 9 + 7 - 12 = 4
Then the 3-digit number is:
N = a*100 + b*10 + c = 9*100 + 7*10 + 4 = 974
N = 974
I NEED HELP ASAP DUE IN 3 MINUTES WHOEVER ANSWERS IT RIGHT GETS BRIANIST
Answers
Answer:
It is D.
Step-by-step explanation:
given vectors u=(-2,3) and v=(-6,9) what is the measure of the angle between u and v?
a. 0
b. 86
c. 91
d. 180
Answers
Answer: 91
Step-by-step explanation:
Angle between the two vectors u and v is option (a) 0 degree
What is Vector?Vector, in mathematics, a quantity that has both magnitude and direction
Given,
u=(-2,3)
v=(-6,9)
Angle between the two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]
[tex]u.v=(-2)(-6)+(3)(9)\\u.v=12+27\\u.v=39[/tex]
[tex]|u|=\sqrt{-2^{2}+3^{2} } \\|u|=\sqrt{13}[/tex]
[tex]|v|=\sqrt{-6^{2}+9^{2} } \\|v|=\sqrt{117}[/tex]
Angle between two vectors θ =[tex]cos^{-1} \frac{u.v}{|u| |v|}[/tex]
θ=[tex]cos^{-1} \frac{39}{\sqrt{13}.\sqrt{117} } \\cos^{-1}\frac{39}{39}\\ cos^{-1}1=0[/tex]
Hence, the angle between the vectors u and v is 0 degree
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Find the cube root of the fraction 27/512.
A 3/8
B -3/8
C Cannot be done
Answers
Answer: can't be done
Step-by-step explanation:
Answer:
The principal, real, root of:
27−−√3
=3
All roots:
3
−1.5+2.59807621i
−1.5−2.59807621i
27 is a perfect cube
Examine the figure below.
B
(4x-16)
6756
(5x+7)
с
A
D
Determine which of the following angle measures are correct. Select all that apply.
OmZBAC = 72°
O
m2BCD = 68°
Om ACB = 112°
m2ABC = 68°
mzBCD=108°
Answers
*see attachment for diagram
Answer:
✔️m<BAC = 72°
✔️m<BCD = 108°
Step-by-step explanation:
Given:
m<ABC = (4x - 16)°
m<ACB = (5x + 7)°
Find the numerical value of m<ABC, m<ACB, m<BAC, and m<BCD.
First we need to determine the value of x.
The ∆ given is an isosceles triangle with two equal sides, therefore, the angles opposite the two equal sides would also be equal.
Therefore:
(4x - 16)° + 2(5x + 7)° = 180° (sum of ∆)
Solve for x
4x - 16 + 10x + 14 = 180
Add like terms
14x - 2 = 180
Add 2 to both sides
14x = 182
Divide both sides by 14
x = 13
Find the measure of each angle by plugging in the value of x where necessary:
✔️m<ABC = (4x - 16)° = 4(13) - 16
m<ABC = 36°
✔️m<ACB = (5x + 7)° = 5(13) + 7
m<ACB = 72°
✔️m<BAC = m<ACB (both are base angles of the isosceles ∆, so they are equal)
Therefore,
m<BAC = 72°
✔️m<BCD = m<ABC + m<ACB (exterior angle theorem of a triangle)
m<BCD = 36 + 72 (Substitution)
m<BCD = 108°
Therefore, the angle measures that are correct are:
✔️m<BAC = 72°
✔️m<BCD = 108°
Does the transformation represent a dilation? Why or
why not?
O no, because each vertex is not multiplied by the
same scale factor
O yes, because each vertex is multiplied by 4/3
O yes, because each vertex is multiplied by 2
Answers
Answer: A: no, because each vertex is not multiplied by the same scale factor.
Step-by-step explanation: got it right on Edge 2020!
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
O {-5 - 134,-5 + 34)
O {-5 -29, -5 + 29)
O {-12, 2)
O {-2, 12}
Plsss
Answers
The value of x from the quadratic equation is x = { 2 , -12 }
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 10x = 24 be equation (1)
Adding 5² on both sides of the equation , we get
x² + 10x + 25 = 24 + 25
( x + 5 )² = 49
Taking square roots on both sides , we get
x + 5 = ±7
Subtracting 5 on both sides , we get
x = 2
And , x = -12
Hence , the quadratic equation is solved and value of x is x = -12 or x = 2
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A clothing bought a shirt from a manufacturer for $85 and marked up the price by 10% . A month later the store reduced the shirts price by 10% . What was the shirts price after that reduction
Answers
Answer: The shirt's price after reduction = $ 84.15
Step-by-step explanation:
Given: Price of shirt= $ 85
Marked up percent = 10%
Reduced percent = 10%
Price after mark up = (Price of shirt) + 10% of (Price of shirt)
= $ (85+10% x 85)
= $ (85+(0.1) x (85))
= $ (85+8.5)
= $ 93.5
Price after 10% reduction = (Price after mark up)- 10% of (Price after mark up)
= $ (93.5-0.1 x 93.5)
= $ (93.5-9.35)
= $ 84.15
Hence, the shirt's price after reduction = $ 84.15
Which Equation represents a Non-Proportional relationship between X and Y?
A. y=x
B. y=7x
C. y= 2/3x -1
D. y=3x + 0
Answers
Answer: C
Step-by-step explanation:
proportional relationship will have an equation that goes through the origin (0,0)
The equation for C will not go through the origin because it has a y-intercept of -1 and the line will be going through (0,-1) instead of (0,0).
All the other equations will be going through the origin because they have no y intercepts.
5(x+3)-3x^2 when x is -1.4
Answers
Answer:
The answer would be C.) 2.12
The length of a rectangle is 3 meters longer than its width. If
the area of the rectangle is 40 square meters, what are the
dimensions?
Answers
Answer:
Length=8 Width=5
Step-by-step explanation:
Set this up as a system of equations with l standing for length and w standing for width.
w+3=l
l×w=40
Substitute rhe first equation into the 2nd one.
w(w+3)=40 --------> w^2+3w=40
Move all the terms to the left side
w^2+3w-40=0
Factor
(w+8) (w-5)
Set both factors equal to 0.
w+8=0 -----> w=-8
w-5=0 ------> w=5
Since distance cannot be negative we can eliminate -8. So w=5
Plug it back into any one of the equations and solve for l.
5+3=l -----> 8=l
So the answer is the length is 8 and the width is 5.
The dimensions of the rectangle are:
Length = 8 meters.
width = 5meters.
We are given that the length of a rectangle is 3 meters longer than its width and the area of a rectangle is 40 square meters.
We need to find the length and width of the rectangle.
What is a rectangle?A rectangle is a closed 2-dimensional shape that has two dimensions, the length, and the width. Length is the longer side and width is the shorter side of the rectangle.
The area of a rectangle is given by :
A = Length x Width.
Let the area, length, and width of the rectangle be A, L, and W.
The length of a rectangle is 3 meters longer than its width.
We can write it as,
L = 3 + W
The area of a rectangle is 40 square meters.
We can write it as,
A = 40 square meters
We can write it as,
L x W = 40
Substituting L = 3 + W.
(3 + W) W = 40
[tex]3W + W^2 = 40\\W^2 + 3W = 40 \\W^2 + 3W - 40 = 0[/tex]
This is a quadratic equation and we will apply middle-term factorization.
[tex]W^2 + 3W - 40=0\\W^2 + (8-5)W - 40=0\\W^2 + 8W - 5W - 40=0\\W(W + 8) - 5 ( W + 8)=0\\(W+8)(W - 5)=0\\W+8 = 0~~and~~W-5=0\\W = -8~~and~~W=5[/tex]
The distance can not be negative so W = -8 is eliminated.
We have, W = 5
Substituting W = 5 in L = 3 + W.
We get,
L = 3 + 5 = 8
L = 8.
The dimensions of the given rectangle are:
Length = L = 8 meters.
Width = W = 5 meters.
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What is the value of 3/8 x - 4.5 when x =0.4
Answers
plz help me answer step by step 2+7/x=-12
Answers
Answer:
x = -1/2
Step-by-step explanation:
First, subtract 2 from both sides to get 7/x alone. Then muliply both sides by x to get rid of 7/x's denominator. Divide both sides by -14 to get rid of x's coefficient and to get x alone. You will then get -1/2 as your answer.
2 + 7/x = -12
-2 -2
7/x = -14
*x *x
7 = -14x
÷-14 ÷-14
- 1/2 =x
x = -1/2
Please help! Me and my bestie are both stuck on this. . .
Use table to solve the inequality 2x<2
Answers
Answer:
x>1
Step-by-step explanation:
Answer:
-2, 0, 2, 4, 6 these are the answers for the boxes and they are in order. solution x<1
Step-by-step explanation:
if you look at the box you will see that it says x and 2x at the bottom. The x at the top is the same as the one at the bottom. So they want you to multiply the number in the row of x by the number below x I hope this helps
1/2x + 3/4 x = 5 - 2.5x
Answers
Answer: I don't know if you wanted it to be solved or re-written but the answer is x=4/3 and re-written is 3x=4
The points (-2, 4) and (1,r) lie on a line with slope 3. Find the missing coordinate r.
Answers
Answer:
-9
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
(r - 11)/(4 - (-1)) = (r - 11)/5
So, (r - 11)/5 = -4
r - 11 = -20
r = -9
I dont know wht
way you are doing this but hope it helps
x-y=11 2x+ y=19 solve using elimanation
Answers
Answer:
the answer is [tex]x=10,\:y=-1[/tex]
Step-by-step explanation:
Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.
hope this helps :)
what is the square root of 674 in simplest radical form
Answers
Answer: Here we answer "What is the square root of 674 (√674) in simplest radical form?"
The square root of 674 in its simplest form means to get the number 674 inside the radical √ as low as possible.
The square root of 674 is already in the simplest radical form. Therefore, the answer is:
√674
hope this helps.. Stay safe and have a great day/night!!! :D
The square root of 674 is expressed as √674 in the radical form.
What is square root?A square root of a number is a value that, when multiplied by itself, gives the number.
Given that, what is the square root of 674 in the simplest radical form,
The square root of 674 is expressed as √674 in the radical form,
The square root of 674 rounded up to 7 decimal places is 25.9615100. It is the positive solution of the equation x² = 674.
Hence, the square root of 674 is expressed as √674 in the radical form.
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HELP ME PLZ I NEED TO GET THIS RIGHT
Answers
Answer:QR = 54
Step-by-step explanation:
what is 149866.37636 rounded as a whole number
Answers
Answer:
149866
Step-by-step explanation:
Hope this helps.
Answer:
149866.
This is because the '.3' part means that you do not have to round the '6' up.
I’ll mark you brainlist I’ll mark you brainlist
Answers
Answer:
The rate of change is 0 because 0/1=0.
Step-by-step explanation:
hope this helps
What’s the answer plzzz hurry
Answers
Answer:
dude i can't even see that sorry
Step-by-step explanation:
I like your cut G
write 3.9 x 10 exponent -4 in standard form
Answers
Answer:
0.00039
Step-by-step explanation:
Which expression can be simplified to find the slope of the trend line in the scatter plot?
D is 8-2
78-87
Answers
(B) [tex]\frac{78-87}{8-2}[/tex]
The slope of the trend line:A linear relationship is depicted by a trend line. [tex]Y=mx+b[/tex], where [tex]x[/tex] is the independent variable, [tex]y[/tex] is the dependent variable, m is the slope of the line and [tex]b[/tex] is the y-intercept, is the equation for a linear relationship.Scatter plot -Data visualization that depicts the relationship between two numerical variables is known as a scatterplot. The values for the two variables are used to depict each member of the dataset as a point with [tex]x-y[/tex] coordinates that correspond to those values.Therefore, (B) [tex]\frac{78-87}{8-2}[/tex] can be simplified to find the slope of the trend line in the scatter plot.
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Plz help I’m getting timed
Answers
Answer:
38
Step-by-step explanation:
Answer:
38
Step-by-step explanation:
1-4 round down 5-10 round up
ASAP pls help me with this
Answers
Answer:
x = 20
Step-by-step explanation:
If A || B, then ∠2 should equal to ∠3 (Alternate angles).
3x - 10 = x + 30
Isolate like terms.
3x - x = 30 + 10
Evaluate like terms.
2x = 40
Find x.
x = 40 ÷ 2
x = 20
Answer:
x = 20.
Angles 2 and 3 are measured as 50 degrees.
Step-by-step explanation:
Angles 2 and 3 are congruent, meaning that they are equal.
Set the two equations equal to each other and solve for x.
3x-10=x+30 (subtract x from the left side and add 10 to the right. This gets the x's and the plain numbers on the same side of the equation)
2x=40 (Divide by 2)
x = 20
Check your work by plugging in 20 for x in each expression. If the two expressions are equal when you do so, then you know you've worked out the problem correctly.
Angle 2:
3(20)-10
60 - 10 = 50
Angle 3:
20 + 30 = 50
Both expressions equal 50 when plugging in 20 for x, so this is the correct answer.
Evaluate 5x - 8.35y when x=12 and y=4
Answers
Answer:
26.6
Step-by-step explanation:
(12*5)-(8.35*4)
60-33.4
26.6