Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function. y=-2(x) and y=-2(x)-3
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The graph of the function y = -2 - 3 is shifted down 3 units from the graph of the function y = -2x.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The equations of the functions are:
y -2x
y = -2x - 3
The graph of the function y = -2x will be a straight line that is passing through origin (0, 0).
Applying transformation to the graph of the function y = -2x
y = -2x - 3
As we can see in the graph:
The graph y=-2x - 3 is shifted down 3 units from y = -2x
Thus, the graph of the function y = -2 - 3 is shifted down 3 units from the graph of the function y = -2x.
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Related Questions
Bill, bob, and barry are hired to paint signs. in 8 hours bill can paint 1 sign, bob can paint 2 signs, and barry can paint 1 and 1 / 3 signs. they all come to work the first day, but barry doesn't like the job and quits after 3 hours. bob works half an hour longer than barry and quits. how long will it take bill to finish 2 signs they were supposed to paint?
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Bill: x = 1/8 signs/h
Bob: y = (2 signs)/(8 h) = 1/4 signs/h
Barry: z = (4/3 signs)/(8 h) = 1/6 signs/h
The job is to paint 2 signs, working together.
In the first 3 hours, the amount painted is
(x+y+z signs/h)*(3 h) = (1/8 + 1/4 + 1/6)*3 = 13/8 signs
Remaining: 2 - 13/8 = 3/8 signs
Barry quits.
In the next 1/2 hour (30 minutes), the amount painted is
(x + y signs/h)*(0.5 h) = (1/8 + 1/4)*0.5 = 3/16 signs
Remaining: 3/8 - 3/16 = 3/16 signs
Now Bob quits.
The time for Bill to finish the job is
(3/16 signs)/(1/8 signs/h) = 3/2 h
Answer: Bill finishes the job in 1.5 hours (or 1 hour, 30 minutes)
It will indeed take Bill 1.5 hours to finish the remaining [tex]\( \frac{3}{16} \)[/tex] signs.
Work done by Bill, Bob, and Barry collectively take the working efficiency in a defined time interval.
Barry's work in 3 hours:
[tex]\(3 \times \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \text{ sign}\)[/tex]
Bob's work in 3.5 hours:
[tex]\(3.5 \times \frac{1}{4} = \frac{7}{8} \text{ sign}\)[/tex]
Bill's work for the same time until Bob leaves (3.5 hours):
[tex]\(3.5 \times \frac{1}{8} = \frac{3.5}{8} = \frac{7}{16} \text{ sign}\)[/tex]
Total work done by all three in the first 3.5 hours:
[tex]\[ = \frac{1}{2} + \frac{7}{8} + \frac{7}{16}\\= \frac{8}{16} + \frac{14}{16} + \frac{7}{16} \\= \frac{29}{16} \text{ signs} \][/tex]
Remaining work to be done:
[tex]\[ = 2 - \frac{29}{16} \\= \frac{32}{16} - \frac{29}{16} = \frac{3}{16} \text{ signs} \][/tex]
Time for Bill to complete remaining work:
Bill’s rate: [tex]\( \frac{1}{8} \text{ signs per hour}\)[/tex]
Time to paint [tex]\( \frac{3}{16} \text{ signs}\):[/tex]
[tex]\[ =\frac{\frac{3}{16}}{\frac{1}{8}} \\= \frac{3}{16} \times 8 = \frac{24}{16} = 1.5 \text{ hours} \][/tex]
Thus, It will indeed take Bill 1.5 hours to finish the remaining [tex]\( \frac{3}{16} \)[/tex] signs. This confirms that the correct answer is 1.5 hours.
Translate each word phrase into an algebraic expression.
The perimeter of a rectangle 24 units long and w units wide.
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WHAT THE VALUE OF 12.5X10 7
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Given: quadrilateral ABCD inscribed in a circle Prove: ∠A and ∠C are supplementary, ∠B and ∠D are supplementary Let the measure of = a°. Because and form a circle, and a circle measures 360°, the measure of is 360 – a°. Because of the ________ theorem, m∠A = degrees and m∠C = degrees. The sum of the measures of angles A and C is degrees, which is equal to , or 180°. Therefore, angles A and C are supplementary because their measures add up to 180°. Angles B and D are supplementary because the sum of the measures of the angles in a quadrilateral is 360°. m∠A + m∠C + m∠B + m∠D = 360°, and using substitution, 180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°. What is the missing information in the paragraph proof?
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Quadrilateral ABCD is inscribed in a circle. Let the measure of arc BAD be a°. Arcs BCD and BAD form a circle and a circle measures 360°, then measure of arc BCD is 360°-a°.
The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle.
Because of the Inscribed angle theorem,
[tex]m\angle A=\dfrac{a^{\circ}}{2};[/tex]
[tex]m\angle C=\dfrac{360^{\circ}-a^{\circ}}{2}.[/tex]
The sum of the measures of angles A and C is
[tex]\dfrac{a^{\circ}}{2}+\dfrac{360^{\circ}-a^{\circ}}{2}=180^{\circ}.[/tex]
Therefore, angles A and C are supplementary, because their measures add up to 180°.
Angles B and D are supplementary, because the sum of the measures of the angles in a quadrilateral is 360°.
m∠A + m∠C + m∠B + m∠D = 360°,
and using substitution,
180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.
Answer: inscribed angle theorem
Answer:A
Step-by-step explanation:
Inscribed angle
List the sides of each triangle from shortest to greatest
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Also, the smallest side, is opposite the smallest angle.
a.[tex]70^o\ \textgreater \ 60^o\ \textgreater \ 50^o[/tex] so [tex]|RQ|\ \textgreater \ |PR|\ \textgreater \ |PQ|[/tex],
because RQ is opposite angle P, the largest,
PR is opposite angle Q , the middle
and PQ is opposite angle R, the smallest.
Greatest side: RQ
b. The sum of the measures of the interior angles of any triangle is 180°,
so
[tex]m(A)+m(B)+m(C)=180^o\\\\50^o+45^o+x=180^o\\\\x=180^o-50^o-45^o=85^o[/tex]
thus, m(C) is the largest angle. This means the largest side is the side AB.
Answers:
a) RQ
b)AB
Number 1. Write an explicit formula for the nth term. Correct answer will get brainliest
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Identify the slope of the line shown in the graph below: Graph of a vertical line with an x intercept of negative 1 slope = -1 slope = 0 slope = undefined slope = 1
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Slope is Undefined because it's just a vertical line and it's not angled...
simplify (8x3-5x-1)-(7x2+6x-10)
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(19x-1)-(8x-10)
19x1-8x+10
11x+9
how do I do this problem ??
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It takes nim 2 2/3 hours to weave a basket. He worked Monday through Friday , 8 hours a day. How many baskets can he make?
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40 / (2 2/3) =
40 / (8/3) =
40 * 3/8 =
120/8 =
15 <=== he made 15 baskets
Answer:
15 baskets
Step-by-step explanation:
In order to solve this question, first we need to know the amount of hours that Nim was able to work.
If Nim worked Monday through Friday, 8 hours a day, then:
Monday to Friday = 5 days
1 day = 8 hours
5 days * 8 hours = 40 hours
Out of these forty hours, Nim needs 2 2/3 hours to weave a basket. Therefore:
40 / (2 2/3) =
40 / (8 /3) =
40 * 3/8 =
120/8 = 15
A package of 10 cans of soup costs $14. An individual can costs $2. You need at least 25 cans.You decide to buy 3 packages of 10 cans. How much do you pay for each can?
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What is 1/4 (5y-3)+1/16 (12y+17
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What is the question? If you are only trying to expand the expression then the answer would be:
1/4 (5y-3)+ 1/16 (12y+17)
(5y/4) – (3/4) + (12y/16) + (17/16)
1.25y – 0.75 + 0.75y + 1.0625
2y + 0.3125
If you are trying to find for y, then you forgot to equate it to 0, that is:
2y + 0.3125 = 0
2y = -0.3125
y = 0.15625
PLEASE HEP ME ANSWER THIS REALLY HARD QUESTION
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When the a value is positive, the parabola has a minimum and opens up. However, when the a value is negative, the parabola is upside down in comparison. It open downward and has a maximum point instead.
Final answer: A
Solve x2 = 144
Select one:
a. 72
b. 12
c. ±12
d. −12
So I chose B which I thought was correct but it was wrong
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Power is the result of multiplying two numbers together. The solution of the x²=144 is ±12. The correct option is C.
What is power?Power is the result of multiplying two numbers together such that both numbers are equal to each other. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.
The solution of the given expression can be written as,
x² = 144
x² = 12×12 or -12×-12
x = √(12×12) or √(-12×-12)
x = 12 or -12
x = ±12
Thus, the solution of the x²=144 is ±12. This is because the multiplication of two positive numbers is positive, also, the sum of the two negative numbers is positive.
Hence, the solution of the x²=144 is ±12
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Juanita is 13 years older than her cousin. The sum of their ages is no less than 103 years.
What is the youngest age Juanita's cousin can be?
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x + y >= 103
substituting for x:-
y + 13 + y >=103
2y >= 90
y >= 45
Answer is 45.
Answer:
45
Step-by-step explanation:
I can confirm, the first guy is right (I did the test)
convert the 5th root of x^3 into a rational expression and explain the steps
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fifth root of n is;
n^(1/5)
And when there is x^3, the fifth root is multiply 1/5 with 3
x^3(1/5)
= x^(3/5)
So, this is the rational expression to write x^3.
explain how you can tell the frequency of a data value by looking at the dot plot
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What is the answer and steps?
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Jackie is wrapping a birthday present. The gift box is in the shape of a rectangular prism. It has a length of 8 inches, a width of 10 inches, and a height of 3 inches. What is the minimum amount of wrapping paper she will need to completely cover the box?
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The surface area of the box with dimensions AxBxC linear units is 2*(AB + AC + BC) square units.
If the condition means conventional/regular rectangular piece of paper, then it is, probably,
the rectangle of 8+3+3 = 14 inches wide and 3+10+3+10 = 26 inches long.
Answer:
D
Step-by-step explanation:
How to solve quadratic inequalities algebraically?
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Solve ( x – 3)( x + 2) > 0.
Solve ( x – 3)( x + 2) = 0. By the zero product property,
Make the boundary points. Here, the boundary points are open circles because the original inequality does not include equality (see Figure 1).
Select points from the different regions created (see Figure 2).
See whether the test points satisfy the original inequality.
Since x = –3 satisfies the original inequality, the region x < –2 is part of the solution. Since x = 0 does not satisfy the original inequality, the region –2 < x < 3 is not part of the solution. Since x = 4 satisfies the original inequality, the region x > 3 is part of the solution.
Represent the solution in graphic form and in solution set form. The graphic form is shown in Figure 3.
The solution set form is { x| x < –2 or x > 3}.
Figure 1. Boundary points.Figure 2. Three regions are created.Figure 3. Solution to ExampleR is the midpoint of QS, if QR=2x and RS=x+3, what is RS?
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suppose this is your line,
R is the mid point
and it's given that
QR = 2x
and
RS = x+3
as R is the mid point of QS
so,
QR = RS
then,
2x = x + 3
2x - x =3
x = 3
as,
it's given that RS = x + 3
then,
RS = 3 + 3
= 6 units.
R is the midpoint of QS, if QR=2x and RS=x+3, then, the value of RS is:
RS is 6 units.
Here, we have that, R is the midpoint of QS, if QR=2x and RS=x+3.
Since R is the midpoint of QS, we know that QR is equal to RS.
Given that,
QR = 2x, and RS = x + 3,
we can set them equal to each other:
2x = x + 3
Now, let's solve for x:
2x - x = 3
x = 3
Now that we have the value of x, we can find RS:
RS = x + 3
RS = 3 + 3
RS = 6
So, RS is 6 units.
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Pls help me out here hope the points are good (no scams pls)
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6/3 =2
15/3 =5
6/15 = 2/5
8/4 =2
20/4 =5
8/20 = 2/5
answer is B 2/5
6/15 = 2/5 (divide by 3)
and
8/20 = 2/5 (divide by 4)
What multiplication do you use to multiply 10 to the power of 4?
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[tex]10^4=10*10*10*10[/tex]
Franklin waters' annual gross pay is $55,400. He takes a married exemption of $4,000. His state income tax rate is 3.5 percent. How much will he pay annually in state tax?
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41,000/ 3.5%= 1799
so he will pay 1,799$
F(x) =8+2x and g(x) =1/2x the value of f/g(5)
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(f/g)(5) = (f(5))/(g(5)) = (-8+2(5))/((1/2))(5) = 2/(5/2)
(f/g)(5) = 4/5
A toy factory creates handmade train sets. One train car takes 0.4 hours to construct and 0.6 hours to paint. A section of wooden track requires 0.2 hours to construct and 0.1 hours to paint. A full train set with x train cars and y sections of wooden track takes 5.2 hours to construct and 4.2 hours to paint. Which system of equations can be used to find the number of train cars and number of sections of wooden track in a full train set?
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0.4x + 0.2y = 5.2.....this one deals with the constructing
0.6x + 0.1y = 4.2 ....this one deals with the painting
To find the number of train cars and sections of wooden track in a full train set, we can set up a system of equations. The equations are 0.4x + 0.2y = 5.2 and 0.6x + 0.1y = 4.2.
Explanation:To find the number of train cars and number of sections of wooden track in a full train set, we can set up a system of equations based on the given information.
Let's use x to represent the number of train cars and y to represent the number of sections of wooden track.
The time to construct 1 train car is 0.4 hours, so the time to construct x train cars is 0.4x hours.The time to paint 1 train car is 0.6 hours, so the time to paint x train cars is 0.6x hours.The time to construct 1 section of wooden track is 0.2 hours, so the time to construct y sections of wooden track is 0.2y hours.The time to paint 1 section of wooden track is 0.1 hours, so the time to paint y sections of wooden track is 0.1y hours.The total time to construct a full train set is 5.2 hours, so we have the equation 0.4x + 0.2y = 5.2.The total time to paint a full train set is 4.2 hours, so we have the equation 0.6x + 0.1y = 4.2.The system of equations that can be used to find the number of train cars and number of sections of wooden track in a full train set is:
0.4x + 0.2y = 5.2
0.6x + 0.1y = 4.2
what's 4/5 + 6/5 equals
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what are the new coordinates for (1,4) when rotated 180 degrees and 90 degrees counterclockwise, and 90 degrees clockwise?
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Hope I helped :)
How do you make $2.161616 as a fraction and a mixed number
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Which names are correct for PM−→− ?
Select each correct answer.
PY−→−
MP−→−
TM−→−
PT−→−
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Therefore, another name for PM is angle MP.
The answers are PT−→− and PY−→−