The graph of f (x) = x + 5 is a vertical translation 5 units
up of the graph of f(x) = x. How can you obtain the graph of
f(x) = x + 5 from the graph of f (x) = x using a horizontal
translation?
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
[tex]\displaystyle f(x)=x[/tex]
To shift vertically n units, we can simply add n to our function. Hence:
[tex]f(x)=x+n[/tex]
So, a vertical shift of 5 units up implies that n=5. So:
[tex]f(x)=x+5[/tex]
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
[tex]f(x-n)=(x-n)[/tex]
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
[tex]f(x-1)=(x-1)[/tex]
Or:
[tex]f(x)=x-1[/tex]
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
I WILL GIVE BRAINLEST!!!!!!
Frank earned x dollars the first week of his new job. He earned 5% more the
second week than the first week. Which expression represents the total amount of
money Frank earned for both weeks?
A. 1.50x
B. 1.05x
C. 2.00x
D. 2.05x
PLSSS SHOW YOUR WORK PLSSSS
Why do scientists use models?
A)
Models are unreliable.
B)
Models waste natural resources.
Models predict not just describe events.
Models are based on scientific laws and principals so they are more
reliable than the real thing.
D)
Solve (x+1)2 = –5.
Question 16 options:
A)
No real solution
B)
x = ±1.75
C)
x = ±5
D)
x = ±1
Answer:
A) no real solutions
Step-by-step explanation:
No real solution. in order to x+1 by itself you must square root both sides. that would mean square rooting -5 which creates an imaginary number. so there are no real solutions. Also cause even if x was a negative, when you'd square it, you'll always get a positive.
Kevin gathered data from his classmates about the number of books they consulted and the total time they spent on a research paper. The scatter plot shows the data he gathered and the line of best fit.
The equation of the line of best fit is y = 70.28x + 425.77.
Based on the line of best fit, approximately how many minutes would a student who consults 3 books spend on a research paper?
211
372
496
637
The student who consults 3 books spends 637 minutes on a research paper based on the line of best fit if the equation of the line of best fit is y = 70.28x + 425.77 option (D) is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have:
Kevin gathered data from his classmates about the number of books they consulted and the total time they spent on a research paper.
The line of best fit is:
y = 70.28x + 425.77
Plug x = 3 in the line of best fit:
y = 70.28(3) + 425.77
y = 21.084 + 425.77
y = 636.61 minutes ≈ 637 minutes
Thus, the student who consults 3 books spends 637 minutes on a research paper based on the line of best fit if the equation of the line of best fit is y = 70.28x + 425.77 option (D) is correct.
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ5
Mark scored 3
more than twice what Nia scored. Nia scored 2
less than 4 times what Lupe scored. If Lupe
scored 2 points, what did Mark score?
Answer:
15
Step-by-step explanation:
2 times 4 is 8 minus 2 equals 6- Nia's Score
2 times 6 is 12 plus 3 equals 15- Mark's Score
xoxo,your highness...Answer:
15
Step-by-step explanation:
2 X 6 is 12 + 3 = 15 (Mark's Score)
Use the diagram below to answer the question. There is a small building that is 24 feet tallThe fire fighter is standing 7 feet away from the building.
Answer:
24- 7 = 17
Step-by-step explanation:
can somebody please help me
Answer:
[tex]C.650,000\ pounds[/tex]
Step-by-step explanation:
[tex]We\ are\ given,\\No.\ of\ superheroes\ =3\ superheroes\\Weight\ in\ Tons\ 3\ superheroes\ can\ lift\ together=975\ tons.\\Hence,\\As\ we\ know\ that,\\1\ ton=2000\ pounds\\Hence,\\Weight\ in\ Pounds\ 3\ superheroes\ can\ lift\ together=975*2000\ pounds\\Hence,\\Weight\ in\ Pounds\ 3\ superheroes\ can\ lift\ together=1,950,000\ pounds\\Hence,\\Weight\ in\ Pounds\ 1\ superhero\ can\ lift=\frac{Weight\ in\ Pounds\ 3\ superheroes\ can\ lift}{No.\ of\ superheroes}\\[/tex]
[tex]Hence\ by\ substituting\ values,\\Weight\ in\ Pounds\ 1\ superhero\ can\ lift=\frac{1,950,000}{3}= 650,000\ pounds[/tex]
Is this true or false? The following graph represents a proportional relationship
A. True
B. False
Answer:
True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Right answer will get brainlist
Answer:
x = -3
Step-by-step explanation:
System of equations has been given as,
y = 2x + 8
y = [tex]-\frac{2}{3}x[/tex]
Since, solution of the system of equations is the point of intersection on the graph.
Therefore, point of intersection or solution of the system will be,
(x, y) = (-3, 2)
This common point will satisfy both the equations.
And x = -3 will also both the equations.
Can someone help please? i’ll give you brainliest, sorry if it’s hard to see
1/4 and 4
Step-by-step explanation:
small to large: 2/8 =1/4
large to small: 8/2 =4
Answer: 2x4=8 , 16x8=128
128x8=1024
Step-by-step explanation: hope I help with your problems and sorry if it wrong
Explain what you would do first to simplify the
expression below. Justify why, and then state the
result of performing this step.
312
1212
2
4+²
Answer:
how do you do this
Step-by-step explanation:
Number the answer like, in the blank type in the answer. Pls help ignore my answers unless correct
1. ____
2____
3______
Answer:
1. 32 2. You got that one correct 3. 1 5/34
Step-by-step explanation:
1. 24 / 3/4
3/4 = .75
24/ .75 = 32
3. Turn into improper fraction
13/4 / 17/6
= 1 5/34
Hope this helps dude
Answer please, be sure your right or don’t answer at all.
Answer:
y > 1/3x -3
Step-by-step explanation:
Just find the equation of the line, which is y = 1/3x -3, and then determine what the symbol is going to be. Since the line is dotted, it will either be < or >. When the shaded area is on top of the line, it's >. Remember that by saying left on the bottom or right on top.
please help me i give 5* along with thanks for quality answer
Answer:
The total number of faces in a pyramid= 1+n
Use your knowledge of similar triangles to solve for x
9514 1404 393
Answer:
x = 10 2/3
Step-by-step explanation:
The ratios of corresponding sides are the same, so we have ...
x/8 = 8/6
x = 8·(8/6) = 64/6
x = 10 2/3
what is the slope..
Answer:
the slope is 2
Step-by-step explanation:
the x's are increasing by 4 each time and the y's are increasing by 2 each time giving you [tex]\frac{4}{2\\}[/tex] which simplifys to 2
Help please!!!!!! HELP
Answer:
number 1
Step-by-step explanation:
what is 0.000 002 in standard form
Answer:
[tex] 0.000 002 = 2 \times {10}^{ - 6} [/tex]
Step-by-step explanation:
It is already in standard form and can be expressed in scientific form as:
[tex]0.000 002 = 2 \times {10}^{ - 6} [/tex]
Answer:
0.000 002 in standard form is NaN x 100^0
Step-by-step explanation:
What is the average rate of change for [-1,2]? I need a answer please!!!!!!!!!
Answer: -2
Hope this helps :)
HELP HELP HELP PLEASE
A line has a slope of 1/4. The line passes through the point (4, 6). The line also passes through the point (12, k). What is the value of k?
A local hamburger shop sold a combined total of 488 hamburgers and cheeseburgers on Friday. There were 62 fewer cheeseburgers sold than hamburgers. How
many hamburgers were sold on Friday?
9514 1404 393
Answer:
275
Step-by-step explanation:
Let h represent the number of hamburgers sold. Then the number of cheeseburgers sold is h-62, and the combined total is ...
hamburgers + cheeseburgers = combined total
h + (h -62) = 488
2h = 550 . . . . . . . . add 62, collect terms
h = 275 . . . . . . . . . .divide by 2
275 hamburgers were sold on Friday.
HELP WILL MARK BRAINLIESTTT!!!!
Answer:
Real= 3 . Imaginary = 3.6
Step-by-step explanation:
mark me brainliest plz
3. Solve (5x – 4)(x – 6). (2 points) O x = 4, x = 6 X = -4, X = -6 X = 1.25, x = 6 0 x = 0.8, x = 6
Answer:
x=0.8
x=6
Step-by-step explanation:
(5x-4)(x-6)=0
1)5x-4=0
2)x-6=0
1)5x=4
x=4/5 or 0.8
2)x=6
If the perimeter of the surface of a cube is 12 metre,
then what is the volume of it?
Answer:
A cube is a solid box whose every surface is a square of same area. ... So the volume of the box will be equal to the volume of 8 unit cubes together. ... The number of cubes are 12, its volume is 12 cu cm. 3. ... When we draw a flat shape on a paper, it occupies a certain ... It's unit is square centimeters or square meters etc.
Step-by-step explanation:
If triangle CAT is similar to triangle DOG, which of the following statements is incorrect?
Answer:
D: AT = OG
Step-by-step explanation:
I just took this quiz so that's how I know
Sociologists have found that information spreads among a population at an exponential rate. How do you think this happens? Describe a piece of good news circulating through your circle of friends or family. How is this exponential?
Answer: Because people talk about important information
Step-by-step explanation: like a virus, information spreads like wildfire. But good news that has spread around my community is that we have a bunch of motivated people looking forward to feeding the homeless and create a homeless shelter to get back on their feet. Thanks to flyers, friends, and family enough money was raised to successfully build a homeless shelter.
Simplify.
34−4x+12x−12+12x
Enter your answer in the box.
Do not use decimals in your answer.
Answer:
22 - 28x
Step-by-step explanation:
34−4x+12x−12+12x
you wanna combine like terms
34 - 16x + 12 + 12x
34 - 28x + 12
22 - 28x
The product of a number below - 7/10 is 2/10
what is the number?
-7/20
7/20
- 5/7
5/7
Answer:
[tex]\frac{5}{7}[/tex]
Step-by-step explanation:
This question can be written algebraically as [tex]-\frac{7}{10} x=\frac{1}{2}[/tex]
And the image below shows step-by-step on how to solve it
Hope this helps! :)
Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: A(3,6) B(11,10)
Line 2: C(-4, 2) D(6, 16)
Parallel, Perpendicular, or Neither:
Answer:
Line 1 : A. Neither B. Parallel__________ Line 2: A. Perpendicular B. Parallel
Step-by-step explanation:
Sorry this was hard to make a picture of it in my head. *Exhausted face* ._.