Mathematics High School

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?

Answers

Answer 1

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.

Related Questions

The vertices of the triangle in the diagram below are A(7,9), B(3,3), and C(11,3).


What are the coordinates of the centroid of triangle ABC?

Please Answer with work shown! I know that the answer is (7,5) But can some one show the work for it?
If you answer it and show the work for me then I will give you the brainiest question reward!
Please Help!

Answers

Answer:

(7 , 5)

Step-by-step explanation:

Add all the x-axis then divide by 3

7 + 3 + 11 = 21

21/3 = 7

Add all the y-axis then divide by 3

9 + 3 + 3 = 15

15/3 = 5

So answer will be (7,5)

The coordinates of the centroid of triangle ABC.

(x, y)

Where,

x = Sum all the x-coordinates of the vertices ÷ 3

y = Sum o

The coordinates of the centroid is (7, 5).

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The vertices of the triangle in the diagram below are:

A(7,9), B(3,3), and C(11,3).

Now,

The coordinates of the centroid of triangle ABC.

(x, y)

Where,

x = Sum all the x-coordinates of the vertices ÷ 3

y = Sum of the y-coordinates of the vertices ÷ 3

Now,

x = 7 + 3 + 11 / 3 = 21/3 = 7

y = 9 + 3 + 3 / 3 = 15/3 = 5

Now,

The coordinates of the centroid is (7, 5).

Learn more about triangles here:

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There are 4,389 dogwood trees in the state park. The park workers are going to plant 342 more trees. How many trees will there be when they are done?

Answers

Answer:

4731

Step-by-step explanation:

4,389+342=4,731

^^^ this too please

Answers

I believe the measurement of CD is 90 degrees

How much time will it take for an amount of ₹9000 to yield ₹810 as interest at 4.5 % per annum of simple interest?
[Irrelevant answers will be reported]​

Answers

Answer:

2 years

Step-by-step explanation:

Let us take the time period be t .

And , we know formula of SI as ,

[tex]\boxed{SI = \frac{PRT}{100}}[/tex]

[tex]\implies Rs 810 = \dfrac{Rs 9000 \times 4.5 \times t }{100}\\\\\implies t = \dfrac{810 \times 100 }{9000\times 4.5 } \\\\\underline{\boxed{\red {\implies Time = 2 \ years }}}[/tex]

Which of the tables represents a function?


Table A
Input Output
5 3
5 2
4 1
Table B
Input Output
1 2
3 2
5 3
Table C
Input Output
0 0
1 2
1 3
Table D
Input Output
4 2
4 3
4 4








Table A
Table B
Table C
Table D

Answers

Answer:

table b i think

Step-by-step explanation:

[Image: Vertical number line ranging from negative 5 to 5.]

On this number line, zero represents sea level. Plot the following points based on the description provided.

• -3 1/2

[Image: Vertical number line ranging from negative 5 to 5.]

On this number line, zero represents sea level. Plot the following points based on the description provided.

• opposite of –5

Answers

Answer:

Positive 5.

Step-by-step explanation:

Opposite of negative 5 is positive 5.

The point will be on the positive side, which is above sea level. So it will be on 5 above the zero.

Answer:positive 5

Step-by-step explanation:

SOLVING SYSTEMS:
I just need the work for each equation.

Answers

S. 2x - 6 = x + 8
+ 6 + 6
2x = x + 14
-x -x
x = 14

y = (14) + 8
y = 22

(14 , 22)

I. 2x - 5y = 16
-2x + 20y = -16
15y = 0
/15 /15
y = 0

x - 10(0) = 8
x = 8

(8 , 0)

F. 10x + 6y = -4
2x - 6y = -8
12x = -12
/12 /12
x = -1

2(-1) - 6y = -8
-2 - 6y = -8
+2 +2
-6y = -6
/-6 /-6
y = 1

(-1 , 1)

N. 24x - 3y = 15
2x + 3y = 11
26x = 26
/26 /26
x = 1

2(1) + 3y = 11
2 + 3y = 11
-2 -2
3y = 9
/3 /3
y = 3

(1 , 3)

T. 3x - 2y = -2
6x + 2y = 2
9x = 0
/9 /9
x = 0

-3(0) + 2y = 2
2y = 2
/2 /2
y = 1

(0 , 1)

O. -8x - 4y = 6
5x + 4y = -3
3x = -3
/3 /3
x = -1

-4(-1) - 2y = 3
4 - 2y = 3
-4 -4
-2y = -1
/-2 /-2
y = 1/2

(-1 , 1/2)

I. 8x - 9 = -2x - 4
+2x +2x
10x - 9 = -4
+9 +9
10x = 5
/10 /10
x = 1/2

y = -2(1/2) - 4
y = -1 - 4
y = -5

(1/2 , -5)

D. -6x - 4 = -3x + 5
+3x +3x
-3x - 4 = 5
+4 +4
-3x = 9
/-3 /-3
x = -3

y= -3(-3) + 5
y = 9 + 5
y = 14

(-3 , 14)

S. -9 = -3x - 3y
8 = 4x + 3y
-1 = x

3 = -1 + y
+1 +1
4 = y

(-1 , 4)

R. -5x - 5y = 25
5x - 4y = 2
-9y = 27
/-9 /-9
y = 3

-x - (-3) = 5
-x + 3 = 5
-3 -3
-x = 2
/-1 /-1
x = -2

(-2 , -3)

A. 8y + 3 = 3x
- 3 - 3
8y = 3x - 3
-3x -3x
-3x + 8y = -3
-3x + 8y = -3

Same equation = infinite solutions

K. 8x - 6y = -4
3x + 6y = 4
11x = 0
/11 /11
x = 0

4(0) - 3y = -2
-3y = -2
/-3 /-3
y = 2/3

(0 , 2/3)

T. -5x - 8y = 0
12x + 8y = 56
7x = 56
/7 /7
x = 8

3(8) + 2y = 14
24 + 2y = 14
-24 -24
2y = -10
/2 /2
y = -5

(8 , -5)

A person standing 130 feet away from the foot of a tall building must look up at an angle of 30° to see the top of the building. There is a radio antenna on the top of the building. The angle of elevation of the top of the radio antenna is 45°.

Answers

Answer:

30 angels

Step-by-step explanation:

1
II
III
IV
X
.
.
X .
-1 | 2
-11-1
-11-4
0 3
2 1-1
-13
0
0
-4-1
--3 0
-1 2
-1 1
0 3
2-5
0 0
2
2
3
3
A. III
B.IV
C.
D
1

Answers

Answer:

X .

-1 | 2

-11-1

-11-4

0 3

2 1-1

-13

0

0

-4-1

--3 0

-1 2

-1 1

0 3

2-5

0 0

2

2

3

3

A. III

B.IV

C.

D

1\

Step-by-step explanation:

Which expression is equivalent to 15x + 3?
15(1x + 1)
5(3x + 1)
3(5x + 1)
2(15x + 3)

Answers

The answer is 3(5x+1)
It is 3(5x + 1). Multiply 3 with 5 and multiply 3 with 1, then you will get 15x + 3

A.) what is the domain?
B.) what is the range?
C.) is this relation a function?

Answers

Answer:

The Domain is the set of all points over which a function is defined.

The range is the set of values the function takes on as output.

In a basketball game, the home team was down by 9 points at the end of the game. They only scored 6 points for every 7 points the visiting team scored. What was the final score of the game? Type both answers with a comma inbetween. Show your work below.

Answers

The final score of the basketball game is  (54, 63).

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, They only scored 6 points for every 7 points the visiting team scored

and they differ by a total of 9 points.

Therefore, The final score would be 6×9, 7×9.

= (54, 63).

If we take the difference between 63 and 54 it would be 9.

learn more about numerical expressions here :

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A Sweater That normally costs $25.00 is on sale for 10 percent Off.
What will the Discount be?
what will the cost of the Sweater be?
Can Someone Please PLEASE help me??

Answers

Answer:

15.00

Step-by-step explanati

the discount is 15% because you need to subtract it

The table below represents a linear function f(x) and the equation represents a function g(x):



Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

(10 points)

Answers

Answer:

Step-by-step explanation:

Part A

for f(x) slope between points (-1,-6) and (1,0)

m= y2-y1/x2-x1 = -6-0/-1-1 = -6/-2= 3

for g(x) slope m=4 because we compare to equation y=mx+b the given equation g(x)=4x-5

The slope of f(x) is 3 and the slope g(x) is 4 so the line of g(x) is steeper

part B

The y intercept for g(x) is  (0, -5)

The equation of f(x) can be found

y-y1 =m(x-x1) take any point for example point (1,0)

y-1 =3(x-0)

y=3x+1 so the y-intercept is at (0,1)

The y-intercept for f(x) is greater at y=1 then the one of g(x) at y=-5

Convert the Following: 5.4 oz=__________ mg

Answers

Answer:

153087 mg

Step-by-step explanation:

6th grade math i mark as brainliest​

Answers

Answer:

There are 5 terms

Step-by-step explanation:

each number is its own term

Solve for x: 10(x + 1) = 2x - 7

Answers

Answer:Simplifying

x = -2.125

Step-by-step explanation:Add '-10' to each side of the equation.

10 + -10 + 8x = -7 + -10

Combine like terms: 10 + -10 = 0

0 + 8x = -7 + -10

8x = -7 + -10

Combine like terms: -7 + -10 = -17

8x = -17

Divide each side by '8'.

x = -2.125

Simplifying

x = -2.125

Answer: x=-17/8


First, distribute the 10

10x + 10 = 2x - 7

Next, move the x-values to one side

8x = -17

Now, isolate the x by dividing both sides by 8

x = -17/8

I don’t understand so please HELPPPPPPPPPPPPPP

Answers

Answer:

C

Step-by-step explanation:

Okay so im going to gudie you thru So what it is asking you is to Count all the cubic squares looking things so what i can see is that You circled 169 aka C that would be correct because it cant be 11 cause it dosent look like 11 square units  lol you get what im saying so the answer is C hope this HELPSS!!

By the way follow my insta. exotic. jaliyah if you need anymore help

C i believe the answer is C

A recipe requires 4 cups of
flour to make 3 dozen
cookies. How many cups of
flour are needed for 10
dozen cookies?

Answers

Answer:

13 1/3 cups

Step-by-step explanation:

The ratio of flour to dozens of cookies is 4:3 or 1 1/3:1

1 1/3 x 10 = 13 1/3

Answer:

13 1/3

Step-by-step explanation:

12 cups cover the first 9 cookies and than just divide 4 by 3 and you will get 1.3 which is 1 1/3 of a cup

the length of a rectangle is 4cm more than double its width. the perimeter of the rectangle is 116cm. Find the length and the width of the rectangle

Answers

Answer:

l = 31 cm

w = 27 cm

Step-by-step explanation:

l = w + 4

p = 2l + 2w

p = 2(w+4) + 2w

116 = 2(w+4) + 2w

116 = 2w + 8 + 2w

116 = 4w + 8

108 = 4w

27 = w

l = w + 4

l = 27 + 4

l = 31

hope this helps, pls mark brainliest :D

Answer:

w=18 L=40

Step-by-step explanation:

 w

---------

|         |

|         | 2w+4

|         |

---------

2(2w+4)+ 2(w)=116

6w+8=116

6w=108

w=18

2(18)+4

36+4

40

If you spend 3$ on 6 apples,what is the unit rate (in dollars) per apple?

Answers

Answer

2 apples per $1

Step-by-step explanation:

because 6 apples cost $3, so take 6 divided by 3 so you get 2 apples per dollar

$Ok so there is $6 per apple

7 chocolate bars cost 19 dollars determine the cost per chocolate bar.

Answers

Answer: .368

Step-by-step explanation:

Answer:

$2.71

Step-by-step explanation:

to find the cost of each chocolate bar you must divide the total cost by the number of chocolate bars

19/7

= 2.714

≈ $2.71

The numbers 22 and 35 are relatively prime. TrueFalse

Answers

Answer: True

Step-by-step explanation:

Answer:

False They are coprime numbers

Step-by-step explanation:

I hope it helps ❤❤

An angle measures 130.4° more than the measure of its supplementary angle. What is the measure of each angle?

Answers

Answer: 24.8 and 155.2

Step-by-step explanation:

x+x+130.4=180

2x=49.6

x=24.8

Answer:

155.2

Step-by-step explanation:

let x be the supplimentary angle

then the angle is

130.4+x

we have

 

130.4+x+x=180

2x=49.6

multiply both sides with 2

x=24.8

then the angle is

130.4+24.8

155.2

Geometry Question:

Find the value of x that makes N the incenter of the triangle (See attached)

Answers

Answer:

.5 or 1/2

Step-by-step explanation:

Y^2x 24^2=25^2

Y=7

7=14x

x=.5

The value of x is 0.5.

The calculation is as follows:

Here we use Pythagoras Theorem

[tex]Y^2 - 24^2=25^2[/tex]

Y=7

Now  

7 = 14x

So, x=.5

Therefore we can conclude that The value of x is 0.5.

Learn more: brainly.com/question/17429689

Sara bought 12 apples, 24 oranges, and 18 bananas for fruit baskets. If Sara wants to create the greatest number of fruit baskets that all have the same amount of fruit without any left over, how many baskets can she create?

Answers

Answer:

Step-by-step explanation:

Apples- 2

Oranges-4

Bananas- 3

In each basket

using the elimination method to solve the system of equations.

3x+6y =36
3x-6y=0


a. 3,6
b. 6,-3
c. 6,3
d. 3,-6

Answers

Answer:

c. (6, 3)

Step-by-step explanation:

subtract

3x + 6y = 36

3x - 6y =  0

12y = 36, y = 3

3x + 6(3) = 36

3x + 18 = 36

3x = 18, x = 6

x = 6, y = 3

Answer:

the answer is b good luck

PLEASE HELP!!!!!!!!!!!!!!

Answers

Answer:

882-28282=9191

Step-by-step explanation:

Find the x- and y-intercepts of the graph of the linear equation 2x+3y=12.

Answers

Answer:

x-intercept= 6

y-intercept= 4

Step-by-step explanation:

Solve for x first then solve for y.

Answer: y= -2/3x+4

The X-Intercept is -2/3

The Y- Intercept is 4

Hope this helps!! Have a wonder day everyone!! (:

Step-by-step explanation:

Step one write out the equation 2x+3y=12

Then move the variable to the right hand side and change the sign. 3y=12-2x

Then divide both sides of the equation by 3. You get y=4-2/3x

Then: Use the Commentative Property to reorder the terms. y= -2/3x+4

What is 23/24 as a decimal rounded to the nearest hundredth?

Answers

Answer:

95.80

Step-by-step explanation:

The number 23/24 rounded to the nearest hundredth is 0.96

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Given data ,

Let the number be A = 23/24

So , in order to round the number

First we need to find the decimal for of the number A

And ,

A = 23/24

A = 0.9583

And , rounding the number to its nearest hundredth is rounding the number to two decimal places

So ,

A = 0.9583

A = 0.96

Hence , The number 23/24 rounded to the nearest hundredth is 0.96

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