Describe the transformations to the basic function. Then, write the equation of the function.

Describe The Transformations To The Basic Function. Then, Write The Equation Of The Function.

Answers

Answer 1

The given function is a graph transformation of the absolute value function.

What are Function Transformations?

A function transformation "moves," "resizes," or "reflects" the parent function's graph. Function transformations are classified into three types: Translation, Dilation, and Reflection. Only dilation alters the size of the original shape; the other two transformations change the shape's position but not its size.

Step 1: Parent function y = f₁(x) = |x|

Step 2: f₁(x) is reflected (Reflection) about x-axis to form f₂(x) = -f₁(x) = -|x|

Step 3: f₂(x) is moved to left by 5 units(Horizontal translation) to form f₃(x) = f₂(x + 5) = -|x + 5|

Step 4: f₃(x) is moved up 1 unit (Vertical translation) to form f₄(x) = f₃(x) + 1 = -|x + 5| + 1

The equation of the given graph is:

y = |x + 5| +1

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Related Questions

1. Here is a graph of the equation 2y - X = 1:

Answers

The given the initial equation

[tex]2y-x=1[/tex]

we can determine the part of the graph to be shaded if the equation changes to the inequality:

[tex]2y-x>1[/tex]

If we make y the subject of the formula, such that

[tex]2y>1+x[/tex]

Then we can put in the values of x and y at (0,0)

so that

[tex]\begin{gathered} 0>1+0 \\ 0>1 \end{gathered}[/tex]

we can see that the expression is false because 0 is not greater than 1

Hence, we will shade away from the origin this means that we will shade above the line

The graph is shown below

So for question B

We will shade above the line

Question C

The points on the line are not included because the inequality does not include an equal sign

[tex]\begin{gathered} \text{Assuming the inequality were} \\ 2y-x\ge1 \\ \\ The\text{ points would have been inclusive because this inequality also have an equal sign } \end{gathered}[/tex]

6. If a = 2, b = 3, Evaluate 15-ab. Show all your work.

Answers

Answer:

9

Step-by-step explanation:

15-2*3

15-6

9

Jesus loves u hope it helps

Step-by-step explanation:

that means "calculate the result with these values".

the expression is

15 - ab

or

15 - a×b

for a = 2, b = 3 this gives us

15 - 2×3 = 15 - 6 = 9

What is the equation of the line that passes through the point
(3,-7) and has a slope of -4/3

Answers

Using point-slope form, the equation is [tex]y+7=-\frac{4}{3}(x-3)[/tex].

Answer:

y = - [tex]\frac{4}{3}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{4}{3}[/tex] , then

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = - 4 + c ⇒ c = - 7 + 4 = - 3

y = - [tex]\frac{4}{3}[/tex] x - 3 ← equation of line

Solve the inequality algebraically x^2+10x+9<0

Answers

Answer:

−9 < x < −1

Step-by-step explanation:

a) Let's find the critical points of the inequality.

x^2 + 10x + 9 = 0

(x + 1)(x + 9) = 0

x + 1 = 0 or x + 9 = 0

x = −1 or x = −9

x < −9 (Wrong)

−9 < x < −1 (Correct)

x > −1 (Wrong)

Your answer is −9 < x < −1

find an equation for the line that passes through the points (-5,-1) and (-1,1)

Answers

answer: y=1/2x + 1.5

Answer:

y = (1/2)x + (3/2)

Step-by-step explanation:

(-5, -1), (-1, 1)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁         1 - (-1)          1 + 1            2            1

m = ------------- = ----------- = ------------ = --------- = --------

        x₂ - x₁        -1 - (-5)        -1 + 5           4            2

y - y₁ = m(x - x₁)

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

y + 1 = (1/2)(x + 5)

y + 1 = (1/2)x + (5/2)

    -1                 -1

---------------------------------

y = (1/2)x + (3/2)

I hope this helps!

Which type of triangle matches the V
following description?
A polygon with 2 sides of length 148 mm
and 2 sides of length 240 mm.
Equilateral
ölölőló
Isosceles
Scalene
Not a triangle
skill code: 1601101

Answers

Answer:

Isosceles

Isosceles triangles have 2 side the same length and one side different

multiplication tables from 2 to 20

Answers

multiplication tables from 2 to 20

table of 2

2 x 1 = 2      

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8

2 x 5 = 10

2 x 6 = 12

2 x 7 = 14

2 x 8 = 16

2 x 9 = 18

2 x 10 = 20

table of 3

3 x 1 = 3

3 x 2 = 6

3 x 3 = 9

3 x 4 = 12

3 x 5 = 15

3 x 6 = 18

3 x 7 = 21

3 x 8 = 24

3 x 9 = 27

3 x 10 = 30

table of 4

4 X 1 = 4

4 X 2 = 8

4 X 3 = 12

4 X 4 = 16

4 X 5 = 20

4 X 6 = 24

4 X 7 = 28

4 X 8 = 32

4 X 9 = 36

4 X 10 = 40

table of 5

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

table of 6

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

6 x 7 = 42

6 x 8 = 48

6 x 9 = 54

6 x 10 = 60

table of 7

7 x 1 = 7

7 x 2 = 14

7 x 3 = 21

7 x 4 = 28

7 x 5 = 35

7 x 6 = 42

7 x 7 = 49

7 x 8 = 56

7 x 9 = 63

7 x 10 = 70

table of 8

8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40

8 x 6 = 48

8 x 7 = 56

8 x 8 = 64

8 x 9 = 72

8 x 10 = 80

table of 9

9 x 1 = 9

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

9 x 6 = 54

9 x 7 = 63

9 x 8 = 72

9 x 9 = 81

9 x 10 = 90

table of 10

10 x 1 = 10

10 x 2 = 20

10 x 3 = 30

10 x 4 = 40

10 x 5 = 50

10 x 6 = 60

10 x 7 = 70

10 x 8 = 80

10 x 9 = 90

10 x 10 = 100

table of 11

11 x 1 = 11

11 x 2 = 22

11 x 3 = 33

11 x 4 = 44

11 x 5 = 55

11 x 6 = 66

11 x 7 = 77

11 x 8 = 88

11 x 9 = 99

11 x 10 = 110

table of 12

12 x 1 = 12

12 x 2 = 24

12 x 3 = 36

12 x 4 = 48

12 x 5 = 60

12 x 6 = 72

12 x 7 = 84

12 x 8 = 96

12 x 9 = 108

12 x 10 = 120

table of 13

13 x 1 = 13

13 x 2 = 26

13 x 3 = 39

13 x 4 = 52

13 x 5 = 65

13 x 6 = 78

13 x 7 = 91

13 x 8 = 104

13 x 9 = 117

13 x 10 = 130

table of 14

14 x 1 = 14

14 x 2 = 28

14 x 3 = 42

14 x 4 = 56

14 x 5 = 70

14 x 6 = 84

14 x 7 = 98

14 x 8 = 112

14 x 9 = 126

14 x 10 = 140

table of 15

15 x 1 = 15

15 x 2 = 30

15 x 3 = 45

15 x 4 = 60

15 x 5 = 75

15 x 6 = 90

15 x 7 = 105

15 x 8 = 120

15 x 9 = 135

15 x 10 = 150

table of 16

16    X 1 = 16

16 X 2 = 32

16 X 3 = 48

16 X 4 = 64

16 X 5 = 80

16 X 6 = 96

16 X 7 = 112

16 X 8 = 128

16 X 9 = 144

16 X 10 = 160

table of 17

17 x 1 = 17

17 x 2 = 34

17 x 3 = 51

17 x 4 = 68

17 x 5 = 85

17 x 6 = 102

17 x 7 = 119

17 x 8 = 136

17 x 9 = 153

17 x 10 = 170

table of 18

18 x 1 = 18

18 x 2 = 36

18 x 3 = 54

18 x 4 = 72

18 x 5 = 90

18 x 6 = 108

18 x 7 = 126

18 x 8 = 144

18 x 9 = 162

18 x 10 = 180

table of 19

19 x 1 = 19

19 x 2 = 38

19 x 3 = 57

19 x 4 = 76

19 x 5 = 95

19 x 6 = 114

19 x 7 = 133

19 x 8 = 152

19 x 9 = 171

19 x 10 = 190

table of 20

20 * 1=20

20*2=40

20*3=60

20*4=80

20*5=100

20*6=120

20*7=140

20*8=160

20*9=180

20*10=200

what is the use of multiplication chart?

A grid including all the times tables is plainly displayed on a multiplication chart. It's a useful tool for remembering multiplication facts. Make a chart of the math multiplication tables and use it for calculations or daily reading. This will aid in your memorization.

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Margaret does the following problem incorrectly.
-0.46 + (-0.54) =
Margaret’s answer: -0.46 + 0.54 = 0.08
Please find the error and resolve the problem to help
PLS HELP FAST ALSO CAN YOU BREAK IT DOWN FOR ME

Answers

The problem is in the parenthesis

Explaination: plus and minus is minus. That means -0.46-0.54=-1.

if x + ay = b then y equals

Answers

x + ay = b

(Isolate y from equation)

ay = b - x

y = (b - x)/a

Hey there!

[tex]x+ay=b\\[/tex] for y

Add -x to both sides:

[tex]ay+x+-x=b+-x\\ay=b-x[/tex]

Now, let's divide both sides by a:

[tex]\frac{ay}{a} =\frac{b-x}{a}[/tex]

[tex]y=\frac{b-x}{a}[/tex]

Hope this helps!

WILL GIVE BRAINLIEST! Please help and explain, thank you! All that is needed is to find the unknown side.

Answers

Answer:

X is 9

Step-by-step explanation:

Answer:

On the smaller figure the measures of it are 6 and 3. On the large figure one of the measures is 18. The number 6 and 18 are congruent, and 6 has be tripled in size, so in order to finding the missing measurement, you will simply triple the 3:

3 times 3 = 9

The missing measure is 9.

Step-by-step explanation:

Hope it helps! =D

Liam buys some fruit for £26.55.
He pays the exact amount using two notes and four coins.
List the notes and coins Liam could have used.​

Answers

Answer:

£20 note, £5 note, 50p,50p,50p, 5p

Step-by-step explanation:

Liam buys some fruit for £26.55 by paying 2 notes of £20 and £5 and 3 coins of 50 cent and one coin of 5 cent.

What is addition?

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Liam buys some fruit for £26.55.

He pays the exact amount using two notes and four coins.

So, possible notes are £1, £5, £10 and £20.

And the possible coins are 1¢, 5¢, 10¢, 25¢, 50¢, and £1.

So, through trial and error,

we get notes of £20 and £5.

And the coins are three coins of 50 cent and 1 coin of 5 cent.

The total amount = adding the amount of notes and coins.

£26.55 =  £20 + £5 + 3(50¢) + 5¢

Therefore, notes of £20 and £5 and the coins are three coins of 50 cent and 1 coin of 5 cent, Liam used.

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what is negative five times negative one third

Answers

Answer:

The answer is to this problem is five over three

Which is an equivalent expression using a positive exponent?
(3/5)^-8 ÷ (3/5)^-4
(3/5)^4
(3/5)^12
(5/3)^32
(5/3)^4

Answers

The equivalent expression using a positive exponent is (5/3)⁴ .

If an expression was created utilizing integer variables, constants, and algebraic operations, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

However, since they are not produced by using integer constants and algebraic operations, transcendental numbers like such and e are not algebraic. The production of is commonly stated as a geometric expression, although the definition of e requires an infinite number of algebraic operations.An expression is said to be rational if it can be reduced to an acceptable fraction using the characteristics of arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

A positive expression is given as (3/5)⁻⁸ ÷ (3/5)⁻⁴ .

Using the properties of exponents we can calculate the expression as:

(3/5)⁻⁸⁺⁴ = (3/5)⁻⁴ = (5/3)⁴

Hence the required expression is (5/3)⁴

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There are 750 students in the seventh grade class and 625 students in the eighth grade class at Brookland Middle School. There are 1,375 total students at the school. About what percent of students attending Brookland MIddle School are in seventh grade? Help asap!!

Answers

The percentage of students in Brookland Middle School who are attending seventh grade is 54.54%

What is percentage?

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it. A% is a number that has no dimensions and is dimensionless (pure).

We know that, to get the value of percentage we have to divide the value for which percentage needs to be calculated by total value and then multiply the resultant by 100.

So, we will divide the number of student in seventh class by the total number of student and then multiply it with 100.

(750/1375)100 = 54.54 %

Therefore, percentage of students attending Brookland Middle School are in seventh grade is 54.54%.

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!!!!!!!!!!!!!!URGENT!!!!!!!
Some information is given about each sphere. Order them from least volume to greatest volume. You may sketch a sphere to help you visualize if you prefer. Sphere A: Has a radius of 4 Sphere B: Has a diameter of 6 Sphere C: Has a volume of 64 Sphere D: Has a radius double that of sphere B.

Answers

The least volume to greatest volume will be sphere B, sphere C, sphere A and sphere D.

What will be the volume of the sphere?

The volume of the sphere is calculated as:

= 4/3 πr³

where r = radius

The volume of sphere A will be:

= 4/3 πr³

= 4/3 × π × 4³

= 85.3π

The volume for sphere B will be:

= 4/3 πr³

= 4/3 × π × (6/2)³

= 4/3 × π × 3³

= 36π

The volume for C is given as 64π.

The volume for D has a radius double that of B. This will be Radius = 3 × 2 = 6

= 4/3 πr³

= 4/3 × π × 6³

= 288π

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A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.

Answers

The length of the pole is 19.15 feet.

What is the angle of elevation?

The angle of elevation is created by the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, the angle formed is an angle of elevation.

Given:

Angle made by straight road = 15°

Angle of elevation of the sun = 57°

Length of the shadow = 75 feet

∠ACB = 90° - 57° = 33°

∠CAB = 57° - 15° = 42°

Using Sine Law to find BC i.e.length of the pole.

[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]

[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]

[tex]BC= \frac{75sin 42}{sin 33}[/tex]

BC ≅ 19.15 feet (to the nearest hundredth.)

Therefore, the approximate length of the pole is 19.15 feet.

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Read image for instructions The shape of the distribution is…

Answers

Ok, so

The shape of a distribution is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity.

Solve the following proportion for v.
8/17=v/7
Round your answer to the nearest tenth.​

Answers

Answer:

your answer is 3.3

Step-by-step explanation:

What is the quotient of 8.252 ÷ 0.4?

Answers

When we divide a number and if it does not get divided completely, we are left with a remainder. Let us understand this with the help of an example. The quotient can be calculated by dividing the dividend with the divisor. Quotient = Dividend ÷ Divisor. The answer is 20.63

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.


The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.


(1, 3), (2, 6), (3, 12), (4, 24)


Write a function to represent the data.

Answers

The data in the question will be represented by a geometric sequence given by 3 (2) ⁿ⁻¹.

A geometric sequence is defined as the sequence in which the ratio between the consecutive terms of the sequence remains constant. The ratio is known as common ratio. The nth term of geometric sequence is written as a (r)ⁿ⁻¹ where a is the first term, r is the common ratio and n is the number of terms. We know from the question that the time in minutes Aurora takes to complete the task forms a sequence as 3, 6, 12, 24.....

The common ratio of this sequence is given by 6/3 = 2. The first term being equal to 3. Now, for the nth term the sequence will be represented as

a (r)ⁿ⁻¹

=> 3 (2)ⁿ⁻¹

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Guys I need help is this right?​

Answers

Answer:

The answer is C.

What are the leading coefficient and degree of the polynomial?
-1+23x² +8x

Answers

It is 12 it’s is 12 it has to be 12

Abby and Lexi each open a savings account on the same day. Both accounts accrue simple interest. The function f(t) = 10t + 500 models the amount of money in Abby’s account over time. The function g(t) = 11.25t + 450 models the amount of money in Lexi’s account over time. Select all the statements that are true of this situation.

Answers

The number of months where they will both have same amount in their accounts is 40 months.

How to illustrate the information?

From the information given, the function f(t) = 10t + 500 models the amount of money in Abby’s account over time and the function g(t) = 11.25t + 450 models the amount of money in Lexi’s account over time.

It should be noted that the number of years when there value will be the same is:

10t + 500 = 11.25t + 450

Collect like terms

11.25t - 10t = 500 - 450

1.25t = 50

Divide

t = 50/1.25

t = 40

In 40 months, Abby and Lexi will have same amount.

Note that an overview was given as the information is incomplete.

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HELP ME PLEASE!!!! will give brainlist , thanks

Answers

Answer:

3

Step-by-step explanation:

1. Subtract 2 y-coordinates.

11 - 8 = 3

2. Subtract the corresponding x-coordinates in the same order.

-1 - (-2) = -1 + 2 = 1

3. slope = (difference in y)/(difference in x) = 3/1 = 3

Solve the equation.

x^2 + 7x = 0

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 0\:\; or \:\: x = -7 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} + 7x = 0 [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}(x + 7) = 0 [/tex]

There are two cases now,

Case 1 :

[tex]\qquad\displaystyle \tt \rightarrow \: x = 0[/tex]

Case 2 :

[tex]\qquad\displaystyle \tt \rightarrow \: x + 7 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = - 7[/tex]

So, the possible values of x are :

[tex]\qquad\displaystyle \tt \rightarrow \: 0 \: \: and \: \: - 7[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]x=0, \quad x=-7[/tex]

Step-by-step explanation:

Given equation:

[tex]x^2+7x=0[/tex]

Factor x from the left side of the equation:

[tex]\implies x(x+7)=0[/tex]

Using the Zero Product Property, set each factor equal to zero and solve for x:

[tex]\implies x=0[/tex]

[tex]\implies x+7=0 \implies x=-7[/tex]

Therefore, the solutions of the equation are:

[tex]x=0, \quad x=-7[/tex]

Zero Product Property: If a⋅b = 0 then either a = 0 or b = 0 (or both).

If I were to solve an equation such as 14x-3=24x+29, would I start inversing the 24x or the 14x first? I have been doing the lower variable number first this whole time but I seem to get it wrong since it's supposed to be negative.

Answers

24-14=10x
3+29=32
32/10
X=3.2

it really does matter how you put it out the big number first like 29-14 make more sense then 14-29=-10
3+29=32
32/-10
-32

Is there a dilation that maps shape I onto shape II? If so, what is the scale factor and is it an enlargement or a reduction?
Give me the actual answer, not explanation, for 10 points

Answers

The scale factor for the graph will be 3 and there will be enlargement.

The scale factor may be defined as the ratio of two dimensions such that one figure is large, and another is small. The scale factor is done due to the unpractical measurement of any figure. For example, if a figure is a scale copy of the scale factor of 6/2 it means 2 is converted into 6. We can use the following points to know about enlargement.

A(1, 1) ⇒ A'(3, 3)

B(2, 1) ⇒ B'(6, 3)

C(1, 2) ⇒ C'(3, 6)

D(2, 2) ⇒ D'(6, 6)

Now, to find the scale factor, simply divide the Point' with the original Point. Use any number.

A'(3, 3)/(A(1, 1)) = 3

B'(6, 3)/(B(2, 1)) = 3

C'(3, 6)/(C(1, 2)) = 3

D'(6, 6)/(D(2, 2)) = 3

which shows that the scale factor is 3.

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Pls tell me the answer thank you

Answers

The answer you have your cursor on is the correct answer

A chef bought 3 bags of oranges at the supermarket and it cost her $8.13. Write an equation that can be used to express the relationship between the total cost(t) and the number of bags of oranges(b) purchased.

Answers

Answer:

8.13=3b

Step-by-step explanation:

8 13 is the total cost and the bags of oranges are three.

Please help me with this question

Answers

First you find the area of the square: 5 x 5 = 25
Next you find you find the area of the circle: (pi x radius) squared
the radius is 4.5, 3.14 x 4.5 = 14.13
square 14.13: 28.26

28.26 is bigger than 25 which is why it can fit.
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