Describe the transformations to the basic function. Then, write the equation of the function.
Answers
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
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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Pls tell me the answer thank you
Answers
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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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]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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if x + ay = b then y equals
Answers
(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!
!!!!!!!!!!!!!!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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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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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 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
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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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.
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.
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
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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Please help me with this question
Answers
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.
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.
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
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
what is negative five times negative one third
Answers
Answer:
The answer is to this problem is five over three
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
Guys I need help is this right?
Answers
Answer:
The answer is C.
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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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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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
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
What are the leading coefficient and degree of the polynomial?
-1+23x² +8x
Answers
find an equation for the line that passes through the points (-5,-1) and (-1,1)
Answers
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!
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
What is the quotient of 8.252 ÷ 0.4?