For each function, identify the transformation from the parent function y=b x . y=7 (x-5)

Answers

Answer 1

Transformation of y= bx into y=7(x-5) will take place by by horizontal translation by 5 units to the right, vertical dilation by a scale factor of 7 .

A parent function is the simplest form of a particular family of functions. A family of functions is a group of functions that have the same highest degree and therefore the same graph shape. Function transformations "move" or "resize" or "mirror" the graph of the parent function. Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means  it is a reflection here,  'a' stands for vertical stretch , 'b' stands for horizontal stretch , 'c' stands for horizontal movement , 'd' stands for vertical movement

We have given two function y=b x   and  y=7 (x-5) which means that first y changes into (x -5 ). i.e., horizontal translation by 5 units to the right. Then it changes into 7 (x - 5). i.e., vertical dilation by a scale factor of 7.

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Related Questions

Manipulating Positive Rational Numbers LC) What is 6 over 8 written as a decimal? 0.6 0.75 1.3 4.8

Answers

Answer:

0.75

Step-by-step explanation:

[tex]\frac{6}{8}[/tex] = 6 ÷ 8 = 0.75

a survey was conducted to study the relationship between the annual income of a family and the amount of money the family spends on entertainment. data were collected from a random sample of 280 families from a certain metropolitan area.

Answers

The scatterplot is the correct answer.

A scatter plot uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.

The dots in a scatter plot not only report the values of individual data points but also patterns when the data are taken as a whole.

Identification of correlational relationships is common with scatter plots. In these cases, we want to know, if we were given a particular horizontal value, what a good prediction would be for the vertical value.

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The measure of each of the
congruent angles of an isosceles
triangle is 9 less than 4 times the
vertex angle. Find the measures of all
the angles in the triangle.

Answers

Answer:

22°, 79° and 79°

Step-by-step explanation:

Let x  be the vertex angle and y each of the congruent angles.

The sum of all angles =180°

So x + y + y = 180

x + 2y = 180 ·········· Equation (1)

Given "The measure of each of the congruent angles of an isosceles triangle is 9 less than 4 times the vertex angle", the equation is

y = 4x - 9

Substitute for y in terms of x in equation 1

⇒ x + 2(4x - 9) = 180

⇒ x + 8x - 18 = 180

⇒ 9x - 18 = 180

⇒ 9x = 180 + 18

⇒ 9x = 198

⇒ x = 198/9 = 22

So vertex angle is 22°

Substituting for x in Equation 1:
22 + 2y = 180
2y = 180 - 22
2y = 158
y = 158/2
y = 79°

So each congruent angle is 79°

What are the solutions for the following equations 2x^2+11x+5=0

Answers

Answer:

x=-5nakalimutan ......................

......


Solve each equation. 3/2log₂4- 1/2log₂x=3

Answers

The value of x using the properties of logarithm is 1.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation for x

We are given a logarithmic expression: 3/2 log₂4 - ½ log₂x = 3

Using properties of the logarithm, we have

3/2 log₂4 - ½ log₂x = 3

3/2 (2 log 2 / log 2) - ½ (log x / log 2) = 3

3 - ½ (log x / log 2) = 3

½ (log x / log 2) = 0

log x = 0

log x = log 1

On applying exponent both sides, we get,

x = 1

Hence, the value of x is 1.

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Which of the statements below are correct?
select all correct statements.
2.8mm = 28cm , 1760 ml < 10 litres, 18g > 0.17 , 1.68 = 168cm

Answers

Answer:

False

True

missing info

missing info

Step-by-step explanation:

2.8mm = 28cm    False since 28 cm = 280 mm

1760 ml < 10 litres     True since 1760 ml = 1.76 l

18g > 0.17    missing units

1.68 = 168cm    missing units

Nethanel Stück receives a monthly income of $600 from a pension and some from Social Security. His wife, Lisha, also receives a monthly income from Social Security, but only 70 percent of Nethanel's amount. If their monthly income is $1,800 per month, how much is Nethanel's monthly Social Security benefit?

Answers

The Nethanel's monthly Social Security benefit is :$ 705.88

What makes the household monthly income of $1,800?

The household monthly income of $1,800 comprises the monthly income and social security of Nethanel Stuck and his wife monthly income from social security which is 70% of Nethanel's

total income=$600+x+(70%*x)

total income=$1,800

Nethanel social security=x

wife's monthly income=70%*x=0.70x

1800=600+x+0.70x

1800-600=1.70x

1200=1.70x

x=1200/1.70

x=Nethanel's monthly Social Security benefit=$ 705.88

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Please help me with this math problem!! Will give BRAINILEST!! :) 15 points!

Answers

Using proportions and the percentage concept, it is found that:

25% of Johnny's apples are the Jonagold variety.75% of Johnny's apples are not of the Jonagold variety.63 apples are not of the Jonagold variety.

What is a proportion?

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for percentage problems.

This is because a percentage of an amount a divided by a total amount b is given by the following proportion:

P = a/b x 100%.

From the image, we have that 3 out of 12 apples are of the Jonagold variety, hence:

3/12 x 100% = 0.25 x 100% = 25%.

25% of Johnny's apples are the Jonagold variety.75% of Johnny's apples are not of the Jonagold variety.

Each apple in the image is equivalent to 7 apples, hence:

9 x 7 = 63.

63 apples are not of the Jonagold variety.

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8+(2)((-2)-3) jjjjjjjjjj

Answers

La respuesta es de 8+(2)(-2)-3) es = a -2

find the magnitude of the sum of these two vector
please vind the direcion too

OK PLEASE I NEED HELP NOW IM RUNNING OUT OF POINTS :(

Answers

The magnitude of the sum of these two vectors is approximately 11.791 units.

How to find the magnitude of the sum of two vectors

In this question we have the representations of two vectors on a Cartesian plane, of which we must find the magnitude of the two vectors. There are different methods to find it, we decide to use a vectorial method. First, sum the two vectors:

R(x, y) = A(x, y) + B(x, y)

R(x, y) = 7.70 · (cos 27.8°, sin 27.8°) + 16.3 · (- sin 20°, - cos 20°)

R(x, y) = (6.811, 3.591) + (- 5.574, - 15.317)

R(x, y) = (1.237, - 11.726)

Second, use the Pythagorean theorem:

R = √[1.237² + (- 11.726)²]

R ≈ 11.791

The magnitude of the sum of these two vectors is approximately 11.791 meters.

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Simplify each number. 4¹.⁵

Answers

The result of simplifying the number (4¹)⁵ using the exponent rules is 1024

To solve this exercise we have to resolve algebraic operations following the exponent rules.

Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

(4¹)⁵ =

4 ⁽¹*⁵⁾ =

4⁵ =

4*4*4*4*4 =

1024

What is an exponent?

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Which equation represents inverse variation between x and y ?
(a) x=y/z (b) x=-15 z/y (c) z=-15 y/x (d) x z=5 y

Answers

The option d ,that is , x= 5y is the equation that represents inverse variation between x and y.

What is inverse variation ?

1: A mathematical connection between two variables that can be described by an equation in which the sum of their products equals a fixed value.

2: an expression of inverse variation by an equation or function; contrast with direct variation.

CALCULATION

In an inverse variation, the inverse percentage establishes the link between two quantities or variables. The inverse relationship between two quantities, x and y, is provided by:

x ∝ 1/y

or

x = k/y

xy = k

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the recode for the Boston marathon wheelchair division is 1 hour 18 minutes and 27 seconds

Answers

Using the relation between velocity, distance and time, it is found that the average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

What is the complete question?

"The record for the Boston Marathon’s wheelchair division is 1 hour,

18 minutes, and 27 seconds.

The Boston Marathon is 26.2 miles long. What was the average speed of the record winner of the wheelchair division?"

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

v = d/t.

For this problem, we have that:

The distance is of 26.2 miles.The time in hours, considering an hour has 3600 seconds and a minute has 60 seconds, is given by: t = 1 + (18 x 60 + 27)/3600 = 1.3075.

Hence the velocity is given by:

v = 26.2/1.3075 = 20.04 miles per hour.

The average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

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Ahmad tutors math. For each hour that he tutors, he earns 30 dollars. His earnings, E (in dollars), after tutoring for h hours is given by the following.
E=30h
How much does Ahmad earn if he tutors for 5 hours?

Answers

He Earns $150 dollars for 5h .
Explanation : multiply 5 & 30 .
He earns $150 in 5 hours

Greg is driving his motorhome. It uses 3 gallons of gas for every 21 miles he travels. Complete the table below showing the number of gallons used and the distance traveled

Answers

Answer:

I think the answer is 234 miles and 78 gallons.

Step-by-step explanation:

Hope this helped :)

Answer:

You didn't show the problem so ill just make it to where you can answer yourself

Step-by-step explanation:

so if he uses 3 gallons per 21 miles just divide 3 by 21(yes 3 by 21)

So 0.142 is used per mile

So because you don't show how many miles he traveled just take the number of miles he traveled and times it by 0.142

Example: 42 x 0.142 = 5.964 which when rounded is 6

p(x)=x^3-4x^2-8x please help me solve

Answers

Answer: The value of p(x) = (-2,6) or p(x) = (-2,0)

Step-by-step explanation:

Given that,

p(x) = x^3-4x^2-8x

p(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] - 8x

and replace with '0'.

x^3-4x^2-8x = 0

Now, factorizing equation is,

(x+2) ([tex]x^{2}[/tex] - 6x) = 0

(x+2) = 0

x= -2

Therefore, x = -2

and,

([tex]x^{2}[/tex] -6x) = 0

([tex]x^{2}[/tex] -6x+0) = 0

using quadratic formula = - [b ± √[tex]b^{2}[/tex]-4ac] / 2a

substitute the values,

a = 1, b = -6 , c = 0

                          p(x) = - [-6 ± √[tex]-6^{2}[/tex]-4.1.0] / 2.1

                           p(x) = - [-6 ± √36-4.1.0] / 2.1

                            p(x) = - [-6 ± √36-(0)] / 2.1

                             p(x) = - [-6 ± √36] / 2.1

                             p(x) = - [-6 ± 6] / 2

                              p(x) = [6 ± 6] / 2

                             p(x) = 3 ± 3

Therefore, p(x) = 3+3 = 6

                  p(x) = 3-3 = 0

So, that we can say the value of p(x) = (-2,6) or p(x) = (-2,0).

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The lengths of the sides of a triangle are 7.6 cm, 8.2cm , and 5.2cm . Find the measure of the largest angle.

Answers

Answer:

arccos(439/1976)

Step-by-step explanation:

The largest angle is opposite the longest side. So, by the Law of Cosines, if we let this angle be x,

[tex]x=\arccos \left(\frac{7.6^2 + 5.2^2 - 8.2^2}{2(7.6)(5.2)} \right) \\ \\ =\arccos(439/1976)[/tex]

You drove at 75 kmh-¹ for 2.25 hours Find the exact distance traveled.​

Answers

Answer:

168.75 km.

Step-by-step explanation:

Distance = speed * time

               = 75 * 2.25

               = 168.75 km.

A bag contains 11 counters five of the count as a white account is taken out of the bag at random and not replaced a second counter is taken out of the bag at random calculate the probability that only one of the counters is white

Answers

The probability that only one of the counter is white is 6/11.

So we know that there are 11 counters, 5 of them are white, 6 are not white.

Let's assume that first we take the white one, the probability is equal to the quotient between the number of white counters and the total number of counters, so we have:

p = 5/11

Now for the second one, we don't want to take a white one, so here the probability is equal to the quotient between the number of non-white counters (6) and the total number of counters (now there are 10, because we took one)

q = 6/10

The joint probability is the product of the individual probabilities, this is:

P = p*q

And, also notice that there are 2 permutations:

first white, then non-white.first non-white, then white.

So we need to add a factor 2.

P = 2*p*q = 2*(5/11)*(6/10) = 6/11

The probability is 6/11

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Match the inequality with its line graph. 1. - x - 5 ≤ -2 2. 6 + x ≤ 3 3. x - 4 < -7 4. 2 x > -6

Answers

The inequalities and their graphs are;

1)  -x - 5 ≤ -2 is represented by the third graph

2) 6 + x ≤ 3 is represented by the fourth graph

3) x - 4 < -7 is represented by the second graph

4) 2x > -6 is represented by the first graph

How to Interpret Inequality Line Graphs?

1) We are given the inequality;

-x - 5 ≤ -2

Rearranging gives us;

-x ≤ -2 + 5

- x ≤ 3

Divide both sides by -1 to get;

x ≥ -3

The graph must be a closed circle starting at -3 and pointing to the right.

It is the third graph in the link at the end of this answers.

2) We are given the inequality; 6 + x ≤ 3

Rearranging gives;

x ≤ -6 + 3

x ≤ -3

The graph must be a closed circle starting at -3 and pointing to the left. Thus, it is the fourth graph.

3) We are given the inequality; x - 4 < -7

Rearranging gives us;

x < -7 + 4

x < -3

The graph must be an open circle starting at -3 and pointing to the left.

Thus, it is the second graph.

4) We are given the Inequality; 2x > -6

Divide both sides by 2 to get;

x > -6/2

x > -3

It must be a graph with an open circle starting at -3 and then to the right.

Thus, it is the first graph as seen in the attached link

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find the constant of proportionality for the relationship plotted, on the graph.
please help, giving branliest. :))

Answers

The constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250

How to find the constant of proportionality for the relationship plotted, on the graph?

The graph is the given parameter

On the graph, we have the following point

(x, y) = (2, 50)

The constant of proportionality for the relationship plotted, on the graph is represented with k, and the formula is

k = y/x

This gives

k = 50/2

Evaluate

k = 25

Substitute k = 25 in k = y/x

25 = y/x

When x = 10. we have

25 = y/10

This gives

y = 250

Hence, the constant of proportionality for the relationship plotted, on the graph is 25 and the distance in 10 seconds is 250

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Translating English to Algebra

Answers

The translations for each sentence are listed below:

x + 5 = 2y - 3 = 96 - x = y5 · x - 6 = - y2 · t < y5 · x · y = zx + y < x - y2 · (a + b) = 153 · (x - 5) > y

How to translate English sentences into algebraic language

Herein we find nine sentences that must be translated in terms of algebraic expressions, that is, combinations of constants, variables and operators. Now we proceed to present the result of each case:

The sum of x and 5 is 2:
Constants: 5, 2
Variables: 2
Operators: +, =
x + 5 = 2
The sum of y and - 3 is 9:
Constants: - 3, 9
Variables: y
Operators: +, =
y + (- 3) = 9
y - 3 = 9
The difference of 6 and x is y:
Constants: 6
Variables: x, y
Operators: -, =
6 - x = y
The difference of five times x and 6 is - y:
Constants: 5, 6
Variables: x, y
Operators: ·, -, =
5 · x - 6 = - y
The product of t and 2 is less than y:
Constants: 2
Variables: t, y
Operators: ·, <
2 · t < y
The product of 5 · x and y is equal to:
Constants: 5
Variables: x, y, z
Operators: ·, =
5 · x · y = z
The sum of x and y is less than the difference of x and y:
Constants: N/A
Variables: x, y
Operators: +, -, <
x + y < x - y
Twice the sum of a and b is 15:
Constants: 2, 15
Variables: a, b
Operators: +, ·, (, ), =
2 · (a + b) = 15
Three times the difference of x and 5 is more than y:
Constants: 5, 3
Variables: x, y
Operators: ·, -, >
3 · (x - 5) > y

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someone please tell me what the equation for this graph is sorry if it’s hard to see

Answers

Answer: y=3(x+3)^3-1

Step-by-step explanation:

ASAP need to turn in in 10 min

Answers

The tank can hold 24 gallons

Answer:

24 gallons

Step-by-step explanation:

The total fuel capacity is 2/(1/24) = 24 gallons.

The greater of two numbers is 3 more than twice the smaller.Their sum is 24. Find the numbers.

Answers

Let the greater number be represented as g and the smaller number as s.

g + s = 24

(2s + 3) + s = 24

3s + 3 = 24

3s + 3 - 3 = 24 - 3

3s = 21

3s / 3 = s

21 / 3 = 7

s = 7

The smaller number is 7. Now, let’s plug 7 into our equation to find the bigger number:

7 + g = 24

7 + g - 7 = 24 - 7

g = 17

g + s = 24

17 + 7 = 24

The smaller number is 7, and the bigger number is 17.

To simplify the expression, which exponent property should you apply first?

Answers

The exponent property which must be applied first to simplify the expression as given in the task content is; The power of a power property.

Which exponent property should be applied first in a bid to simplify the expression as given in the task content?

It follows from the task content that the exponent property which must be applied first in a bid to simplify the expression be determined.

Since the expression given is;

(4y)³ • (2g)² • y • g

Consequently, to solve the parentheses, the power of a power property must be used first so that we have;

4³•y³ • 2²•g² • y • g

The expression can then be further simplified by using the the product of a power property on like terms so that the simplified form is therefore;

256g³y⁴.

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could someone please help me on this worth 10 points 7(x+3y)=

Answers

According to the distributive property:

[tex] \alpha ( \beta + \gamma ) = \alpha \beta + \alpha \gamma [/tex]

So, applying this to our equation:

[tex]7(x + 3y) = 7 \times x + 7 \times 3y \\ 7(x + 3y) = 7x + 21y[/tex]

A company sold 1 million shares of common stock at $10 book value and the stock price then rose to $25 per share on the new york stock exchange. what amount of equity capital did the firm raise from this sale

Answers

The equity capital the firm raise from this sale is $15 million.

Equity capital refers to the funds paid into a business by investors in exchange for common or preferred stock. It can be solved by subtracting the total liabilities from the total assets.

Equity Capital = Total Assets – Total Liabilities

If a company sold 1 million shares of common stock at $10 book value, then its total liabilities is $10 million.

If the stock price then rose to $25 per share on the New York stock exchange, then the total assets is $25 million.

Equity Capital = Total Assets – Total Liabilities

Equity Capital = $25 million – $10 million

Equity Capital = $15 million

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Nicole and Daniel are splitting a pizza. Nicole eats 1/4 of the pizza and Daniel eats 2/3 of it. How much pizza is left? Write an equation to represent this situation.

Answers

The number of pizza left is 1/12

How to calculate the number of pizza left ?

Nicole and Daniel are splitting a pizza

Nicole gets 1/4 of the pizza

Daniel gets 2/3 of the pizza

let 1 represent the total amount of pizza

1- (1/4 + 2/3)

1- 11/12

= 1/12

Hence 1/12 of the pizza is left from the total amount of pizza

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Alan is driving on a highway. He uses one gallon of gas every 25 miles he drives. The distance, D (in
miles), he travels on g gallons of gas is given by the following function.
D(g)=25g
How far does Alan drive if he uses 4 gallons of gas?

Answers

Alan drive if he uses 4 gallons of gas is 75 miles distance

The following function calculates the distance (in miles) he travels on gallons of gas. D(g)=25g

Where D(g) is the distance traveled in gallons.

and g denoted the quantity of gasoline used

We are asked to calculate the distance traveled in three gallons of gasoline. To do this, we will set the value of g to 3 in our function.

D(3)=25 x 3 = 75

As a result, Chris's automobile traveled 75 miles on three gallons of petrol.

The length of the line segment connecting two places, for example, is the distance between them. a two-dimensional plane, which may also be  in a three-dimensional plane. In coordinate geometry, there are several forms of distance formulae.

Distance between two locations in a two-dimensional plane

Distance between two locations in a three-dimensional plane

Distance in 2D from a point to a line

2D distance between two parallel lines

3D distance from a point to a line

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