Find g(x), where g(x) is the translation 2 units left and 13 units up of f(x)=–7x+7.

Answers

Answer 1

Answer:

[tex]g(x)=-7x+6[/tex]

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]f(x)=-7x+7[/tex]

Translation of 2 units left:

[tex]\implies f(x+2)=-7(x+2)+7[/tex]

Translation of 13 units up:

[tex]\implies f(x+2)+13=-7(x+2)+7+13[/tex]

Simplifying:

[tex]\implies g(x)=-7(x+2)+7+13[/tex]

[tex]\implies g(x)=-7x-14+7+13[/tex]

[tex]\implies g(x)=-7x+6[/tex]

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Related Questions

Write the equation y=-3x+3 in function notation using f(x) to denote the function.

Answers

The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.

What is the function notation form of the equation?

According to the task content, the equation given; y = -3x +3 is to be written in function notation.

Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;

f(x) = -3x +3.

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If the volume of the cone is 180 in³, what is its surface area? ​

Answers

Answer:

Hi, to find the surface area of a cone is πrl

if your radius and length is given.

hope this helps (•‿•)

in mongolia the temperature can dip down to -45C in January. The temperature in July may reach 40C. What is the temperature range in Mongolia?

Answers

Answer:

85 C

Step-by-step explanation:

Temperature range means the difference between the maximum and minimum in temperature for an area. 40C-(-45C)=85 C

Find the measure of XY

Answers

Answer:

18

Step-by-step explanation:

For this problem, you have to look at the ratios of the corresponding sides.

Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18

Jason wants to receive monthly payments of $3,250 for 15 years. How much does he have to invest now in an annuity that has an annual interest rate of 3.6% to achieve his goal? Round your answer to the nearest hundred.

Answer: $451,500​

Answers

The amount she should invest today in the annuity is $455,450.40.

How much should be invested today?

The first step is to determine the future value of the monthly annuity.

Future value = monthly payment x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

r = interest rate = 3.6/12 = 0.3%n = number of periods : 15 x 12 = 180

Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92

The second step is to determine the present value of this future annuity:

774, 171.92 / (1.036^15) = $455,450.40

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A 2-liter bottle of juice costs $2.80. A box containing six 1/2 liter bottles sells for $3.90. Which option has a higher cost per liter? What is that cost?

A. 2-liter bottle; $1.40
B. Box of six 2-liter bottles; $1.30
C. 2-liter bottle; $2.80
D. Box of six-liter bottles; $3.90

Answers

Answer:

A. 2-liter bottle;$1.40

Step-by-step explanation:

We have to find out which option has the higher cost per liter. To do this we must find out how much each option would be if it was a liter.

1st set up each equation
2-liter = $2.80 we can divide by 2 on both sides of the equal sign and we get 1 liter = $1.40.
6(1/2) liter bottles = $3.90 this becomes 3 liters = $3.90 then we divide by 3 on both sides of the equal sign and we get $1.30

2nd we compare
$1.40(2 liter bottle) > $1.30 (6 1/2 liter bottles)

The probability that Greg is on time for a given class is 14% . If there are 30 classes during the semester, what is the best estimate of the number of times out of 30 that Greg is on time to class? Round your answer to the nearest integer.

Answers

The number of times that Greg is on time to class is 4

How to estimate the number of times that Greg is on time to class?

The given parameters are:

Probability that Greg is on time, p = 14%

The sample size, n = 30

The estimate of the number of times that Greg is on time to class is

E(x) = np

Substitute the known values in the above equation

E(x) = 30 * 13%

Evaluate the product

E(x) = 3.9

Approximate

E(x) = 4

Hence, the number of times that Greg is on time to class is 4

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A regular octagon has side lengths of 8 centimeters. What is the approximate area of the octagon?

Answers

Answer:

The answer is B if the octagon has side lengths of 8

What is the LCM of the denominators? 8/ab^6, 9/ab^5

Answers

Answer:

8

Step-by-step explanation:

because all the number is over 1

So confused please help me thank u

Answers

True

The inverse of the statement would be “If an angle is acute, then it measures less than 90°.” This is true as the definition of acute is an angle measuring less than 90°

Find the value of z.
answer choices
A. 40
B. 56
C. 62
D. 80

Answers

Answer:

40°

Step-by-step explanation:

Using external angle intercepted arcs calculation:

    50° = 1/2 (210-x)    shows x = 110°

then z = 360 - 210 -110 = 40°

Ramiro was on a 2-day road trip. On the first day he drive at an average speed 40 mph. On the second day he drove at an average speed of 60 mph. If he drove 2 hours. If he drove 2 hours longer and went 20 miles farther on the first day, find the total distance Ramiro traveled on his first road trip

Answers

X = first day hours
Y = second day hours

x = y + 2
40x = 60y + 20

40(y + 2) = 60y + 20
40y + 80 = 60y + 20
60 = 20y
y = 3 hours on day 2

x = y + 2
x = 3 + 2
x = 5 hours on day 1

Miles = 40(5) + 60(3)
200 + 180
380 miles

The total distance Ramiro travelled is 380 miles.

What is equation?

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

let x be the first day hours

let y be the second day hours.

now,

x = y + 2

40x = 60y + 20

Putting x= y+2

40(y + 2) = 60y + 20

40y + 80 = 60y + 20

60 = 20y

y = 3 hours

For, first day

x = y + 2

x = 3 + 2

x = 5 hours

Thus,

Total distance = 40(5) + 60(3)

=200 + 180

=380 miles

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Find one value of x for which h(x)=4 and find h (-2)

Answers

the solutions are:

h(x) = 4  for x = 0h(-2) = 2

How to find the value of x for which h(x) = 4?

The only information of h(x) that we have is the given graph.

To find the value of x, we need to go to the vertical axis and find y = 4, then we move horizontally to the left until we meet the curve.

That intersection will give the value of x for which h(x) = 4.

Doing that, we conclude that h(x) = 4 when x = 0 (on the vertical axis).

Now we want to find h(-2), and we can do that using the graph.

By finding x = -2 on the horizontal axis and then moving up until we intercept the graph, we can see that:

h(-2) = 2

Concluding, the solutions are:

h(x) = 4  for x = 0h(-2) = 2

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A rhombus is a four-sided figure with all sides the same length. Points F(-2,-2), G(-2, 3), and H(2, 6) are three vertices of rhombus FGHJ. Vertex J is directly below vertex H. What is the perimeter of the rhombus? Show your work.​

Answers

Answer:

  20

Step-by-step explanation:

The sides of the 4-sided figure are the same length, so we can find the perimeter (sum of side lengths) by multiplying one side length by 4.

Side length

Points F(-2, -2) and G(-2, 3) lie on the same vertical line: x = -2. The distance between them is the difference of their y-coordinates:

  FG = (3 -(-2)) = 5

Each side is 5 units long.

Perimeter

The length of the four sides is ...

  P = 4s = 4(5) = 20

The perimeter of the rhombus is 20 units.

The next two terms of 2;6;18;54

Answers

Hello there! The next two terms in this arithmetic sequence are 162 and 486.

This set of terms has a rule that for each corresponding number, we multiply by 3.

2 x 3 = 6

6 x 3 = 18

18 x 3 = 54

By following this rule, we can multiply our last used number by 3 to get what our next term is.

54 x 3 = 162

Our terms now look like this:

2; 6; 18; 54; 162

Again, we multiply the last used number.

162 x 3 = 486

Now our set looks like this:

2; 6; 18; 54; 162; 486

By multiplying each corresponding term by 3, we have identified the rule and the next two terms in our set.

The next two terms of 2; 6; 18; 54 are 162 and 486. If you need any extra help, let me know and I will gladly assist you.

(y-5)/2=(y+6)/3 solve

Answers

The solution of the given equation represented in the task content can be determined by first evaluating the LCM and hence is; y= 27.

What is the solution of the equation as given in the task?

The given equation is; (y-5)/2=(y+6)/3.

Hence, by multiplying the equation by 6, we have;

3(y-5) = 2(y+6)

3y -15 = 2y +12

y = 27.

Hence, it follows that the value of y which is a solution to the equation is; y = 27.

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What length of skirting board is needed for a room which is 4m by 4m square if the room has a 800mm door?​

Answers

Answer:

15.2m2

Step-by-step explanation:

hope it helps.good day

15. Find the young modulus of a brass rod of diameter 25mm and of length 250mm which is
subjected to a tensile load of 50KN when the extension of the rod is equal to 0.3mm.

Answers

The Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².

How to find the young modulus of a brass rod?

Given: Physical Properties of the Brass rod exist

Length, L = 250 mm

Radius, R = Diameter / 2 = 25/2 mm

Load of 50 kN hanging on the brass rod which results in elongation of the rod to 0.3 mm.

To estimate the Young Modulus of the brass rod we will require Stress on the rod, Ratio of elongation to the total length.

To find the stress on the rod,

Stress(Pressure) = Force / Area

⇒ Stress = 50,000 / (Area of cross-section)

The rod exists shaped like a cylinder then the area of its cross-section will be πR² ( R = radius)

⇒ Stress = 50000 / (π (25/2 mm)² )

The force exists given in newton, then we must convert the unit of the area into m² to obtain the solution in pascal.

1 mm = 0.001 m

⇒ Stress = 50,000 / 22/7 ( 25/2 × 10⁻³ m)²

take, π = 22/7

⇒ Stress = 50000 / ( 22/7 × 625 / 4 × 10⁻⁶ )

⇒ Stress = 50000 / ( 11/14 × 625 × 10⁻6 )

⇒ Stress = 50000 × 14 × 10⁶ / 625×11

⇒ Stress = 80 × 14 × 10⁶ / 11

Stress = 1120/11 × 10⁶ Pa

Now, that we maintain Stressed, to estimate Strain (ratio of elongation to original length),

Strain = (Elongation) / (Original length)

⇒ Strain = 0.3 / 250

⇒ Strain = 3 / 2500

Therefore, Young Modulus, Y = Stress / Strain

⇒ Y = 1120/11 × 10⁶ / 3/2500

⇒ Y = 1120/11 × 2500/3 × 10⁶

⇒ Y = 101.8 × 833.3 × 10⁶

⇒ Y = 84829.94 × 10⁶

Y ≈ 8.5 × 10¹⁰ Pa

Therefore, the Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².

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ASAP HELP ME WITH THIS

Answers

Answer:

isosceles trapezoind

Step-by-step explanation:

An isosceles trapezoid is a trapezoid with congruent base angles.

Work out the upper quartile of this list of numbers: 3,4,1,2,9

Answers

Answer:

23 24

it is the answer it is answered

JD Scott I have no idea how to go but she is kind I don't really care about

john likes to walk the steps of the department he works for during lunch break. There are s steps in his department. Today John would like to walk the steps of the taller building next door. The number of steps in the taller building next door is 27 less than 6 times the number of steps in John's department. Which expression represents the number of steps in the taller building next door in terms of s?

Answers

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍ ‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍ ‍ ‍ ‍ ‍

You are offered two jobs selling college textbooks. One company offers an annual salary of $30,000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $25,000 plus a year-end bonus of 2% of your total sales. How much would you need to sell in a year to make the second offer the better offer?

Answers

Answer:

at least $500,000 in sales

Step-by-step explanation:

Translate the sentence into an equation using n to represent the unknown number. Then solve the equation for n.
a number subtracted from 46 is -21
a.
46 minus n = negative 21. n = 67
b.
46 minus 21 = n. n = 67
c.
46 minus 21 = n. n = 25
d.
46 minus n = negative 21. n = 75

Answers

Answer: a.

Step-by-step explanation:

46 is subtracted by n to get -21 so the equation is 46 - n = -21

Add n on both sides; 46 - n + n = -21 + n; 46 = -21 + n

Add 21 on both sides; 46 + 21 = -21 + n + 21; 67 = n

So n = 67

5 and 6 thousandths in standard form

Answers

5 and 6 thousandths in standard form is 5.006

How to express the number in standard form?

The number is given as:

5 and 6 thousandths

This can be rewritten as

5 +  6 thousandths

Express as numbers

5 +  0.006

Evaluate the sum

5.006

Hence, 5 and 6 thousandths in standard form is 5.006

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which of the following rational functions is graphed below?

Answers

Answer:

c

Step-by-step explanation:

Oblique Asymptotes

R(x) will have oblique asymptote if it can be represented in the form

1 / (Q)x

5) What problems have a negative slope?

Answers

A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.

What is a negative slope

It should be noted that a negative slope implies that two variables are negatively related.

This implies that when x increases, y decreases, and also when x decreases, y increases.

Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.

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Exercise 18: 3 1. The populations of a city increased from 4 million to 1.1 million. Write in digits the number by which the population increased.​

pls as fast as u can!!!!!!!!!!!!!!!!

Answers

Answer:

bro it had been decreased

so total had been decreased is (4,000,000-2,900,000)=1,100,000

Find the sum of the infinite geometric sequence that begins 1/12, 1/18, 1/27, …

Answers

Answer:

  1/4

Step-by-step explanation:

The sum of an infinite geometric series is given by the formula ...

  S = a/(1 -r)

where 'a' is the first term, and r is the common ratio.

Application

Here, the first term is 1/12, and the common ratio is ...

  (1/18)/(1/12) = 12/18 = 2/3

Then the sum is ...

  S = (1/12)/(1 -2/3) = (1/12)/(1/3) = 3/12 = 1/4

The sum of the infinite series is 1/4.

Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur​

Answers

The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.

How to calculate the profit?

From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.

It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.

The loss will be:

= 2,000,000 - 1,500,000

= 500,000

Therefore, the information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.

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Which of the following is equivalent to √√8?
02
O√√2
2√√√2
2 + √2

Answers

Answer:

The correct answer is √2 (√√2)

Step-by-step explanation:

√8 = √(4.2) = 2 √2

√√8 = √(2√2) = √2 (√√2)

Answer:

2 √2 (C)

and to the second question the answer is..

1 (B)

9 (C)

Step-by-step explanation:

I answered it on ed 2022

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