The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?

g(x) = (x + 9)2 + 4
g(x) = (x + 9)2 − 4
g(x) = (x − 4)2 + 9
g(x) = (x + 4)2 + 9

Answers

Answer 1

Answer:

The function that represents g(x) is the third choice: g(x) = (x − 4)^2 + 9

Step-by-step explanation:

The original function has been shifted 9 units up (a vertical transformation). To show a vertical transformation, all we have to do is either add or subtract at the end of the function.

To show a shift upwards, we add the value of change.

To show a shift downwards, we subtract the value of change.

In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 9 units up. Since we shifted up, we simply add 9 to the end of the function: g(x) = [tex]x^{2}[/tex] + 9

The original function has also been shifted 4 units to the right. This is a horizontal transformation. To show a horizontal transformation, we need to either add or subtract within the function (within the parenthesis).

To show a shift to the left, we add the value of change.

To show a shift to the right, we subtract the value of change.

*Notice: Moving left does NOT mean to subtract while moving right does NOT mean to add. The rules above are counterintuitive so pay attention when doing horizontal transformations.

In this case, the original function f(x) = [tex]x^{2}[/tex] was translated 4 units to the right. Since we shifted right, we must subtract 4 units within the function/parenthesis: g(x) = [tex](x-4)^{2}[/tex]

When we combine both vertical and horizontal changes, the only equation that follows these rules is the third choice: g(x) = (x − 4)^2 + 9

Answer 2

Answer: C

Step-by-step explanation:


Related Questions

the cost of an article is Rs 10,000 and it is sold at same profit. if a customer bought it for Rs 12430 with 13% VAT calculate the profit percent on the article.​

Answers

Answer:

Percentage profit = 11.3%

Step-by-step explanation:

Given the following data;

Vat = 13% = 13/100 = 0.13Cost price = 10,000Selling price = Rs 12430

To calculate the profit percentage on the article;

First of all, we would determine the value-added (vat) tax levy;

Vat levy = 0.13 * 10000

Vat levy = Rs. 1300

Profit = selling price - cost price

Profit = 12430 - 10000

Profit = 2430

Profit after vat;

Profit after vat = Profit - Vat levy

Profit after vat = 2430 - 1300

Profit after vat = 1130

Next, we would calculate the profit percentage on the article;

[tex] Percentage \; profit = \frac {Profit \; after \; vat}{Cost \; price} * 100 [/tex]

Substituting the values into the formula, we have;

[tex] Percentage \; profit = \frac {1130}{10000} * 100 [/tex]

[tex] Percentage \; profit = \frac {113000}{10000} [/tex]

Percentage profit = 11.3%

Find the length of PR from the given figure ( step by step ). ​

Answers

Answer:

PR = 39 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

PR² + PQ² = QR² , that is

PR² + 80² = 89²

PR² + 6400 = 7921 ( subtract 6400 from both sides )

PR² = 1521 ( take the square root of both sides )

PR = [tex]\sqrt{1521}[/tex] = 39

Answer:

[tex]PR=39[/tex]

Step-by-step explanation:

The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:

[tex]a^2+b^2=c^2[/tex]

Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,

[tex]a^2+b^2=c^2[/tex]

Substitute,

[tex]a^2+b^2=c^2[/tex]

[tex]PQ^2+PR^2=QR^2[/tex]

[tex]80^2+PR^2=89^2\\[/tex]

Simplify,

[tex]80^2+PR^2=89^2\\[/tex]

[tex]6400+PR^2=7921[/tex]

Inverse operations,

[tex]6400+PR^2=7921[/tex]

[tex]PR^2=1521\\\\PR=39[/tex]

what number is smallest 2,-3,-10,-5,-2-1

Answers

Answer:

2,-3,-10,-5,-2-1

The smallest number is -10

Answer:

it's -10

Step-by-step explanation:

Well, if you look at the number line, numbers start from the left going to the right and the ones before the 0 ( the negative ones) are the smaller ones. And here if you arrange them from the smallest, -10 is the smallest and 2 is the biggest.

hope this helps

highest common factor of 9 and 29 ​

Answers

Answer:

1

Step-by-step explanation:

See pic for steps :)

The highest common factor of 9 and 29 is: 1

Please help explanation if possible

Answers

Answer:

y=-11

Step-by-step explanation:

A line can be represented by a linear equation of

[tex]y = mx + b[/tex]

where m is the slope and y is the y intercept.

The slope is 0 so this function will be

[tex]y = b[/tex]

Which is also called a constant function. The y intercept is -11. So the answer is

[tex]y = - 11[/tex]

What is the value of x in the equation -5/4x=-160

Answers

[tex] \\ \sf \longmapsto \: - \frac{ 5}{4} x = - 160 \\ \\ \sf \longmapsto \: \frac{5}{4} x = 160 \\ \\ \sf \longmapsto \: x = 160 \times \frac{4}{5} \\ \\ \sf \longmapsto \: x = 32 \times 4 \\ \\ \sf \longmapsto \: x = 128[/tex]

Step-by-step explanation:

-5/4x=-160

5/4x=160

x=160×4/5

x=640/5

x=128

Anybody help please ! Step by step

Answers

Your answer is -6.

Hope my answer is helpful to you. Stay blessed .

[tex]\\ \large\sf\longmapsto {27}^{x} = {9}^{x - 3} \\ \\ \large\sf\longmapsto ( {3}^{3} ) {}^{x} = ({3}^{2} ) {}^{x - 3} \\ \\ \large\sf\longmapsto 3 {}^{3x} = 3 {}^{2(x - 3)} \\ \\ \large\sf\longmapsto {3}^{3x} = 3 {}^{2x - 6} \\ \\ \large\sf\longmapsto 3x = 2x - 6 \\ \\ \large\sf\longmapsto 3x - 2x = - 6 \\ \\ \large\sf\longmapsto x = - 6[/tex]

solve for x with step by step explanation
0.85x - 100 < 80

;-; i don't understand how to solve this help

Answers

0.85x-100<80

collect like terms

0.85x<80+100

0.85x<180

divide by 0.85

x<211.8

5a + 18 < −27 pre algibra

Answers

Answer:

X < -9

Step-by-step explanation:

5a +18 < -27

5a < -27 -18

5a < - 45

5a/5 < - 45/5

a < - 9

Answred by Gauthmath

Answer: -9

Step-by-step explanation:

5a+18 < -27

5a< -27-18

5a<-45

a< -45/5

a< -9

Given Isosceles Trapezoid TRAP, if mP=98, find mT

Answers

Answer:

∠ T = 82°

Step-by-step explanation:

In a Isosceles trapezoid, any lower base angle is supplementary to any upper base angle , so

∠ T + ∠ P = 180°

∠ T + 98° = 180° ( subtract 98° from both sides )

∠ T = 82°

Please help explanation if possible

Answers

Answer: y = -1x + 1

Step-by-step explanation:

(choose two points on the line to find the slope)

(0,1) and (2,-1)

(slope = m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-1}{2-0}=\frac{-2}{2} =-1[/tex]

y = mx + b, (0,1), (2,-1), m=-1

(both points work and yield the same equation)

[tex]y=mx+b\\1=-1(0)+b\\b=1\\y=-1x+1[/tex]

Solve for a. a+|-23+6|=-32
Plz help

Answers

Answer:

a = -49

Step-by-step explanation:

a+|-23+6|=-32

Simplify the absolute value term

a+|-17|=-32

a+17=-32

Subtract 17 from each side

a +17-17 = -32-17

a = -49

Answer:

a = −49

Step-by-step explanation:

a + ∣ − 17∣ = −32

a + 17 = −32

a = −32 − 17

Simplify.

-32 - 17 to -49.

james cuts 2 of his neighbor's lawn the first is 1000 m long and 100 m wide what is the area

Answers

The formula for area is l(w). This stands for length and width, or long and wide in this problem. I can multiply 1000(100) to get 100,000m. The area of the lawn is 100,000m.

Step-by-step explanation:

The formula for area is l x b. This stands for length and breadth. I can multiply 1000(100) to get 100,000m. The area of the lawn is 100,000 m.

HOPE IT HELPS YOU

MARK ME BRAINLIEST

A piece of fabric 20m long sew 4/5 of that cloth, the rest of the fabric is sewn for each bag 2/3m, how many bags can be sewn in all?

Answers

Answer: 16 bags

Step-by-step explanation:

(20) (4/5) = 16

(16) (3) / 2 = 24

pls help its a optional math question
Find the length of a pendulum which describes an arc of 33cm when it turns through and angle 27º. ​

Answers

Answer:

70cm

Step-by-step explanation:

33=27/360*2*22/7*r

33*2520/1188=r

83160/1188=r

r=70cm

hope it's right

help please ASAP!!! Got a lot of math to do here comes an all nighter :(

Answers

Answer:

110

Step-by-step explanation:

2 ( wl+hl+hw ) = 2 (7·1+6·1+6·7 ) = 110

Here Enjoy :)

Will Mark Brainlest helpppp plssss​

Answers

Answer:

C = [tex]\left[\begin{array}{ccc}-2&-4\\-1&1\\\end{array}\right][/tex]

Step-by-step explanation:

A = B+ C then

C = A - B

C = [tex]\left[\begin{array}{ccc}2&-5\\-1&4\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&-1\\0&3\\\end{array}\right][/tex] (subtract corresponding elements )

   = [tex]\left[\begin{array}{ccc}2-4&-5-(-1)\\-1-0&4-3\\\end{array}\right][/tex]

   = [tex]\left[\begin{array}{ccc}-2&-4\\-1&1\\\end{array}\right][/tex]

hlpppppppppppppppppppppppppppppppp

Answers

Answer:

c

Step-by-step explanation:

-7.5 is less than 6.5

HELP ME PLS ITS URGENT

Answers

Answer: -3 (option D) is the answer.

(-8)-(-5)= -8+5 = -3

Answer:
-3
Explanation:
= (-8)-(-5)
= -8+5 (- and - is equal to +)
= -3
So the correct answer is D)-3
YOUR WELCOME☺️⭐️

the difference of 8 and 3 is multiplied by one quarter of the sum of 7 and 5​

Answers

Answer:

15

Step-by-step explanation:

the difference of 8 and 3 : 8-3 = 5

sum of 7 and 5 : 7+5 = 12

a quarter of that sum : 12/4 = 3

the difference from before is now multiplied by that quarter : 5 × 3 = 15

I know, you are a beginner, but you don't know basic arithmetic calculation of +, -, × , / ? really ?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The solution of the difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 is 15.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The statement can be solved as shown below,

1.   The difference between 8 and 3,

     8 - 3 = 5

2.   The difference between 8 and 3 is multiplied by one-quarter of the    sum of 7 and 5,

    ​[tex](8-3) \times \dfrac{(7+5)}{4}\\\\= 5 \times \dfrac{12}{4}\\\\= 15[/tex]

Hence, the solution of the difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 is 15.

Learn more about Multiplication:

https://brainly.com/question/14059007

#SPJ2

x^3+(y+z)^3 factorise it broefly.​

Answers

Answer:

x^3 + y^3 + z^3

Step-by-step explanation:

x^3+(y+z)^3

Remove brackets

x^3 + y^3 + z^3

The sides of an equilateral triangle measure 0.2(10x+90)cm each. If the perimeter of the triangle is 612.6 cm, what is the side length?


Write the equation to solve the problem.


Solve for x


Find the side of the triangle

Answers

Answer:

204.2 cm

Step-by-step explanation:

equilateral means all sides are of equal length.

the perimeter of such a triangle is simply 3 times one of these sides.

so,

612.6 = 3×0.2×(10x + 90) = 0.6×(10x+90) = 6x + 54

6x = 558.6

x = 93.1

so, a single side is

0.2×(10×93.1 +90) = 0.2×(931 + 90) = 0.2×1021 = 204.2 cm

to check

3×204.2 = 612.6 = the original perimeter.

so, correct.

Pears cost 38p how much for 15 pears?

Answers

Answer:

if pears cost 38p

then 15=15×38

=570p

If onee moderator was typing why this website is bad every 20 minutes and the other was trying to update this site every 30 minutes by what time will the one updating the site find out about the insults

Answers

Answer: 60 minutes or 1 hour.

Step-by-step explanation:

Since one moderator was typing every 20 minutes while the other moderator was typing every 30 minutes, then the time the other one will find about the insult simply means that we should find the lowest common multiple of 20 and 30. This will be:

20 = 20, 40, 60, 80, 100, ..

30 = 30, 60, 90, 120 .....

Here, we can see that the lowest common multiple is 60. Therefore, the other one will find about the insults in 60 minutes.

Cual es la respuesta 5%9(12-32)

Answers

Answer:

i need more detail

Step-by-step explanation:

PLEASE HELP!!! I dont understand

Answers

Answer:

x^4+x^2+5

Step-by-step explanation:

f(x) = x^2 -3x+7

g(x) = x^2+2

f(g(x) =  Place g(x) in for x in the function f(x)

       = (x^2+2)^2 -3(x^2+2) +7

FOIL and Distribute

       = x^4 +2x^2+2x^2 +4 - 3x^2 -6 +7

Combine like terms

    = x^4+x^2+5

Problema de Matematicas En una fábrica de papel se han elaborado, 238 942 rollos de papel higiénico, 763 924 rollos de papel toalla y 73 947 rollos de servilletas, del total de rollos se vendieron 875 394 rollos la cantidad de rollos que faltan por vender son.

Answers

Answer:

Se faltan por vender 201,419 rollos.

Step-by-step explanation:

Total de rollos:

238 942 rollos de papel higiénico

763 924 rollos de papel toalla

73 947 rollos de servilletas

Entonces:

[tex]T = 238942+763924+73947 = 1076813[/tex]

Se vendieron 875 394 rollos la cantidad de rollos que faltan por vender son?

Total subtraído por la cuantidad vendida. Entonces:

[tex]V = 1076813 - 875394 = 201419[/tex]

Se faltan por vender 201,419 rollos.

Help memememememe please

Answers

Answer:

good evening good evening good evening good evening

Step-by-step explanation:

w

Answer:

∠b = 54°

they add up to 180

7x + 14 + 5x - 26 = 180

12x = 192

x=16

thus ∠b = 54°

Step-by-step explanation:

Identify the vertex of this absolute value function: f(x) = -2|x + 1| + 2. Type the correct answer in each box. Use numerals instead of words.

Answers

Answer:

Step-by-step explanation:

x+1=0

then f(x)=2

x=-1

vertex is (-1,2)

Answer:

-1,2

Step-by-step explanation:

Plato

easy algebra question below first correct answer gets brainliest

Answers

Answer:

Y = 27

Step-by-step explanation:

To find the the value of y when x = 4 simply substitute the given value of x

into the equation and solve for y

Equation given: y - 3x = 15

x = 4 * substitute 4 for x in given equation *

y - 3(4) = 15

Now solve for y

simplify multiplication

y - 12 = 15

Add 12 to both sides

y - 12 + 12 = 15 + 12

y = 27

So we can conclude that when x = 4 y = 27

Answer:

y = 27

Step-by-step explanation:

y - 3x = 15

Let x = 4

y - 3(4) = 15

y - 12 = 15

Add 12 to each side

y -12 +12 =15+12

y = 27

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