The function g(x) = (x + 2)2 + 4 is a transformation of the parent function f(x) = x2. Select all the statements that are true about the transformation.
A. Function g is the result of f being translated right 2 units and down 4 units.
B. Function g is the result of f being translated left 2 units and up 4 units.
C. The graph of function f opens upward.
D. The graph of function g opens downward.
E. The graph of function f is compressed by a factor of 2.

Answers

Answer 1

Answer:

Step-by-step explanation:

B

C

Answer 2

Using translation and parabola concepts, it is found that the correct options are:

A. Function g is the result of f being translated right 2 units and down 4 units.

C. The graph of function f opens upward.

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

The parent function is: [tex]f(x) = x^2[/tex]Function g is given by: [tex]g(x) = (x + 2)^2 + 4[/tex]Shifting a function f(x) a units to the right is the same as finding f(x + a).Shifting a function f(x) a units up is the same as finding f(x) + a.From the last two bullet points, option A is correct and option B is incorrect.In both functions, f and g, the term that multiplies [tex]x^2[/tex] is positive, thus, both open upward, which means that option C is correct and option D is incorrect.Both are multiplied by the same factor, 1, thus none are compressed, and option E is incorrect.

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Related Questions

Tara has 3/4 cup of ice cream. How many 1/5 -cup servings are in 3/4 cup of ice cream?​

Answers

Answer:

4/15

Step-by-step explanation:

because 1/5÷3/4=4/15

11037







































have fun figuring out what i mean

Answers

Answer:

????????????????????

Answer:

I think 11037 is a clue to tell what the murder is

Step-by-step explanation:

Is it correct? Please tell me I’m not sure lol I’ll give brainliest

Answers

you are correct
and omg i love your handwriting!

please answer i need help

Answers

Answer:

h < 2

Step-by-step explanation:

Given

5(2h + 8) < 60 ( divide both sides by 5 )

2h + 8 < 12 ( subtract 8 from both sides )

2h < 4 ( divide both sides by 2 )

h < 2

Answer:

h<2

Step-by-step explanation:

5(2h+8)<60

2h+8<12

2h<4

h<2

someone please help me with this! please write out the steps as well, thank you!

Answers

Answer:

60°

140°

Step-by-step explanation:

From the given figures,

 a. we use the concept of alternate angles.

   Two parallel lines cut by a transversal will have equal alternate angles;

  So;

       6x + 12 = 7x + 4

    collect like terms and solve for x;

     6x - 7x = 4 - 12

         -x = -8

         x = 8

Now, 6x + 12 = 6(8) + 12

                     = 48 + 12

                     = 60°

b. Here we use alternate angles and angles on a line;

     4x is an alternate angle to that angle to the left of 13x + 10

   

And sum of angles on a line = 180

    4x + 13x + 10 = 180

        17x = 170

          x = 10

Now,  13x + 10 = 13(10) + 10 = 140°

answer the question(s) will give brainliest if correct
---
thanks

for 2) please explain

Answers

Answer:

d=r*2

πtimes the diameter

Step-by-step explanation:

diameter is twice the radius

there is nothing like that

HELP WILL MARK YOU BRAINLIEST NO GUESSES PLZ!!!!

Answers

Answer: B 4,5

Step-by-step explanation:

Can someone explain how to find the slop and y-intercept?

Answers

Answer:

slope: 4/5

y-intercept: (0,4)

slope intercept form: y = 4/5 x + 4

Step-by-step explanation:

to find the slope, you have to find the difference of the x coordinants and the difference of the y coordinants. since the two coordinants we have are 0,4 and 5,0 and we know that 0 - 5 is -5 and 0 - 4 is -4 we then have to divide the two. so now we get -4/-5. since a negative divided by a negative is a positive, the negative signs cancel out. since the fraction is in simplest form, that is our answer. also, since its rise over run, it means that everytime you go up or down 4 and over 5, you will reach a whole number on the graph.

okay, now the y-intercept is when the line crosses the y-axis/when x=0. the y-intercept for this example would be 4 or (0,4). i hope that makes sense. like i said ill get back to you on the slope thing in a minute just a second...

Rasha and Scott went to a bakery. Rasha bought 4 plain bagels and 2 chocolate donuts for a total of $8.70. Scott
bought 3 chocolate donuts for a total of $2.55.
What is the cost of one plain bagel at the bakery?​

Answers

Answer:

Step-by-step explanation:

Let b = bagels , d = donuts

Rasha bought 4 plain bagels and 2 chocolate donuts for a total of $8.70

We can write this as :

4b + 2d = 8.70

Scott bought 3 chocolate donuts for $2.55

3d = 2.55

First, let's find out the cost of 1 donut.

To do this, divide 2.55 by 3.

1d = 2.55/3 =0.85  (1 donut costs $0.85)

Substitute the value of d ( d = 0.85 ) into the equation 4b + 2d = 8.70

4b + 2d = 8.70

4b + 2 (0.85) = 8.70

4b + 1.7 = 8.70

Subtract 1.7 from both sides.

4b = 8.70 - 1.7

4b = 7

Divide both sides by 4 to find how much one bagel costs.

b = 7/4 = 1.75

Therefore, one bagel costs $1.75

Make Sense and Persevere A submarine
descends to of its maximum depth. Then it
descends another of its maximum depth. If it
is now at 650 feet below sea level, what is its
maximum depth?

Answers

Answer: 325 feet

Explanation: you cut the amount of feet below sea level in half since it only depended twice. And you get 325

What percent of 462 is 851?

Answers

Answer:

It is 54.29%.

Answer:

54.29

Step-by-step explanation:

Percentage Calculator: 462 is what percent of 851? = 54.29.

A dolphin swam7 1/2 miles in 3/8 hour. what is its average speed in miles per hour?

Answers

Answer:

20 mph

Step-by-step explanation:

To find miles per hour you divide the number of miles by the number of hours

 

(7 1/2)/(3/8) = (15/2)(8/3) = 20 mph

The formula for the circumference, C, of a circle with radius r is given.

C=2pi

Amanda made a circular toy hoop using a plastic tube. The circumference of the hoop is 125.6 inches. What is the radius of the hoop? Use 3.14 for pi.

A.
80 inches
B.
10 inches
C.
20 inches
D.
40 inches

Answers

The formula for the circumference, C, of a circle with radius r is given.

C=2pi

Amanda made a circular toy hoop using a plastic tube. The circumference of the hoop is 125.6 inches. What is the radius of the hoop? Use 3.14 for pi.

The answer is
D.
40 inches

Find the equation perpendicular to y =1/2x - 3 and goes through the point (6, -3).

Answers

Perpendicular equations have opposite reciprocal slopes, so any equation perpendicular to the equation y = 1/2 x - 2 would have the slope -2.

Now plug in the point (6, -3) into the equation y = -2x + b to find out what b is.

-3 = -2(6) + b

Multiply -2 by 6.

-3 = -12 + b

Add 12.

9 = b

So the equation is y = -2x + 9

Hope this helps

Alejandra correctly wrote the equation y – 3 = y minus 3 equals StartFraction 1 Over 5 EndFraction left-parenthesis x minus 10 right-parenthesis.(x – 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

Answers

Answer:

y – 3 = 2(x – 10)

Step-by-step explanation:

Hope this helps!!!

If QR = 2x, RS = x + 7, and QS = 16, what is QR?
2x
R
x + 7
S
16

Answers

Answer: QR = 6 units

Step-by-step explanation:

QR + RS = QS

2x + x + 7 = 16

3x = 9

x = 3

QR = 2x = 2*3 = 6

On her first science test, Whitney scored a 92%. On the second test, she scored an 80%. What is the approximate percent of decrease in her score?

Answers

Answer:

Step-by-step explanation:

Decrease = 92 - 80 = 12

Percent of decrease in her score = [tex]\frac{12}{92}*100\\[/tex]

                                                       = [tex]\frac{1200}{92}\\[/tex]

                                                       = 13.04

                                                      = 13 %

Answer:

it would be a 12 percent

Step-by-step explanation:

Scottie has 3 dimes and 1 nickel. Kristin has 2 quarters. What percent of a dollar do they have all together?

Answers

Answer: 85%

Step-by-step explanation:  

It all adds up to a total of 85 cents, and since there are 100 cents in a dollar, 85 cents equals 85% of a dollar.

Hope that helps!

It took Jill two hours to drive 100 miles. What was her average speed?

Answers

Answer:

50 miles per hour

Step-by-step explanation:

Divide 100 by 2

50

Hope this helped :)

Factor completely 4p2 - 25q2 =

Answers

Answer: 2(4p - 25q)


Explanation: 4p*2 = 8p - 25q*2 = 8p - 50q = 2(4p - 25q)

Yumiko has a rectangular-shaped patio. She wants to double the area of the patio by increasing the length and the width by the same amount.
The length is 14 and the width is 10.

a. Write a function, in factored form, to calculate the number of feet Yumiko would need to add to the length and width.

b. What are the dimensions of the patio, rounded to the nearest hundredth feet?

I am not very good with completing the square and would like to understand it better. Any help would be very appreciated!

Answers

Answer:

For a rectangle of length L and width W, the area is:

A = L*W

In this case, we start with:

L = 14ft

W = 10ft

Then the initial area is:

A = 14ft*10ft = 140ft^2

a) Now she wants to increase the same amount in each measure, then the new measures will be:

L = 14ft + x

W = 10ft + x

Now we want this new area to be twice the one that we got before, then the equation will be:

(14ft + x)*(10ft + x) = 2*140ft^2 = 280ft^2.

b) Let's solve the equation:

(14ft + x)*(10ft + x) = 280ft^2

First lets distribute the multiplication:

140ft + x*10ft + 14ft*x + x^2 = 280ft

Now let's group terms with the same power of x.

x^2 + (10ft + 14ft)*x + 140ft - 280ft = 0.

x^2 + 24ft*x  - 140ft = 0.

Now we need to solve this quadratic equation, here we must use the Bhaskara equation for quadratic equations, and we will get two solutions for x.

[tex]x = \frac{-24ft +- \sqrt{(24ft)^2 - 4*140ft*1} }{2*1} = \frac{-24ft +- 33.7ft}{2}[/tex]

Then the two solutions are:

x = (-24ft - 33.7ft)/2 = -28.9 ft

This solution is negative, so it does not make sense and we can discard it.

x = (-24ft + 33.7ft)/2 = 4.85ft

This is positive, so we can use this.

Now we can find the new length and width:

L =  14ft + 4.85ft = 18.85ft

W = 10ft + 4.85ft = 14.85ft

If y = -5 when x = 2, find y when x = 8. *

Answers

Answer:

y=1

Step-by-step explanation:

you add how many you went to one side

Ally is interested in the following classes. She wants to know the total time for each class before she decides to sign up. Complete the table to show the total time for each class.

Answers

I need a table to solve this

If a diameter of a circle has endpoints (-3, 5) and (5, 7), then the center of the circle is

Answers

The center of the circle is (1,6)

Answer:

The midpoint formula is ( (x1 + x2)/2, (y + y2)/2 ) The answer will be an ordered pair.

(-7 + 5)/2, (3 + 1)/2

(-2/2, 4/2)

(-1, 2)

The center of the circle is at (-1,2)

Is 50/33 and 117% equivalent?

Answers

Answer:

no

Step-by-step explanation:because 117% would be 1.17  and 50/33 is 1.5151...

The fraction can be converted into percentage by multiplying it by 100. The given fraction is not equivalent to 117%.

What is percentage?

A percentage is a value that indicates hundredth part of any quantity.

To convert percentage into a fraction it is divided by 100.

The given fraction is 50 / 33

In order to check whether the given fraction is equal to 117%, convert the given fraction to percentage by multiplying it by 100 as follows,

(50 / 33) × 100%

=  50 × 3.33%

=  166.5%

Thus, the given fraction is not equal to 117%.

Hence, 50 / 33 and 117% are not equivalent.

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Water is steadily dripping from a faucet into a bowl. You want to write an equation that represents the number of milliliters y of water in the bowl after . What is the constant of proportionality for the relationship between the number of milliliters y of water in the bowl and the time in seconds​ x? What is the​ equation? Water from Dripping Faucet Time in Seconds​ (x) Milliliters in Bowl​ (y) 20 320 35 560 45 720 60 960

Answers

9514 1404 393

Answer:

k = 16y = 16x

Step-by-step explanation:

y is proportional to x when it satisfies the equation ...

  y = kx

where k is the constant of proportionality. The equation can be solved for k by dividing by x:

  k = y/x

The value of k for the given relation is ...

  k = (320 mL)/(20 s)

  k = 16 mL/s . . . the constant of proportionality

Then the equation is ...

  y = 16x

The post office is selling 7 cent stamps and 9 cent stamps. If a package requires 43 cents to mail, how many 9 cent stamps will you need?

Answers

4 9 cent stamps and 1 7 cent stamp

If a package requires 43 cents to mail, the number of 9 cent stamps that will be needed is 41cent  is the value needed.

What is meant by  mathematical equation?

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

Identify the question that is being asked. Write the pertinent details in straightforward statements. Give values that need to be discovered symbols. Find the mathematical connections between the assertions.

The most well-known equation in the entire universe is E=mc2. Just like that. It is succinct, elegant, and expresses a phenomenon that is so important that everyone should be aware of it.

Given,

The equation will be:

7x + 9y = 43

7(2) + 9(3) =41

14+ 27 = 41

Since the value that's is gotten not equal to 43  

Therefore  The value is  41 cent  is needed to 9 cent stamps

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I need helppp?!
What is the slope of the line??? Please give right answer :(((

Answers

the slope of the line is 2

Answer:

hello

Step-by-step explanation:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m.

m = slope

in a survey 8 out of 32 students preferred vanilla ice cream if 252 students are surveyed how many should theoretically prefer vanilla ice cream make a prediction?

Answers

Answer:

63

Step-by-step explanation:

8 / 32 = 0.25

Multiply 0.25 with 252

0.25 * 252 = 63

This process simply applies the same ratio from the first test to the second test.

6. Complete la tabla con el número 4.956: Dígito Valor posicional Notación estándar Notación en potencia De esta forma el número 4.956 puede escribirse como: 7. Fernando tiene 12 cuadrados de cartulina y Catalina tiene 16. Si ambos disponen sus cuadrados uno aliado del otro, ¿cuál de los dos niños puede formar un cuadrado? 8. Escriba las siguientes cifras como notación científica. Número: Notación científica: 45000000 0,000000000000056 0,000000000034

Answers

Answer:

6. Miles  [tex]{}[/tex]     cientos       decenas      unidades

  4   [tex]{}[/tex]              9                5               6

7. Catalina podrá hacer un cuadrado con longitud lateral de 4 cartones

8. 45000000 = 4.5 × 10⁶

0.000000000000056 = 5.6 × 10¹⁴

0.000000000034 = 3.4 × 10¹¹

Step-by-step explanation:

6. Los valores posicionales de dígitos son;

Miles  [tex]{}[/tex]     cientos       decenas      unidades

4   [tex]{}[/tex]              9                5                   6

 

7. El número de cuadrados que tiene Fernando = 12

El número de cuadrados que tiene Catalina = 16

El largo y el ancho de un cuadrado son iguales, por lo tanto tenemos;

largo × ancho = Área del cuadrado

largo = ancho = lado del cuadrado

Lado del cuadrado × Lado del cuadrado = Área del cuadrado

(Lado del cuadrado) ² = Área del cuadrado

Lado del cuadrado = √ (Área del cuadrado)

Para Fernando, Área del cuadrado = 12

Lado del cuadrado para Fernando = √12 = 2 · √3 cartones

Para Catalina, Área del cuadrado = 16

Lado del cuadrado para Catalina = √16 = 4 cartones

Por tanto, Catalina podrá realizar un cuadrado con longitud lateral de 4 cartones

8. 45000000 = 4.5 × 10⁶

0.000000000000056 = 5.6 × 10¹⁴

0.000000000034 = 3.4 × 10¹¹

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