11. Write y = 2x² +12x+14 in vertex form.

Please show work if possible so I know how to do it

Answer:

[tex]g(x) = |x-3|[/tex]

Step-by-step explanation:

We are given the parent function:

[tex]f(x) = |x|[/tex]

And we want to find the equation after a reflection in the y-axis followed by a translation of three units right.

To reflect a function over the y-axis, we multiply the input by a negative. That is:

[tex]\displaystyle f(x) \rightarrow f(-x)[/tex]

In other words, a reflection over the y-axis will be given by:

[tex]f(-x) = |-x|[/tex]

To shift horzontally, we add if we are moving leftwards or subtract if we are moving rightwards. That is:

[tex]f(x) \rightarrow f(x-k)[/tex]

Where k is the horizontal translation.

Since we are translating three units rightwards, k = 3. Hence:

[tex]\displaystyle f(-(x-3)) = |-(x-3)|[/tex]

Recall that |ab| = |a||b|. Hence:

[tex]\displaystyle f(-(x-3)) = |-(x-3)| = |-1||(x-3)| = |x-3|[/tex]

Hence, f reflected over the y-axis followed by a translation of three units right is given by:

[tex]g(x) = |x-3|[/tex]

Answer:

D. F-1(x) = 3x + 6

Brainliest, please!

Step-by-step explanation:

y (F(x)) = 1/3x - 2

x = 1/3y - 2

x + 2 = 1/3y

y (F-1(x)) = 3x + 6

Answer:

your answer should be D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter = 2W +  2L

160 = 2W + 2L

width = 16 feet less than length

W = L - 16   ------------(I)

Finding the dimensions of the court:

2W + 2L = 160

2*(L-16) + 2L = 160       {from (I) }

2*L - 2*16 + 2L = 160     {Distributive property}

2L - 32 + 2L = 160

2L + 2L - 32 = 160         {Combine like terms}

4L - 32 = 160              {Add 32 to both sides}

4L = 160 +32

4L = 192         {Divide both sides by 4}

L = 192/4

L = 48

W = 48 - 16

  W = 32

Answer:

20 is the mean length of rainbows

Answer:

12,04

Step-by-step explanation:

17^2 - 12^2 (pythagoras theorem)

=145

=square root of 145

=12.04 (rounded off)

Answer:

x=4±sqrt(17)

Step-by-step explanation:

x^2+4=8x+5

x^2-8x-1=0

Use quadratic formula

x=(8±sqrt(64+4))/2

Simplify it

x=4±sqrt(17)

Answer:

-12.8

Step-by-step explanation:

Replace the letters with the respective values ( a = 4, b = 2, c = 3).

So (-3a+4b)^3 would become (-3 (4) + 4 (2))^3 = (-12 + 8)^3 = -4^3 = -64

And the bottom part (2c -1) would become (2 (3) - 1) = 6-1 = 5

So the final result would be -64 / 5 which is approximately -12,8

Answer:

1500

Step-by-step explanation:

Basically 5*3 then add the two zeroes. One from 50 and 30.

Hello :D

2 x $4.52 = $9.04

$9.04 + $11.47 = $20.51

2 x $20 = $40.00

$40.00 - $20.51 = $19.49

With change:

$40.00 + $7.72 = $47.72

$47.72 - $20.51 = $27.21

Answer:

here you go mate.

These are the solutions

Answer:

Step-by-step explanation:

buenas tardes .....

solucion

Volumen de un cilindro: es igual al área de la tapa por la altura del mismo

A = πD² * h / 4

Lata grande y lata pequeña

Para la lata grande, el diámetro y la altura han aumentado un 20%.

Lata pequeña:

d = 4 cm

h = 3 cm

A 1 = π * (4) ² * 3/4

A1 = 37,70 cm²

Lata grande:

d = 4 * 1,2 = 4,8 cm

h = 3 * 1,2 = 3,6 cm

A2 = π (4,8) ²3,6 / 4

A2 = 65,14 cm²

Si 37,7 representa el 100%

  65,14 representación x

x = 170%

El incremento del volumen es de un 70%

Answer:  Area = 16*pi m^2

               Circumference = 8*pi

Step-by-step explanation:  The circumference and area of a circle are given by:

Area = pi*r^2

Circumference  = 2 pi*r

Radius = Diameter/2, or 4 meters (m)

Area = 16*pi m^2  (50.27 m^2)

Circumference = 8*pi  (25.13 m)

Answer:

[tex]x - 3(x + 2) > 4 \\ x - 3x - 6 > 4 \\ - 2x > 4 + 6 \\ - 2x > 10 \\ x = 10 \div ( - 2) \\ x = - 5[/tex]

Answer:

x=2, y=2

Step-by-step explanation:

3x + y = 8

2x + 4y = 12

Multiply the first equation by -4

-12x -4y = -32

Then add to the second equation

-12x -4y = -32

2x + 4y = 12

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

-10x + 0y = -20

-10x = -20

Divide by -10

-10x/-10 = -20/-10

x =2

Now find y

3x+y = 8

3(2)+y = 8

6+y = 8

y = 8-6

y =2

Answer:

[tex]\huge\boxed{\sf Solution Set = \{(2,2)\}}[/tex]

Step-by-step explanation:

3x + y = 8 ----------------------(1)

2x + 4y = 12 -------------------(2)

Multiply Eq. (1) by 4

4(3x+y) = 8*4

12x + 4y = 32 -----------------(3)

Subtract Eq. (3) from (2)

2x + 4y - (12x + 4y) = 12 - 32

2x + 4y - 12x - 4y = -20

2x - 12x = -20

-10x = -20

Divide both sides by -10

x = 2

Put x = 2 in Eq. (1)

3(2) + y = 8

6 + y = 8

Subtract 6 to both sides

y = 8 - 6

y = 2

Solution Set = {(x,y)} = {(2,2)}

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

Among all shapes with the same area, a circle has the smallest/shortest perimeter.

Answer:

Step-by-step explanation:

x² + 16x + 9 = - 3

x² + 16x + 12 = 0

D = 16² - 4(1)(12) = 208

√D = 4√13

[tex]x_{1}[/tex] = ( - 16 - 4√13 ) ÷ 2 = - 8 - 2√13 ≈ - 15.21

[tex]x_{2}[/tex] = ( - 16 + 4√13 ) ÷ 2 = 2√13 - 8 ≈ - 0.79

Answer:

5.5

Step-by-step explanation:

3x + 15 - 7x = -7

-4x + 15 = -7

-4x = -7 -15

-4x = -22

x = -22/-4 = 5.5

Answer:

a=2 b=3

Step-by-step explanation:

all you'll gat in pic

Actual perimeter:-

[tex]\\ \tt\longmapsto 0.251\times 1000[/tex]

[tex]\\ \tt\longmapsto \dfrac{251}{1000}\times 1000[/tex]

[tex]\\ \tt\longmapsto 251m[/tex]

Answer:

$40

Step-by-step explanation:

she owed $25 at first then she borrowed $15 so now she owed her $40.

25+15=40

Answer:

40

Step-by-step explanation:

Once you add 25 and 15

5+5=10

so you put the 1 over the 2 than add 2+1 and add 1 from the 10.

So the answer is 40

Answer:

(x - 4)³

Step-by-step explanation:

"The cube of x" would be x³.  The difference of a number and 4 would be x - 4.

Therefore, "the cube of the difference of a number and 4" would be

(x - 4)³

Answer: y = -1/2x

8(x - 2y) = 16x

8x -16y = 16x

-16y      = 16x-8x

-16y      = 8x

-16y/-16= 8x/-16

        y = -1/2x

Answer:

(-2,4)

Step-by-step explanation:

-2+6=4

Answer:

x = 7

Step-by-step explanation:

RT= RS+ST

70 = (7x +2 ) + (2x+5)

70 = 9x + 7

9x= 70 - 7

9x = 63

x= 63/ 9

x = 7

I hope I helped you^_^

Answer:

[tex]given \: that \: total \: length \: rt = 70 \\ \: then \: rs + st = rt \\ 7x + 2 + 2x + 5 = 70 \\ 9x + 7 = 70 \\ 9x = 63 \\ x = \frac{63}{9} \\ x = 7 \\ thank \: you[/tex]

Answer:

m is the slope so plug in y=6x+b

and b is the y intercept so the equation is y=6x+5

Step-by-step explanation:

-6a + 10 = -27

First step: subtract 10 from both sides:

-6a = -37

Now divide both sides by -6:

A = -37/-6

Simplify:

A = 37/6

Answer:

a = 37/6

Step-by-step explanation:

-6a +10 = -27

Subtract 10 from each side using the subtraction property of equality

-6a+10-10 = -27-10

-6a = -37

Divide each side by -6 using the division property of equality

-6a/-6 = -37/-6

a = 37/6

Answer:

60 km

"How long does it take to travel 30 minutes"... 30 Minutes !

If you want to know how FAR did it travel in 30 minutes then

that would be 60 km

Step-by-step explanation:

Answer:

60km

Step-by-step explanation:

distance= speed × time

=120×(30/60)

=60km