What is the standard form of function f ?

What Is The Standard Form Of Function F ?

Answers

Answer 1

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

f(x) = 4(x + 6)² + 5

The above expression can be written as: f(x) = ax² + bx + c, by doing the following:

1. Expand (x + 6)²

(x + 6)² = (x + 6)(x + 6)

(x + 6)(x + 6)

x(x + 6) + 6(x +6)

x² + 6x + 6x + 36

x² + 12x + 36

(x + 6)² = x² + 12x + 36

2. Substitute x² + 12x + 36 for (x + 6)² in

f(x) = 4(x + 6)² + 5

This is illustrated below:

f(x) = 4(x + 6)² + 5

(x + 6)² = x² + 12x + 36

f(x) = 4(x² + 12x + 36) + 5

Clear bracket

f(x) = 4x² + 48x + 144 + 5

f(x) = 4x² + 48x + 149

Therefore, the standard of the function:

f(x) = 4(x + 6)² + 5

is

f(x) = 4x² + 48x + 149


Related Questions

15. Paul is scuba diving and is 3.5 feet below
sea level. He is descending at a rate of 0.5
feet per minute. If Paul is now at 12 feet
below sea level, how many minutes has he
been diving?

Answers

Answer:

24min.

Step-by-step explanation:

he descends 0.5 feet per min. Its just like counting by 2's. I hope this helped!!

Answer:

17 minutes

Step-by-step explanation:

This equation can be expressed as .5m+3.5=12 where m = minutes. I put this in a graphing calculator but to solve this you can

12-3.5=8.5

8.5/.5 = 17

Please answer this question now

Answers

Answer:

112°

Step-by-step explanation:

Arc CD is part of arc BCD, which is intercepted by the inscribed angle A.

Based on the inscribed angle theorem on circle, the sum of arc CD and CB is twice the measure of angle A.

That is:

CD + CB = 2(129°)

CD + 146 = 2*129

CD + 146 = 258

Subtract 146 from both sides to find CD

CD + 146 - 146 = 258 - 146

CD = 112°

piz help me!!!!

[tex]look \: at \: pic \: piz[/tex]

Answers

Here is my solution to this question worked out on paper:

please help will give you a 5 star rating

Answers

Answer:

3

Step-by-step explanation:

To find the average rate of change

f(0) - f(-2)

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

0 - -2

Taking the values for f(0) = 6 and f(-2) =0  

6 - 0

---------

0+2

6/2

3

Answer:

Slope I think its says, so: 3

Step-by-step explanation:

Take

6 = y2 , 0 = y1 , 0 = x2 , -2 = x1

y2 - y1 over x2 - x1

6-0

0+2 (because 2 is negative)

=

6/2

which reduced makes 3!

Hope this helps, and have a good day.

And for the 0 + 2:

its

0 - ( - 2 )

- ( - makes a big plus so add :)

s=(n(a_(1)+a_(n)))/(2)

Answers

Answer:

tokyo

Step-by-step explanation:

0.135 written as a fraction is _____.

27/200
5/37
27/100

Answers

Answer:

27/200

Step-by-step explanation:

To write 0.135 as a fraction you have to write 0.135 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 0.135 = 0.135/1 = 1.35/10 = 13.5/100 = 135/1000

Answer:

27/200

Step-by-step explanation:

your teacher tried to be tricky.

0.135 is simply 135/1000.

that is how you can express any finite decimal number.

anyway, now, we need to transform that fraction into one of the provided fractions. so, which one fits ?

with experience you see it right away. otherwise by simply trying.

in any case, the first option is the right one.

proof :

27/200 = 135/1000 ?

the denominator is our driver : what factor do I need to turn 200 into 1000 ? right, 5 ! 200×5 = 1000

so, we multiply numerator and denominator by 5 (it is important to do that for both, so that the value of the fraction does not change).

27/200 × 5/5 = (27×5) / (200×5) = 135/1000

and that is the proof. 27/200 is indeed 0.135

Gregg’s phone plan charges $.50 per text message plus $.70 a day. Howard’s plan charges $.30 a text plus $2.50 a day. For what number of texts, a day are the cost of the phone plans the same? Show work.

Answers

Answer:

x=9

Step-by-step explanation:

.5x+.7 = .3x+2.5

     -.7   -.3x

.2x=1.8

/.2    /.2

x=9

.5(9)+.7=5.2

.3(9)+2.5=5.2

Paul, a dentist, determined that the number of cavities that develops in his patient's mouth each year varies inversely to the number of seconds spent brushing each night. His patient, Lori, had 4 cavities when brushing her teeth 30 seconds each night. Write the equation that relates the number of cavities, c, to the time, t, spent brushing. How many cavities would Paul expect Lori to have if she had brushed her teeth for 120 seconds each night?

Answers

Answer:

Step-by-step explanation:

Inverse variation is written as

[tex]y=\frac{k}{x}[/tex] which, in words, says "y varies inversely with x". If cavities varies inversely with time brushing, then

[tex]c=\frac{k}{t}[/tex]

We are given the initial condition for which we need to solve for k:

c = 4 when t = 30:

[tex]4=\frac{k}{30}[/tex] so

k = 120.

Now we will use that value of k to solve the problem of how many cavities, c, would she have if she brushed her teeth 120 seconds, t, each night:

[tex]c=\frac{120}{120}[/tex] (the 120 on top is the k value and the 120 on the bottom is the number of seconds she brushed) to get

c = 1

Answer:

1 cavity

Step-by-step explanation:

The inverse equation is x*y=k, where x is the amount of cavities, y is the time brushed, and k is a constant number. In your scenario, x is c and y is t, but you can really use any name for the variable. In the first equation 23 have 4*30=120, which is just a constant number. now that we know our constant, we can plug is into our second equation, and we get c*120=120. By dividing both sides by 120, c=1. This means that Paul will have 1 cavity.

Can i please have help thanks.

Answers

Answer:

[tex] q = 2(3r + 8) [/tex]

Step-by-step explanation:

There are two variables, q and r in the expression given. To make r the independent variable, it simply means, make q the subject of the formula, so that variable q would be dependent on variable r. As r changes, q changes also.

Thus,

[tex] q - 10 = 6(r + 1) [/tex]

Open the parenthesis

[tex] q - 10 = 6r + 6 [/tex]

Add 10 to both sides

[tex] q - 10 + 10 = 6r + 6 + 10 [/tex]

[tex] q = 6r + 16 [/tex]

[tex] q = 2(3r + 8) [/tex]

trigonometric identities help

Answers

Answer:

5/13

Step-by-step explanation:

Sin = 12/13

cos= 5/13

Tan= 12/5

A circle has a circumference of 153.86153.86153, point, 86 units.
What is the radius of the circle?

Answers

Answer=24.49 I’m not 100% sure but I believe this is the answer :)
Hope it helps

Answer:

Step-by-step explanation:

C=153.86153...

100000C=15386153.86153...

subtract

99999C=15386000

C=15386000/99999

2 π r=15386000/99999

r=7693000/99999π≈24.5

Convert the following as a. 2 hours to second​

Answers

1. First convert hrs into min by multiplying 60

= 2 *60=120min

2. Then multiply 60 in 120 to convert it into seconds

120*60=7200 sec

MARK AS BRANLIEST.

please please please help me with this assignment :)

Answers

Answer:

$45.63

Step-by-step explanation:

[tex]50,145 cm^{3} * 2.6 g/cm^3 = 130,377 g\\130,377 g = 130.377 kg\\130.377 kg * $0.35/kg = $45.63\\[/tex]

or all together    

50,145 cm³  *  2.6 g/cm³ * 0.35/kg =  $45.63

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Answers

Answer:

Option C, 93.6 mi³

Step-by-step explanation:

Volume of the triangular prism,

(8×3.9/2)×6

= 93.6 mi³

What is the value of 1/4m +n 8 - 6 = 12 *​

Answers

Answer:

i dont know if you want me to solve for m

Step-by-step explanation:

Let's solve for m.

MP Find the Error Katrina states that
3.5 X 104 is greater than 2.1 x 106 because
3.5 > 2.1. Explain her mistake and correct it.

Answers

Answer:

3.5 X 10^4 < 2.1 x 10^6

Step-by-step explanation:

3.5 X 10^4 < 2.1 x 10^6

The first thing we look at is the exponent

10 ^4 is less than 10^6

10000 < 1000000

If the exponents are the same, then we look at the numbers out front

A poll of a registered voters is a small town is taken to determine their preferences in the national Presidential election. The results are then used to estimate the national vote. This sample is _______.
A. impartial
B. not representative
C. representative
D. unbiased

Answers

D is going to be your answer:)

Convert 7.5 gallons to quarts using a unit multiplier

Answers

Answer:

30 quarts

Step-by-step explanation:

4 quarts = 1 gallon

7.5 gallons * 4 quarts/ 1 gallon = 30 quarts

ANSWER QUICK !!
Yuri is participating in a tund-raiser at school. She will receive donations from 2 people. A cousin will donate $0.40 for every 1/8 mile that Yuri walks.
A friend will give Yuri a one-time donation of $30
What is the minimum number of miles Yuri needs to walk to raise at least $507 Enter the answer in the box,

Answers

507 - 30 =  477

477 / 0.4 = 1192.5

1192.4 / 8 = 149.0625 miles or 150 miles

i don't know if this is right cause the answer seems so absurd

△ABCis reflected to form​​ ​△A′B′C′​. The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). Which reflection results in the transformation of ​△ABC​​ to ​△A′B′C′​​? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x

Answers

Answer:

reflection across y = x

Step-by-step explanation:

Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.

If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)

If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)

If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)

If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)

The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form​​ ​△A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged

Answer:

reflection across y = x

Step-by-step explanation:

in a 10 team league, each teams play every other team exactly twice. find the total number of games played in the league

Answers

Since it’s a 10 team league and each team plays with the other team twice then 10+10=20, thus there would be 20 games played

Addition can be defined as the process of adding two numbers. The total number of games played in the league is 90.

What is Addition?

Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.

Given that in a 10-team league, each team play every other team exactly twice. Therefore, the total number of games that will be played by the first team is 18, similarly, the number of games that will be played by the second team is 16.

Therefore, as mentioned above the series will continue with a common difference of -2 and will continue till 0. Thus, the total number of games played in the league is,

Total number of games = 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 = 90

Learn more about Addition:

https://brainly.com/question/13167637

#SPJ2

2.2.4.4.4=
plzz help

Answers

Answer:

what is this question ??

This answer will also same 2.2.4.4.4=2.2.4.4.4

Pls help Q16 thx guys

Answers

Answer:

35°

Step-by-step explanation:

Extending line BC to point E on line AD

angle CED = 20° + 95°= 115°

ang|BCD|= ang|CED| + y

150°=115° + y

y= 150° - 115°

y= 35°

Answer:

y = 35°°

Step-by-step explanation:

∠BCD = 360 - 150 = 210°

Sum of angles of quadrilateral = 360°

210 + 20 + 95 + y = 360

325 +y = 360

Subtract 325 form both sides

y = 360 - 325

y =35°

find the surface area of each figure. Round to the nearest tenth if necessary.​

Answers

Answer: 318 km²

Let's find the areas of the triangles

Formula: base x height / 2

9 x 6 = 54

54/2 = 27

Multiply by 2 since there are two triangles (I know, we already got the areas from 9 x 6)

27 x 2 = 54

Now let's try to find the areas of all the rectangular sides

Formula: length x width

9 x 11 = 99

8 x 11 = 88

7 x 11 = 77

99 + 88 + 77 = 264

Add up all the areas

264 + 54 = 318

4/5x - 1/10 = 3/10
what is the value of x ?

Answers

Answer:

x = 1/2

Step-by-step explanation:

[tex]\frac{4}{5}x-\frac{1}{10}=\frac{3}{10}\\\\\mathrm{Add\:}\frac{1}{10}\mathrm{\:to\:both\:sides}\\\\\frac{4}{5}x-\frac{1}{10}+\frac{1}{10}=\frac{3}{10}+\frac{1}{10}\\\\\frac{4}{5}x=\frac{2}{5}\\\\\mathrm{Multiply\:both\:sides\:by\:}5\\\\5\times \frac{4}{5}x=\frac{2\times \:5}{5}\\\\4x=2\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4x}{4}=\frac{2}{4}\\\\x=\frac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

isolate variable

solve

Please help me on this question

Answers

Answer:

you need to add 11 red circles

Step-by-step explanation:

1:3     one red and three blues

r=12   b=3

r:b  =12:3

12:3 is the same as 4:1

you have to add 11 red circles

What is the value of x ?

Answers

Answer:

x = 3

Step-by-step explanation:

Given two secants drawn from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

x(x + 21) = (x + 1)(x + 1 + 14)

x² + 21x = (x + 1)(x + 15) ← expand using FOIL

x² + 21x = x² + 16x + 15 ( subtract x² + 16x from both sides )

5x = 15 ( divide both sides by 5 )

x = 3

Which is NOT a reasonable estimate?
A 683 + 431 = 1100
B 8236 X 387 = 3200
C 943 – 682 = 200
D 6247 + 312 = 20

Answers

D the answer to 6247 + 312 is not 20. The answer to that would be 6559 so I think D isn’t reasonable

how do you do this with always never one solution 3х – 12 = 4х + 3 is this true or never true​

Answers

3x - 12 = 4x + 3

3x - 4x = 3 + 12

-x = 15 / : (-1)

x = -15

Answer:

One solution

Step-by-step explanation:

3х – 12 = 4х + 3

3x - 4x = 3 + 12

-x = 15

x = -15

This is a one solution because x only equals 1 number.

Help me come up with a YT name plz. I’m looking for something that POPS, but I keep coming up with the same names/words.

Answers

ACEMaster52 u like that I made it up
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