the equation 3x^2-6x=8 is rewritten in a form of 3(x-p)^2+q=0.

Answers

Answer 1

Answer:

[tex]3(x - 1)^2 - 11= 0[/tex]

Step-by-step explanation:

Given

[tex]3x^2 - 6x = 8[/tex]

Required

Rewrite in form of [tex]3(x - p)^2 + q = 0[/tex]

[tex]3x^2 - 6x = 8[/tex]

Subtract 8 from both sides

[tex]3x^2 - 6x - 8 = 8 - 8[/tex]

[tex]3x^2 - 6x - 8 = 0[/tex]

Express -8 as 3 - 11;

So, we have:

[tex]3x^2 - 6x + 3 - 11= 0[/tex]

Expand [tex]3x^2 - 6x + 3[/tex]

[tex]3(x^2 - 2x + 1) - 11= 0[/tex]

Factorize the expression in the bracket;

[tex]3(x^2 - x -x + 1) - 11= 0[/tex]

[tex]3(x(x - 1) -1(x - 1)) - 11= 0[/tex]

[tex]3((x - 1)^2) - 11= 0[/tex]

[tex]3(x - 1)^2 - 11= 0[/tex]

By comparison: [tex]3(x - p)^2 + q = 0[/tex]

[tex]p= 1[/tex]

[tex]q = -11[/tex]


Related Questions

PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!
Square TUVW with vertices T(-6,1), U(-1,0), V(-2,-5), and W(-7,-4):
(a) Reflection: in the y-axis (b) Translation (x,y) —> (x-5,y+7)
A. (4,7)
B. (-5,7)
C. (1,0)
D. (-4,7)

Answers

Answer:

093006570

Step-by-step explanation:

Rut ectjyvtjyhrjtjtj5j6

a point is ____
•imaginary
•real

Answers

Answer:

a point Is an imaginary line

Answer:

imaginary

Step-by-step explanation:

asking questions is super in this education life

Find the value of the expression below.
15 + 5 × 3
-------------- (fraction)
3² + 6

5
4
2

Answers

Answer:

2

Step-by-step explanation:

15 + 5 × 3

________

  3² + 6

For this question, we need to use PEMDAS to solve the question correctly. PEMDAS stands for "parentheses, exponents, multiplication, division, addition, subtraction". In this question, for the numerator, we see 5 x 3 so that's multiplication. So we multiply those together to get 15. In the denominator, there's an exponent which is 3². We have to find the square of 3 so that we can simplify the denominator as well. That simplifies to 9:

(15+15)/(9+6)

Next, we just have to add the 15+15 in the numerator together and 9+6 in the denominator together:

30/15

Finally, we divide 30/15 to get 2 as our answer

2

Plz help quick >_< What is the best estimate for 81.9 x 4.6?
O A) 100
OB) 360
OC) 400
OD 8,000

Answers

Answer:

B.

Step-by-step explanation:

When you multiply the two decimals you get 376.74 which is closer to 360 than 400

Answer:
it's b
Step-by-step explanation:
I took the test

Please help me!!!

Michael's parents doubled his pocket money. His sister paid $1 for ice-cream from her pocket money and he paid $3 of his poket money for an new toy. After making these payments, they have the same money left. If his sister's pocket money is $6, what was Michael's pocket money before doubling it?


1. How much money did they together have after making the payments?

2. How much money did Michael have after his pocket money was doubled. Find the value of x.

3. How much did Micheal's sister have before making the payment?

(ONLY THE ANSWER)

Answers

Answer:

x = $4

1. $10

2. $8

3. $6

Step-by-step explanation:

Let

Michael's doubled pocket money = 2x

He spends $3

Balance = 2x - 3

His sister's pocket money = $6

She spends $1

Balance = $6 - $1

= $5

2x - 3 = 5

2x = 5 + 3

2x = 8

x = 8/2

= 4

x = $4

After making the payments, they both together have $10

After Michael's pocket money was doubled, he has 2x

= 2(4)

= $8

His sister's has $6 before making the payments

Combine like terms

9w-w =

Answers

9w-w=8w because its 9 positive w plus 1 negative w

What is the growth of the rule y=3x+5 ?
Need a number answer

Answers

As I see the slope is 3 and the y-intercept is 5 so the graph would be x=0 then y=5 then the next x=1 and Y=8

here's the image for the question I have:

Answers

Answer:

c

Step-by-step explanation:

Answer:

C::10:15

Step-by-step explanation:

It is C because he had 15 hours of first aid and 10 hours of cpr and the question says CPR TO FIRST AID therefore the number of CPR training hours will come before the number of First Aid training hours. If it would have asked you to reduce the ratio it would have been 2:3 because you would have had to divide both sides by 5 resulting in the smallest possible ratio.

HOPE THIS HELPS YOU OUT!

12⁴x 9³ x 4
6³ x 8² x 27​

Answers

Answer:

12⁴ × 9³ x 4 = 60,466,176

6³ × 8² × 27 = 373,248

Step-by-step explanation:

You could use the expanded form to calculate the answer

12⁴ = 20,736

9³ = 729

4 = 4

20,736 × 729 × 4 = 60,466,176

6³ x 8² x 27​

6³ = 216

8² = 64

27 = 27

216 × 64 × 27 = 373,248

Hector had $98.70. He spent $52.67 for school clothes. How much money does Hector have left?

Answers

Answer:

$46.03

Step-by-step explanation:

Answer: A) $ 46.03

Step-by-step explanation: I took away $98.70 and $52.67 and I got A as answer :)

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

need answer asap Whole numbers: ___ + ___ + ___ = _____ cups of soup mix.

Answers

Answer:

1+2+3=6 lol jk i dont have the numbers that they gave you

Step-by-step explanation:

1) What is the VERTEX of the Quadratic Graph below?*

Answers

( 0, -4 ) is the vertex of the parabola

A concert organizer learned from a market survey that when the admission price is $30, there is an average attendance of 800 people. For every $1 drop in price, there is a gain of 20 customers. Each customer spends an average of $5 on concessions. The concert hall has 1,000 seats.

Answers

Answer:

[tex]\mathbf{ P =D(x)= 70 -\dfrac{ x}{20}}[/tex]

Step-by-step explanation:

From the information given :

The objective is to find the demand function which is expressed in p, the price in dollars charged for each ticket, as a function of x, and the number of average attendance is:

Suppose the admission price P = D(x) = 30 and number of average attendant = x = 800 people

Then:

ΔP = -1

Δx = 20

[tex]\left \{ \dfrac{\Delta x}{\Delta P }= -20 }}\ \right.[/tex]

According to point line form :

[tex]\dfrac{\Delta x}{\Delta P }= -20[/tex] where the point is (30, 800)

x - 800 = -20 (P - 30)

x - 800 = -20P + 600

collect like terms

x + 20P = 800+ 600

x + 20P = 1400

x = 1400 - 20P

[tex]\mathsf{ P = 70 -\dfrac{ 1}{20}x}[/tex]

Thus, price in dollars for each ticket P = D(x) is:

[tex]\mathbf{ P =D(x)= 70 -\dfrac{ x}{20}}[/tex]

[tex]\frac{x^{2} }{3x^{2}+8x-3 } divided \frac{x-3}{x+2}[/tex]

Answers

Answer:

ddsdvffgdf gddccd fddf

En la figura, la suma de las medidas p + q + r + s =/In the figure, the sum of the measures p + q + r + s =

And if someone know the explanation please write it​

Answers

Answer:

I think its 300

Step-by-step explanation

This is from my understanding, so I may be a bit wrong.

1. First observe the amount of triangles that form, you have two main triangles and one isosceles triangle that forms in the middle by how these are joined together.

2. Using this idea we will come up  with the equations of  each triangle that has been formed.

3. We can observe that almost all angles are named with a variable except the one in the middle, being an isosceles we will name the missing variable y.

4. Triangle 1(left side) or T1 equals 180 degrees but what angles form this triangle, these would be p+q+y = 180, T2(right side) = r+s+y = 180

5. After creating these two triangles we notice that we have not taken into account the triangle in the middle, we are given 1 angle of this isosceles. There is a mathematical property which I don't remember the name, but essentially the angle below is the same as the angle above, this being 120 degrees. This will result in T3 = 2y + 120 = 180

6. Solve for y, which gives us y=30, *simple triangle math you know*

7. Finally we fix our equations for p+q+r+s, essentially T1 and T2 will transform into p+q = 180-y and r+s = 180-y, we add them up forming p+q+r+s = 2(180-y)

8. Solve the equation p+q+r+s = 360 - 2y which when adding y becomes p+q+r+s = 360-60 = 300

Notes: when doing these exercises it is important to take into account every triangle, the isosceles triangle is very vital for solving it, as it gives us a way for making an equation that is single handedly dependent on y a constant we can find and use. A good approach for these issues would be writing every piece of information as separate sets and then trying to join them using algebra.

Is the following figure a parallelogram? Why?
P
O No, opposite angles are congruent.
O Yes, opposite sides are congruent.
O No, opposite sides are congruent.
O Yes, opposite angles are congruent.

Answers

Yes because opposite sides are congruent

The annual gas bill for a town household are considered to be normally distributed with a mean of $ 1130 and a standard deviation of $ 150. If one household is randomly selected, what is the probability that the gas bill will be between $900 and $1100?

Answers

Answer:

The probability is  [tex]P(900 < X < 1100) = 0.358102[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 1130[/tex]

    The standard deviation is  [tex]\sigma = \$ 150[/tex]

   

Generally the probability that the gas bill will be between $900 and  $1100 is mathematically represented as

      [tex]P(900 < X < 1100) = P(\frac{900 - 1130 }{150 } < \frac{X - \mu}{\sigma } < \frac{1100 - 1130 }{150 } )[/tex]

=>  [tex]P(900 < X < 1100) = P(-1.533 < \frac{X - \mu}{\sigma } < -0.2 )[/tex]

Generally [tex]\frac{X - \mu}{\sigma } = Z (The\ standardized \ value \ of \ X)[/tex]

So

    [tex]P(900 < X < 1100) = P(-1.533 < Z< -0.2 )[/tex]

   [tex]P(900 < X < 1100) = P( Z< -0.2 ) - P(Z < -1.533)[/tex]

From the z  table  

     [tex]P(Z < -0.2 ) = 0.42074[/tex]

and

     [tex]P(Z < -1.533) = 0.062638[/tex]

So

     [tex]P(900 < X < 1100) = 0.42074 - 0.062638[/tex]

=> [tex]P(900 < X < 1100) = 0.358102[/tex]

Given g(x)=-x-1, find g(-4)

Answers

Answer:

g(-4)=3

Step-by-step explanation:

g(x)=-x-1

g(-4)=-(-4)-1

g(-4)=4-1

g(-4)=3

Answer:3

Step-by-step explanation:

(x2 – 2x – 2)(3x2 - 4x +4)

Answers

Answer:

10-4x

Step-by-step explanation:

The answer to the equation is 10-4x

A toy company manufactures sealed cubes that contain a colored liquid that glows in the dark. The liquid completely fills the cubes. If 8 cubic blocks with a side length of m are needed to find the volume of each cube, how much of the liquid can each cube hold?

Answers

Answer:

[tex]Volume = 8m^3[/tex]

Step-by-step explanation:

Given

[tex]Cubes = 8[/tex]

[tex]Length = m[/tex] for each

Required

Determine how much all cubes can hold

First, we need to determine the volume of each.

[tex]Volume = m * m * m[/tex]

[tex]Volume = m^3[/tex]

For the 8 cubes, we have:

[tex]Volume = 8 * Volume\ of\ 1[/tex]

[tex]Volume = 8 * m^3[/tex]

[tex]Volume = 8m^3[/tex]

A poll conducted the day before the student- body presidential election at a midwestern university showed that 53.9 percent favored Mario, the rest favoring Yin Ling. The margin of error was 4.2 percentage points. Should Yin Ling have conceded the election?

Answers

Answer:

No

Step-by-step explanation:

The confidence interval of the percentage of people that favored Mario = number of votes favoring Mario ± Margin of error

The confidence interval = 53.9% ± 4.2% = (49.7%, 58.1%)

This means that between 49.7% to 58.1% of the people would have voted for Mario.

Hence Yin Ling would not have won the election, since there is a probability that 50% would have voted for Mario

Solve for v

-39v=4v+7(v+7)

Answers

Answer:

-49/50

Step-by-step explanation:

-39v=4v+7(v+7)

Distribute

-39v = 4v +7v+49

Combine like terms

-39v = 11v+49

Subtract 11 v from each side

-39v-11v = 11v-11v +49

-50v = 49

Divide by -50

-50v/-50 = 49/-50

v = -49/50

Answer:

v= - 49/50

Step-by-step explanation:

-39v=4v+7(v+7)

open the parentheses by multiplying both v&7 by 7:

-39v=4v+7v+49

add like terms:

-39v-4v-7v=49

-50v=49

divide both sides by -50:

v= - 49/50

-4 = - 17 + x linear equations

Answers

add 17 to both sides

13 = x

hope this helps

See attachment for math work and answer.

Two equations are shown: I will give 40 pts if someone answers


Equation 1: (x – 12) = 12

Solve each equation.

Answers

Answer:

x and y both equal 24

Which expressions are equivalent to 46 ?

Answers

Answer:

frus

ggyfhhfgggdg the nearest whole number is the nearest whole thing that is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number is the nearest whole number of the nearest and the product of the nearest and we are all in this together to to 21211111111wwethkuff

I need help if you can.

Answers

Answer:

I cant see the equation that well, but i got 5/16

Step-by-step explanation:

Hope this helps!

Answer:

I got C) 1 and 1/4

Step-by-step explanation:

-0.5 + 0.75 = 0.25

1/5 = 0.20

0.25 divided by 0.20 would be over 1 because a fraction divided by another fraction brings the number while a whole number divided by a fraction would bring the number down.

0.25 divided by 0.20 = 1.25

The cost of parking a car in an hourly lot can be represented by the following equation y = 3x + 2 What does the 3 tell you about the cost of parking?

A) The hourly rate is $3

B) You can only park for 3 hours

C) There is a $3 fee to park

D) it costs 5 dollars to park all day​

Answers

Answer:

A

Step-by-step explanation:

The three represents the amount it costs for each hour parked, and is continuous, which is a rate.

It’s A ... sorry if I’m wrong

write the sentence as an equation.241is the same as 364 fewer than f​

Answers

Answer:

241 = f - 364

Step-by-step explanation:

The answer is 241 = f - 364

Have a nice day / night! :)

Please help me with this. This is my last one and when you are answering PLEASE SHOW STEPS FOR BRAINSLT. THIS IS DUE TOMORROW

Answers

X= -2

Explanation: the photos are in order :)

Answer:

x = -2

Step-by-step explanation:

3/5 +3/10x = 4/5 + 2/5x

Step 1. Change every fraction into the same denominator

6/10 + 3/10 x = 8/10 + 4/10x

Step 2. Subtract 3/10x

6/10 = 8/10 + 1/10x

Step 3. Subtract 8/10

-2/10 = 1/10x

x = -2

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