Find the constant a, P and Q such
that 3x²-12x+16=a(x+p) +q​

Answers

Answer 1

Answer:

Step-by-step explanation:

Rewrite 3x²-12x+16 as follows:

3(x^2 - 4x) + 16

Complete the square of x^2 - 4x; it is (x - 2)^2 - 4.  We then have:

3( (x - 2)^2 - 4) + 16, or:

3(x - 2)^2 - 12 + 16, or

3(x - 2)^2 + 4

Then a = 3, p = -2 and q = 4

********************************************************************

Completing the square of x^2 - 4x is done as follows:

1.  Identify the coefficient of x:  It is -4.

2.  Take half of this result:  It is -2

3.  Square this, and then add the square to x^2 - 4x, and then subtract it:

    x^2 - 4x = x^2 - 4x + 4 - 4

4.  Rewrite this result in the form (x - a)^2 - c:

    (x - 2)^2 - 4  

5.  Now follow the remainder of the problem solution (given above)


Related Questions

Two boats are traveling toward a cliff that is 225 feet above sea level. When the two boats are exactly 200 feet apart, the boat closest to the cliff has an angle of elevation to the top of the cliff of 36 degree, as shown.

Answers

Answer:

[tex]x=23.82^o[/tex]

Step-by-step explanation:

[tex]Solve ~for~x, first ~ we~ need ~ to ~know~y[/tex]

[tex]tan~36=\frac{225}{y}[/tex]

[tex]y=\frac{225}{tan ~36}[/tex]

[tex]y=309.6859321[/tex]

[tex]tan(x)=\frac{225}{y+200}[/tex]

[tex]x=tan^{-1}(\frac{225}{309.6858321}[/tex]

[tex]x=23.81898048[/tex]

[tex]x=23.82^o[/tex]

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

hope it helps...

have a great day!!

23.82° is derived as the value of x according to nthe diagram shown.

What is Angle of elevation?

This is referred to the angle from the horizontal upward area to an object.It is measured in degrees.

36 = 225/y

y = 225/tan 36

  = 309.686.

tan(x) = 225 / y+200

x = tan -1 (225/309.686)

x = 23.82

Read more about Angle of elevation here https://brainly.com/question/88158

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Please help me on this :/

Answers

Answer:

4. obtuse

5. right

6. obtuse

6. acute

Step-by-step explanation:

4. not a triangle, 2+4 = 6

5. 100 + 576 = 26^2 -> right

6. 8, 16 < 36 -> obtuse

7. 43.6 > 42.25 -> acute

3. A mysterious metal medallion has a mass of 3,088 grams. Water is poured into a graduated glass container with a 10-by-10 cm square base with a water level of 53.0 cm. The medallion is dropped into the container and the water level rises to 54.6 cm. Find the volume and the density of the​

Answers

Answer:

Initial volume:

10*10*53 = 5300 cm³

Increased volume:

10*10*54.6 = 5460 cm³

Volume of the medallion:

5460 - 5300 = 160 cm³

Density = mass / volume

Density is:

3.088/160 = 19.3 g / cm³

1. Combine the like like terms
14 + 8x + 2y -5x - 2

Answers

Answer:

12 + 3x + 2y

Step-by-step explanation:

14 + 8x + 2y -5x - 2

14 + -2 + 8x -5x + 2y

12 + 3x + 2y

Answer:

3x + 2y + 12

Step-by-step explanation:

In the photo.

what is the perimeter of the triangle?

Answers

Answer:

the picture is messed up

Step-by-step explanation:

Answer:

34?

Step-by-step explanation:

P=a+b+c=10+12+12=34

Anne-Marie bought a new couch at Buykea for $225. She used a 20% off coupon in her purchase. What was the original price of the couch?

Answers

Answer:

$270

Step-by-step explanation:

20% of 225 is 45. So, 225+45=270

From a group of 5 counselors and 8​ teachers, 3 counselors and 2 teachers will be selected to attend a conference. In how many ways can the selection be​ made?
A.
38
B.
3360
C.
280
D.
240

Answers

It would probably be A

NEED HELP ASAP
NO LINKS AND NO JUST SAYING HI, PLEASE ANSWER LEGITIMATELY! THANK YOU!!!! <3

Answers

Answer:

x=42.5

Step-by-step explanation:

First, start by setting up the equation

these are both same side interior angles, so they both add up to 180

(3x+10) + x = 180

4x+10 =180

subtract both sides by 10

    -10    -10

4x=170

divide both sides by 4

x=42.5

ASAP

Just the answer pls

Answers

Answer:

D

Step-by-step explanation:

An isosceles triangle has an angle that measures 26°. Which other angles could be in that
isosceles triangle? Choose all that apply.

Answers

Answer:

26° 26° 128°

77° 77° 26°

Step-by-step explanation:

So we have two scenarios here.

One of them is if the base angles are 26°.

If that's true, the other angle is 128°

The other scenario is the opposite.

This means the base angles are 77°

An office manager spent $4870 on a
total of 14 chairs and desks. Each chair
costs $125, and each desk costs $515.
How many chairs and how many desks
did he buy?

Answers

Answer:

6 chairs

8 desks

Step-by-step explanation:

First, we assume that all 14 items he bought were chairs, if that was to be true then the office manager would spend...

125 x 14 =  1750$

We see that he spent less then he should have so now we start to substitute desks instead of chairs, and we have to keep in mind that if we change 1 chair to a desk then the total will increase by...

515 - 125 = 390$

Now we just find the difference between the needed total and the total that we get if the office manager would by only chairs and then divide the result by 390 in order to find the number of desks, and so we get...

(4870 - 1750) / 390 = 3120 / 390 = 8 desks

And now that we know the number of desks we just subtract the number of desks from 14 and get the number of chairs, and so...

14 - 8 = 6 chairs

ILL BRAINLIEST YOU PLEASE HELP ME

Answers

Answer:

D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hope it helped :) If you need a explantion step by step then tell me.

Gregg deposits the money he makes from mowing lawns into his
savings account, adding it to the money his father gave him to
open the account.
Lawns
Mowed
Money
Saved
5
110
10
170
15
230
20
290
What is the slope and y-intercept of the table?
A.
Slope: -12, y-intercept is -50
B
Slope: 50, y-intercept is 12
C.
Slope: 12, y-intercept is 50
D.
Slope: 50, y-intercept is -12

Answers

Answer:

c

Step-by-step explanation:

c

Which of the following sets of angle measurements determines a triangle? Select all that apply.
60, 80
90, 110
70, 90
100, 80
50, 70

Answers

Answer: 70,90 is the measurements determined

find the value of x. round your answer to the nearest tenth.

Answers

Answer:

x = 56.7

Step-by-step explanation:

cos theta = adjacent/hypotenuse

cos x = 17/31

x = arccos(17/31)

x = 56.7

what can 16 and 4 both be divided by​

Answers

Answer: They can both be divided by 4, 2, and 1

Answer:

1, 2 and 4

explanation:

16/1, 16/2, 16/4

4/1, 4/2, 4/4

/=division sign

You just got an order of 8 apples and you need to break them up accordingly:

25% of the apples should be baked into a pie
25% of the apples should be baked into a tart
37.5% of the apples will be used for juice
you may eat the remaining apples. of?

Answers

Answer:

⟟ got 12.5 remaining

Step-by-step explanation:

Just add all the percentages then subtract from 100

plss help help help can someone plss help me
~plss respect my question~

I really need this right now so please​

Answers

Answer:

1) The stars are not constant in their position.

2) No. The stars aren't in original position because of apparent movement of stars in the sky.

3) Due to rotation of earth on its axis , the stars appear to move from west to east in the sky. Actually stars don't move as they are constant in their position but they appear to move with respect to earth.

4) Both the motion of stars & motion of sun are similar because both are an example of apparent motion. Both appear to change their respective positions but in reality , sun & stars are constant in their positions. But as earth is rotating , it appears like sun & stars are changing their positions.

what 9/2-11/4 plz help i only have 10 mins till due

Answers

Answer:

7/4

Step-by-step explanation:

9/2 - 11/4

Get a common denominator of 4

9/2 *2/2  - 11/4

18/4 - 11/4

7/4

Answer:

The answer is 7/4

Step-by-step explanation:

9/2 - 11/4

Here, we will Cross Multiply

9/2 - 11/4

9 × 4 - 11 × 2 ÷ 4 × 2

36 - 22 ÷ 8

14 ÷ 8 = 7/4

Thus, The answer is 7/4

-TheUnknownScientist

Write the ratio, Explain what the ratio means . 6 basketballs to 4 soccer balls

Answers

Answer:

6:4

This ratio means that for every 6 basketballs there are 4 soccer balls.

Use the distributive property to simplify 5( x + 3).

(A). 8 x
(B). 5 x + 3
(C). 5 x + 8
(D). 5 x + 15

Answers

Answer:

D) 5x+15

Step-by-step explanation:

5×x+5×3

5x+15

plz mark as brainliest

D, is the correct answer


Help me please I don't know it​

Answers

Answer:

65

Step-by-step explanation:

Method 1(Algebra):

m - 14 = 51

Add 14 to both sides of the equation.

m - 14 + 14 = 51 + 14

Combine like terms.

m = 65

Method 2:

m - 14 = 51

Move negative fourteen(- 14) to the other side of the equation. Because we moved it, it is now positive fourteen( + 14)

m = 51 + 14

Combine like terms.

m = 65

Suppose you leave your house and travel 13 mi due west. Then you travel 3 mi due south. How far, in miles, are you from your house as the crow flies (a straight line)? Round your answer to the nearest tenth if necessary.

Answers

Answer: [tex]13.34\ \text{miles}[/tex]

Step-by-step explanation:

Given

First the person travels 13 mi west and then 3 mi due to south

The distance traveled by crow is represented by line BO

using Pythagoras theorem, we can write

[tex]\Rightarrow AO^2+AB^2=BO^2\\\Rightarrow BO^2=13^2+3^2\\\Rightarrow BO^2=178\\\Rightarrow BO=\sqrt{178}\\\Rightarrow BO=13.34\ \text{miles}[/tex]

What is the length of the longest side ?

Answers

Answer:

11 feet (Option C)

Step-by-step explanation:

Let the longer side be l and the shorter side be b.

We know that,

Perimeter of rectangle = 2 ( longer side + shorter side )

Here,

Perimeter of rectangle is 32 feet.

→ 32 = 2 (l + b)

→ 32 = 2l + 2(5)

→ 32 = 2l + 10

→ 32 - 10 = 2l

→ 22 = 2l

→ [tex] \sf \dfrac{22}{2} [/tex] = l

→ 11 = l

11 feet = longer side

[tex] \therefore [/tex] Length of the longer side is 11 feet.

A Rectangle has diagonals of length 13 cm and width is 5 cm. Find the length of its side?

Answers

Answer:

Length = 12 cm

Step-by-step explanation:

using the Pythagorean theorem:

Length² = 13² - 5² = 169 - 25 = 144

Length = √144 m= 12 cm

Answer:

It's 34 cm

Step-by-step explanation:

Width of a rectangle = 5 cm

Diagonal of a rectangle = 13 cm

By Pythagoras Theorem,

Length of a rectangle = √(13² - 5²)

Or, Length of a rectangle = √(169 - 25)

Or, Length of a rectangle = √144

Or, Length of a rectangle = 12 cm

Perimeter of a rectangle = 2(12+5)

Or, Perimeter of a rectangle = 2×17

Or, Perimeter of a rectangle = 34 cm

Therefore, the perimeter of a rectangle = 34 cm

What is an equation of the line that passes through the points (-4,-3) and (3,-3)

Answers

Answer:

y=-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-3-(-3))/(3-(-4))

m=(-3+3)/(3+4)

m=0/7

m=0

y-y1=m(x-x1)

y-(-3)=0(x-(-4))

y+3=0(x+4)

y+3=0

y=0-3

y=-3

heeeeeeeeeelp meeeeeee

Answers

Answer:

81

Step-by-step explanation:

Find out the percentage of people who had mispriced item.

3/50 = 0.06

6% of people had mispriced items.

Find 6% of 1,350.

81

81 people would have mispriced items.

Answer:

81

Step-by-step explanation:

I did this by doing 1,350 ÷ 50, which gave me 27. I then did 27 times 3, the average amount of people with a mispriced item per 50 people, which gave me 81 as a result. And with that, I can conclude that you would expect there to be 81 people per day who have a mispriced item.

A rope that is 6 meters long will be cut into 24 pieces that are all of the same
length. What will be the length of each piece, in centimeters?

Answers

Answer: I would say 4 centimeters

Step-by-step explanation: Well if 24 divided by 6 equals 4 then I would say 4

Based on the length of the rope and the number of pieces it is to be cut into, the length of each piece will be 25 cm long.

First covert the length of the rope to centimeters:

= 6 x 100

= 600 cm

The length of each piece will be:

= Length of rope / Number of pieces

= 600 / 24

= 25 cm

In conclusion, each piece will be 25 cm long.

Find out more at https://brainly.com/question/17563021.

Johhny earns $2,334.50 from his job each month. He pays $1,437 for monthly expenses. Johnny is planning a vacation in 3 months' time that he estimates will cost $1,750 total. How much will Johnny have leftover from three months of saving once he pays for his vacation?

Answers

Answer:

2,302,63

Step-by-step explanation:

................

Answer:

942.50

Step-by-step explanation:

First, multiply 2334.50 by 3 to get 7003.50. Then multiply 1437x3= 4311

7003.50-4311=2692.50 Then take away 1750. 2692.50-1750=942.50

I hope this helps! UWU

what was the total number of gallons of paint sold?

Answers

Answer:

1,600

Step-by-step explanation:

Divide 240 by 3. This is 80, or 5% of the total.

Multiply 80 by 20, to get 1,600, 100% of the total

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