a) Show that x² - 8x + 20 can be written in the form (x - a)² + a where a is an integer.
b) Hence explain how you know that x² - 8x + 20 is always positive.

I have worked out the first bit of the question and the answer is:
x²-8x+20
x²-8x+16-16+20
(x-4)²+4
(x-a)²+a
a= 4

I just need help with part b and I'm struggling to do it. Please help.

Answers

Answer 1
b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.
You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive.
Answer 2

Answer:

Step-by-step explanation:

b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.

You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive


Related Questions


Factor completely: y6 - 1.

Answers

Answer:

(y times 6) -1

Step-by-step explanation:

I don't know what to say it is already simplified

Plz help it would mean a lot

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Answer:

proportional/equal

Step-by-step explanation:

doesnt need

PLEASE HELP!!!!!!!
The temperature is 56°F. The temperature decreases for 6 hours. Each hour, the temperature decreases by 3°F. Then the temperature rises 12°F in one hour. What is the temperature after 7 hours?

Answers

Answer:

50 degrees

Step-by-step explanation:

3 x 6 = 18

56 - 18 = 38

38 + 12 = 50

what is 58+67÷34×21-34​

Answers

65.38235294117647 I got this answer
58+67= 125
125 divided by 34 = 3.6764
3.6764 x 21 = 77.2044
77.2044 - 34 = 43. 2044

Write 2/3 as a decimal and round to 3 significant figures

Answers

Answer:

0,66

Step-by-step explanation:

You can put it into a calculator, that might be just as helpful and less time-consuming, because 2/3 is the same as 2÷3

Answer:

0.667

Step-by-step explanation:

[tex]\frac{2}{3} =0.6666666666666666[/tex]

A case of woods screws wieghs 18 2/3 pounds.each individual box of woods screws wieghs 1 1/3 pounds. How many individual boxes of wood screws are in the case?

A. 5
B. 9
C. 14
D. 20

Answers

B maybe I’m not sure

In a fruit basket there are 9 bananas 4 apples and 3 plums 1. The ration of bananas to apple is ________:_________. 2. The ration of plums to apples is __________to________. 3. For every __________apples, there are ______plums. 4. For every 3 bananas there is one _________.

Answers

Answer:

1. 9:4 2. 3:4 3. for every 4 apples there are 3 plums 4. plum

Step-by-step explanation:

1. there are 9 bananas and there are 4 apples.

2. there are 3 plums and there are 4 apples

3. there are 4 apples so there are 3 plums

4. 9 divided by 3 = 3. 3 divided by 3 = 1

A scuba diver is swimming at an elevation of 52 feet below sea level. She sees it'school of fish and rises 16 feet to watch the fish. What is her elevation now?​

Answers

-46

52-16=negative 46 because shes still below sea level

Answer:

36 feet below sea level.

Step-by-step explanation:

if you subtract 52 by 16 you'd get 36. See for yourself.

Please help I need these quickly. Please answer sensibly! I will give brainliest to the correct answer.

Answers

Answer:

n+n= 2n

[tex](3n) ^{2} = 9n ^{2} [/tex]

5(n+2)=5n+10

2(n+1)=2n+1

[tex]n \div 4 = \frac{n}{4} [/tex]

[tex]n(n - 2 = n{2} - 2n[/tex]

What is the absolute value of the complex number 4-V3/?
O 32
O 14
O 18

Answers

Answer:

[tex]3\sqrt{2}[/tex]

Step-by-step explanation:

The Magnitude of a Complex Number

A complex number is expressed in rectangular form as:

[tex]Z=a+ b\mathbf{ i}[/tex]

The absolute value or magnitude of Z is calculated as follows:

[tex]\mid Z\mid=\sqrt{a^2+b^2}[/tex]

We are given the number

[tex]Z=-4-\sqrt{2}\mathbf{ i}[/tex]

Here: a= -4, b=[tex]-\sqrt{2}[/tex]

Calculating the absolute value:

[tex]\mid Z\mid=\sqrt{(-4)^2+(-\sqrt{2})^2}[/tex]

Operating:

[tex]\mid Z\mid=\sqrt{16+2}=\sqrt{18}[/tex]

Factoring 18:

[tex]\mid Z\mid=\sqrt{3^2*2}[/tex]

Taking the square root of 3^2:

[tex]\mid Z\mid=3\sqrt{2}[/tex]

Answer: [tex]\mathbf{3\sqrt{2}}[/tex]

what is 60,000,000,000+800.000,000,000=?

Answers

Answer:

130.000,000,000

:)

Step-by-step explanation:

888383883838383dStep-by-step explanatio

7925 divided by 25 can you help

Answers

Answer:

317

Step-by-step explanation:

hope this helped:))))))

Answer:317Step-by-step explanation:25 x 317 = 7925Hope this helps!!

what is the correct evaluation of 3x-x+2,when x is equal to -4?

14

-6

6

-14​

Answers

-6 is the correct answer !


3(-4)-(-4)+2
-12+4+2
-8+2
-6

Answer:

(b) -6

Step-by-step explanation:

=3x-x+2

=3(-4)-(-4)+2

=-12+4+2

=-12+6

=-6

Use the 3 trig ratios to find each unknown side length. Round all answers to 1 decimal

Answers

Note: As you missed to add the graph of mentioning the complete question.

So, I am solving your concept based on an assumed graph which I have attached. It would anyways clear your concept.

Answer:

Please check the explanation!

Step-by-step explanation:

Given the attached graph below, it is clear that the right angle triangle ABC is shown.

Here are some of the information we can get from the right angle triangle ABC such as:

The angle at C = 30°side AB = 8 units

We have to determine the unknown side 'x' using the trigonometric ratios

As

tan Ф = opp/adjacent

From the diagram it is clear that

Ф = 30°

opp=8

adjacent = BC = x

so

tan Ф = opp/adjacent

tan 30 = 8/x

1/√3 = 8/x

x = 8×√3

x = 13.9

Therefore, the missing length will be: x = 13.9

8. If Alice only has $10 dollars, and she sends 27 text messages, how much data can she use?

Answers

Answer: 37 cents per text message

Answer:

200 mintes

Step-by-step explanation:

Any hypothesis that an analyst has accepted to be true and which forms the basis of an assessment is a: ______

Answers

Answer:

The correct answer is the alternate hypothesis.

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

For instance, H₀: µ = µ₀, where µ₀ is some null value or some claimed value.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by Hₐ.

Thus, the correct answer is the alternate hypothesis.

hmmmmmmmmmmmm please help uwu

Answers

Answer:

10.50 per hour

Step-by-step explanation:

I divided 26.25 by 2.5 and got 10.5. Hope this helps!

First answer is brainiest
Explain you're answer even if its just a bit because I'm tired of people giving me random answers so I fail its annoying.

Answers

Answer:

D

Step-by-step explanation:

So you are looking for the inverse equation. The original can be written as y=1/2x-6. For the inverse, your variables switch places. It's reflecting across the line y=x (that's what the inverse does). So you write it as x=1/2y-6. Now solve for the new equation:

Move 6 over: x+6=1/2y

Isolate y: 2(x+6)=y

This gets you D.  

PLEASE HELP!!!!! -x+y= -2

A 5,3

B 4,2

C 3,1

D 2,0

Answers

The answer is all of the above

Answer:

All of the above.

Step-by-step explanation:

All of the above are equal to 5,2. I hope this cleared things up! ^w^

what is order of operations for 20-5x2+6

Answers

Answer:

multiply, add, then subtract so your answer should be 4

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

(please excuse my dear aunt sally)

Angle W measures 68 degrees more than angle F. Angles Wand
Fare supplementary. What is the measure of angle W?

Answers

Answer: The measure of angle W is 124°.

Step-by-step explanation:

Given: Angles W and  F are supplementary.

We know that the sum of two supplementary angles is 180 degrees.

So, ∠W + ∠F = 180°   (i)

As per given,

∠W = ∠F + 68°   (ii)

Put value of ∠W from (ii) in (i)

∠F + 68°+∠F = 180°  

⇒ 2 ∠F =  180°- 68°

⇒ 2 ∠F = 112°

⇒ ∠F = 56°

From (ii),

∠W = 56° + 68°

⇒ 124°

Hence, the measure of angle W is 124°.

13. Find the slope of any PLZ HELP!!!! 13. Find the slope of any line parallel to the line passing through (1,5) and (-1,0).
a. 5/2
b. 2/5
c. -5/2
d. -5/2

Answers

Answer:

a

Step-by-step explanation:

5- 0 = 5

1- -1 = 2

5/2

The answer might be B. I’m not entirely sure.

Use the vertical line test to determine if the relation {(–6, –2), (–2, 6), (0, 3), (3, 5)} is a function

Answers

Answer: Its a function

Step-by-step explanation:

what is an equation with more than one variable called
a.a literal equation
b.a variable
c.an expression
d.a quadratic equation​

Answers

Answer:

option A

a variable is a number which is always changing

an  expression doesn't have an equal sign

a quadratic equation is an equation which has one variable but the highest power of that variable is 2

so the answer is a literal equation or linear equation in two variables

A) literal equation

2.5 divided by 1.5 round to nearest tenth

Answers

Answer:

1.7

Step-by-step explanation:

2.5÷1.5

5/3

1.66666

1.7

The divisions of 2.5 divided by 1.5 gives to 5/3 or 1.6667.

What is Division?

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

2.5 divided by 1.5

So, 2.5 / 1.5

= 25 x 10 / 15 x 10

= 25/15

= 5 x 5 / 5 x 3

= 5/3

Hence, the divisions results to 5/3 or 1.6667

Learn more about Division here:

https://brainly.com/question/21416852

#SPJ2

PLEASE PLEASE HELP ME

Answers

Answer:

Is the line going through negative dot or positive? Think about it.

Step-by-step explanation:

Anyway my teacher came into me anyway its a positive answer. so A or B

show work and ill give credit

Answers

9514 1404 393

Answer:

  5

Step-by-step explanation:

To solve the inequality, we can do the following.

  4.55g + 8.50 ≤ 35 . . . given

  4.55g ≤ 26.50 . . . . . . subtract 8.50 from both sides

  g ≤ 5.82... . . . . . . . . . . divide both sides by 4.55

The number of games must be an integer value, so the maximum number of games they can bowl is 5.

which expression is equivalent to to 4(3+5)-3.92

Answers

Answer:

C: 12+20-54

Step-by-step explanation:

4(3+5)-3.92= -22

12+20-54= -22

:))

An electronics store has a current inventory of 50 stereo systems. The lowest priced stereo system in the store sells for $800, The lowest priced stereo system in the store sells for 800 dollars, and the highest priced stereo system sells for $3000. and the highest priced stereo system sells for 3000 dollars. Which of the following is the maximum amount of $3000 systems on hand Which of the following is the maximum amount of 3000 dollar systems on hand if the current inventory totals $111,000?

The answer is 32, I need an explanation how to find the answer.

Answers

B) 32

Explanation:

let H = number of expensive high price stereo

systems

let L = number of less expensive low price

stereo systems

H +L = 50 =

3,000H + 80OL = 110,000

H = 50 - L (now replace)

3,000 (50 - L) + 800 L = 110,00

150,000 - 3,000L + 800L = 110,000

150,000 - 110,000 = 3,000L - 800L =

40,000 = 2,2OOL

L = 40,000 / 2,200 = 18.18 = 18 lower priced = =

stereo systems H = 50 - 18 = 32 higher priced stereo systems

=

=

(3,000 x 32) + (800 x 18) = 96,000 + 14,400 = 110,400

Even though the answer is not exact, if you had 33 high cost stereo systems, your inventory's cost = $112,600 which is $1,600 off

The mean score on a set of 16 tests is 90. What’s the sum of all the test scores?

Answers

It should be 90 because in question it says that
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