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1 year ago

Find the values of a and b such that x^2-2x+2=(x-a)^2+b

Mathematics

1 answer:

vekshin11 year ago

6 0

Answer:

a = 1, b = 1

Step-by-step explanation:

Expand the right side and compare the coefficients of like terms on both sides, that is

right side

(x - a)² + b ← expand factor using FOIL

= x² - 2ax + a² + b

Compare to left side x² - 2x + 2

Compare the coefficients of the x- term

- 2a = - 2 ( divide both sides by - 2 )

a = 1

Compare the constant terms

a² + b = 2 ( substitute a = 1 )

1² + b = 2

1 + b = 2 ( subtract 1 from both sides )

b = 1

Thus a = 1, b = 1

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If 5 gallons cost $ 6.60 how much do 29 gallons of gasoline cost

ikadub [295]

Answer:

Should be 38.28

Step-by-step explanation:

Dividing 6.60 by 5 is $1.32, aka the cost of one gallon. multiply by 29, answer is that it costs $38.28 to get 29 gallons of gasoline.

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1 year ago

A military cannon is placed at the base of a hill. The cannon is fired at an angle toward the hill. The path

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Answer:

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1 year ago

Use the greatest common factor and the distributive property to write and an equivalent expression: 20g+24h

n200080 [17]

4(5g+6h)

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2 years ago

Find a number in the sequence<br><br> 1) 100, 400, 610, ?, 652<br><br> 2) 342, 128, ?, 26

dsp73

Answer:

1. 460

2. 216

Step-by-step explanation:

From the series ,

100 , 400 , 610 , ? , 652

Writing the the digits in the revere order , i.e

001 , 004 , 016 , ? , 256

Now,

Now , getting the number in the form of the multiple of 4 as -

1 , 1 * 4 = 4 , 4 * 4 = 16 , ? , 64 * 4 = 4

Hence , the value for ? = 16 * 4 = 64 .

Again , reversing 64 to get the missing number of the series -

460 .

Hence ,

The value for ? is 460 .

From the series ,

342 , 128 , ? , 26

Now, multiplying the first digit with the second digit and merging it to the product of the second and third digit -

3 * 4 and 4 * 2 , 1 * 2 and 2 * 8 , ?

128 , 216 , ?

Hence ,

The value for question mark = 1 * 2 and 1 * 6 = 216

Hence ,

The value for ? is 216 .

4 0

2 years ago

The area of the regular pentagon is 6.9 cm2. What is the perimeter? 2 cm 5 cm 10 cm 20 cm

disa [49]

Given

Area of the regular pentagon is 6.9 cm².

Find out the perimeter of a regular pentagon

To proof

Formula

Area of regular pentagon is

$= \frac{1}{4}\sqrt{5(5+2\sqrt{5})}\ a^{2}$

As given in the question

area of regular pentagon = 6.9 cm²

now equating the area value with the area formula.

$6.9 =\frac{1}{4}\sqrt{5(5+2\sqrt{5})} a^{2}$

Now put

√5 = 2.24 ( approx)

put in the above equation

$\frac{6.9\times 4}{\sqrt{5(5+2\times2.24)}}=a^{2}\\\frac{27.6}{\sqrt{47.4}}=a^{2}\\\frac{27.6}{6.88}=a^{2}$

thus

a² = 4.01

a = √ 4.01

a = 2.0 cm ( approx)

As perimeter represented the sum of all sides.

i.e regular pentagon have five sides of equal length.

Thus

perimeter of the regular pentagon = 5 × side length

= 5 ×2.00

therefore the perimeter of the regular pentagon = 10cm

option c is correct

Hence proved

3 0

2 years ago

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