Use the completing the square method to transform the equation x2 + 2x = 13 into an equation of the form (x + a)2 = b, where ɑ and b are real numbers What are the values ​​of ɑ and b?

Answers

Answer 1

Answer:

(x+1)² = 14

a = 1, b = 14

Step-by-step explanation:

Given the equation, x² + 2x = 13

We are to use the completing the square method to express in the form

(x + a)² = b

x² + 2x = 13

Add the square of half of the coefficient of x to both sides

Coefficient of x = 2

Half of the coefficient of x = 2/2

Square of the result = (2/2)²

Square of the result = 1²

Add (1/2)² to both sides

x² + 2x + (1)² = 13 + (1)²

(x+1)² = 13 + 1

(x+1)² = 14

Compare with  (x+a)² = b

a = 1 and b = 14


Related Questions

Find the value of x in The parallelogram.

Answers

Answer:

48 degrees

Step-by-step explanation:

x+132 should be equal to 180, property of a parallelogram (and same side interior angles)

180-132=48

Answer:

x = 48

Step-by-step explanation:

Consecutive angles in a parallelogram sum to 180° , so

x + 132 = 180 ( subtract 132 from both sides )

x = 48

a rectangular solid box measures 2.17 feet by 4.05 feet by 480 inches. in cubic yards, what is the volume of the box? express your answer as a decimal to the nearest tenth

Answers

Answer:

117.18 yards

Step-by-step explanation:

480in=40ft

2.17x4.05x40=351.54tf

351.54ft=117.18yrds

Scarlett can bake 10 cookies with each scoop of flour. Write an equation that shows the relationship between the scoops of flour x and the cookies y. Write your answer as an equation with y first, followed by an equals sign.

Answers

y = 10x

Where y is equal to the amount of cookies and x is the scoops of flour.

Use a net of the square pyramid, if necessary, to find the surface area of the pyramid.

Answers

Answer:

128 if it wants the whole thing than 192

Step-by-step explanation:

Guys This is one of the most difficult question .
I salute the person who answer it correctly
The question goes like this :

The present price of a Camera is $32400. After day to day use, its price depriciates !! in such a way that its price will be $0 in 12 years ,, Then calculate the ptice of the Camera after 4 years. ​

Answers

Answer:

$21,600

Step-by-step explanation:

32400÷12=2700

2700×4=10,800

32400-10800=21600

Answer: $21,600

Step-by-step explanation: 32400÷12=2700

2700×4=10,80032400-10800=21600

does the equation define y as a function of x? y^2 = 7 - x^2

Answers

I would say No hope this helps you.

Complete the Steps to Solve the Equation -13x-11=-37

-13x-11=-37
-13x=

Answers

Uhhmmm sorry to my friend I have to go

Answer:

x=2

Step-by-step explanation:

-13x-11=-37                             Original equation

-13x=-26                                 Add 11 to both sides

x=2                                         Divide both sides by -13

Need help please!! :)

Answers

Answer:

[tex]A: (-3,1)[/tex]

[tex]B:(-1,-1)[/tex]

[tex]d=\sqrt{(-3-(-1)^{2} +(-1(-1))^{2} }[/tex]

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

[tex]=\sqrt{4+4}=\sqrt{8}[/tex]

[tex]=2\sqrt{2} =2.8[/tex]

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

hope it helps..

have a great day sis ^_^!!!

Answer:

Coordinates of :-

A= (-3,1)

B= (-1,-1)

Distance AB= [tex]\sqrt{-2+3)^{2}+(-1-1)^{2} }[/tex]

[tex]\sqrt{(2)^{2} +(-2)^{2} }[/tex][tex]=\sqrt{4+4}[/tex][tex]=\sqrt{8}[/tex][tex]=2.8[/tex]

OAmalOHopeO

Can anyone help with this?

Answers

The pints should be a line that passes throughout (-2,1) and (0,0)

Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below:

Answers

Answer:

The answer is "158.489"

Step-by-step explanation:

for san francisco earthquake:

[tex]\log(\frac{a_1}{T}) + B = 7.8\\\\\log(\frac{a_1}{T})+\log(10^{B}) = 7.8\\\\\log(\frac{a_1}{T} \times 10^{B})=7.8\\\\(\frac{a_1}{T} \times 10^B=10^{7.8}...............(i)[/tex]

similarly , for coloumbia earthquake:

[tex]\frac{a_2}{T}\times 10^B = 10^{5.6}.................(ii)[/tex]

divide equation (i) and (ii):

[tex]\frac{a_1}{a_2}=\frac{10^{7.8}}{10^{5.6}}\\\\\frac{a_1}{a_2}=10^{2.2}\approx 158.489[/tex]

Which expression is equivalent to 4(2x + 1)?
8x + 1
8x +4
6x + 5
O
2x + 4

Answers

Answer:

8x + 4

Step-by-step explanation:

You just gotta distribute 4(2x+1) and it gives you the expression 8x + 4

in a survey of 100 cars,47 were white,23 were blue and 30 were red.express each of these numbers as a percentage of the total.

Answers

Answer:

white- 47%   Blue-23% Red- 30%

Step-by-step explanation:

White cars- (47/100)*100= 47%

Blue cars- (23/100)*100=23%

Red cars- (30/100)*100=30%

2. The direct distance between city A and city B is 200 miles. The direct distance
between city B and city C is 300 miles. Which could be the direct distance between city
C and city A?
1) 50 miles
2) 350 miles
3) 550 miles
4) 650 miles

Answers

Answer:

2

Step-by-step explanation:

Please give real answers with an explaination. 50 points + I will follow + I will give brainliest + 5-star rated. No Docs/No Files/No Links only answer with explaination.

Answers

Answer:

B

Step-by-step explanation:

Look at the figures below.

Figure A.

The median of a quadrilateral was drawn as the red segment. It split the interior angle of the quadrilateral into angles 1 and 2. Angles 1 and 2 are clearly not congruent. Statement A is false.

Figure B.

The red segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. Statement B is true.

Figure C.

The red midsegment cuts the triangle into two areas, crosshatched in blue and green. The areas are clearly not equal, so statement C is false.

Which expression can go in the blank to make the equation true?
-2.9 + 2.8 + ____________ = 0

Answers

Answer:

+0.1

Step-by-step explanation:

when we subtract 2.9 and 2.8 we get -0.1 and to make it zero we have to keep +0.1

When u subtract the to u get -0.1 so u got to add the the zero to get the positive 0.1

365.12x =36,512 please help ​

Answers

Answer:

x = 100

Step-by-step explanation:

365.12 x = 36512

36512 / 365.12 = x

x = 100

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Which of the following does not represent a function?

Answers

C, the circle because it fails the vertical line test.
It’s C because I did the math I hope you get the right answer and a good day

The circumference of a circle can be found using the formula C = 2r.

Which is an equivalent equation solved for r?

r = C
r = C(2)
r = r equals StartFraction C Over 2 pi EndFraction.
r = r equals StartFraction 2 pi Over C EndFraction.

Answers

Answer:

r = C/(2π)

Step-by-step explanation:

C = 2πr

Divide both sides by 2π

C/(2π) = r

r = C/(2π)

Given that the circumference of a circle, its radius r becomes r = C/2π.

Option C) r equals StartFraction C Over 2 pi EndFraction is the correct answer.

What is a circle?

A circle is simply a closed 2-dimensional curved shape with no corners or edges. The total length of the boundary of a circle is referred to as a circumference. It is expressed as;

C = 2πr

Where r is radius and π is constant pi ( π = 3.14 )

Now, if the circumference C = 2πr, lets make radius r the subject of the formula.

C = 2πr

Divide both sides by 2π

C/2π = 2πr/2π

C/2π = r

r = C/2π

Given that the circumference of a circle, its radius r becomes r = C/2π.

Option C) r = start fraction C over 2 pi end fraction is the correct answer.

Learn more about circles here: brainly.com/question/11952845

#SPJ2

An airplane covers 1824 km in an hour How much distance will it cover in 3.7 hours​

Answers

Answer:

6748.8 km

Step-by-step explanation:

in 1 hour = 1824

in 3.7 hour = 1824×3.7

=6748.8 km

Find the area of PQRS. (Hint: Use the Pythagorean Theorem to find the height .)

Answers

Height = sqrt(5^2 - 4^2) = sqrt(9) = 3

Area = length x height
Area = 8 x 3 = 24m^2

Now solve this equation for y. Remember the roller coaster is above ground, so you are only interested in the positive root.

Answers

Answer:

[tex]y = \sqrt{ 900 - x\²[/tex]

Step-by-step explanation:

In the complete question, the area of  the roller coaster is:

[tex]x\² + y^2 = 900[/tex]

Required

Solve for y

We have:

[tex]x\² + y^2 = 900[/tex]

Subtract [tex]x\²[/tex] from both sides

[tex]y^2 = 900 - x\²[/tex]

Take positive roots of both sides

[tex]y = \sqrt{ 900 - x\²[/tex]

A prism with a volume of 148 cubic cm is dilated by a factor of 5.5.

The volume of the dilated prism is ___ cubic cm.

Answers

volume = 148 × 5.5 cube

= 24623.5 cubic cm

P= -4b^2+6b-9
Q= 7b^2-2b-5
P-Q=

Answers

Answer:

P - Q = - 11b² + 8b - 4

Step-by-step explanation:

P - Q

= - 4b² + 6b - 9 - (7b² - 2b - 5) ← distribute parenthesis by - 1

= - 4b² + 6b - 9 - 7b² + 2b + 5 ← collect like terms

= - 11b² + 8b - 4

37 + (-37) im looking for the answer

Answers

Answer:

0

Step-by-step explanation:

37 + (-37)

open the bracket

remember when u multiply the bracket - sign and + sign also gets multiplied and (-) * (+) is( -) . So

37 - 37

0

Find the value of x and the measure of the exterior angle. (9x+16) (5x-14)

Answers

Answer:

[tex]x = 15 \: \: .....(5(15)- 14) = 61[/tex]

[tex](9x + 16 )= (5x - 14) + 90 \\ 9x - 5x = 90 - 14 - 16 \\ 4x = 60 \\ x = \frac{60}{4} \\ x = 15[/tex]

WHOEVER ANSWERS FIRST WINS BRAINLIEST!
Multiply.
4 1/6 × 5 3/5

Answers

Answer and Step-by-step explanation:

Convert the numbers into improper fractions.

[tex]\frac{25}{6} ,\frac{28}{5}[/tex]

Now, multiply the numbers.

[tex]\frac{700}{30}[/tex]

Finally, simplify.

[tex]\frac{70}{3}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

CUAL ES LA MITAD DE 30

Answers

Answer:

15

Step-by-step explanation:

30/2=15

in . 3.5 in 4 9 in 4 in . The triangular prism above has been created with two equilateral triangles and three congruent rectangles . The height of the triangles is 3.5 inches . Find the surface area of the triangular prism . square inches

Answers

Answer:

122 in²

Step-by-step explanation:

Applying,

S.A =  bh+ bl+bl+bl............. Equation 1

Where S.A = Surface area of the prism, b = base of the triangle, h = height of the triangle, l = lenghth of the prism

From the question,

Given: b = 4 in, h = 3.5 in, l = 9 in

Substitute these values into equation 1

S.A = 4×3.5+9×4+9×4+9×4

S.A = 14+108

S.A = 122 in²

Hence the surface area of the prism is 122 in²

Question: A sample contains 68 grams of radioactive Bruinium. Sixteen days later, the sample had decayed to 47 grams.

A) what is the decay rate, k?
B) what is half-life of bruinium to the nearest 0.1 day?
C) how much bruinium would be left in another 10 days? (After the first 16)
D) how much time is required for the sample to decay to 25 grams (from t=0)?

Answers

The answer is B......

The triangle inequality

Answers

The answer is the first choice: 7, 15, 20.
When you want to know what three numbers can make up a triangle. All you have to do is take the first two numbers and add them up. If the sum is larger than the third number, it can form a triangle. If the sum of the first two numbers are smaller than the third number, it cannot form a triangle.
Hope this helped
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