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

There is a 15% chance it will snow and a 15% chance it will rain. What is the probability that it will be a dry day (meaning that it will neither snow nor rain)? HELP PLS

Answers

Answer:

70%, obviously

Step-by-step explanation:

15 + 15 = 30, 100 - 30 = 70

I NEED THIS ANSWER PLEASE LAST QUESTION FOR EXAM PLEASE SHOW WORK

Answers

Answer:

x = 8

Step-by-step explanation:

b². b⁵ = b¹⁵/ bˣ

b²⁺⁵ = b¹⁵⁻ˣ

2 + 5 = 15 - x

7 = 15 - x

x = 15 - 7

x= 8

Which equation represents a proportional relationship that has a constant of proportionality equal to 2?
y = x + 2
y = x/2
y = 2 x
y = 2


pls hurry

Answers

Y = 2. Is proportional equal
Not sure how to work this out but if you figure it out let me know as I struggle with this too!

x=3, and y=-4: -5(x-2) + 3y

Answers

-17 -5(3-2)+3x-4= -17

Answer:

-17

Step-by-step explanation:

Substitute 3 for x and -4 for y

-5(x-2) + 3y

-5 ( 3 - 2 ) + 3 * -4

-5 * 1 + 3 * -4

-5 - 12

-17

¿Numeros entre 0,1 y 0,5?

Answers

Answer:

0.2

0.3

0.4

Step-by-step explanation:

If it takes star 1/2 a can of sauce to cover 3/4 of a pizza,compute the unit rate in terms of cans of sauce per pizza

Answers

I think it might take 4/6, or 2/3

Explanation: because 1/2 a can of sauce covers 3/4 of the pizza, you still need 1/4 of the pizza covered. 1/4 if 1/3 of 3/4. That means you need an additional 1/3 of the 1/2 can of sauce - 1/3 of 1/2 is 1/6. So, if we add the original 1/2, which is equal to 3/6, with the additional 1/6, we get 4/6. 4/6 can be simplified to 2/3. I’m not sure if I’m right cause I’m bad at math but you could give it a try. :)

Write an algorithm to find sum of first ten even numbers?

plz do it ... if you do i will mark brainliest ​

Answers

Answer:

n(n+1)

This is the answer I know

Can someone help me with this question please

Answers

Answer:

A. Conditional Statement

Step-by-step explanation:

In a conditional statement, A would be the premise, and B would be the conclusion.

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Have a great summer :)

The evolutionary pathways of ten different species are represented in the diagram below. SA Which two species are the most closely related?

E and I
G and J
A and F
O and D​

Answers

Answer:

I don't see an O in the picture at all.

but here's how you solve it: just count the nodes between the species, the fewer the closer

I would go for E and I, only one step between them

The length of the triangle for the pool table is the twice the sum of 5 and a number. If the rack is equilateral, what is the perimeter, in inches, of the triangle?​

Answers

Answer:  

30 + 6x inches

Step-by-step explanation:  

Let the required number be x

If the length of the triangle for the pool table is twice the sum of 5 and a number

L = 2(5+x)

L = 10+2x

Since the triangle is quadrilateral, this means that all sides are equal

Perimeter = 3L

Perimeter = 3(10+2x)

Perimeter = 30+6x

Hence the perimeter, in inches, of the triangle is 30 + 6x inches

Melissa has a spray paint that covers about 6,500 square centimeters. Can melissa apply two coats of paint to the entire sculpture?

Answers

Answer:

This question cannot be solved. It does not say anything about a statue in the first sentence and it doesn't give you the area of the statue.

Step-by-step explanation:

Answer:

Actually, in my math book I had that question. The answer was yes, I don’t remember why, but there was a picture included of the sculpture.

Step-by-step explanation:

You have to find the surface area of the cube and the surface area of the cylinder, but you don’t count the faces (circles). Then you total them, and find your answer. You do 6,500 times 2.

in Lisa’s school, 53% of students take a bus to school, 38% go the bus riders were late one snowy morning. 25% of students who don’t take a bus to school were not late that morning. What percent of students who do not take the bus was late that morning?

Answers

Answer:

I got 53% but I'm not sure

Step-by-step explanation:

if 53% of students take the bus, then 47% of students DON'T.

25% (the percent of non-riding students who were late) of 47 is about 53%

How many kilograms are equivalent to 5 pounds?

Answers

Answer: the answer is 2.25 kg

Step-by-step explanation:

Find a round to the nearest tenth a 150 12 10cm c a=?cm

Answers

Answer:

[tex]Using~ the ~ law~ of ~sinse:-[/tex][tex]\frac{a}{SinA} =\frac{b}{SinB}[/tex][tex]\frac{a}{Sin150}[/tex][tex]=\frac{b}{SinB}[/tex][tex]a=\frac{10~sin~150}{Sin~12}[/tex][tex]a=[24] ~cm[/tex]-----------------------hope it helps..have a great day!!

As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions shown. Abigail sloshes \dfrac23 3 2 ​ start fraction, 2, divided by, 3, end fraction of the water out of her cup before she gets a chance to drink any. What is the volume of water remaining in Abigail's cup?

Answers

Answer:

Volume of water remaining in Abigail's cup = 25.12 cm³

Step-by-step explanation:

As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions radius 3 cm and height 8 cm. Abigail sloshes 2/3 of the water out of her cup before she gets a chance to drink any. What is the volume of water remaining in Abigail's cup? Use 3.14 for Pi

Volume of a cone cup = πr²h/3

Radius, r = 3 cm

Height, h = 8 cm

Pi, π = 3.14

Volume of a cone cup = πr²h/3

= (3.14 * 3² * 8) / 3

= (3.14 * 9 * 8) / 3

= 226.08 / 3

= 75.36 cm³

Abigail sloshes 2/3 of the water out of her cup.

What is the volume of water remaining in Abigail's cup

Volume of water Abigail slosh = 2/3 of 75.36 cm³

= 2/3 * 75.36

= 150.72 / 3

= 50.24 cm³

Volume of water remaining in Abigail's cup = Volume of water in the cup - Volume of water Abigail slosh

= 75.36 cm³ - 50.24 cm³

= 25.12 cm³

Volume of water remaining in Abigail's cup = 25.12 cm³

Answer:

25.12

Step-by-step explanation:

I checked in khan

what is the relationship between vectors u={1,0} and v={0,-3}?

Answers

Answer: Hi, your answer would be  

C) The vectors are orthogonal because the angle between them is 90°.

24 : 56 is equivalent to 3 : __

Answers

Answer:

3 : 7

Step-by-step explanation:

24/56 = 3 / 7

Answer:

3:7 helpful answer to your question have a nice evening

Aidan is saving money to buy a new computer. He made a scatter plot and a linear model for the amount of money he has saved over the past eight weeks. The equation of the line is y = 17.63x + 27.52 . Use the model to predict how much aidan saved over five weeks

Answers

Answer:

Aidan saved 115.67 over five weeks.

Step-by-step explanation:

After x weeks:

The amount of money saved by Aidan is given by:

[tex]y(x) = 17.63x + 27.52[/tex]

How much aidan saved over five weeks?

This is y when x = 5. So

[tex]y(x) = 17.63x + 27.52[/tex]

[tex]y(5) = 17.63*5 + 27.52 = 115.67[/tex]

Aidan saved 115.67 over five weeks.

Solve for x in this equation.
7^3x-17 = 49^x

Answers

Answer:

X = 17

Step-by-step explanation:

If you created equivalent expressions with equal bases that should be the answer.

Answer: x=17

Write in exponential form: 7^3x-17 = 7^2x
3x-17=2x
-2x -2x
————-
X=17

Which equation represents a relationship where y is a nonlinear function
of x?
O x = -6y

O y = IxI- 3

O 3x + 4y = 8

O 4x - 3y + 2 = 8x-5y+12929

Answers

Step-by-step explanation:

if you use the online graphing calculator it will help you

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of (u circle v) (x)?

Answers

Answer:

A≈1075.21

d Diameter

37

d

r

r

r

d

d

C

A

Using the formulas

A=

π

r

2

d=

2

r

Solving forA

A=

1

4

π

d

2

=

h1

4

π

37

2

1075.21009

Step-by-step explanation:

Your gross pay is $1,878.96, net income is $1,196.34, and fixed expenses are $1,338.54. What is your discretionary income?

Answers

Answer:

$0

Step-by-step explanation:

32% of a number is 64 what is the number

Answers

Answer:

If you take 32 percent of a number and get 64, then what is that number? In other words, you know that 32 percent of a number is 64 and you want to know what that initial number is. Therefore, the answer to "64 is 32 percent of what number?" is 200, and you can also derive that 32 percent of 200 equals 64.

Step-by-step explanation:

200

Step-by-step explanation:

32% x = 64

(32/100)x= 64

0.32x=64

x=64÷0.32

x=200

This was wrong.. Why?

Answers

Answer:

I think it's 9/22

Step-by-step explanation:

Probability of A given B = (probability of A and B)/probability of B

[tex]\frac{(14/22)(9/22)}{14/22} \\=\frac{9}{22}[/tex]

P(B) = P(1 checked bag) = 14/22

P(A) = P(silver status) = 9/22

P(A ∩ B) = (14/22)(9/22)

8(2x - 9) = 4(5 + 4x) solve for x

Answers

Answer:

No solutions

Step-by-step explanation:

8(2x - 9) = 4(5 + 4x)

Distribute the 8

16x - 72 = 4(5 + 4x)

Distribute the 4.

16x - 72 = 20 + 16x

Add 72 to both sides

16x = 92 + 16x

Subtract 16x from both sides

0 = 92

0 does not equal 92 therefore there are no solutions

Answer:

No solution

Step-by-step explanation:

8(2x - 9) = 4(5 + 4x)

Simplify

8(2x−9).

Start simplifying.

0+0+8(2x−9)=4(5+4x)

Simplify by adding zeros.

8(2x−9)=4(5+4x)

Apply the distributive property.

8(2x)+8(−9)=4(5+4x)

Multiply 2 by 8.

16x+8(−9)=4(5+4x)

Multiply 8 by −9.

16x−72=4(5+4x)

Simplify

4(5+4x).

Apply the distributive property.

16x−72=4×5+4(4x)

Multiply 4 by 5.

16x−72=20+4(4x)

Multiply 4 by 4.

16x−72=20+16x

Move all terms containing x to the left side of the equation.

Subtract 16x from both sides of the equation.

16x−72−16x=20

Combine the opposite terms in

16x−72−16x.

Subtract 16x from 16x.

0−72=20

Subtract 72 from 0.

−72=20

Since −72 ≠ 20, there are no solutions.

Hope it is helpful...

Math help please urgent

Answers

Answer:

area of circle is 2πr²

= 2 x 3.14 x 8 x 8

= 402 cm

tan145+tan85/1-tan145*tan85 as asingle funciton

Answers

Answer:

Step-by-step explanation:

Tan 145 = - 0.7002

Tan 85 = 11.43

Tan 145 + tan 85 =  10.7298

1 - tan(145)* tan(85) = 9.003

(Tan(145) + Tan(85)) / (9.003)

= 10.73 / 9.003

= 1.1918

I misread the question. If you mean

(Tan145+tan85) /1-tan145*tan85   (brackets are really important here)

then the answer is

Tan(145 + 85)

= Tan(230)

= 1.1918

Luis wants to change companies for his phone service. Company SaveMore charges $16 for the initial service plus $0.20 for every 1 text of use.Write an equation that represents the cost of the service, with the cost of the constant number of text, t added After how many texts will the two companies be the same charge for the service?

Answers

Answer:

[tex]y = 16 + 0.2t[/tex] --- the equation of SaveMore company

Step-by-step explanation:

Given

SaveMore

[tex]Initial = 16[/tex]

[tex]Additional\ Rate = 0.20[/tex]

Required

Determine the equation

Let

[tex]y \to cost[/tex]

[tex]t \to texts[/tex]

So, we have:

[tex]y = Initial + Additional\ Rate * t[/tex]

[tex]y = 16 + 0.20 * t[/tex]

[tex]y = 16 + 0.2t[/tex]

The equation for the second company is not given. So, the (b) part cannot be correctly answered.

A general solution to the (b) part is:

Assume the equation is:

[tex]y = 10 + 0.4t[/tex]

Next, we equate both

i.e.

[tex]y = y[/tex]

This gives:

[tex]16 + 0.2t = 10 + 0.4t[/tex]

Collect like terms

[tex]0.4t - 0.2t = 16 - 10[/tex]

[tex]0.2t = 6[/tex]

Divide by 0.2

[tex]t = 30[/tex]

Hence, the charges will be the same after 30 texts

Any answers for this question

Answers

Step-by-step explanation:

hear is your both answer

How will she know if 5(3x – 6) is equivalent to 15x – 30?

Answers

Answer:

By distributing the parenthesis

Step-by-step explanation:

Given

5(3x - 6) ← multiply each term in the parenthesis by 5

= 15x - 30 ← as required

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