Solve each equation by completing the square. Write both answers separately.

Solve Each Equation By Completing The Square. Write Both Answers Separately.

Answers

Answer 1

Answer:

37) ±√29 - 4

Completing the square utilizes this formula [tex](\frac{b}{2})^{2}[/tex]. We know that b=8, 8 can be plugged into this formula to get [tex](\frac{8}{2})^2[/tex]. Simplify to get 16. Now, we can add this into the equation to get [tex]k^{2}+8k+13=26[/tex]. Subtract 26 to both sides, so the equation can equal to 0. [tex]k^{2} +8k-13=0[/tex] would be the resulting equation. Now, let's use quadratic formula to find the solution. The quadratic formula is (-b+-√b^2-4ac) / 2a. Plug in all of our values to get (-8+-√8^2-4(1)(-13)/2(1). Simplify the equation to get ±√29 - 4.

38) ±√21 - 2

Let's use the same formula. b=4, so [tex](\frac{4}{2} )^2[/tex]. Simplify to get 4. Add that into the equation to get [tex]x^{2}+4x-5=12[/tex]. Subtract 8 on both sides, so the equation can equal to 0. [tex]x^{2}+4x-17=0[/tex] would be the result. Use the quadratic formula again to find the solution. Plug in all of the values to get ±√21 - 2

If you're confused on any part of the explanation, feel free to ask :)


Related Questions

If ABCD is a square, and the area covered by the blue equilateral triangle is 49√3cm², what will be the area covered by the yellow region (in cm²)?



a. 139
b. 98
c.42
d. 154

no spam answers please!

Answers

Area of equilateral triangle = √3/4 a²

49√3 = √3/4 a²

49×4 = a²

a = 7×2

a = 14 cm

Side of equilateral triangle = Side of square ABCD = 14cm

Area of square ABCD = a²

A = 14×14

A = 196 cm²

Now diameter of circle = side of square = 14cm

Radius = D/2 = 7 Cm

There are two half circle in the square = one whole circle

Area of circle = πr²

A = 3.14 ×7 ×7

A = 153.86

Area of yellow region = Area of square - Area of circle

Area of yellow region = 196 - 153.86 = 42.14 Cm²

The area covered by the yellow region (in cm²) in the given diagram is 42cm². The correct option is c.42

From the question, the area of the blue equilateral triangle in the given diagram is 49√3cm².

The area of an equilateral triangle can be calculated by finding half the product of the square of a side (all sides are equal in an equilateral triangle) and sin 60° (each interior angle of an equilateral triangle is 60°)

Hence, the area of the blue triangle is given by

[tex]A = \frac{1}{2}/AB/^{2}sin60\°[/tex]

Where A is the area

Therefore,

[tex]49\sqrt{3} = \frac{1}{2}/AB/^{2}sin60\°\\2 \times 49\sqrt{3} = /AB/^{2} \times \frac{\sqrt{3} }{2}[/tex]

[tex]2 \times2 \times 49\sqrt{3} = /AB/^{2} \times \sqrt{3}[/tex]

[tex]196 \sqrt{3} = /AB/^{2} \times \sqrt{3}[/tex]

∴ [tex]/AB/^{2} = \frac{196 \sqrt{3} }{\sqrt{3} }[/tex]

[tex]/AB/^{2} = 196[/tex]

∴ [tex]/AB/ = \sqrt{196}[/tex]

[tex]/AB/ = 14cm[/tex]

Hence, the length of a side of the square is 14 cm and the diameter of the circle is also 14 cm (since the length of a side of the square cuts the circle into equal halves, hence it is the diameter)

Area covered by the yellow region = Area of the square - ( sum of the areas of the two semicircles)

Sum of the areas of the two semicircles = Area of one circle

Area of a circle is given by the formula

[tex]A = \pi r^{2}[/tex]

But r = d/2

where r is radius and d is diameter

∴ r = 14/2 cm

r = 7cm

Hence

Area of the circle = [tex]\pi \times 7^{2}[/tex]

A = [tex]49\pi[/tex]

Taking π = 22/7

∴ A = [tex]49 \times \frac{22}{7}[/tex]

A = 154cm²

This is the sum of areas of the two semicircles

Now, for the area of the square

Area of the square = /AB/²

Area of the square = 196 cm²

Now, as stated earlier,

Area covered by the yellow region = Area of the square - ( sum of the areas of the two semicircles)

∴ Area covered by the yellow region = 196 cm² - 154cm²

Area covered by the yellow region = 42cm²

Hence, the area covered by the yellow region (in cm²) in the given diagram is 42cm²

The correct option is c.42

Learn more on area of shapes here: https://brainly.com/question/24220654

Lori had $126.89 in her bank account. She deposited $21.49 into it and then wrote a check for her car repairs for $156.61.
What was the ending balance in her account?
O -$51.21
O $8.23
O $8.23
O $51.21

What is the answer?

Answers

Answer:

-8.23

Step-by-step explanation:

If Lori had $126.89 in her bank account and she deposited $21.49, she would be adding that to the amount of money in her bank account.

126.89+21.59= 148.48

Then subtract the amount of money the repairs costed.

148.48 - 156.61 = -8.23

Therefore Lori would have a balance of -$8.23.

Answer:

Lori had $126.89 in her bank account.

She deposited $21.49 into it and then wrote a check for her car repairs for $156.61  

126.89+ 21.49=148.38

148.38-156.61=−8.23

the answer is -8.23

1/5(6+3+1){2
answer the question

Answers

Answer:

The answer is 4 to the equation

State six ordered pairs for this function.
f(x)=4^x

Answers

Answer:

Step-by-step explanation:

x     y = 4^x    (x, y)

-2    1/16         (-2, 1/16)

-1    1/4           (-1, 1/4)

0      1              (0, 1)

1      4                1, 4

3      64             3, 64

5    1024           (5, 1024)

Someone help!

If there are 365 days in a year and you buy 365 $15 Starbucks gift cards. How much will that cost?

Answers

Answer:

If you buy a 15 dollar gift card every day for a year, it will cost $5,475.

Just take the price, multiply it by the amount.

Answer:

$5475

Step-by-step explanation:

365 X 15 =

(365 x 10) + (365 x 5) =

3650 + 1825 =

$5475

Logic puzzle ANSWER AS QUICKLY AS POSSIBLE PLS!


Answers

Answer:

what do i do is this math or science

Step-by-step explanation:

WILL GIVE BRAINLIEST!
Ify is floating freely in outer space. The gravitational forces pulling on her body are negligible except for the forces from a nearby asteroid (a) the nearest planet (p) and the nearest star (s) The asteroid, planet, star, and Ify all lie in the same plane.
a= (2,4)
p=(-1.-3)
s=(8,2)

Answers

Answer:

The magnitude of the net gravitational force acting on Ify is 9.1 newtons.

Ify is getting pulled in a direction of 6.2 radians.

Step-by-step explanation:

The vector g = (9,-1)   describes the net gravitational force acting on Ify.

We can find the magnitude of  g, using the Pythagorean theorem.

Find the value of x in the triangle shown below.
ac
5

Answers

the value of x is equal to 3

What is the area of the following circle?
Either enter an exact answer in terms of 7 or use 3.14 for TT and enter your answer as a decimal.
d=10
units?

Answers

Answer:

78.5 is the answer

10/2 = 5

5 x 5 = 25

3.14 x 25 = 78.5

Tan?cos? Sin? What is the m

Answers

Answer:

45º

Step-by-step explanation:

Since we know the relatiionship of a 45-45-90 degree triangle, we can go two ways. Either we can use this to find CA and get the tangent of (6/6) or we can go straight to it. The hypotenuse in a 45-45-90 is always 6√2 and we know it is a right triangle so we can confirm this. So, measure of angle B is 45º.

Gisella has 4 pints of chicken broth. She uses 5 cups of the broth to make soup.

How much chicken broth is left?

Answers

Answer:

3 cups would be left or 1.5 pints.

Step-by-step explanation:

1 pint is equal to 2 cups.

1.5 US pints according to the test I had.

Solve the system by eliminating one of the variables by addition or subtraction

2x-y=4
3x+y=6

Answers

Answer:

(2,0)

Step-by-step explanation:

2x-y=4 equation 1

3x+y=6 equation 2

5x=10 eliminate y by adding equations

x=2

solve for y

2x-y=4

2(2)-y=4

4-y=4

-y=0

y=0

check answer:

3x+y=6

3(2)+0=6

6=6

Plz answer i'll give brainliest but it has to be right.

Answers

3 -3/4 and 2 pls brainlest

Can someone help pls

Answers

C) how many sweets did they share altogether. We must know how many sweets they had in order to simplify the ratio with this information nothing can be done

Answer:

Age of Sean = 15

Age of Ricki  = 10

[tex]Ratio \ of \ their \ age = 15 : 10 = 3 : 2[/tex]

[tex]Sum \ of \ the \ ratio = 5[/tex]

[tex]Let \ number\ of sweets \ be \ x[/tex]

[tex]Number \ of \ sweets \ Sean \ got = \frac{3}{5} * x\\\\48 = \frac{3}{5} * x\\\\x = \frac{48*5}{3} = 80[/tex]

[tex]Total \ number \ of \ sweets = 80\\Sean \ got \ 48\\Number \ of \ sweets \ Ricki \ got = 80 -48 = 32[/tex]

Ans : a) 3  : 2

       b) 32 sweets

       c) 80 sweets

good luck on finals week :)

Answers

you too ty :)

ilysm and you matter <3

Please help me quick please solve in inequality form

Answers

Answer:

Answer OPTION C

AT LEAST... means that she needs 80% and more

Meaning its must be equal to 80% or greater than 80%

Average has to do with Mean.

Her mean would have to be

The sum of the 3 last algebra tests plus the unknown one she's supposed to have to complete 80%

So

Thatll be

80+75+86 + x /(4) ≥ 80

241 + x/(4) ≥80

Option C

Practice test question, help please

Answers

Answer:

ask ur teacher

Step-by-step explanation:

talk

I need help! would appreciate it

Answers

Answer:

stay safe healthy and happy....

3x-8y=24
y=x-8
Please show
work

Answers

Answer:

3x - 8y = 24   --------(1)

y = x - 8  ---------(2)

substitute  y in (1)

3x - 8( x - 8) = 24

3x - 8x + 64 = 24

-5x = 24 - 64

-5x = -40

5x = 40

x= 8

substitute x in (2)

y = 2 - 8

y = - 6

Answer:

x = 8, and y = 0

Step-by-step explanation:

We can solve this by taking y as (x-8), as it states there.

Since y is equal to x-8, we can rearrange the system of equations into one single equation.

We can multiply y by 8, as it shows in the first equation, which is something like 8x-64.

Since it is a negative 8 being multiplied by y, it would be the inverse of 8x-64, which is -8x+64.

We can now organize our equation here.

3x - 8x + 64 = 24.

We can use subtraction property of equality by subtracing 64 from both sides to get rid of it.

We will get something like:

3x - 8x + 64 - 64 = 24 - 64.

Simplify by solving like terms like the x value and the integers.

-5x = -40

Divide both sides with division property of equality:

-5/5x = -40/5

x = 8

We can then plug the 8 back into x, lets use the second equation because I'm lazy and it looks the easiest to solve for.

y = (8) - 8

y = 0

Therefore, x = 8, and y = 0.

Marking brainliest if you answer all 3 of them n

Answers

1) Equation: y = 5x + 1

Missing Value: 51

2) Equation: y = 4x

Missing Value: 28

3) I have no idea for this one... sorry!

Which equation is a linear function?

Answers

Either the first or last but I think it is first

Answer:

B. y = x

Step-by-step explanation:

Linear function has the form of:

y = mx + b

Only one of the choices, B is representing the linear function:

y = x

3800 divided by 4, I know it’s 950 but I need to know how to get 950

Answers

Here you go hope this helps :)

write -5.6 x 10^-3 in standard form?

Answers

Answer:

-0.0056

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/math/scientific-notation-converter.php

Janet is comparing prices of bottled drinks. She finds one bottle of water that costs $1.92 and contains 12 ounces. She then finds one bottle of soda that costs $2.40 and contains 16 ounces. Which bottle costs less per ounce?

it a short answer response

Answers

Answer:

1 ounces of water= $0.16

1 ounces of soda= $0.15

Water costs $0.16 per ounces while soda costs $0.15 per ounces which means soda costs less than water per ounces.

You spin a spinner labeled 1-10 evenly. what are the chances you will get an odd number?

Answers

Answer:

1/2

Step-by-step explanation:

Which equation is equal to 4a + 2b = 10?

options:
b = -2a + 10
b = 2a + 10
b = -2a + 5
b = 2a + 5

Answers

b = -2a + 5
good luck :)))

Which expresion is equivalent to -5 -(-7)?
HURRY 20 POINTS

Answers

Answer:

2 (the answer should have a positive sign.)The equivalent to -5-(-7) is -5+7.

Step-by-step explanation:

To solve this problem, use the order of operations.

PEMDAS

Parentheses

Exponents

Multiply

Divide

Add

Subtract

[tex]\sf{-5-(-7)=-5+7}[/tex]

[tex]\sf{-5+7}[/tex]

Add or subtract.

Solve.

[tex]-5+7=2[/tex]

[tex]\large\boxed{2}[/tex]

So, the correct answer is 2.

Answer:3+(px6)

Step-by-step explanation:

Veronica and Helga both have collections of trading cards.

Veronica has 752 trading cards.
Veronica has 16 times as many trading cards as Helga.
If Veronica and Helga put their cards together, how many cards would there be?

Answers

752 x 16 = 12032
12032 + 752 = (12785)

PLEASE HELP IM GIVING 70 POINTS Figure A is a scale image of Figure B, as shown Х 3 Figure A Figure B The scale that maps Figure A onto Figure B is 1:7- 4​

Answers

Answer:

stretching trifling preheated prejudicial irresistible

If the scale factor is 1:7 1/4. Then x = 7.25 * 3 = 21.75 or 21 3/4

Given the following equation, solve for x.
y = mx+b


Answers

Answer:

c

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

Other Questions
Select the closing entry that RB Auto would make at the end of the accounting period to close their revenue accounts and income statement accounts with credit balances. Multiple Choice debit Sales and credit Income Summary for $15,000. debit Sales $15,000; debit Purchase Returns and Allowances $200 and credit Income Summary for $15,200. debit Sales for $15,000; debit R Holloway, Capital for $13,000 and credit Income Summary for $28,000. debit Income Summary for $15,000 and credit Sales for $15,000. Can someone answer this Finding probability Which of the following was legal under slave codes?A.enslaved people meeting in large numbersB.teaching enslaved people to read and writeC.an enslaved person owning a weaponD.the killing of an enslaved person by his or her master Which factors increase the heat absorbed by a land surface? Select the two correct answers.A. becoming wetterB. becoming smootherC. removing plantsD. removing showE. becoming paler Compare a to b (which one is greater or insufficient information meaning that there is not enough information to determine which one is greater) if a is a counting number and b is an integer. use either < or > or say insufficient information) PLEASE HELP will give first answer brainliest if u get it right Can someone pleaseeee help and if youre correct ill give brainliest According to the excerpt, which best describes Aung San Suu Kyi's position regarding junta rule? A. She wishes to overthrow the government. B. She is calling for peaceful opposition. C. She supports the junta's policies. D. She is calling for an armed, anti-junta rebellion. PLEASE ANSWER THIISSSISISIIS Who do you think should have decided whether slavery was legal in the United States? Solve for XSolve for XSolve for XSolve for XSolve for XSolve for XSolve for XSolve for XSolve for XSolve for XSolve for X Which of these is a compound sentence?AThe Herald, a prominent newspaper, had been in business for more than 100 years.B. At first its circulation was only 500 papers daily.C. However, circulation grew and grew, reaching 100,000 papers by 1998.DThen, people began reading the news online, circulation fell, and the paper folded. Brsinlirst if correct(4) Kevin is scanning old images from his college library. He might use these scanned images in the college magazine. He might also use them on the college website. What is the best practice for Kevin to follow when scanning the images?A. scan the images with 72 DPIB. scan only the images that are ideal for a websiteC. scan the images with 150 DPID. scan the images with 600 DPIE. scan the images that are ideal for a magazine according to john locke what was the purpose of the government PLS HELP!!! Where does the light and thermal energy given off when burns food come from?A Light and thermal energy given off from burning food comes from the lighter used to light the food.B. Light and thermal energy given off from burning food is converted from the chemical energy stored inthe food.C. Light and thermal energy given off from burning food comes from oxygen.D. Light and thermal energy given off from burning is created when food burns.3. Why do two grams of fat provide a different amount of energy than two grams of carbohydrate? Which of these descriptions defines general characteristics of a symbol?Symbols are subtle and intangible thoughts or details.Symbols have a concrete, physical existence.Symbols carry alternate, associated meanings.Symbols are always explicitly stated in the text. At the city Museum child admission is $6.20 an adult admission is $9.90 on Sunday 142 tickets were sold for a total sales of $1183.80 how much adult tickets were sold that day 2) determine the length of the hypotenuse from the picture A) 21 cmB) 28 cmC) 35 cmD) 49 cmDont put the answerIn a link Answer plsssssssssssssssssssssssssssssss