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

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.

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


Answers

Answer:

c

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

Practice test question, help please

Answers

Answer:

ask ur teacher

Step-by-step explanation:

talk

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

good luck on finals week :)

Answers

you too ty :)

ilysm and you matter <3

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!

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

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

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)

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

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

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 :)))

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.

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:

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.

I need help! would appreciate it

Answers

Answer:

stay safe healthy and happy....

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

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

Answers

Answer:

The answer is 4 to the equation

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)

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.

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

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

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

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.

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

Answers

3 -3/4 and 2 pls brainlest

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

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 :)

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

Answers

the value of x is equal to 3

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:

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