Mathematics College

Solve the equation x^2 - 16x+ 54 = 0 by completing the square.
Fill in the values of a and b to complete the solutions.

Solve The Equation X^2 - 16x+ 54 = 0 By Completing The Square.Fill In The Values Of A And B To Complete

Answers

Answer 1

Answer:

[tex]x = 8\±\sqrt{10[/tex]

[tex]a =8[/tex]    [tex]b = 10[/tex]

Step-by-step explanation:

Given

[tex]x^2 - 16x + 54 = 0[/tex]

Required

Complete the square

[tex]x^2 - 16x + 54 = 0[/tex]

Subtract 54 from both sides

[tex]x^2 - 16x + 54 -54= 0-54[/tex]

[tex]x^2 - 16x = -54[/tex]

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

Take half of - 16

[tex](-16/2) = -8[/tex]

Square the result

[tex](-8)^2 = 64[/tex]

Add the squared result to both sides of the equation

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

So, we have:

[tex]x^2 - 16x +64= -54+64[/tex]

[tex]x^2 - 16x +64= 10[/tex]

Expand

[tex]x^2 - 8x - 8x + 64 = 10[/tex]

Factorize

[tex]x(x - 8) - 8(x - 8) = 10[/tex]

Factor out x - 8

[tex](x - 8)(x - 8) = 10[/tex]

[tex](x - 8)^2 = 10[/tex]

Take square roots

[tex]x - 8 = \±\sqrt{10[/tex]

Solve for x

[tex]x = 8\±\sqrt{10[/tex]

We have:

[tex]x = a - \sqrt{b}[/tex]

[tex]x = a + \sqrt{b}[/tex]

By comparing the above with: [tex]x = 8\±\sqrt{10[/tex]

Answer 2

Answer:

Step-by-step explanation:

Solve The Equation X^2 - 16x+ 54 = 0 By Completing The Square.Fill In The Values Of A And B To Complete

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Guys can you help me please :( ASAP

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Answer:

The answer is 25 + 11

Step-by-step explanation:

Hope this helps

Tammy harvested pounds of nuts from her pecan tree. If she divides the nuts into pound bags, how many bags will she have?

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Answer: Tammy would have 9

Step-by-step explanation:

(6 3/4) / (3/4) =

= 27/4 / 3/4

= 27/4 * 4/3

= 27/3 * 4/4

= 9

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What are you asking here? Are you asking if D is the right answer? If so then I can’t see D.

it’s a non calc question

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Answer:

60 Degrees

Step-by-step explanation:

trust me

HELP ME PLEASEEEEEEEEEEEE

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the answer is b (-3,3) can i have brainliest

UN


2. What is the conversion from cubic metres to litres?​

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Answer:

1 cubic meter equals 1000 liters

Step-by-step explanation:

i think this is right

What is the product?

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Answer:

I believe that it is the 2nd option x(x-1)/2 but I could be wrong sorry if I am

Comparative financial statement data for Carmono Company follow: This Year Last Year Assets Cash $ 8.50 $ 16.00 Accounts receivable 54.00 47.00 Inventory 97.50 84.40 Total current assets 160.00 147.40 Property, plant, and equipment 237.00 198.00 Less accumulated depreciation 47.20 35.40 Net property, plant, and equipment 189.80 162.60 Total assets $ 349.80 $ 310.00 Liabilities and Stockholders’ Equity Accounts payable $ 58.50 $ 48.00 Common stock 126.00 97.00 Retained earnings 165.30 165.00 Total liabilities and stockholders’ equity $ 349.80 $ 310.00 For this year, the company reported net income as follows: Sales $ 950.00 Cost of goods sold 570.00 Gross margin 380.00 Selling and administrative expenses 360.00 Net income $ 20.00 This year Carmono declared and paid a cash dividend. There were no sales of property, plant, and equipment during this year. The company did not repurchase any of its own stock this year. Required: 1. Using the indirect method, prepare a statement of cash flows for this year. 2. Compute Carmono’s free cash flow for this year.

Answers

this ain’t work 5 points ...

Select the correct answer.

A home-based sign company uses this function to model its monthly profit, where x is the price of each sign it sells.

p(x) = -10x^2 + 498x - 1,500

what is the company's profit if it sells each sign for $20?

A. $18,020
B. $4,460
C. $14,420
D. $1,402

Answers

The profit made id each sign is sold for $20 is $4460

The profit model, P(x) = -10x² + 498x - 1,500

Where, x = price per sign sold

If the price per sign sold is $20. Hence, x = $20

The profit made can be calculated thus :

Put x = 20 in the profit function :

P(20) = -10(20)² + 498(20) - 1,500

P(20) = - 10(400) + 9960 - 1500

P(20) = - 4000 + 9960 - 1500

P(20) = $4,460

The profit made is $4,460

Learn more : https://brainly.com/question/18109354

Answer:

$4,460

Step-by-step explanation:

I got a 100% on my test

The square of an integer is 5 more than 4 times the integer. Find the integer.

Answers

Answer:

The integer can be -1 or 5.

Step-by-step explanation:

Let an integer is x.

ATQ,

The square of an integer is 5 more than 4 times the integer.

[tex]x^2=5+4x[/tex]

or

[tex]x^2-5-4x=0\\\\x^2-4x-5=0[/tex]

It is a quadratic equation. Using middle term splitting,

[tex]x^2-5x+x-5=0\\\\x(x-5)+1(x-5)=0\\\\(x+1)(x-5)=0\\\\x=-1,5[/tex]

So, the integer can be -1 or 5.

If the square of an integer is 5 more than 4 times the integer, the integers are -1 and 5

Let the unkown integer be "x"

The square of an integer is expressed as x^2

5 more than 4 times the integer is expressed as [tex]4x +5[/tex]

Equate both expressions to have:

[tex]x^2 = 4x + 5\\[/tex]

Equate to zero and factorize:

x^2 - 4x - 5  = 0

x^2 - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x + 1)(x - 5) = 0

x = -1 and 5

Hence the integers are -1 and 5

Leearn more here: https://brainly.com/question/13805464

PLS HELP 40 POINTS

A rectangular prism has a surface area of 8 square feet. A similar rectangular prism has a surface area of 200 square feet. How many times larger are the dimensions of the larger prism?

25
625
5
10

Answers

Answer:

C. 5

Step-by-step explanation:

The area is the product of two dimensions.

If the ratio of sides is k, then the ratio of areas is k²

We have:

k² = 200/8k² = 25k = √25k = 5

Correct choice is C

Answer:

5

Have a great day/night!

Write the equation of the line in fully simplified slope-intercept form.

Answers

the answer is y=-5x+5

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Answers

Here’s what I got
A 43
B137
C137

Answer this for 10 points

Answers

Answer:

Equations would be;

30 + 50 + y = 180

and

y = 180 - 80

Additional:

If you are looking for y and u value then here they are:

y = 100°

u = 25°

Hope this helps!

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8x2 9x2 y2 5y yx3

Explanation:

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Answers

Answer:

20meter per second is tw correct answer

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Step-by-step explanation:

1km/h = 1000m/3600s = 5m/18s

⇒ 72 × 5 ÷ 18 = 20 (m/s)

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a.
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b.
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c.
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d.
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Answers

I think the answer is D

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Answers

Answer:

Gross margin= $50

Step-by-step explanation:

Giving the following information:

Selling price= $264

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To calculate the gross margin, we need to deduct from the selling price the unitary cost:

Gross margin= selling price - unitary cost

Gross margin= 264 - 214

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A woman drives her car 180 miles in 3 hours. At this rate how far will she travel in 5 hours?

Answers

Answer:

288

Step-by-step explanation:

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Answers

First lets find the total number of cookies

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Number of cookies eaten

5*2=10

10 were eaten

Cookies left

48-10=38

38/48=19/24

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Answer:

38 are left

Step-by-step explanation:

What is the total Fatima paid?

Answers

A.
You have to $129.95 * 5 because 5 were purchased and that would give you $649.75 then you add delivery fee $76.20 for delivery fee.

olve the system of linear equations by graphing. =3+3 - 2x - 3 ​

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Answer:

If the equation is actually typed like that the answer will be

3-2x

If is typed like this 3-2x-3+3=

It will be

-2x+3

Devin has a rectangular vegetable garden. He planted tomatoes in section of the garden with an area of 6 square yards. There were 30 square yards remaining for Devin to plant zucchini. Let g represent the total area of the garden. Which equation models the problem? Solve the equation to find the total area of the garden. g =

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

(a) 18.5ft

(b) 388.5 ft²

Step-by-step explanation:

(a)

She has 79ft of fence = the perimeter will be 79.

Perimeter of a rectangle = 2(length) +2(width)

79 = 2(21)+2(width)

2(width) = 79 - 42

width = 37/2

width = 18.5ft

(b)

Area of a rectangle = (length)(width) = (21)(18.5) = 388.5 ft²

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ts
43
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<<
43 = [?]

Answers

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Please please help!!!!

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Answer:

4.75

Step-by-step explanation:

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Answers

Answer:

(6⋅2)−(9/3)

Simplify each term.

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Step-by-step explanation:

an aquarium at the zoo is shaped like a cylinder. it has a height of 4 feet and a base radius of 2.5 feet. the aquarium is being filled with water at a rate of 12 gallons per minute. if one cubic foot is about 7.5 gallons, how long will it take the aquarium to fill? round to the nearest whole minute.

Answers

Answer:

49 minutes

Step-by-step explanation:

Volume

v = πr²h

v = π(2.5²)4

v = 78.5 ft³

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

Gallons needed

78.5 * 7.5 = 588.75 gallons

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

Time to fill

588.75 / 12 = 49.0625

Rounded

49 minutes

IK ANSWERS AREN’T CLEAR LOOK AT PHOTO!! HELP ASAP I WILL MARK BRAINIEST!

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Step-by-step explanation:

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The answer is (B) hope it helps
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