Mathematics High School

Solve the quadratic equation below by completing the square. What are the solutions?
x^2 - 16x + 50 = 21
A. X= -8+sqrt 7
B. X= 8 + sqrt 7
C. X= 8 +sqrt 35
D. X= -8+sqrt 35

Answers

Answer 1

By completing squares we will see that the solutions are:

[tex]x =\pm \sqrt{35} + 8[/tex]

How to complete squares?

Here we have the quadratic equation:

[tex]x^2 - 16x + 50 = 21[/tex]

We can rewrite it as:

[tex]x^2 - 2*8*x + 50 - 21 = 0\\\\x^2 - 2*8*x + 29= 0[/tex]

Then we must have a 8² term to complete squares, then we need to add and subtract 35.

[tex]x^2 - 2*8*x + 29 +35 - 35= 0\\\\(x - 8)^2 - 35 = 0\\\\(x - 8)^2 = 35[/tex]

Now we can solve this:

[tex]x =\pm \sqrt{35} + 8[/tex]

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Related Questions

9s - 5g=4u, for s i need the answer pls

Answers

Answer:

9s-5g=-4u

*Isolating the S variable*

9s = -4u+5g

s = (-4u + 5g)/9

The answer is option B.

The correct answer choice is B.

You want to isolate the variable so you add 5g on both sides of the equation. Which gives you 9s = -4u + 5g. Then you divide both sides of the equation by 9 which would get you s= -4u+ 5g/9.

Find FG. (idk how to write the question but apparently it needs to be longer)

Answers

Answer:

FG = 18

Step-by-step explanation:

FG + GH =  FH

FG + 31 = 49

Subtract 31 from each side

FG +31-31 = 49-31

FG = 18

Answer: FG is 18

Step-by-step explanation: FG + GH is FH, GH is 31 and then you substitute 31 in for GH which makes the equation FG+31=49 49-31 is 18 which means FG is 18

A statement that two ratios are equal is called a
​

Answers

The answer is proportion. A proportion basically equates two ratios.

A statement that two ratios are equal is called a proportion.

In a proportion, the four quantities involved are related in such a way that the first ratio is equal to the second ratio. It can be represented in the form of "a:b = c:d," where "a" and "b" are the terms of the first ratio, and "c" and "d" are the terms of the second ratio.

Proportions are used in various mathematical applications, such as solving problems involving ratios, scaling, similarity, and solving for unknown values. They provide a way to compare quantities and establish relationships between them based on their relative sizes.

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6) The wind blew away 35 of your muffins.
That was 5/6
of all of them! With how
many did you start?

Answers

Answer:

42 muffins

Step-by-step explanation:

In order to find the answer, you would divide 35 by 5/6 which would equal 42. So you started with 42 muffins.

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Solve the inequality:


2x−9≥17

Select one:

x≤13

x≥3

x≤3

x≥13

Answers

Answer:

x≥13

Step-by-step explanation:

add 9 to both sides

2x≥26

divide both sides by 2

x≥13

If m<5=63°, find the measure of <3.

Answers

Answer:

angle 3's measurement should be 117 degrees

hope this helps :)

The measure of angle 3 is 117 degrees.

Calculation of an angle:

In terms of geometry, an angle refers to the figure i.e. credited by two rays that should be met out at a common endpoint. An angle should be presented by the symbol ∠.

Since the angle 5 is 63 degrees

and, the total of two angles is 180 degrees

So, the angle 3 is

= 180 - 63

= 117 degrees

hence, The measure of angle 3 is 117 degrees.

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The original price of a play ticket was $36.00. Yolanda bought the ticket at original price and then marked it up 10% and resold the ticket. How
much did she resell the ticket for?
What

Answers

she sold the ticket for $39.50
explanation: you take 36 and time it by 10% and it will give you $3.60 and you add it to 36

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 18 minutes. The other bucket dumps water every 16 minutes. It is currently 2:45 P.M. And both buckets dumped water 15 minutes ago. Find the next two times that both buckets dump water at the same time.

Answers

Answer:

The next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

Step-by-step explanation:

From the question, one bucket dumps water every 18 minutes, say bucket A;

and the other bucket dumps water every 16 minutes, say bucket B.

Also, It is currently 2:45 P.M. and both buckets dumped water 15 minutes ago,

that is, both buckets dumped water at 2:30 P.M.

For bucket A, the next times it will dump water will be:

2:48 P.M, 3:06 P.M, 3:24 P.M, 3:42 P.M, 4:00 P.M, 4:18 P.M, 4:36 P.M, 4:54 P.M, 5:12 P.M, 5:30 P.M, 5:48 P.M, 6:06 P.M, 6:24 P.M, 6:42 P.M, 7:00 P.M, 7:18 P.M, 7:36 P.M, 7:54 P.M, 8:12 P.M, 8:30 P.M etc.

For bucket B, the next times it will dump water will be:

2:46 P.M, 3:02 P.M, 3:18 P.M, 3:34 P.M, 3:50 P.M, 4:06 P.M, 4:22 P.M, 4:38 P.M, 4:54 P.M, 5:10 P.M, 5:26 P.M, 5:42 P.M, 5:58 P.M, 6:14 P.M, 6:30 P.M, 6:46 P.M, 7:02 P.M, 7:18 P.M, 7:34 P.M, 7:50 P.M etc.

From above, we observe that the next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

Hence, the next two times both buckets dump water at the same time are 4:54 P.M and 7:18 P.M.

solve 3(x-4)=16+5x show work

Answers

Answer:

hi… I think it's written that way

What do the two lines in the graph below have in common?

Answers

Answer: Parallel and same slope

Step-by-step explanation: Parallel means that the lines will never cross, which is shown in the picture. Basically they won't intersect.

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expand (2a +36) (2a-3b​

Answers

Use the binomial expansion theorem to find each term. The binomial theorem states
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Simplify the exponents for each term of the expansion.
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Tap for more steps...
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which list shows the numbers 2/3, 9/11 and 7/9 arranged from least to greatest​

Answers

Answer:

2/3; 7/9; 9/11

Step-by-step explanation:

You have to divide them and you will get a decimal that is how you put them in numerical order

What is the equation of the line that is parallel to the the line y-1 =4 (x+3) and passes through th point (4,32)

Answers

I used Symbolab to calculate my answer. It is y=4x + 16.

Calculation of slope: y-1=4(x+3) m= 4 and b=16

A number that is at most 30 as an inequality

Answers

Answer:

n  ⩽ 30

Step-by-step explanation:

What is the equation in point-slope form of the line that passes through (-9, 12) with a slope of 5/6?
A. y-12=6/5(x+9)
B. y-12=5/6(x+9)
C. y-9=5/6(x-12)
D. y-12=6/5(x-9)​​

Answers

Answer:

The equation of the line is y - 12 = [tex]\frac{5}{6}[/tex] (x + 9) ⇒ B

Step-by-step explanation:

The slope-point form of the linear equation is

y - y1 = m(x - x1), where

m is the slope of the line(x1, y1) are the coordinates of a point lie on the line

∵ The slope of a line is [tex]\frac{5}{6}[/tex]

∴ m = [tex]\frac{5}{6}[/tex]

∵ The line passes through point (-9, 12)

∴ x1 = -9 and y1 = 12

→ Substitute these values in the form of the equation above

∵ y - 12 = [tex]\frac{5}{6}[/tex] (x - -9)

→ Remember (-)(-) = (+)

∴ y - 12 = [tex]\frac{5}{6}[/tex] (x + 9)

∴ The equation of the line is y - 12 = [tex]\frac{5}{6}[/tex] (x + 9)

1. Which of the following is a pair of parallel lines? W = 1/4x - 7 V=1/44+2 W = 4x - 7 V = 1/4x + 2 W = 1/4x - 7 V= 1/4x + 2 W = 4x - 7 V = -4x + 2 C​

Answers

V=1/4x+2 and W=1/4x-7 are parallel because they have the same slope and different y-intercepts.

There are a total of 75 motorcycles and cars in a shop. There are 270 wheels in all. How many motorcycles and how many cars are in the shop? ​

Answers

Answer: 15 motorcycles and 60cars

At an auction a company sells 150 television sets for an
average of $65 each. The production cost was $10 000.
How much loss did the company make?

Answers

Answer:

They lost $250 total

Step-by-step explanation:

[tex]150 \times 65 = 9750[/tex]

[tex]10000 - 9750 = 250[/tex]

[tex]250[/tex]

2. Tamara has to go on a business trip. Including taxes, her round trip airfare is $400 and her room costs $150 per night. The cab fare from the airport to the hotel is $40. If Tamara stays for two nights, how much does the trip cost, not including the cost of food?

Answers

Answer:1180,740

Step-by-step explanation:

2 night, so (400x2)+(150x2)+(40x2)=800+300+80=1180 this is cost to go and come back.

400+300+40=740 this is the cost for only going there and not coming back.

prime factorization of 45 expanded form

Answers

The prime factorization of 45 would be 5×9, and 9 is 3×3, so 45 would be 5×3^2.

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These triangles are congruent by _____.

A. AAS
B. SAS
C. HL
D. Not enough information

Answers

Answer:

AAS

Step-by-step explanation:

Angles in left and right corner are congruent (isosceles triangle)

Two right angles in the middle

If the leading coefficient is negative, always factor out the negative.
-x^2+5x-6​

Answers

Answer:

-1(x-2)(x-3)

Step-by-step explanation:

first we factor the negative:

-1 (x^2 - 5x +6 )

the next step, (if possible) is to guess 2 numbers that multiplied are 6

and added are -5

in this case is easy to see that those numbers are -2 and -3

The solution then is:

-1(x-2)(x-3)

If guessing the 2 numbers doesn't work, you need to complete the square

Question:

What is the other term of removing sets from a universal set?

Thank you. ​

Answers

Answer:

Subset

Step-by-step explanation:

A subset is a group of elements whose values were obtained from a larger set known as the universal set.

For example, say we have a universal set of all the numbers from 10 to 20

{10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A subset of the even numbers include;

{10, 12, 14, 16, 18, 20}

A subset of the odd numbers include;

{11, 13, 15, 17, 19,}

These figures in the subset were derived from the universal set which is the larger set.

heyyy so like hellpppp me out

Answers

Answer:

gotta be C

Step-by-step explanation:

The perimeter of a rectangle is 70cm. If the length of the rectangle is 5cm more than its breadth, find the dimensions of the rectangle.

Plsss help I put 15 points

Answers

Hope it helps man .....

The fifth term of a non-linear sequence is 9.
The term-to-term rule is divide by 3'.
Work out the second term of the sequence.​

Answers

Answer:

a₂ = 243

Step-by-step explanation:

The term to term rule from left to right in the sequence is divide by 3

The term to term rule from right to left is the opposite, multiply by 3

Given

a₅ = 9, then

a₄ = 9 × 3 = 27

a₃ = 27 × 3 = 81

a₂ = 81 × 3 = 243 ← required term

Find the area of a rectangle with length of 3 inches and width of 8 inches.
Area = _____ square inches.

Answers

Answer:

24 in

Step-by-step explanation:

L × W = A3 × 8 = 24 in

I hope this helps!

Answer:

24

Step-by-step explanation:

lXw= area

-4x-2y = -6

a. y = -2x + 3
b. y = 2x - 3
C. y = 2x + 3
d. y=-2x - 3

Answers

Answer:

B

Step-by-step explanation:

y = 2x - 3

.....20 characters smh

Which expression represents “7 more than x” 7+x x-7
x÷7 7x

Answers

Answer:

7+x

Step-by-step explanation:

this could also be written as “x + 7” and it means 7 more than (+) x

Answer:

It is 7+x (✿◠‿◠)

Please help a girl out!! :(( im really confused and it would mean a lot if someone helped!

Answers

Answer:

$7.69

Step-by-step explanation:

2.48+2.48+2.48= $7.44

then add 0.25 which is

$7.69

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please help me with this thank you:) 4.- Choose the right answer. A: Hace cuatro horas que mi hermano juego videojuegos.B: Hac tres horas que mi hermano juga videojuegos.C: Hace dos horas que mi hermano juega videojuegos.D: Hace una hora que mi hermano juegan videojuegos. What is the following sum? Selected Information from Balance Sheets (As of Year End for Years 0 and 1) Year 0 Year 1 Cash 1,000 2,000 Accounts Receivables 1,000 5,000 Inventory 5,000 4,000 Property, Plant and Equipment (net) 12,000 11,000 Accounts Payable 5,000 4,000 Unearned Revenue 2,000 1,000 Bonds Payable 5,000 6,000 Common Stock 3,000 4,000 Retained Earnings 5,000 7,000 Income Statement (Year 1) Sales 20,000 Costs of Goods Sold (8,000) Wage Expense (4,000) Depreciation Expense (2,000) Loss from PP&E Sale (1,000) Net Income Before Tax 5,000 Tax Expense (2.000) Net Income 3.000 In the space provided, prepare the Operating section of the statement of cash flow for Year 1, using the indirect approach. What claim does the author make in her argument in this selection? A stream of oxygen enters a compressor at 298 K and 1.00 atm at a rate of 127m3/h and is compressed to 358 K and 1000 atm. Estimate the volumetric flow rate of compressed O2 using the compressibility-factor equation of state. Could you please put the answer with the letter? Does not need to be in order too. Which of the following was a military advantage that the Americans enjoyed over the British during the Revolutionary War?OA. A single top commander served throughout the entire conflict.OB. Public support for the cause was strong throughout the war.OC. Reliable pay ensured that troop morale was always high.OD. A single manufacturer produced all of the weapons used. Which sentences in the section "AuthoritarianRegimes" support the idea that ordinary peoplehave very little power in authoritarian governments?AIt is dangerous to categorize a nation simplyby the moment in time during which they wereexamined.BKings, military leaders, emperors, a smallgroup of aristocrats, dictators and evenpresidents or prime ministers may ruleauthoritarian governments.CAuthoritarian governments may holdelections. They may even have contact withtheir citizens.DThe leaders decide what the people can orcannot have. Citizens, then, are subjects whomust obey. What character traits make Achilles in hector and Achilles Heroic? 1/5t+2- =171/5t.1/5tT= Both Lone Dog and Playing Robinson Crusoe are about animals.How is the poem and story alike?Both passages explain what life is like from the point of view of a dog.Lone Dog describes dogs positively, but Playing Robinson Crusoe describes good and bad things about cats.Lone Dog compares the behaviors of two types of dogs, while Playing Robinson Crusoe compares the life of an indoor cat who must survive outside.Both passages discuss the loving relationship between pets and humans. Can someone plz plzzz help me out with these problems I been stuck on them for the past hour and a half is there an edge to the universe? 1/2 inch is equal to ____ /16 inch a. 8 b. 2c. 6d. 4 How have you dealt with failure and bounced back from it? 24 is what percent of 300 which of the following sentence uses the correct verb tense A your science class won't meet yesterday. B my mother goes running every day. C currently, my favorite food was ice cream. D the candied yams were delicious tomorrow Global strategic planning is a primary function of a company's managers, and the process of strategic planning provides a formal structure for undertaking this process. Companies are confronting a set of environmental forces that are increasingly complex, global, and subject to rapid change. In response, many international firms have found it necessary to institute formal global strategic planning to provide a means for top management to identify opportunities and threats from all over the world. Required:Formulate strategies to handle them, and stipulate how to finance and manage the implementation of these strategies? On Tuesday, a local hamburger shop sold a combined total of 435 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Tuesday?