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

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

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)

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...
8
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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

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.

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

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.

A number that is at most 30 as an inequality

Answers

Answer:

n  ⩽ 30

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 .....

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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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

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

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 (✿◠‿◠)

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



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

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

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

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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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.

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]

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

-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 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

heyyy so like hellpppp me out

Answers

Answer:

gotta be C

Step-by-step explanation:

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

Answers

Answer:

hi… I think it's written that way

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.

Hope this helps and pls do mark me brainliest if you can:)

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.

branliest plssss :)

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.

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.

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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