20 POINTS !!!!!!!!!
Solve the quadratic equation by completing the square.
x^2 - 18x + 68 = 0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.

Answers

Answer 1

Answer:

x =  x = 9 ±[tex]\sqrt{13}[/tex]  or x ≈ 12.61 or  x ≈ 5.39

Step-by-step explanation:

x² - 18x + 68            Solve by completing the square.

x² - 18x = - 68    

Now complete the square and add that number to both sides of the equation.

1/2 (of the coefficient of the x term)² = (1/2 · -18)² = 81 .

x² - 18x + 81  = -68 + 81

(x - 9) (x - 9) = 13                  Now find the square root of both sides

[tex]\sqrt{(x - 9)(x - 9)}[/tex] =[tex]\sqrt{13}[/tex]            Solve

x - 9 = ±[tex]\sqrt{13}[/tex]                         Solve for x

x = 9 ±[tex]\sqrt{13}[/tex]  

x = 9 + [tex]\sqrt{13}[/tex]    or  x = 9 - [tex]\sqrt{13}[/tex]      

x ≈ 12.61      or x ≈ x  5.39            


Related Questions

May u give all the answers to these? please and thank you! <3
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Write an equation for the statement
(this applies for all of them <3)


1. The product of nineteen and a number x is seven

2. The sum of a number x and negative thirty is two

3. A number x divided by negative twenty-seven is eight

4. Twelve less than a number x is five

5. One-third of a number x is three​

Answers

Answer:

1. 19 (x) = 7

2. -32 + x = 2

3. x ÷ -27 = 8

4. x - 12 = 5

5. 1/3 (x) = 3

Step-by-step explanation:

:)

Solve the system of equations by the substitution method. x+4y=6 y=3−x

Answers

Answer:

x = 2, y = 1

Step-by-step explanation:

x + 4y = 6 and y = 3 - x have to be rearranged: x + 4y = 6 and x + y = 3

You subtract the equations to eliminate one of the variables (x) so that the other can be found

v + w at v = 2, w =5

Answers

Answer:

7

Step-by-step explanation:

if v=2 and w=5 you add 5 and 2 and get 7

Mike´s fitness center charges $30 per month for a membership. All-Day fitness club charges $22 per month plus an $80 initiation fee for a membership. After how many months will the total amount paid to the two fitness clubs be the same?

Answers

Answer:

10 months

Step-by-step explanation:

30x=22x+80

8x=80

x=10

Which equation in standard form has a graph that passes through the point (-2, 6) and has a slope of !.A. 3x — 2y = 12 B. 3x — 2y = 6 C. 3x — 2y = -18 D. 3x — 2y = 18

Answers

Answer:

Your answer should be C

Step-by-step explanation:

Answer:

3x - 2y = -18

Step-by-step explanation:

3x - 2y = -18 and (-2, 6)

(3)(-2) - (2)(6) = -6 - 12 = -18

What is the equation of the line that passes through the point (-6, -7) and has a slope of 0

Answers

Answer:

x = - 6

Step-by-step explanation:

A line with a slope of zero is a horizontal line parallel to the x- axis with equation

x = c ( where c is the value of the x- coordinates the line passes through )

The line passes through (- 6, - 7 ) with x- coordinate - 6 , then

x = - 6 ← equation of line

Both Tyrone and Albert walk to and from school every day. Qlbert has to walk 1.25 miles farther than Tyrone does each way. If Tyrone's house id 0.6 mile from school, how far do the two boys walk altogether?​

Answers

Answer: 0.6 + 1.25 = 1.85

0.6 + 1.85 = 2.45

Is the triangle isosceles, equilateral, or
neither?
70°
55°
55°
A. isosceles
B. equilateral
C. neither

Answers

Answer:

It is isosceles triangle because its base angles are equal .

plz mark me brainest

Answer: A. isosceles

Step-by-step explanation:

an isosceles triangle is a triangle that has two sides of equal length.

You can read about isosceles triangle more : https://en.wikipedia.org/wiki/Isosceles_triangle

please give me a brainliest answer

What is the value of x

Answers

Answer:

23. because there is a 90 degree angle and then the 67 degree angle, and triangle law says that all angles add up to 180.

Step-by-step explanation:

Im not smart but hope this helps

What is the slope of a line parallel to y = 4x + 3.​

Answers

Answer:Using the slope-intercept form, the slope is −4 - 4 .

Step-by-step explanation:To find an equation that is parallel to y=−4x−3 y = - 4 x - 3 , the slopes must be equal.

Answer:

the slope is −4 - 4

sorry if it’s wrong

A 5-pound bag of dog food costs $11.25. What is the unit price of the dog food in dollars per pound?

Answers

Answer:

$2.25

Step-by-step explanation:

5 lbs = $11.25

The unit price in this context means the price of a 1-pound bag of dog food so you would divide $11.25 by 5:

$11.25 ÷ 5 = $2.25

Hope this helps!

Answer:

2.25 ($) per pound

Step-by-step explanation:                                                                               11.25 /  5 = 2.25 per pound   Alternative workings we simply divide by 10  to find   11.25 / 10  = 1.125 then multiply by 2                                                      1.125 * 2  = 2.25 ($) per pound

help me pleaseeeeeeeee​

Answers

Answer:

Open your dictionary, Find the word you are looking for and reread the Sentence and find the right definition that BEST fits the Sentence

Thank me Later :D

Step-by-step explanation:

which company offers the best deal?why?​

Answers

Answer:

where question?

Step-by-step explanation:

i dont know the question it cant be solve

Answer:

I don't see the question. it cannot be solved

What the answer?????

Answers

Okay,

So this equation is non existent. It is not an equation nor expression.

Key Info:

x - variable

0.256 - decimal

10.3 - decimal

Hope this helps.

Add more information to your answers. ( GIVE CONTEXT )

How many solutions does this equation have?
9p + 5 = 5 + 9p

Answers

Answer:

Infinite solutions

Step-by-step explanation:

9p + 5 = 5 + 9p

Since both sides are equal, therefore the equation has infinite solutions

[tex]\sf 15=2x-9[/tex]

Answers

Answer:

x=12

Step by step explanation:

Step by step explanation:Add 9 to both sides :

15 = 2x - 9

15 + 9 = 2x - 9 + 9

Simplify:

24 = 2x

Divide both sides to get the result:

24 = 2x

24/2 = (2x)/2

Result:

x=12

[tex]\boxed{\sf Answered \: By\: Subhash} [/tex]

[tex]\boxed{\sf Good\: luck \: for \: your \:assignment} [/tex]

Answer:

x=12

Step-by-step explanation:

[tex]15=2x-9[/tex]

[tex]2x-9=15[/tex]

[tex]2x-9+9=15+9[/tex]

[tex]2x=24[/tex]

[tex]\cfrac{2x}{2}=\cfrac{24}{2}[/tex]

[tex]x=12[/tex]

I need help with this question:

Answers

Answer:

a)    #4    vertical angles are congruent

b)    # 1   ∠3 ≅ ∠7

c)    # 6   Transitive property

Step-by-step explanation:

    a. Vertical angles - opposite angles that are equal.

    b.  corresponding angles - in the same place but on different parallel lines

          and are equal.

     c. a = b, b = c  so a = c

The perimeter of a triangle is 65 cm. The
lengths of the sides are x cm, x+8 cm, and
X+ 12 cm.
What is the length, in cm, of the longest side of
the triangle?

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The longest side measures :

[tex]27\: \: cm[/tex]

[tex] \large \boxed{ \mathfrak{Explanation}}[/tex]

Perimeter of a triangle is equal to sum of measures of its all three sides, that is :

[tex]x + x + 8 + x + 12[/tex]

and according to the question, the perimeter of the triangle is = 65 cm

so, let's equate both the expressions to find value of x :

[tex]x + x + 8 + x + 12 = 65[/tex][tex]3x + 20 = 65[/tex][tex]3x = 65 - 20[/tex][tex]3x = 45[/tex][tex]x = 45 \div 3[/tex][tex]x = 15[/tex]

The longest side of the Triangle is :

[tex]x + 12[/tex][tex]15 + 12[/tex][tex]27 \: \: cm[/tex]

27cm

Step-by-step explanation:

(xcm) + (x+8cm) + ( x+ 12cm) = 65cm

Open Bracket

xcm + x+8cm + x+12cm = 65cm

3x+ 20cm = 65cm

Collect like terms

3x = 65cm - 20cm

3x = 45cm

Divide both sides by 3

3x/3 = 45cm/3

x = 15cm

The longest side of the triangle =( x+12cm)

= (15+12)cm= 27cm

Find the distance between P(2, 5 ) and Q( 7 , 3)

Answers

Answer:

PQ = √(7-2)²+(3-5)²

= √ 5²+(-2)²

= √ 25+4

=√29 units

Hope it helps !

Don't forget to mark me as brainliests.

I need help asap please

Answers

Answer:

A= 90 , b= 12 , c=60,

Step-by-step explanation:

cuz im smart like that

Explain how you can use mental math to
calculate 2^8.

Answers

Answer:

think about what 2 times 8 equals

Step-by-step explanation:

Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)

Answers

Answer:

[tex]x = 2\sqrt{55}[/tex]  

Step-by-step explanation:

Given the values for the leg and hypotenuse:

a (leg) = 6 cm

c (hypotenuse) = 16 cm

Use the Pythagorean Theorem to find the value of the other leg, x:

[tex]x = \sqrt{c^{2} - a^{2} }[/tex]

[tex]x = \sqrt{16^{2} - 6^{2} }[/tex]

[tex]x = 2\sqrt{55}[/tex]  

Answer:

Your answer is [tex]\sqrt{220}[/tex] or 14.8323969...

Step-by-step explanation:

[tex]A^{2} +B^{2} =C^{2} \\x^{2} + 6^{2} =16^{2}[/tex]

[tex]x^{2} =16^{2} -6^{2} \\[/tex]

[tex]x^{2}[/tex] = 256 - 36

x = [tex]\sqrt{220}[/tex]

Find the slope of the line that contains the points (2,5) and (4,8).

Answers

Answer: Slope = 3/2 or 1.5

Answer: y= 1.5 x+2 or y=3/2x+2

Step-by-step explanation:Slope (m) =

ΔY

ΔX

=

3

2

= 1.5

θ =

arctan( ΔY )

ΔX

= 56.30993247402°

ΔX = 4 – 2 = 2

ΔY = 8 – 5 = 3

Distance (d) = √ΔX2 + ΔY2 = √13 = 3.605551275464

y = 1.5x + 2

or

y =

3 x

2

+ 2

When x=0, y = 2

When y=0, x = -1.3333333333333

What is an equation of the line that passes through the point (8,0) and is parallel to the line x-4y=20?

Answers

Answer:

y= 1/4 (x -8)

Step-by-step explanation:

x -4y= 20

-4y= -x + 20

y= 1/4 × -5

y - y1 = m (x - x1)

y - 0 = 1/4 (x -8)

y= 1/4 (x -8)

Lamar made $110 for 5 hours of work.
At the same rate, how much would he make for 12 hours of work?

Answers

Answer:

264

Step-by-step explanation:

to find one hour

110÷5=22 per hour

12×22=264

Answer: Lamar would make $264 in 12 hours of work.

First we would try to find how much he would make in an hour, so technically the unit rate.

TO find the unit rate we have to do 110/5 which is equal to $22

Then we know that Lamar is working for 12 hours and that he makes $22 per hour. SO,  12 times 22 is 264.

Step-by-step explanation:

I hope this helps, if you are having a tough time with math you can use:

khan academy

math nation

and many more free sites!

Can someone please help me with this I really need help.

Answers

Answer:

The angle mPQO is 86°

Step-by-step explanation:

123°-37°

The difference of twice a number and three is​

Answers

Answer:

2

Step-by-step explanation:

given the difference of twice a number and one is three to find "number" let the number be x

2x - 1 =3

2x = 4

x= 2

thus the number is 2

Help pleaseeeeeeeeeeee

Answers

Answer:

[tex]f(x) = 2x + 5 \\ y = 2x + 5 \\ x = 2y + 5 \\ 2y = x - 5 \\ y = \frac{1}{2} x - \frac{5}{2} \\ y = {f}^{ - 1} (x) = \frac{x - 5}{2} [/tex]

if a 280g with 32 pieces chocolate bar contains 20% of fat. How much fat is in 4 pieces?

Answers

Answer:

0.8%

Step-by-step explanation:

4*20%=4*(1/5)=4/5=0.8%

what is the value of the expression 1/2 (m-2/3n) when m=3/2 and n= 1/2 ?

a. 5/12

b. 7/12

c. 11/12

d. i don’t know

Answers

Answer:

B.[tex]\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]m=\frac{3}{2}\\n=\frac{1}{2\\} \\\frac{1}{2} (m-\frac{2}{3} n)=\frac{1}{2} (\frac{3}{2} -\frac{2}{3} .\frac{1}{2} )\\=\frac{7}{12}[/tex]

So B is the correct answer.

Expression is a combination of operators, variables and numbers.. The value of the expression 1/2 (m-2/3n) when m=3/2 and n= 1/2 is 7/12.

What is Expression?

Expression is a combination of operators, variables and numbers.

The given expression is one by two  times of m minus two by three times n.

1/2 (m-2/3n)

where m and n are two variables with values m equal to three by two 3/2 and n equal to one by two.

1/2 (3/2-2/3(1/2))

Firstly we solve the value in parenthesis.

1/2 (3/2-1/3)

LCM of two, three is six

1/2 ((9-2)/6)

Subtract nine and two we get seven

1/2 (7/6)

Now one by two times of seven by six

7/12

So value of the expression 1/2 (m-2/3n) when m=3/2 and n= 1/2 is 7/12.

To learn more on expressions click:

https://brainly.com/question/14083225

#SPJ2

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