What is the intermediate step in the form (x + a)2 = b as a result of completing the
square for the following equation?
x2
12x + 32 = 4
Answers
Given:
The equation is:
[tex]x^2-12x+32=4[/tex]
To find:
The result of completing the square for the given equation.
Solution:
We have,
[tex]x^2-12x+32=4[/tex]
It can be written as:
[tex]x^2-12x=4-32[/tex]
[tex]x^2-12x=-28[/tex]
Now, we need to add half of square of coefficient of x, to complete the square.
Adding [tex](\dfrac{-12}{2})^2[/tex] on both sides, we get
[tex]x^2-12x+(\dfrac{-12}{2})^2=-28+(\dfrac{-12}{2})^2[/tex]
[tex]x^2-2(x)(6)+(-6)^2=-28+(-6)^2[/tex]
[tex]x^2-2(x)(6)+(6)^2=-28+36[/tex] [tex][\because (-a)^2=(a)^2][/tex]
Using the formula [tex](a-b)^2=a^2-2ab+b^2[/tex], we get
[tex](x-6)^2=8[/tex]
Therefore, the required equation after completing the square is [tex](x-6)^2=8[/tex].
Related Questions
4. Gloria makes $750 a week PLUS
3% commission on her sales.
Her sales were $1000 for the week.
How much did Gloria earn for the
week?
Answers
write 3.402 as a fraction.
Answers
Answer:
that as a fraction is 3 and 201 over 500
Answer:
3 402/1000 = 3 201/500 simplified or 1701/500 as an improper fraction
Step-by-step explanation:
y = 2x - 8
I need the answer
Answers
Then substitute x with 4, to get y.
2(4) - 8 = 0, y = 0
So x = 4 and y = 0
Which is bigger 1/7 or 0.14
Answers
Answer:
Both are equal
Step-by-step explanation:
please mark me brainliest
Answer:1/7
Step-by-step explanation:
Solve for v.
6v – 4v – 3 = 9
V =
= [?]
Answers
Answer: v=6
Step-by-step explanation:
Answer:
6 it's because I did this stuff in 6th grade.
Step-by-step explanation:
2 x ? -3=9. 2 x 6 - 3 = 9
PLEASE HELP I'M ON THE FINAL MATH TEST AND GOT A 64 ON THE FIRST ATTEMPT AND I DON'T WANT TO FAIL AGAIN I'LL GIVE 100 POINTS BUT I HAVE SEEN A LOT OF PEOPLE SAYING IT'S 81 AND THAT IS WRONG
In the map below, the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks.
A map of the aquarium at the City Zoo. A triangle has points whales, sharks, dolphins. The distance from Whales to sharks is 54 feet and from whales to dolphins is 30 feet. A triangle with points Dolphins, fish tanks, penguins. The distance from dolphins to fish tanks is 45 feet, and from penguins to fish tanks is x feet.
What is the distance between the penguins and the fish tanks?
25 feet
36 feet
69 feet
81 feet
Answers
Answer:
A. 25 feet
Step-by-step explanation:
A baby pool contained 50 gallons of water. Water leaked out of the pool at a rate of 10 gallons every 3 days. At this rate, how many days did it take all 50 gallons of water to leak out of the barrel?
Answers
Answer:
15 days
Step-by-step explanation:
The floor of the school music room is being tiled. The room is shaped like a parallelogram. The parallelogram has a base of 25 feet and a height of 11 feet. Each package of tile will cover 5 square feet. How many packages of tile will be needed to tile the music room floor? A=bh *
Answers
Answer:
Number of tile package need = 55 package of tile
Step-by-step explanation:
Given:
Base of parallelogram = 25 feet
Height of parallelogram = 11 feet
Each package of tile cover = 5 square feet
Find;
Number of tile package need
Computation:
Area of parallelogram = Base of parallelogram x Height of parallelogram
Area of parallelogram = 25 x 11
Area of parallelogram = 275 square feet
Number of tile package need = Area of parallelogram / Each package of tile cover
Number of tile package need = 275 / 5
Number of tile package need = 55 package of tile
Consider the diagram.
Which equations are true? Select all true equations.
Answers
Answer:
Sum of angles of a triangle is 180, so x + y + w = 180
Straight angle is 180 , so y + z = 180
From the first 2 conditions :
=>x + y +w = y + z
=> x + w = z
Option 1, 2, 5
The equations which are true are given by,
w + x + y = 180w + x + y = 180y + z = w + x + yw + x + y = 180y + z = w + x + yw + x = z What is an Equation?Equation is a mathematical relation between more than one variable, number or mathematical quantities involving mathematical operations using equal sign in between them.
From angle sum property of triangle says that the sum of all interrior angles of a triangle is 180.
Here all interrior angles of triangle are x,y,w
So, x+y+w = 180
Hence first option is correct.
Again the exterrior angle of a triangle is equal to the sum of the opposite two interrior angles.
here exterrior angle is z and opposite two interrior of z are x,w
So, w+x = z
Hence last option is correct.
Again y+z = y+w+x
so second option is also true.
Hence correct options or equations are given by:
w + x + y = 180w + x + y = 180y + z = w + x + yw + x + y = 180y + z = w + x + yw + x = zLearn more about Equation here -
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0.16x^2-49, factor using special products
Answers
Answer:
(.4x+7)(.4x-7)
Step-by-step explanation:
11m −4/3=2m+5/3
pls tell me this answer is the answer 3
Answers
Answer:
m=1/3
Step-by-step explanation:
11m- 4/3=2m+5/3
-2m. - 2m
9m -4/3=5/3
+4/3.+ 4/3
9m= 9/3
m=1/3
Point A is at (-1,8) and point B is at (7,3).
What is the midpoint of line segment AB?
Answers
Answer:
( 3, 5.5 )
Step-by-step explanation:
Let,
( x1, y1 ) = ( 7, 3 )
Where,
x1 = 7
y1 = 3
Let,
( x2, y2 ) = ( - 1, 8 )
Where,
x2 = - 1
y2 = 8
Formula : -
Midpoint = ( x1 + x2 ) / 2, ( y1 + y2 ) / 2
Midpoint of AB
= ( - 1 + 7 ) / 2, ( 8 + 3 ) / 2
= 6 / 2, 11 / 2
= ( 3, 11 / 2 )
= ( 3, 5.5 )
please answer question 4
Answers
They reject if the pie is more than 3.2oz from 28oz.
The scale shows positive number if its more than 28oz.
The scale shows negative number if its less than 28oz.
The scale shows zero if its 28oz.
A . Scale reads -2.8oz which means less than 28oz, So accepted.
B. Scale reads 3.5oz which means 3.5oz more than 28oz. So rejected.
C. Scale reads -3.3oz which means less than 28oz, So accepted.
D. Scale reads 28oz which means more than 28oz, So rejected.
PLEASE HELP PLEASE HELP
Answers
Answer:
B) 24
Step-by-step explanation:
The area of the rectangle is 48 units (8 x 6).
The base of the is 6 units and the height is 8 units. The formula for the are of a triangle is A = [tex]\frac{1}{2}[/tex]bh.
b = base
h = height
A = [tex]\frac{1}{2}[/tex](6)(8)
A = 24
Answer:
[tex]24[/tex]
Step-by-step explanation:
If the area of a rectangle is bh, and the area of a triangle is bh/2, then a triangle's area is half a rectangle's area. Hence, if the area of the rectangle is 48, the area of the triangle is half of 48, or 24.
y−3x=5 what is m and c
Answers
Answer:
✺ [tex] \large \tt \: E \: X\: P\: L\: A \: N \: A \: T \: I \: O\: N : [/tex]
☃ [tex] \large{ \tt{GIVEN \: EQUATION}} : [/tex]
[tex] \large{ \bf{y - 3x = 5}}[/tex]
[tex] \large{ \bf{↬y = 3x + 5}}[/tex] [ Move 3x from left hand side to right hand side and change it's sign to addition since the opposite of subtraction is addition ]
Comparing y = 3x + 5 with equation of straight line in slope intercept from [ y = mx + c ] , We get :[tex] \boxed{ \large \:⟿ \tt \:Slope \: (m) = \boxed{ \tt{3} }}[/tex]
[tex] \boxed{ \large { \tt{⟿ \: Y - intercept \: (c \: ) = \boxed {\tt{ 5}}}}}[/tex]
☏ And we're done! Yay , We found our answer !
♕ [tex] \large{ \tt{STUDY \: TIP}}[/tex]
Schedule daily study time : This is the time to review your readings and lecture notes that help prepare for exams. Plan this as a cumulative review , not working on new information. ♪♡ Hope I helped! ✎
☄ Have a wonderful day / night ! ☂
#StayInAndExplore ! ♨
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
AB is parallel to ED.
ACD and BCE are straight lines.
AB = 8 cm
AC = 4.8cm
BC = 6.4cm
ED = 20 cm
Work out the length of BE.
Answers
Answer:
BE = 22.4 cm
Step-by-step explanation:
Δ CAB and Δ CDE are similar , then ratios of corresponding sides are equal, that is
[tex]\frac{CB}{CE}[/tex] = [tex]\frac{AB}{DE}[/tex] , substitute values
[tex]\frac{6.4}{CE}[/tex] = [tex]\frac{8}{20}[/tex] ( cross- multiply )
8 CE = 128 ( divide both sides by 8 )
CE = 16 cm
Then
BE = BC + CE = 6.4 + 16 = 22.4 cm
The diagram shows a solid triangular prism. Height 6cm width 4cm length 10cm the prism is made from wood with a density of 0.8 g/cm3 work out the mass of this prism
Answers
Answer:
Step-by-step explanation:
The mass of the given triangular prism with a density of 0.8 g/cm³ is 96 grams.
What is the volume of a prism?The volume of a prism is the total space occupied by it.
What is the density of a prism?The density of a prism is the mass occupied by the 1 cubic unit volume of the prism. The formula for the density of a prism is:
Density = Mass/Volume
How do we solve the given question?In the question, we are given a triangular prism of height 6cm, width 4cm, and length 10cm. Its density is given as 0.8 g/cm³.
We first find the volume of the prism.
The volume = Area of triangle*length = ((1/2)*6*4)*10 cm³ = 120 cm³.
Let the mass of the prism be m grams.
We know the density of the prism is given by the formula,
Density = Mass/Volume
or, 0.8 = m/120
or, m = 120*0.8
or, m = 96
∴ The mass of the given triangular prism with a density of 0.8 g/cm³ is 96 grams.
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A rectangle has an area of 70 m^2 and dimensions, in meters, of x and x + 2. Estimate each dimension of the rectangle to the nearest meter.
Answers
-7 and - 9
Step-by-step explanation:
Area of rectangule is length * width
A triangle has vertices at (3, 2), (-4,4), and (-2,5). What are the coordinates of the vertices of the image
after the translation (x,y) → (x +5, y - 1)?
Prin
The coordinates are (3, 2) →
and (-2,5)
Complete the description of the translation.
The triangle is translated
unit(s) to the right and
unit(s) down.
Answers
Answer:
The triangle is translated 2 units down and 4 units to the right.
Step-by-step explanation:
please help w this question! would appreciate if you explained how you got it but its okay if you don't
Answers
Answer:
22
Step-by-step explanation:
49 (the whole length of the angle) - 27 (part of the angle) = 22 (the other part)
A ladder that is 30 feet long is placed against a house. The location of the ladder is 8 feet from the base of the house. How far up the house does the ladder reach? Round your answer to the nearest tenth of a foot
Answers
Answer:
28.9 m
Step-by-step explanation:
30²-8²=900-64= 836
√836 = 28.9 m
The Ladder reach 28.91 ft. up the house which is 8 ft. away from the base.
What is pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Here, Given, length of ladder ( Hypotenuse ) = 30 ft.
Distance from base = 8 ft.
By Pythagoras theorem,
Hypo.² = perp.² + base²
30² = x² + 8²
900 = x² + 64
x² = 900 - 64
x² = 836
x = √836
x = 28.91 ft.
Thus, the Ladder reach 28.91 ft. up the house which is 8 ft. away from the base.
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what is 2/3 of 1/4 THANKS!
Answers
Answer:
1/6
Step-by-step explanation:
[tex]2/3 \text{ of } 1/4 = (2/3)*(1/4) = 2/12 = 1/6[/tex]
Answer:
1/6
Step-by-step explanation:
(2/3)(1/4)=2/12=1/6
What is 9 x 7 squared
Answers
Answer: 441
Step-by-step explanation:
7. The local theatre performed a Saturday matinee to a crowd of 215 people. Tickets cost $11 child and $15 per adult, bringing in a total of $2877. Use an inverse matrix to determine the number of each type of ticket sold .
Answers
Answer:
The total number of child ticket sold = 87
The total number of adult ticket sold = 128
Step-by-step explanation:
Given - The local theatre performed a Saturday matinee to a crowd of 215 people. Tickets cost $11 child and $15 per adult, bringing in a total of $2877.
To find - Use an inverse matrix to determine the number of each type of ticket sold .
Proof -
Let the total number of child ticket sold = x
Let the total number of adult ticket sold = y
Given that, The local theatre performed a Saturday matinee to a crowd of 215 people.
⇒x + y = 215
Also,
Given that, Tickets cost $11 child and $15 per adult, bringing in a total of $2877
⇒11x + 15y = 2877
So,
The equations becomes
x + y = 215
11x + 15y = 2877
So,
The matrix form becomes
[tex]\left[\begin{array}{ccc}1&1\\11&15\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}215\\2877\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}1&1\\11&15\end{array}\right| \left\begin{array}{ccc}215\\2877\end{array}\right ] \\\left[\begin{array}{ccc}1&1\\0&4\end{array}\right| \left\begin{array}{ccc}215\\512\end{array}\right ] \\\left[\begin{array}{ccc}1&1\\0&1\end{array}\right| \left\begin{array}{ccc}215\\128\end{array}\right ]\\\left[\begin{array}{ccc}1&0\\0&1\end{array}\right| \left\begin{array}{ccc}87\\128\end{array}\right ][/tex]
By comparing, we get
x = 87
y = 128
So, we get
The total number of child ticket sold = x = 87
The total number of adult ticket sold = y = 128
A triangle has angles measuring 25 degrees and 45 degrees. What is the measure of the triangle's third angle
Answers
Answer:
110°
Step-by-step explanation:
Let the third angle be x. All the angles in a triangle add up to 180°. From the previous statement, we can write the equation:
25° + 45° + x = 180°
70° + x = 180°
x = 110°
please help!!
show work(factoring)
u^4 - 3u^2 - 4
Answers
1) Devin wants to play lazer tag for his birthday. He is comparing the cost of two companies. Lazer Zone charges $50 for parties, and an additional $10 per guest. Fun Palace charges $90 for parties, and an additional $6 per guest. For how many guests is the cost of both companies the same?
Answers
Answer:
10 guests
Step-by-step explanation:
Devin wants to play lazer tag for his birthday. He is comparing the cost of two companies.
Let us represent additional guests = g
Lazer Zone charges $50 for parties, and an additional $10 per guest.
=$50 + $10 × g
50 + 10g
For fun place
Fun Palace charges $90 for parties, and an additional $6 per guest.
= $90 + $6 × g
90 + 6g
For how many ?
We equate both Equations together
= 50 + 10g = 90 + 6g
Collect like terms
10g - 6g = 90 - 50
4g = 40
g = 40/4
g = 10
Hence, g = 10 guests
Therefore, the number of guests for which the cost of both companies is the same is 10 guests
what is the answer? help
Answers
Answer:
close to (4, 2)
Step-by-step explanation:
Given
PQ 1 PS
mZQPR = 73 – 9°
mZRPS = 4x + 22
Find mZQPR:
87
R.
Р
S
Answers
Answer:
The answer is in the picture.
Which function describes the graph below?
Answers
Answer:
Step-by-step explanation:
There are no pics