13. Write
y = 2x^2 -12x+16 in vertex form.
Please show work if possible so I know how to do it
Answers
First off, we factor out the expression:
[tex] \displaystyle \large{y = 2 {x}^{2} - 12x + 16} \\ \displaystyle \large{y = 2 ( {x}^{2} - 6x + 8) }[/tex]
In the bracket, separate 8 out of the expression.
[tex] \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}[/tex]
In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:
[tex] \displaystyle \large{ {(x - 3)}^{2} = {x}^{2} - 6x + 9}[/tex]
So we add +9 in x^2-6x.
[tex] \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}[/tex]
Convert the expression in the small bracket to perfect square.
[tex] \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}[/tex]
Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.
[tex] \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}[/tex]
Then we distribute 2 in.
[tex]\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ [/tex]
[tex]\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }[/tex]
Remember that negative multiply positive = negative.
Hence the vertex form is y = 2(x-3)^2-2 or first choice.
Related Questions
Help me with this one
Answers
9514 1404 393
Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:
[tex]x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}[/tex]
_____
Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
_____
* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a. What is the area of the pool cover?
b. What is the length of the rope?
You must show all of your work to receive credit
Answers
Answer:
The cover has diameter of:
20 feet + 2*12 inches = 20 feet + 2 feet = 22 feeta.
Area of the pool cover:
A = πd²/4 = 3.14*22²/4 = 379.94 ft²b.
The length of the rope:
C = πd = 3.14*22 = 69.08 ftAnswer:
346.19ft65.94ftStep-by-step explanation:
Add the length of the pool and the extent the pool cover [ 12in = 1ft ] has over the pool.
20 + 2 = 22ft
Part A:
The formula for the area of a circle is πr².
To find the radius just divide by two; 22 / 2 = 11ft
= π(11)²
= 121π
≈ 379.94ft
Part B:
We can use the circumference formula [ dπ ] to find how long the rope is.
= 22(3.14)
= 69.08ft
Best of Luck!
-2u+(-1)=-13
---------------
Answers
Answer:
Solution given
-2u+(-1)=-13
open bracket
-2u-1=-13
add 1 on both side
-2u-1+1=-13+1
-2u=-12
divide both side by -2
-2u/-2=-12/-2
u=6
[tex]\huge\text{Hey there!}[/tex]
[tex]\textsf{-2u + (-1) = -13}\\\textsf{-2u - 1 = -13}\\\large\text{ADD 1 to BOTH SIDES}\\\textsf{-2u - 1 + 1 = -13 + 1}\\\large\text{CANCEL out: -1 + 1}\\\large\text{KEEP: -13 + 1}\\\rightarrow\textsf{-2u = -12}\\\large\text{DIVIDE -2 to BOTH SIDES}\\\mathsf{\dfrac{-2u}{-2}= \dfrac{-12}{-2}}\\\textsf{CANCEL out: }\mathsf{\dfrac{-2}{-2}}\\\textsf{KEEP: }\mathsf{\dfrac{-12}{-2}}\\\mathsf{u = \dfrac{-12}{-2}}\\\mathsf{u = \bf 6}\\\huge\boxed{\mathsf{Answer: u = 6}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]
1.1x + 1.2x -5.4 =-10
Show answer
Answers
I circled the answer and put an example hope it helps
A 180-inch pipe is cut into two pieces.one piece is three times the length of the other.find the length of the shorter piece.
Answers
So the shorter length (n) plus the longer length (3n) add up to 180
n + 3n = 180
4n = 180
n = 45
so the shorter board is 45 inches, and the longer one is 3 x 45, or 135 inches.
Hope this helps!
The length of the shorter piece is 45 inches.
How to determine the length of the shorter piece.Let's represent the length of the shorter piece as "x" inches.
According to the information given, the length of the longer piece would be three times the length of the shorter piece, which means it's 3x inches.
Since the total length of the pipe is 180 inches, we can set up an equation:
x (shorter piece) + 3x (longer piece) = 180
Now solve for x:
4x = 180
x = 45
Therefore, the length of the shorter piece is 45 inches.
Learn more about length at https://brainly.com/question/26589728
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pls ans the question step by step
then i wil mark it as brainlist ans
Answers
Answer:
i hope it helped U
stay safe stay happy
in which figures is segment AB a median?
WILL RATE BRAINLIEST!!!
HELP
Answers
Answer:
B, D, H, I, J
Step-by-step explanation:
Median: A line segment that joins the vertex of a triangle to the midpoint of the opposite side.
Write this in set notation [-13; 4 )
Answers
Answer:
[tex]13\leq x<4[/tex]
Explanation:
If a side has a bracket [] then it is less than or equal to, meaning that it can reach that exact number.
However, if a side has a parentheses () then it is simply less than. It cannot be that exact number, but it can be even slightly less than that number.
URGENT!!
1-84. Find the perimeter and area of each figure.
9.85 m
15 m
9 m
Answers
Answer:
total = 99m² + 39.4m²
= 148.4m²
how do you solve 3-(-7)?
Answers
Answer:
10
Step-by-step explanation:
Subtracting a negative is like adding
3 +7
10
Determine the geometric mean of 8 and 12, to the nearest tenth.
A) 10.0
B) 4.5
C) 48.0
D) 9.8
Answers
Answer:
D) 9.8
Step-by-step explanation:
The geometric mean of two numbers x and y is
[tex]\sqrt{xy}[/tex]
so [tex]\sqrt{8*12}[/tex] = [tex]\sqrt{96}[/tex] [tex]\approx 9.7979[/tex]
Which, since the 9 in the hundredths place is greater than 5, we can round up to 9.8
Like what is this and how do you do it please explain clearly and understandable
Answers
Answer:
1/4
Step-by-step explanation:
HT represent the probability of tossing a head then Tail.
There is 4 possible results and only 1 give us HT.
We call this theoretical probability. which is
[tex] \frac{x}{y} [/tex]
where x is favorable outcomes and y is total number of outcomes.
So there is a 1/4 probability of getting a head followed by a tail.
1) A head followed by a head.
2) A head followed by a tail.
3) A tail followed by a head.
4) A tail followed by a tail.
Therefore,
Total possible outcomes = 4
Now, the given condition is a head followed by a tail. In the possible outcomes there is only one (i.e; 2) that satisfies this condition.
Therefore, outcome of getting head followed by tail = 1
Finally,
P(getting head followed by tail) = outcome of getting head followed by tail / Total possible outcome.
Which is 1/4.
Hope this helps.
In the triangle above, the cosine of a is 0.8.What is sine of b?
Answers
Answer:
sin b = 0.8
Step-by-step explanation:
Since a and b are complementary angles , then
sin b = cos a = 0.8
The sine of angle b is 0.8
What is right triangle?"It is a triangle in which one of the angle measures 90° "
What is hypotenuse?"It is the longest side of the right triangle."
What is sine angle?"In a right triangle, sine of angle [tex]\theta[/tex] is the ratio of the opposite side of angle [tex]\theta[/tex] to the hypotenuse."
What is cosine angle?"In a right triangle, cosine of angle [tex]\theta[/tex] is the ratio of the adjacent side of angle [tex]\theta[/tex] to the hypotenuse."
What are complementary angles?"Two angles are complementary if the sum of their measures is equal to 90 degrees."
For given question,
We have been given a right triangle.
here,
∠a + ∠b = 90°
∠b = 90° - ∠a ................(i)
This means, a and b are complementary angles.
The cosine of a is 0.8
cos(a) = 0.8
We need to find the sine of angle b.
sin(b)
= sin(90 - a) .............(from (i))
= cos(a) .............(Since [tex]sin(90-\theta)=cos(\theta)[/tex])
= 0.8 ............(Given)
So, sin(b) = 0.8
Therefore, the sine of angle b is 0.8
Learn more about the sine angle here:
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area of the shape...
Answers
Which is 1/2(13+16)4
If this is correct pls mark brainliest
28+12
—————
13-5
7th Grade Math Book (McGraw-Hill) page 9 exercise 26
Answers
can someone help me with this question
Answers
Answer: The guage block height is 4.98 m
The base of the right triangle that is formed is 7.3784 m
The last angle in the triangle is 56 degrees
Step-by-step explanation:
Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base. Now we can use trig (SOHCAHTOA) to find the answaers.
Using sine, we can first find the gauge block height, O (Opposite). Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.
Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)
O = (8.9)*(0.5592)
O = 4.98 m, the height of the gauge block,
The base of the triangle, A, can be determined with cosine.
Cosine(34) = A/O, or A = Cosine(34)*O
A = (0.82904)*(8.9)
A = 7.3784 m
The sum of all angles in a triangle is 180 degrees.
180 = X + 34 + 90
X = 56 degrees
Solve by using the quadratic formula: (3x + 3)^2 = 25
Answers
Step by Step:
3x+3=+/- 5
3x+3=5 and 3x+3=-5
x=-8/3 and x=2/3
Use the given graph to determine the limit, if it exists. A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1.5, a closed point at 3, 7, and a horizontal line starting at the open point 3, 2. Find limit as x approaches three from the left of f of x..
Answers
Explanation:
The given limit notation means we're approaching x = 3 from the left side. So start at say x = 0 and approach x = 3. We don't actually get to x = 3 itself, but instead just get closer and closer. Note how y gets closer to y = 1.5
Will someone help me please?
Answers
Answer:
Ok so
Step-by-step explanation:
Yes yes yes yes its C
It is the third answer from above photo
answer choices:
A. 182.3
B. 164.2
C. 288
D. 144
PLSSSS HELP
Answers
Answer:
288m^3
Step-by-step explanation:
the volume is base* height
to find the second side, use the Pythagorean theorem : [tex]\sqrt{10^2-8^2} = \sqrt{100-64}= \sqrt{36} = 6[/tex],
now find the area of the triangle: 6*8/2=24
now multiply it by the height and you get the volume: 24*12=288
It is midpoint please help
Answers
Step-by-step explanation:(2, -3)
[tex]thank \: you[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{5+8}{2},\dfrac{3.5+10}{2}\right)[/tex]
[tex]\\ \sf\longmapsto (x,y)=\left(\dfrac{13}{2},\dfrac{13.5}{2}\right)[/tex]
a different way of proving the angle sum of a triangle is to use diagram
Answers
a.yes
Step-by-step explanation:
a.angle BCD =b because angle BCD is alternate angle of angle ABC
b.the two angles angle BAC and angle ACD is co-interior angle because they are inside a parallel line
4. Find the quotient. -7 ÷ 14/3
Answers
As a mixed number, this is -1 and 1/2
As a decimal this is -1.5
-3/2
As a mixed number this is -1 1/2
as a decimal this is - 1.5
-(-5.6g + 2h – 9)
Does anyone know this ?
Answers
Answer: 5.6g - 2h + 9
Explanation:
Flip the sign of each term inside the parenthesis.
The -5.6g becomes +5.6g or simply 5.6gThe +2h becomes -2hThe -9 becomes +9These sign flips occur because of the negative out front the parenthesis. It's the same as having -1 outside, and we distribute the -1 through.
K-5+1-5k please I need help
Answers
Explanation:
The like terms k and -5k combine to -4k
The like terms -5 and 1 combine to -4
So overall, that's how we end up with -4k-4
Answer:
-4k - 4Step-by-step explanation:
1). (k - 5k) + (-5 + 1) {Collect like terms}
2). -4k - 4 {Simplify}
Help anyone can help me do this question 2,I will mark brainlest.
Answers
Answer:
see explanation
Step-by-step explanation:
For the triangle to be isosceles it must have 2 equal sides.
Calculate the length of the sides using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = B (3, 5)
AB = [tex]\sqrt{(3-(-1))^2+(5-2)^2}[/tex]
= [tex]\sqrt{(3+1)^2+3^2}[/tex]
= [tex]\sqrt{4^2+9}[/tex]
= [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5
Repeat with (x₁, y₁ ) = A (- 1, 2) and (x₂, y₂ ) = C (3, - 1)
AC = [tex]\sqrt{(3+1)^2+(-1-2)^2}[/tex]
= [tex]\sqrt{4^2+(-3)^2}[/tex]
= [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = 5
Consider B (3, 5) and C (3, - 1)
Since both x- coordinates are 3, this is a vertical line and its length is the difference of the y- coordinates, that is
BC = | - 1 - 5 | = | - 6 | = 6
Then
AB = AC = 5 , BC = 6
Since AB = AC = 5 then the triangle is isosceles
Order the numbers in each group from least to greatest 7/11, 0.63 and 0.636
Answers
7/11 , 0.636, and 0.63
Hope this helps
Answer:
Least to Greatest
7/11 , 0.636, 0.63
Step-by-step explanation:
7/11 = 0.6363636363636364
so this number is least
Write -0.450 as a fraction in simplest form.
Answers
Answer:
-0.450 as a fraction is -9/20
Step-by-step explanation:
Since there 3 decimal places, divide it by 1000
-450/1000 and simplify it
8^2 x 6{4 + 8^2(10 - 6)}^2
Answers
Answer:
25958400
Step-by-step explanation:
[tex] {8}^{2} \times 6(4 + {8}^{2} \times (10 - 6) {)}^{2} [/tex]
[tex] = 64 \times 6(4 + {2}^{6} \times 4 {)}^{2} [/tex]
[tex] = 64 \times 6(4 + {2}^{6} \times {2}^{2} {)}^{2} [/tex]
[tex] = 64 \times 6(4 + {2}^{8} {)}^{2} [/tex]
[tex] = 64 \times 6(16 + 2048 + 65536)[/tex]
[tex] = 64 \times 6 \times 67600[/tex]
[tex] = 25958400[/tex]
The measure of an angle is 87°. What is the measure of its supplementary angle?
Answers
Answer:
180-87 = 93
Step-by-step explanation:
supplementary angles add up to 180°
so (the other angle + 87)=180°
other angle =180-87=93°
Answer:
93 degrees
Step-by-step explanation:
Supplementary angles add up to 180 degrees. Therefore, the equation for finding the supplementary angle to 87 would be:
[tex]87 + x = 180\\x=180-87\\x=93[/tex]
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