Complete the square to transform the expression x2 - 2x - 2 into the form a(x - h)2 + k
Answers
Answer:
A
Step-by-step explanation:
Find the vertex form of the quadratic function below.
y = x^2 - 4x + 3
This quadratic equation is in the form y = a{x^2} + bx + cy=ax
2
+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…
y = a(x - h)^2 + k
This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.
Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.
STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.
STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).
STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.
Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.
STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.
After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).
Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.
Example 2: Find the vertex form of the quadratic function below.
The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a
=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.
STEP 1: Factor out 22 only to the terms with variable xx.
STEP 2: Identify the coefficient of the xx-term or linear term.
STEP 3: Take that number, divide it by 22, and square.
STEP 4: Now, I will take the output {9 \over 4}
4
9
and add it inside the parenthesis.
By adding {9 \over 4}
4
9
inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(
4
9
)=
2
9
to the entire equation.
Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.
STEP 5: Since I added {9 \over 2}
2
9
to the equation, then I should subtract the entire equation by {9 \over 2}
2
9
also to compensate for it.
STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.
It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(
2
−3
,
2
−11
).
Example 3: Find the vertex form of the quadratic function below.
Solution:
Factor out - \,3−3 among the xx-terms.
The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}
4
1
inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(
4
1
)=
4
−3
is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}
4
3
outside the parenthesis.
Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(
2
1
,
4
11
).
Example 4: Find the vertex form of the quadratic function below.
y = 5x^2 + 15x - 5
Solution:
Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}
4
9
.
Add {9 \over 4}
4
9
inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(
4
9
)=
4
45
is the number that we need to subtract to keep the equation unchanged.
Express the trinomial as a square of binomial, and combine the constants to get the final answer.
Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}
2
−3
,
4
−65
.
Answer:
(x - 1 )^2 - 3
Step-by-step explanation:
( x - 1 )^2 + ( -3)
x^2 - 2x + 1 - 3
x^2 - 2x - 2
Related Questions
for which prime p,p4+8 is also a prime number
Answers
Answer: p = 3.
Step-by-step explanation:
Ok, this must be:
p and p^4 + 8
ok, it may be useful to remember the first prime numbers:
2, 3, 5, 7, 11, 13...
So let's play with those and see what happens, this is solving a problem by brute force, this means that we will input those values in the equation p^4 + 8 and see if the result is also prime:
First, p = 2 is not the solution, because 2^4 + 8 = 24: not prime.
now let's try p = 3.
3^4 + 8 = 81 + 8 = 89, and 89 is a prime number, so the solution is p = 3.
A movie theater conducted a survey to see what customers preferred at the concession stand. The theater asked every fifth person who entered the movie theater every Friday for a month what his or her favorite movie snack was. Were the results of the survey valid? A. No, because the theater did not survey everyone in the theater. B. Yes, because the theater only surveyed children. C. Yes, because the theater surveyed a random sample. D. No, because the theater did not use a random sample.
Answers
Answer:
A) No because the theater did not survey everyone in the theater.
Answer:
Yes, because the theater surveyed a random sample.
Step-by-step explanation:
The survey is valid because there was a random sample. They surveyed every fifth person, so there was a variety of age groups, genders, and preferences included in the sample. Therefore, the correct answer is yes, because the theater surveyed a random sample.
Square Roots and Cube Roots - Tutorial - Level H
Pepper Jackie has 225 square inches for the area for her square mosaic.
How can she figure out how long each side should be?
Area of a Square
A= 225 in.
S
S
Find the positive square
root of 225.
Divide 225 by 4.
Divide 225 by 2.
She doesn't have enough
information to do this.
Answers
Answer:
s = 15 in (positive square root of 225)
Step-by-step explanation:
A = 225 in²
side of square mosaic is sq. root of 225 = 15 in
therefore the side (s) = 15 in
Identify the Mapping MNJ —> EDC
Translation
Rotation
Reflection
Glide Reflection
Answers
Answer:
The answer is rotation.
Please help!!!
Simplify: (sin 0 - cos 0)2 + (sin 0 + cos 0)2 (5 points)
Select one:
a. 1
b. 2
c. sin^2theta
d. cos^2theta
Answers
Answer:
B
Step-by-step explanation:
(To save time, I'm going to use x instead of θ)
So we have the expression:
[tex](\sin(x)-\cos(x))^2+(\sin(x)+\cos(x))^2[/tex]
First, expand these binomials:
[tex]=(\sin^2(x)-2\sin(x)\cos(x)+\cos^2(x))+(\sin^2(x)+2\sin(x)\cos(x)+\cos^2(x))[/tex]
Combine like terms:
[tex]=\sin^2(x)+\sin^2(x)+\cos^2(x)+\cos^2(x)-2\sin(x)\cos(x)+2\sin(x)\cos(x)\\=2\sin^2(x)+2\cos^2(x)[/tex]
Factor out a 2:
[tex]=2(\sin^2(x)+\cos^2(x))[/tex]
The expression inside the parentheses is the Pythagorean Identity:
[tex]\sin^2(x)+\cos^2(x)=1[/tex]
Substitute:
[tex]=2(1)\\=2[/tex]
The answer is B.
HELP ME PLEASE The student's in Roberto's school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet. What are the length and width of the scale drawing in feet
Answers
Answer:
Length = 3.2feets ; width = 6feets
Step-by-step explanation:
Given the following :
Actual dimension of Mural:
8feets by 15feets
Scale drawing ratio of Mural :
2feets : 5feets
This means :
2 Feets on paper equals 5 Feets of actual drawing:
Therefore, with actual dimension of Length = 8feets ;
Length of scale drawing = (2/5) * 8 = 3.2feets
Actual dimension of width 15feets ;
Width of scale drawing = (2/5) * 15 = 6 Feets
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
When and , the value of the expression is
Answers
Answer:
-2, 6
Step-by-step explanation:
(x - 6)(x + 2) = 0
x - 6 = 0 x+ 2 = 0
x = 6 x = -2
The values of x that would result in the given expression being equal to 0, in order from least to greatest, are -2 and 6.
help me with this promblem THXXXX
Answers
Function 1 = negative y intercept
Function 2 = positive y intercept
====================================================
Explanation:
A. This is false because function 2 has a positive y intercept. Each time x goes up, y goes down. Reverse this and decreasing x leads to increasing y.
B. False. Function 1 has a negative y intercept. The y intercept occurs where the diagonal line crosses the y axis.
C. True. The graph shows a negative y intercept. The y intercept of function 2 is (0,2).
D. False. This contradicts choice C.
solve for y. -y/3 = -23 simplify your answer as much as possible
Answers
Answer:
69
Step-by-step explanation:
-y/3 = -23
=> -y = -23 x 3
=> -y = -69
=> y = 69
Answer:
69
Step-by-step explanation:
We multiply both sides of the equation by 3 to cancel out the denominator. That gives us -y=-69. Since we cannot have a negative variable, we change the values on both sides, giving us y=69
If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answers
Answer:
7800 brownies will be produced in an 8 hour shift
Step-by-step explanation:
Given : The production rate is 975 brownies per hour at a bakery
To Find : how many brownies will be produced in an 8 hour shift?
Solution:
No. of brownies produced in 1 hour = 975
We are supposed to find No. of brownies produced in 8 hour
No. of brownies produced in 8 hour = 975 x 8=7800
Hence 7800 brownies will be produced in an 8 hour shift
Hope this helps ФωФ
A survey asked students at Wilson Academy which status they would prefer—to be happy, healthy, or rich—and how much pressure they felt from their homework. The two-way table of row relative frequencies below shows the data.
Answers
Answer:
A. A student who prefers to be healthy is more likely to feel very little pressure from homework than a student who prefers to be rich.
Step-by-step explanation:
Answer:
A THE RIGHT ANSWER
Step-by-step explanation:
PLEASSSSSEEE HELPPP ASPPP PLEASEEE
Answers
Answer:
x=1
i hope this helps!
Step-by-step explanation:
x+2/-1 =3
x+2 (1) =3
x+2 = 3
x=1
Hopes this answers your question
How do I solve 3(x+1)=5(x−2)+7?
Answers
Answer:
x = 3Step-by-step explanation:
[tex]3\left(x+1\right)=5\left(x-2\right)+7\\Expand\\3x+3 =5x -10+7\\Collect \:like\: terms\\3x-5x = -10+7-3\\-2x = -6\\Divide \:both\:sides\:of\:the\:equation\:by\:-2\\\frac{-2x}{-2} = \frac{-6}{-2}\\ \\x = 3[/tex]
Answer:
x = 3
Step-by-step explanation:
3(x+1)=5(x−2)+7
Use the distributive property to multiply 3 by x+1.
3x+3=5(x−2)+7
Use the distributive property to multiply 5 by x−2.
3x+3=5x−10+7
Add −10 and 7 to get −3.
3x+3=5x−3
Subtract 5x from both sides.
3x+3−5x=−3
Combine 3x and −5x to get −2x
−2x+3=−3
Subtract 3 from both sides.
−2x=−3−3
Subtract 3 from −3 to get −6.
−2x=−6
Divide both sides by −2.
x = -6/2
Divide −6 by −2
x = 3
calculate the area of the shaded region in each figure. use 3.14 for π and round to the nearest 10th if nessary
Answers
Answer:
7.6 cm²
Step-by-step explanation:
Area of rectangle= l x w
3 x 4 = 12 cm
Area of circle= πr²
π x 2.5²= 19.625
Area of shaded= Area of circle - area of rec
19.625- 12= 7.625 cm²
≈7.6
I HOPE THIS HELPED
8 is subtracted from the square of a number
Answers
Answer:
n^2-8 is the answer
Step-by-step explanation:
Harley is trying to save $25,000 to put a down payment on a condominium. if she starts with $10,000 saved and saves in additional $750 each month, which equation represents how far Holly is from her goal of reaching $25,000? X stand for months and Y stand for dollars.
Answers
Answer:
10,000+750x=25,000
Step-by-step explanation:
This is because shes starts with 10,000 and gets 750 per month so she needs x months to get to 25,000 you can also do 25,000-10,000/750 = x
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Use digits to write the value of the 6 in this number.
672,180
Answers
Six hundred thousand
Hope it helps :)
Whats the volume of the cylinder? Round your answer to the nearest hundred the top is B the left side of the cylinder is 13cm the bottom of the cylinder is 4cm so whats the volume of it?
Answers
Answer:
The volume of the cylinder is 163.3 m³.
Step-by-step explanation:
Given that,
Height = 13 cm
Base = 4 cm
So, radius = 2 cm
We need to calculate the volume of the cylinder
Using formula of cylinder
[tex]V=\pi r^2h[/tex]
Where, r = radius
h = height
Put the value into the formula
[tex]V=\pi\times(2)^2\times13[/tex]
[tex]V=163.3\ cm^3[/tex]
Hence, The volume of the cylinder is 163.3 cm³.
Judy's heart beats 70 times a minute. At this rate, how many times does it beat per hour?
Answers
Answer:
4200 timesStep-by-step explanation:
[tex]70\:times = 1\:minute\\x\:times\:= 60\:minute\\\\Cross\:multiply\\ x = 70 \times 60\\\\x = 4200\\\\= 4200 \:times\:in\:an\:hour\\\\Note: 60\:minutes = 1 \:hour[/tex]
Answer:
4200 beat per hour
Step-by-step explanation:
70 beat per min to beat per hour
70 beat 60 min
------- x ----------- = 4200 beat per hour
min 1 hour
The chess club has 18 students. How many different teams of 4 can be formed for competition?
A. 3,060
B. 18,360
C. 73,440
Answers
The number of 3060 teams of 4 can be formed for competition.
The correct answer is A.
What is a combination?A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.
Given:
The chess club has 18 students.
To find the number of combination of teams of 4 can be formed for competition:
¹⁸C₄
Solving the combination,
¹⁸C₄
= 18! / 4! x (18-4)!
= 18! / 4! x 14!
= 18 x 17 x 16 x 15 / 4 x 3 x 2 x 1
= 3060
Therefore, the number of teams are, 3060
To learn more about the combination;
https://brainly.com/question/29594894
#SPJ5
Is this answer correct?
Answers
Answer:
yes
The statement 'C' explains the difference between a plane and a ray.
i.e. A plane does not have a formal definition, and a ray is described through undefined terms.
Step-by-step explanation:
A plane does not have a formal definition, and a ray is described through undefined terms. The statement is true because
A plane is basically an undefined term as it could be named using three non-straight points - also called noncollinear points. A plane is basically a flat two-dimensional object having no thickness.
In Geometry, we have a variety of undefined terms, including point, line and plane. All other terms in Mathematics (Geometry) could be defined from the mentioned three undefined terms.
Therefore, the statement 'C' explains the difference between a plane and a ray.
i.e. A plane does not have a formal definition, and a ray is described through undefined terms.
Keywords: plane, point, line, ray
Learn more about plane and ray form brainly.com/question/14471549
#learnwithBrainly
Mukat has five times as many book as usha.If mukat gave 16 books to usha,they each would have the same number.how many books did each girl have?
Answers
Mukat gets 40, Usha gets 8
Step-by-step explanation:
Mukat = 5 × Usha
After Mukat gives Usha 16 books ,Usha gets (16 + initial number of books) and Mukat gets (5 × Usha - 16)
Then Mukat = final number of books for Usha
5 × Usha - 16 = Usha + 16
(5 × Usha ) - Usha = 16+16
4 × Usha = 32
Usha = 8 i.e her number of books.
Mukat = 5×8=40.
I HOPE IT'S OK
HELP!!!!!!!! PLEASE!!!!!! Matthew works as a painter. He is currently doing a project painting a house. He is left with 7 1/5 liters of paint and one wall of a room requires approximately 1 2/3 liters of the paint. How many more walls of the rooms can he paint? A 5 B 4 C 6 D 3
Answers
Answer:
C
Step-by-step explanation:
1 2/3*3 = about 5
5+1 2/3= 6 2/3<7 1/5
6 2/3+1 2/3 =8 1/3> 7 1/5
C is the best answer because it is the closest to the total amount of paint
27 – 4 + 2a = 4a + 10 what is the answer
Answers
Answer:
13/2 = a
Step-by-step explanation:
27 – 4 + 2a = 4a + 10
Combine like terms
23 +2a = 4a +10
Subtract 2a from each side
23+2a-2a = 4a-2a +10
23 = 2a+10
Subtract 10 from each side
23-10 = 2a+10-10
13 = 2a
Divide by 2
13/2 = a
Answer: a = 13/2
I assume you don't need a step - by - step, you're just asking for the answer. Hope this helps!
Pls halp is due today >_<. Thank you
Answers
Answer:
The square root of 38.
Step-by-step explanation:
The square root of 38 is about 6.16.
The square root of 35 is about 5.91.
The square root of 45 is about 6.70.
The square root of 48 is about 6.92,
So the most reasonable one is the square root of 38, since it is much closer to 6.
Las dos compañías cobran el mismo precio por viaje, cada viaje vale $100.00 pesos, los pobladores dicen que uno de los camiones tiene una capacidad de 3 toneladas y el otro de 4 toneladas, en total se hicieron 23 viajes y se transportaron 80 toneladas de tierra.
Answers
what is this supposed to be bro pls help
Answers
Answer: 1
Step-by-step explanation:
so i put the amount of flour to servings into ratios (fractions)
28:14
9:12
10:13
then I put them into the same denominators
2184:1092
819/1092
840/1092
the first one is the greatest
The ratio of boys and girls in the class is 4:3. How many boys and girls are in the class if there are 35 students?
Answers
Explanation:
Boy = 35 x 4/7 = 20
Girl = 35 x 3/7 = 15
Answer:
20boys and 15girls
Step-by-step explanation:
Let no of boys be 4x
no of girls be 3x
4x+3x=35
7x=35
x=35/7
x=5
no of boys=4×5=20
no of girls=3×5=15
20+15=35 students
help me please pelase please
Answers
look at the image to get ur question thank u for ansering
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate the slope using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 0) ← 2 points on the line
m = [tex]\frac{0-3}{-1-0}[/tex] = [tex]\frac{-3}{-1}[/tex] = 3
The line crosses the y- axis at (0, 3) ⇒ c = 3
y = 3x + 3 ← equation of line
