Mathematics High School

Write y = 3x^2-12x+11 in vertex form. I know the answer, just dont know how to show the work.

Answers

Answer 1

I'll write it out instead of typing it. I think it would be easier to read.

Write Y = 3x^2-12x+11 In Vertex Form. I Know The Answer, Just Dont Know How To Show The Work.

Answer 2

The equation in vertex form is given as:

y = a (x - h) ² + k where a, h, and k are constant.

The equation y = 3x² - 12x + 11 in vertex form is y = 3(x - 2)² + 7.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation in vertex form is given as:

y = a (x - h) ² + k where a, h, and k are constant.

We have,

y = 3x² - 12x + 11

3x² - 12x can be written as:

Taking out common value.

3(x² - 4x).

Now,

y = 3(x² - 4x) + 11 _____(A)

x² - 4x can be written as:

Squaring we get,

= x² - 2.2x + 2² - 2²

= (x² - 2.2x + 4) - 4

[ (a - b)² = a² - 2ab + b ]

= (x - 2)² - 4 ________(B)

Now,

From (A) and (B) we get,

y = 3 (x - 2)² - 4 + 11

y = 3(x - 2)² + 7

Thus,

The equation y = 3x² - 12x + 11 in vertex form is y = 3(x - 2)² + 7.

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Related Questions

What is the value of 3x ( 2x²+6x+3) when x is -3?

a. -27
b. 0
c. 27
d. 54

Answers

3x ( 2x²+6x+3)=
3(-3)(2*3²+6*3+3)
-9 (2*9-18+3)=
-9 (18-18+3)=
-9 (0+3)
-9*3=
-27

The equationoflinevis y + 10 = 2 3 ( x – 8 ) . line w , which is parallel to line v , includes the point (6, -5) . what is the equation of line w ?

Answers

You know that if 2 lines are parallel, they have the same slope.

First, find the slope of the given line;

y+10 = 23(x-8)
y=23x-184-10
y=23x-194

Slope is 23

Write out the basic format;

y=mx+c
y=23x+c <--- replace x and y values here
-5=23(6)+c
-5-138=c
-143=c

Therefore, this equation would be y=23x-143

Hope I helped :)

It is 4 kilometers from chris's house to the nearest mailbox. how far is it in meters?

Answers

1km=1000m
therefore, 4km=4000m

Victoria is 4 years older than her neighbor. the sum of their ages is no more than 14 years. 1. enter an inequality that can be used to represent this situation in the first box, where x represents victoria's neighbor's age. 2. enter the oldest age victoria's neighbor in the second box.

Answers

V = x + 4
x = neighbors age

x + x + 4 < = 14...here is the inequality
2x + 4 < = 14.....this is just a simplified form of the inequality
not sure which one u want to write, because they are both basically the same...one is just simplified a little

2x + 4 < = 14
2x < = 14 - 4
2x < = 10
x < = 10/2
x < = 5.....the oldest age of the neighbor is 5

For the equations given above, which statement is true?

Answers

Consider the first equation : -3x-8=19.

Adding 8 to both sides, we get -3x=27. Dividing by -3 yields the solution x=-9.

Consider the first equation : -3x-2=25.

Adding 2 to both sides, we get -3x=27. Dividing by -3 yields the solution x=-9, again.

Thus, the 2 equations have the same solution.

We could have achieved this result also by noticing that the second equation is equivalent to first one, adding 6 to both sides.

Answer: A) The equations have the same solution because the second can be obtained by adding 6 to both sides of the first equation.

PLZ HELP!!!!!!!!! WILL GIVE BRAINLIEST!!!!!!!! 15 PTS!!!!!!

What is the value of x?

angle PIR
angle SIM

Answers

they intersect so therfor PIR=SIM

so therefor 4x+24=7x+3
minus 4x both sides
24=3x+3
minus 3 both sides
21=3x
divide both sides by 3
7=x
x=7

An architectural drawing of a building shows the elevation of the basement floor to be â12 feet. the elevation of the roof is 32 feet. what is the total distance from the roof to the basement floor?

Answers

The total distance from the roof to the basement floor is 20 feet. If the elevation of the basement floor is 12 feet and the elevation of the roof is 32 feet, then you must subtract the elevation of the basement floor from the elevation of the roof to get the distance between them.

If a car rental costs $35 per day plus $0.79 per mile, and you are traveling for 4 days, 389 miles, how much is the total rental?

Answers

35$×4=140$ rental costs for 4 days
0,79$×389=307,31$ for the miles you drove
140$+307,31$= 447,31$
So the total rent is 447,31$

Answer:

Total rent costing for traveling for 4 days, 389 miles is $447.31

Step-by-step explanation:

Given : a car rental costs $35 per day plus $0.79 per mile.

We have to find the total rent costing for traveling for 4 days, 389 miles.

Since, Cost of car rent per day is $35

Thus, Cost of car rent for 4 days is $ 35 × 4 = $140

Also, Cost of car rent per miles is $0.79

Thus, Cost of car rent for 389 miles is $ 0.79 × 389 = $307.31

Thus, total car rental cost = Cost of car rent for 4 days + Cost of car rent for 389 miles.

Total car rental cost = $140 + $307.31

Total car rental cost = $447.31

Thus, total rent costing for traveling for 4 days, 389 miles is $447.31

What is the median of 150.8, 149.5, 151.2, 153.1, 150.6, 149.9, 146.5, 151.5, 153.5?

Answers

150.8 is your median

Can you please explain to me what the end behavior of the function f(x)=-2x^4-x^3+3 looks like?
I have trouble putting it into terms of approaching infinities as well.Thank you!

Answers

The dominant term is -2x⁴.

As X approaches infinite, y is naturally going to be really large as well.

Remember that a number with an even exponent, regardless of whether it's positive or negative, will be positive.
As x approaches infinite, y will approach -2 * ∞, or -∞. Therefore, the end behavior in the positive direction is y=-∞
As x approaches negative infinite, y will approach -2 *∞ again. This is because -∞⁴ = ∞. Therefore, the end behavior in the negative direction is also y=-∞

Basically, due to the dominance of the -2x^4 term, the function will look more or less like a downward facing parabola with a y-intercept of 3.

What is the component form of the vector?

Answers

Final answer:

The component form of a vector represents it as the sum of its scalar components along the coordinate axes. It is used to describe a vector's individual directional effects in a Cartesian coordinate system, often denoted by Axi + Ayj for 2D vectors, and an additional Azk for 3D vectors.

Explanation:

The component form of a vector refers to its representation as the sum of its separate parts along the coordinate axes. In a two-dimensional system, a vector can be broken down into the x and y components. Each component is essentially the projection of the vector along one of the coordinate axes. For example, in a rectangular (Cartesian) coordinate system, a two-dimensional vector A with an initial point and a terminal point can be represented by the difference in the x-coordinates (horizontal component) and the difference in the y-coordinates (vertical component).

The formula to represent a two-dimensional vector in component form is A = Axi + Ayj, where Ax and Ay are the scalar components of the vector along the x-axis and y-axis, respectively, and i and j are the unit vectors in the direction of the x-axis and y-axis. In three-dimensional space, an additional z-component is included, resulting in the component form A = Axi + Ayj + Azk, with k being the unit vector along the z-axis.

I am a 2 digit number, add my digits together and you get 5, I am not an odd number, I am greater than 45, what am I?

Answers

the only possibility is 50.

Carol earns $8.50 per hour plus 6% commission. She worked 40 hours last week. What is her salary if her total sales were $250

Answers

40x$8.50=$340
$250x6%=$15
$340+15=$355

Choose the correct pair !!

Answers

Greetings!

Find the POI.
[tex] \left \{ {{3x+2y=12} \atop {6x+3y=21}} \right. [/tex]
Multiply Equation #1 by 2.
[tex] \left \{ {{2(3x+2y)=2(12)} \atop {6x+3y=21}} \right. [/tex]
[tex] \left \{ {{6x+4y=24} \atop {6x+3y=21}} \right. [/tex]
Eliminate with subtraction.
[tex] \frac{\left \{ {{6x+4y=24} \atop {6x+3y=21}} \right. }{0x+y=3} [/tex]
[tex]y=3[/tex]

Substitute the value of y.
[tex]6x+3y=21[/tex]
[tex]6x+3(3)=21[/tex]
Simplify.
[tex]6x+9=21[/tex]
Add -9 to both sides.
[tex](6x+9)+(-9)=(21)+(-9)[/tex]
[tex]6x=12[/tex]
Divide both sides by 6.
[tex] \frac{6x}{6}= \frac{12}{6} [/tex]
[tex]x=2[/tex]

The Solution/POI is:
[tex](2,3)[/tex]

Hope this helps.
-Benjamin

???????help please :)

Answers

it is 5 > the check thingy 18 because if you do 18 then put the check it is 4.242640687119285

hope i help pls give bristliest to me

it is 5 > the divided 18 because if you do 18 then put the divided it is 4.24.And 5 is greater than 4.24. which is 5>4.24

Which expression equals 1?
a. sin(x) + cos(x)
b. sin^2(x) + cos^2(x)
c. sin^2(x) - cos^2(x)
d. sin(x) - cos(x)

Answers

b. sin^2 (x) + cos^2 (x)

What is the difference between linear and nonlinear equations

Answers

Thank you for posting your question here at Brainly!~

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

A non-linear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

Hope I helped!~ Brainliest appreciated.

The table below lists the number of floors in the 10 tallest buildings in the world. Note: The buildings are organized by height, not by the number of floors. Skyscraper Number of Floors Taipei 101 Shanghai World Financial Center 101 Petronas Tower 1 88 Petronas Tower 2 88 Greenland Square Zifeng Tower 69 Sears Tower 108 Jin Mao Tower 88 Two International Financial Centre 88 Citic Plaza 80 Shun Hing Square 69 What is the difference between the median and the mode for the number of floors?

Answers

Median - 88

Mode - 88

Mean - 0

the median is a value or quantity that lies at the midpoint of a frequency of observed quantity, the median of 10 and 1 is 5 the mode of a set of numbers is one of the numbers that occurs most often so in set 5595659 5 is the mode.

So in this case the median is 88 and the mode is 88 the mean is 0

Work out the value of 6x^2 when x= -2

Answers

6(-2)^2
-18^2
-324
HOPE IT HELPS!!!

We are given the expression 6x² and a value of x, -2. Starting off, we need to plug in the value of x into 6x², which, when doing so, gives us 6(-2)². By the law of PEMDAS, we will need to do the exponent first. -2² is 4, and when we multiply 4 by 6, we get 24. Therefore, the value of 6x² when x = -2 is 24. Hope this helped and have a phenomenal day!

geometry help will give brainliest

Answers

m<b=19 (Supplementary Angles)
m<c=101 (Triangle Angle Sum Theorem)

what angle measure forms a linear pair with an angle that measures 125

Answers

It would be obtuse, but are you asking for numbers or obtuse, acute, and right angles.

I need help with 1-3 I just don’t understand how to do it at all please help

Answers

1. The transitive property
-if a=band b=c, then a=c
2.Add
3.Subtraction Property of Equality
Hope this helps

I need help with #20 and #21. Show work if possible. Thank You! :)

Answers

20)
3x-1 = 4x-2
x=1
she had 1 hit

21)
2(3t+1) =4(2t-1)
6t+2 = 8t-4
6=2t
t=3
3 fish

Simplify the expression. â€“9z â€“ 13z

A. 4z

B. 4

C. â€“22z

D. 22z

Answers

i wish i could help soryy

The amount of money at a gas stations varies directly with the number of gallons purchased. When 14 gallons were purchased the cost was $27.16. Determine the cost for 18 gallons of gas.
Please answer as soon as possible!!!!!! I appreciate it guys!!!!!!

Answers

The answer is 488.88

It should be 108.64
hope this helped if it did please give me 5 stars and hit the heart button to let me know it did if it didn't please tell me the correct answer.

WILL MARK THE BRAINLIEST

Your local shoe store anticipated giving away 2,500 pairs of shoes in one month, but they only sold 2,215 pairs of shoes. What was the approximate percent error? Show your work to find the percent error.

Answers

The answer is 11.4% where 2500-11.4%=2215.

Answer:

11.4 there now mark that person brainliest

Step-by-step explanation:

Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.

Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?
A. x=-2
B. x=-1
C. x=1
D. x=5
Those are the choices

Answers

the answer is A. x= -2 the first choice

Answer:

Option A is correct

x= -2 is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex]

Step-by-step explanation:

As per the statement:

Fran graphs the equations

[tex]y=2x^2-2[/tex] and

[tex]y = -0.5x + 4[/tex]

Equate these two equations:

[tex]2x^2-2 = -0.5x+4[/tex]

You can see the graph for these equations as shown.

Since, the line and the parabola intersects at x = -2 and x = 1.5.

From the given options:

x = -2 is the solution for these equations.

Therefore, the value is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex] is, x = -2

A business owes $8000 on a loan. Every month, the business pays 12 of the amount remaining on the loan.

How much will the business pay in the sixth month?

Answers

Final answer:

The business will pay $506.99 on the loan in the sixth month, after making monthly payments of 12% of the remaining balance on an $8000 loan.

Explanation:

To determine how much the business will pay in the sixth month on a loan where they pay off 12% of the remaining balance each month, we need to use a decay formula. This is a type of exponential decay since the amount owed is decreasing by a fixed percentage each month. The formula to find the remaining balance after each payment is:

Balance after n payments = Initial amount * (1 - rate)^n

Starting with an initial loan amount of $8000 and a monthly payment rate of 12% (or 0.12 in decimal form), we calculate the remaining balance each month until the sixth month:

Month 1: 8000 * (1 - 0.12) = 8000 * 0.88 = $7040 remainingMonth 2: 7040 * 0.88 = $6195.20 remainingMonth 3: 6195.20 * 0.88 = $5455.78 remainingMonth 4: 5455.78 * 0.88 = $4801.09 remainingMonth 5: 4801.09 * 0.88 = $4224.96 remainingMonth 6: 4224.96 * 0.88 = $3717.97 remaining

Now we can find out how much will be paid in the sixth month by calculating 12% of the balance at the end of the fifth month:

Sixth month payment = 12% of 4224.96
Sixth month payment = 0.12 * 4224.96
Sixth month payment = $506.99
The business will pay $506.99 in the sixth month.

10. Which transformations result in a preimage and image with opposite orientations?
1 point
Dilations only
Translations and rotations
Rotations and reflections
Reflections and glide reflections

Answers

Reflections and glide reflections both give you a transformation where the preimage and image have opposite orientations.

Final answer:

In geometry, reflections and glide reflections are transformations that result in a preimage and an image with opposite orientations. This happens because a reflection flips an object over a line, creating a mirror image with reverse orientation. A glide reflection combines a translation and a reflection, also leading to opposite orientation.

Explanation:

In mathematics, particularly in geometry, when we talk about a preimage and an image, we refer to the original shape and the shape after transformation respectively. The transformation that results in a preimage and image with opposite orientations is reflections and glide reflections. A reflection is a transformation that flips a figure over a line, thus turning it into its mirror image. This reverses the orientation of the figure. A glide reflection involves a translation (or glide) followed by a reflection. Again, the result will have an orientation opposite to the original (or preimage).

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Which statement describes a parallelogram that must be a square?
A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.
B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
C. A parallelogram with a right angle and diagonals that are congruent
D. A parallelogram with diagonals that bisect each other.

Answers

Answer: B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

Step-by-step explanation:

We know that a parallelogram is a quadrilateral having congruent opposite sides and its diagonals bisect each other.

A square is a kind of parallelogram having all its consecutive sides equal and both diagonals congruent to each other.

Its all 4 angles are right angle.

let's check all the statements :

A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.

→It can be rhombus ∵ it also has same characteristics.

B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

→ It only occurs in square.

C. A parallelogram with a right angle and diagonals that are congruent .

→ it can be a rectangle ∵ it has all its angles right angle and diagonals are congruent.

D. A parallelogram with diagonals that bisect each other.

→ It is the basic property of parallelogram , it can describe a rhombus or rectangle both.

The statement that must be true is (b) A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.

A parallelogram has parallel and congruent opposite sides

However, the following must be true about parallelograms that can be regarded as squares:

There are congruent consecutive sidesThe diagonals are congruent

Hence, the true statement is (b)