What is the vertex of the parabola defined by the equation(x − 2)^2 = -12(y − 2)?

Answers

Answer 1

x^2-4x+4=-12y+24
(x^2-4x-20)/-12=y
quadratic => vertex is (-b/2a,f (-b/2a))
Note it is a minimum since coefficient a is positive

Answer 2

I got (2,2) as the answer

Related Questions

Constructing a box. From a rectangular piece of cardboard having dimensions 20 inches x 30 inches, an open box is to be made by cutting out identical squares of area x^2 from each corner and turning up the sides.

(a) Show that the volume of the box is given by the function V(x)=x(20-2x)(30-2x).

(b) Find all positive values of x such that V(x)>0. ...?

Answers

height=x length=20-2(what u cut out)=20-2x width=30-2(what u cut out)=30-2x so v(x)=l*w*h=x(20-2x)(30-2x) b) (0,10)

What is the average rate of change of the function below on the interval from x = 0 to x = 2?

f(x)=250(0.5)x

A. -93.75

B. 62.5

C. 0

D. -0.25

Answers

B. 62.5 hope this works for ya

A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings?
hours of tutoring hours as a teacher's aide What is the maximum profit? $

Answers

since he gets paid more for tutoring, he should work as many hrs tutoring as possible. He can only work at most 20 hrs. He has to work at least 3 hrs tutoring but no more then 8 hrs.....to maximize profit, he needs to work 8 hrs tutoring...leaving 12 hrs as a teachers aide. He should work 20 hrs to maximize his earnings.

maximum profit is : 8(10) + 12(7) = 80 + 84 = 164

He should work 20 hours every week to optimize his profits. The maximum profit will be $164.

What is a numerical expression?

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

He should tutor as many hours as possible because he is paid more for it. He may only work for a maximum of 20 hours every day. He must tutor for at least 3 hours but no more than 8 hours to optimum profit, he must tutor for 8 hours leaving 12 hours as a teacher's helper.

To optimize his profits, he should work 20 hours every week.

⇒ 8(10) + 12(7)

⇒ 80 + 84

⇒ 164

Therefore, he should work 20 hours every week to optimize his profit and the maximum profit will be $164.

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A line tangent to a circle is ________ to a radius of the circle at the point of tangency.
congruent
perpendicular
parallel
similar

Answers

The answer is perpendicular

Answer:

Perpendicular... I had the same question and I got a 100%! Hope this helps!

A once thriving company in Teaneck had its monthly profits, in thousands of dollars, modeled by the equation?
f(t) = t^2 + 9/ 1t^2 + 2

where t is in months after June 1st, 2002.

Estimate the company's profits on June 1st, 2002.
Estimate the company's profits many years into the future

Answers

- The company`s profits on June 1st, 2002:
t = 0
f ( 0 ) = ( 0² + 9 ) / ( 0² + 2 ) = 9/2 = 4.5 ( or $4,500 )
- The company`s profits many years into the future:
[tex] \lim_{t \to \infty} \frac{ t^{2}+9}{ t^{2} +2}= \\ = \lim_{t \to \infty} \frac{2t}{2t} = 1 [/tex]
( or $1,000 )

Answer:

1) 4.5% 2)1%

Step-by-step explanation:

Given equation The monthly profits: [tex]f(t) = \frac{t^2 + 9}{t^2 + 2}[/tex]

where t is in months after june 1st,2002

To find : The company's profits on June 1st, 2002

which means t=0

⇒ [tex]f(0) = \frac{0^2 + 9}{0^2 + 2}[/tex]

⇒ [tex]f(0) = \frac{9}{2}[/tex]

⇒ [tex]f(0) = 4.5[/tex]

The company's profits on June 1st, 2002 = 4.5%

To find :The company's profits many years into the future

we take limit tends to infinity

[tex]\lim_{n \to \infty}( \frac{t^2 + 9}{t^2 + 2})[/tex]

[tex]\lim_{n \to \infty}( \frac{2t}{2t})=1[/tex]

The company's profits many years into the future = 1%

When you pay a bill in full, you are

Answers

paying it off. when you pay a bill in full you have to pay it all off

When n = energy efficiency and Pin = energy input and Pout = energy output, how can you mathematically represent the correct relationship between the energy you put in something and the energy you get out?
A. n = P out * P in
B. n = P out / P in
C. n = P out - P in ...?

Answers

Energy efficiency computes the amount of input power converted into output power. Thus, n = Pin / Pout. Therefore, B.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer:

[tex]n=\frac{P_{out}}{P_{in}}[/tex]

Step-by-step explanation:

We know that,

[tex]\text{Energy efficiency}=\frac{\text{Energy out put}}{\text{Energy in put}}[/tex]

If [tex]P_{in}[/tex] represents the energy input,

[tex]P_{out}[/tex] represents the energy output,

And, n represents energy efficiency,

Hence, the required formula would be,

[tex]n=\frac{P_{out}}{P_{in}}[/tex]

i.e. OPTION B is correct.

What are the common factors of 30 and 300?

Answers

1, 2, 3, 5, 6, 10, 15, 30

Your math teacher manages a campground during summer vacation. He loves math so much that he has mapped the campground on a coordinate grid. The campsites have the following coordinate: Brighton Bluff at B(2,2), ponaganset peak at P(4,10) and harmony hill at h(12,2) he wants to build showers that are equidistant from all three campsites. Find the coordinates of the point where the shower should be placed.

Answers

Answer:

(5,5)

Step-by-step explanation:

Step 1) Find the perpendicular bisector of BP Step 2) Find the perpendicular bisector of BH Step 3) The intersection point of the perpendicular bisector is where the showers would be built. This is the circumcenter of the circumscribed circle. After doing all of this, you should get that answer.. (5,5)

A triangular tent flap measures 3 1/2 ft along the base and has a height of 4 1/2 ft. How much canvas is needed to make the flap

Answers

Assuming the equation is asking us for Area...

Area of a triangle is:

A = [tex] \frac{1}{2} [/tex]b*h

with b = base
and h = height

so area = (0.5)(3.5)(4.5)

=7.875 ft^2

*NOTE: not sure how to show area in feet and also brainiest answer would be nice :D

You're finding area which is 1/2(b(h)) so it's 1/2(3.5(4.5)) = 1/2(15.75) = 7.875 (which is 7 7/8) feet squared of course. Thanks for letting me help!

8 less than a number n is less than 11

Answers

take 11 and add 8 that gives you n so n= 19

Final answer:

To find the number n in the inequality '8 less than a number n is less than 11', we can set up and solve the inequality n - 8 < 11. The answer is that the number n is less than 19.

Explanation:

The question states that 8 less than a number n is less than 11. To solve this, we can set up the inequality:

n - 8 < 11

To isolate n, we can add 8 to both sides:

n < 11 + 8

n < 19

So, the answer is that the number n is less than 19.

Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have?

Answers

The answer is 70,000 sales.

Bob gets paid an annual salary of $30,000, which means that monthly he gets:
$30,000 : 12 months = $2,500 per month

x - number of sales
Bob earns 5% commission on all sales he makes: x * 5% = x * 0.05 = 0.05x

The function is:
f(x) = 2,500 + 0.05x

Bob wants to make $6,000 this month: f(x) = 6,000

2500 + 0.05x = 6000
0.05x = 6000 - 2500
0.05x = 3500
x = 3500 : 0.05
x = 70000 sales

Answer: Correct answer is 70,000 just took the test

how do i find the finite approximation to estimate the area using the lower sum of 4 rectangles for f(x)= 4-x^2 between x=-2 and x=2?
...?

Answers

the primary rectangle would be from - 2 to - 1.
f(- 2) = 0
f(- 1) = 2
this rectangle has 0 stature, subsequently it has no territory. A = length * width = 0.

second rectangle from - 1 to 0
f(- 1) = 2
f(0) = 4
this rectangle has stature of 2 (the base). range = stature * width = 2 * 1 = 2

third rectangle from 0 to 1 is the same
A3 = 2
fourth rectangle from 1 to 2 is the same as the first:
A4 = 0 * 1 = 0
Add up to range = A1 + A2 + A3 + A4 = 4

HELP ME ASAP!! Some red white and blue candies were placed in a bowl. Some contain nuts, and some do not. Suppose one of the candies were chosen randomly from all the candies in the bowl. According to the table below, if the candy is blue, what is the probability that is does not contain any nuts?
Red with nuts=10. Red without nuts=10. White with nuts=20. White without nuts=10. Blue with nuts=20. Blue without nuts=30.
A. 20%
B. 40%
C. 60%
D. 10%

Answers

Answer:

Option C: 60%

Step-by-step explanation:

The number of blue candies with nuts = 20

The number of blue candies without nuts = 30

The total number of blue candies = 20 + 30 = 50

As the chosen candy is blue, the probability that is does not contain any nuts will be = (The number of blue candies without nuts)/(Total number of blue candies)

So, the probability = 30/50 = 0.6 *100% = 60%

Answer: 20%

Step-by-step explanation:

If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis,and rotated 180°, where would point A' lie?

[Hint: Place your coordinates in the blank with no parantheses and a space after the comma in the form: x, y.] (5 points)

Answers

The answer to the problem is as follows:

(x,y)−−−>(−x,y)
---->it is reflect across y axis
(x,y)−−−−>(x,−y)
--->across x axis

rotate 180 (x,y) ---> (-x,-y)

so it's (-4,1) i am right

I hope my answer has come to your help. God bless and have a nice day ahead!

Point A is (-4,1) .Point A is reflected along y axis so y will remain same and x coordinate will have opposite sign .The reflected point A' ---(4,1) .The point is now reflected along x axis so its x ordinate will remain same and y will be at an equal distance from x axis The new reflected point is A" (4,-1) .The point is now rotated 180 degrees the x and y coordinate changes sign so the rotated final point is A"'( -4,1).

Solve for u
3(2u+5)=33
Simplify your answer as much as possible.

Answers

6u+15=33
6u=33-15
6u=18
u=3

U = 3 Is the answer!!!
HOPE THIS HELP!! :D

y=f(x)=1/x. Use algebra to find a simplified rational expression for the slope of the line between (3, f(3)) and (3+h, f(3+h))?? h cannot=0. ...?

Answers

[tex]f(x)= \frac{1}{x} \\ \\ (3,f(3))=(3,\frac{1}{3} ) \\ \\ (3+h,f(3+h))=(3+h,\frac{1}{3+h} ) \\ \\ m= \frac{\frac{1}{3+h}-\frac{1}{3}}{3+h-3} =\frac{ \frac{3-(3+h)}{3(3+h)}}{h} =\frac{ 3-3-h}{3(3+h)h} = \frac{-h}{3(3+h)h} =- \frac{1}{3(3+h)} [/tex]

Find an equation of the tangent line to the curve
y = 8x sin x at the point (π/2, 4π).
y'=8(sinx)+8xcosx
8(sinπ)+8π(cosπ)
0+(-8π)

Answers

Hello
We know that upon differentiating a function at a certain point, we can obtain its gradient at that point. That will also be the gradient of its tangent line. Thus,
y = 8x * sin(x)
y' = 8x * cos(x) + 8sin(x)
Evaluating the gradient at the given point, we insert pi/2 for x.
gradient = 8(pi/2) * cos(pi/2) + 8sin(pi/2)
= 2pi*sqrt(2) + 4(sqrt(2))
The equation of the line will be in the form y = mx + c; where m is the gradient and c is the y intercept. To calculate the y-int, we insert the given x and y values:
4pi = [2pi*sqrt(2)+4(sqrt(2))]*(pi/2) + c
c = -1.98
Thus, the equation is:
y = 14.5x - 1.98

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram?

A)2 cm and 2 cm
B)4 cm and 7 cm
C)7 cm and 9 cm
D)13 cm and 19 cm

Answers

To find this, set the opposite ends equal to one another and solve for n

5n-6 = 3n-2 subtract 3n from both sides
2n-6 = -2 add 6 to both sides
2n = 4 divide both sides by 2
n=4

now use this to solve for the sides
5n-6
5(2) -6
4
and
2n+3
2(2) +3
7
adjacent means next to each other so it is 4 and 7 +B

Brainliest is always appreciated !

A dolphins heart beats 688 times in 6 minutes

Answers

In one minute, the heart beats 114 2/3 times

That's 114 .7 beats per minute (rounded to nearest tenth)

Which Equation represents this problem?

Pauline can spend $36 on bus fare each week. She needs to ride the bus 5 days a week. How much can she spend each day on bus fare?
A.
36 + b = 5

B.
5 x b = 36

C.
5 ÷ b = 36

D.
36 – b = 5

Answers

The answer has to be C

Determine whether the following relation is a function.
{(3,7), (3,8), (3,-2), (3.4),(3,1)}
A) it is a function because the ordered pairs all have the same x-value.
B) it is not a function because there are multiple y-values paired with a single x-value.
C) it is a function because none of the ordered pairs have the same y-value.
D) it is not a function because none of the ordered pairs have the same y-value.

Answers

The relation is not a function it is not a function because there are multiple y-values paired with a single x-value. Option B.

Is the relation a function?

A relation is a function only if every input is mapped into a single output.

Here we have the relation {(3,7), (3,8), (3,-2), (3.4),(3,1)}

Remember that the first number of each pair is the input, so we can see that all the inputs are the same one

So the input x = 3 is mapped into different outputs, thus, this is not a function.

Learn more about functions:

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The correct option is B) it is not a function because there are multiple y-values paired with a single x-value.

To determine if a relation is a function, one must check if each x-value is associated with exactly one y-value. In other words, for every x, there should be one and only one y. This is known as the vertical line test in the context of graphs.

Let's examine the given set of ordered pairs: {(3,7), (3,8), (3,-2), (3,4), (3,1)}.

We can see that the x-value of 3 is repeated with different y-values: 7, 8, -2, 4, and 1.

This means that the x-value of 3 is associated with multiple y-values, which violates the definition of a function.

Therefore, the relation is not a function because it fails to satisfy the condition that each x-value must correspond to exactly one y-value.

The presence of multiple y-values for a single x-value is the key indicator that the relation is not a function.

What is the negative reciprocal of 3/4 or three over 4

Answers

I believe it would be -4/3.

Final answer:

The negative reciprocal of 3/4 is -4/3. This is found by inverting the fraction to get 4/3 and then applying the negative sign.

Explanation:

The negative reciprocal of a number refers to the value that, when multiplied by the original number, results in -1. For the fraction 3/4 (three over four), taking the reciprocal involves flipping the numerator and the denominator, which gives us 4/3. Making this reciprocal negative results in -4/3. The concept of reciprocals relates to the broader mathematical principles of multiplication and division, where negative exponents indicate the inverse of the corresponding positive exponent. For example, x to the power of -1 is equal to 1 divided by x to the power of 1, which demonstrates how negative exponents introduce division into the operation.

Solve for x. -3(x-5)-2x=-10

Answers

-3x+15-2x=-10
-5x+15=-10
-5x=-10-15
-5x=-25
X=5
Ask me if you have a question. :D

mrs. fletcher bought 5 coins for $32 each later she sold all the coins for $300 how much more did mrs. fletcher receive for each coin that she paid

Answers

She recieved 28 more dollars for each coin that she paid.

Answer:

She received $60 for each coin.

Step-by-step explanation:

Mrs. Fletcher bought 5 coins for $32.Then, she sold them for $300.

We need to divide to know how much Mrs. Fletcher received for the coins

[tex]\frac{\$300}{5}=\$60[/tex]

She received $60 for each coin.

Now, each coin had a cost of

[tex]\frac{\$32}{5}= \$6.40[/tex]

So, he earned a profit of

[tex]\$60 - \$6.40=\$53.60[/tex]

What is the smallest positive value for x where y=sin2x reaches its maximum? How do you figure this out? ...?

Answers

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

The amplitude of sin(x) is 1, so we want

sin (2x) =1

taking inverse sin, we get
2x = [tex] \pi /2[/tex]

divide by 2 and we get
x = [tex] \pi /4[/tex]

Final answer:

To find the smallest positive value for x where y = sin^2x reaches its maximum, we can set sin^2x = 1 and solve for x. The smallest positive value of x where y = sin^2x reaches its maximum is pi/2.

Explanation:

To find the smallest positive value for x where y = sin^2x reaches its maximum, we need to consider the properties of the sine function. The sine function oscillates between -1 and +1, with the maximum value of sin^2x being 1. Since the maximum value of sin^2x is 1, we can set sin^2x = 1 and solve for x.

Applying the property of sin^2x = 1, we have:

sin^2x = 1
Taking the square root of both sides, sinx = ±1
Since we are looking for the smallest positive value of x, we take sinx = 1
This means that x = π/2 + 2πn, where n is an integer.

Therefore, the smallest positive value for x where y = sin^2x reaches its maximum is π/2.

The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?

Answers

9(u – 2) + 1.5u = 8.25
9u - 18 + 1.5u = 8.25
10.5u = 8.25 + 18
10.5u = 26.25
u = 26.25 / 10.5
u = 2.5

Answer:

2.5

Step-by-step explanation:

Given: The equation [tex]9(u - 2) + 1.5u = 8.25[/tex]models the total miles Michael traveled one afternoon while sledding.

To Find: Which is the value of u?

Solution:

[tex]9(u - 2) + 1.5u = 8.25[/tex]

[tex]9u - 18+ 1.5u = 8.25[/tex]

[tex]10.5u = 8.25+18[/tex]

[tex]10.5u =26.25[/tex]

[tex]u =\frac{26.25}{10.5}[/tex]

[tex]u =2.5[/tex]

Hence the value of u is 2.5

Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.

(–3, –2)

(–2, 1)

(–1, –2)

(–1, 2)

(1, –2)

(1, 2)

Answers

The answer is (1,-2) and (1,2)

Answer:

Points (-3,-2), (-1,-2), (1,-2) and (1,2) are solutions to the given inequality.

Step-by-step explanation:

We are given the following inequality in the question:

[tex]y < 0.5x + 2[/tex]

We have to check which points give the solution to the given inequality.

1) (-3,-2)