Write an equation for a parabola that has a vertex (1, 2) and passes through the point (3, -6).

Answers

Answer 1

Answer:

y= -2x²+4x.

Step-by-step explanation:

the common equation of the parabola is y=ax²+bx+c, where a, b, c - numbers.

1) the coordinates of the vertex are:

[tex]x_0=-\frac{b}{2a} \ and \ y_0=\frac{4ac-b^2}{4a}.[/tex]

2) if according to the condition x₀=1, then b= -2a.

If according to the condition y₀=2, then   [tex]2=\frac{4ac-b^2}{4a}=\frac{4ac-4a^2}{4a}=c-a;[/tex]

it means that c=a+2.

3) if b= -2a; c=a+2 and the point (3;-6) belongs to the given parabola, then it is possible to substitute them into the common equation of the parabola:

-6=3²*a-6a+a+2; ⇔ a= -2.

4) if a= -2, then b=-2a=4, and c=a+2=0.

5) if a=-2, b=4 and c=0, then the required equation of the parabola is:

y= -2x²+4x.


Related Questions

A insurance office keeps track of the number of car insurance claims filed each day. Based on the data collected, it determines that the following probability distribution applies: Number of Claims Probability 0 .25 1 .15 2 .25 3 .25 4 .10 a. What is the expected number of new claims filed each day

Answers

Answer:

The expected number of new claims filed each day is 1.8.

Step-by-step explanation:

We are given the following probability distribution:

[tex]P(X = 0) = 0.25[/tex]

[tex]P(X = 1) = 0.15[/tex]

[tex]P(X = 2) = 0.25[/tex]

[tex]P(X = 3) = 0.25[/tex]

[tex]P(X = 4) = 0.1[/tex]

a. What is the expected number of new claims filed each day

Multiplication of each outcome by its probability, so:

[tex]E(X) = 0*0.25 + 1*0.15 + 2*0.25 + 3*0.25 + 4*0.1 = 1.8[/tex]

The expected number of new claims filed each day is 1.8.

Nick buys a bag of cookies that contains 9 chocolate chip cookies, 8 peanut butter cookies, 4 sugar cookies and 5 oatmeal cookies. What is the probability that Nick reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie

Answers

Answer:

7/26

Step-by-step explanation:

Add all of it up.

9 + 8 + 4 +5 = 26

26 cookies, but done twice so,

26 × 2 = 52

14/52 = 7/26

10v-6v=28
Simplify your answer as much as possible

Answers

Step-by-step explanation:

10v-6v=28

4v=28

v=28/4

v=7

Answer:

10v-6v=28

or, 4v = 28

or, v = 28/4

or, v = 7

hence 7 is the required value of v

the bath tap was left dripping at 18 :00. The water dripped out at a rate of 3 drops per minute. each drop contains 2ml of water. how much water had been lost by 06 :00 the next morning​

Answers

so first, we need to figure out how long the tap had been dripping for. To do this, we have two values: 6:00 pm and 6:00 am. From 6 pm to 6 am is 12 hours.

Then, we convert this to minutes, so it can be easier to figure out the rate of water dripping in minutes, not hours. So we do, 12*60, which is 720 minutes.

Next, we need to find out how many drips of water there was. So, if 3 drops come out of the tap in 1 minute, we need to multiply 3 and 720 to give us the amount of drops that come out in 720 minutes. 720*3 is 2160.

Then, we need to figure out how much millilitres of water that it. So, we do 2160*2 which is 4320 ml.

So, 4320 ml of water had been lost by 6 am.

Feel free to ask any questions if anything isn't clear x

if √3CosA = sin A , find the acute angle A​

Answers

Answer:

Here is your answer.....

Hope it helps you....

Which of the following choices is the correct range for the function
h(x) =-3x^2if the domain is (0.-2. 1)?
(0, -6, -3)
(0,6, -3)
None of the choices are correct.
(0, 12, 3)
(0, -12,3)

Answers

9514 1404 393

Answer:

  None of the choices are correct

Step-by-step explanation:

The squared term (x²) is never negative, so all non-zero range values will be negative. For the given domain values, the range is {0, -12, -3}.

None of the choices are correct.

A subcommittee of six is to be selected from a committee containing 10 democrats and 12 republicans. In how many ways can at least 1 democracy be selected for the subcommittee?

Answers

Answer:

the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways

Step-by-step explanation:

Given;

number of the subcommittee, = 6

number of democrats = 10

number of republicans, = 12

The number of ways to select at least 1 democrat in the subcommittee is calculated as follows;

Let D represent Democrats

let R represent Republicans

= (1D & 5R) or (2D & 4R) or (3D & 3R) or (4D & 2R) or (5D & 1R) or (6D)

= 10C₁ x 12C₅  +  10C₂ x 12C₄  +  10C₃ x 12C₃  + 10C₄ x 12C₂ + 10C₅ x 12C₁  + 10C₆

[tex]=( \frac{10!}{9!1!} \times \frac{12!}{7!5!} )+ (\frac{10!}{8!2!} \times \frac{12!}{8!4!})+ (\frac{10!}{7!3!} \times \frac{12!}{9!3!})+ (\frac{10!}{6!4!} \times \frac{12!}{10!2!})+ (\frac{10!}{5!5!} \times \frac{12!}{11!1!}) \\\\ +(\frac{10!}{4!6!})\\\\= (7,920) + (17,820) + (26,400) + (13,860)+ (3,276) + (210)\\\\= 69,486 \ ways[/tex]

Therefore, the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways

PLEASE HELPPPP
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.

Answers

Given:

The cost function is:

[tex]C(x)=0.28x^2-0.7x+1[/tex]

where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.

To find:

The minimum production cost.

Solution:

We have,

[tex]C(x)=0.28x^2-0.7x+1[/tex]

It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:

[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,

[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]

[tex]-\dfrac{b}{2a}=1.25[/tex]

Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.

[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]

[tex]C(x)=0.28(1.5625)-0.875+1[/tex]

[tex]C(x)=0.4375+0.125[/tex]

[tex]C(x)=0.5625[/tex]

Therefore, the minimum production cost is 0.5625 million dollars.

Answer:

The minimum cost is 0.5625.

Step-by-step explanation:

The cost function is

C(x) = 0.28x^2 - 0.7 x + 1

Differentiate with respect to x.

[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]

The minimum value is

c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1

C = 0.4375 - 0.875 + 1

C = 0.5625

Midpoint for
(-2,3) and (4,-1)

Answers

Midpiont=(_2+3\2), (4+_1/2)

=2/2,6/2

=1,3

Find z such that 6% of the standard normal curve lies to the right of z.

Answers

P(Z ≥ z) = 1 - P(Z ≤ z) = 0.06

==>   P(Z ≤ z) = 0.94

==>   z1.7507

Consider a set of data in which the sample mean is 26.826.8 and the sample standard deviation is 7.97.9. Calculate the z-score given that x.

Answers

Answer:

The answer is "0.59".

Step-by-step explanation:

Please find the whole question in the attached file.

Given:

[tex]\mu=26.8\\\\\sigma=6.4\\\\X=30.6[/tex]

Using formula:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

   [tex]=\frac{30.6-26.8}{6.4}\\\\=\frac{3.8}{6.4}\\\\=\frac{380}{640}\\\\=\frac{38}{64}\\\\=\frac{19}{32}\\\\=0.59375\approx 0.59[/tex]

Help plz help needed i need the answer

Answers

Answer:

x = ±sqrt(26)

Step-by-step explanation:

ln ( x^2 -25) = 0

Raise each side to base e

e^ln ( x^2 -25) = e^0

x^2 -25 = 1

Add 25 to each side

x^2 -25 +25 = 1+25

x^2 = 26

Take the square root of each side

sqrt(x^2) = ±sqrt(26)

x = ±sqrt(26)

Answer:

The third option

Step-by-step explanation:

If we rewrite this in log form, we get

[tex]e {}^{0} = {x}^{2} - 25[/tex]

Remeber anything to the 0 power is 1, so simplifying the equation first

[tex]1 = {x}^{2} - 25[/tex]

Add 25 to both sides

[tex]26 = {x}^{2} [/tex]

Take the square root of both sides

[tex]x = \sqrt{26} [/tex]

Square root are both so

[tex]x = - \sqrt{26} [/tex]

Is also a answer.

The third option is the answer

What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}​

Answers

Answer:

Range → {y| y ≥ -11}

Step-by-step explanation:

Range of a function is the set of of y-values.

Given function is,

f(x) = 2x² + 6x - 8

By converting this equation into vertex form,

f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]

     = [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]

     = [tex]3[(x+1)^2-\frac{11}{3}][/tex]

     = [tex]3(x+1)^2-11[/tex]

Vertex of the parabola → (-1, -11)

Therefore, range of the function will be → y ≥ -11

The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}

What is the range of a function?

The range of a function is the set of output values of the function

Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.

So, df(x)/dx = d(3x² + 6x - 8)/dx

= d(3x²)/dx + d6x/dx - d8/dx

= 6x + 6 + 0

= 6x + 6

Equating the experssion to zero, we have

df(x)/dx = 0

6x + 6 = 0

6x = -6

x = -6/6

x = -1

From the graph, we see that this is a minimum point.

So, the value of y = f(x) at the minimum point is that is a t x = - 1 is

y = f(x) = 3x² + 6x - 8

y = f(-1) = 3(-1)² + 6(-1) - 8

y = 3 - 6 - 8

y = -3 - 8

y = -11

Since this is a minimum point for the graph, we have that y ≥ -11.

So, the range of the function is {y|y ≥ -11}

So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}

Learn more about range of a function here:

https://brainly.com/question/25915612

SAQ 5.1

1. Find the first four terms of the sequence whose general term is given by

i.

ii.

7 x 3"

n-2 5 x

2. Say what the pattern of is for each of the following sequences and give the next three

terms

i.

ii.

2, 6, 12, 20

8, 0.8, 0.08, 0.008

1 1 1 '2'3'4

Answers

Answer:

1. (i) 7, 21, 63, 189

(ii) 20, 10, 5, 2.5

2. (i) n²+n (where n = 1, 2, 3, ..)

(ii) 8/(10^n) (where n = 1, 2, 3, ..)

(iii) 1/(n+1) (where n = 1, 2, 3, ..)

In order for the parallelogram to be a
rectangle, x = [?]
Diagonal AC = 7x - 35
Diagonal BD = 3x + 45
A
B.
D
C С

Answers

Answer:   20

Explanation:

For any rectangle, the diagonals are the same length.

AC = BD

7x-35 = 3x+45

7x-3x = 45+35

4x = 80

x = 80/4

x = 20

Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O

Answers

Answer: Volume of Cylinder A is                          pi times the area of the base times the height

                                                             π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3

Volume of Cylinder B is likewise             pi times the area of the base times the height

                                                             π r2 h = (3.1416)(6)(6)(7)   = 791.68 ft3

After pumping all of Cyl A into Cyl B

there will remain empty space in B         791.68 – 753.98 = 37.7 ft3  

The percentage this empty space is

of the entire volume is                            37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth  

.

Step-by-step explanation: I hope that help you.

Answer:  7.4%

Note: you may not need to type in the percent sign.

===========================================================

Explanation:

Let's find the volume of water in container A.

Use the cylinder volume formula to get

V = pi*r^2*h

V = pi*5^2*8

V = 200pi

The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.

We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.

-----------------------

Now find the volume of cylinder B

V = pi*r^2*h

V = pi*6^2*6

V = 216pi

Despite being shorter, tank B can hold more water (since it's more wider).

-----------------------

Now divide the results of each section

(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%

This shows us that 92.59% of tank B is 200pi cubic feet of water.

In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.

This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%

Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.

Which is an x-intercept of the graph of the function?

Answers

Answer:

D

Step-by-step explanation:

X intercept=y=0. 0=tan(x-5pi/6). x-5pi/6=0, x=5pi/6

The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.

Answers

Answer:

60 sq in

Step-by-step explanation:

Perimeter = 2l + 2w

If l = w+4

Perimeter = 2(w+4) + 2w

Perimeter = 4w+8

32 = 4w + 8

24 = 4w

6 = w

If w = 6, l = 6+4 = 10

Area = l * w

Area = 10 * 6

Area = 60

Which statement is true about the slope of the graphed line?

Answers

Answer: positive

Step-by-step explanation: because it is going up from the left to the right

Evaluating functions (pic attached)

Answers

f(x) = 2x³ - 3x² + 7

f(-1) = 2(-1)³ - 3(-1)² + 7

=> f(-1) = 2(-1) - 3(1) + 7

=> f(-1) = -2 -3 + 7

=> f(-1) = 2

f(1) = 2(1)³ - 3(1)² + 7

=> f(1) = 2(1) - 3(1) + 7

=> f(1) = 2 -3 + 7

=> f(1) = 6

f(2) = 2(2)³ - 3(2)² + 7

=> f(2) = 2(8) - 3(4) + 7

=> f(2) = 16 - 12 + 7

=> f(2) = 11

simplify -2/5(sqrt(75))

Answers


-2√3
Decimal form:-3.46410161

Answer:

= - 2√3/75

Step-by-step explanation:

Remove parentheses: (a) = a

= -2/5√75

Apply the fraction rule: -a/b = -a/b

= -2/5√75

= - 2/5 . 5√3

Multiply the numbers: 5 . 5 = 25

= - 2/25√3

= - 2√3/75

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation
p = −0.00051x + 5 (0 ≤ x ≤ 12,000)
where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by
C(x) = 600 + 2x − 0.00002x2 (0 ≤ x ≤ 20,000).
Hint: The revenue is
R(x) = px,
and the profit is
P(x) = R(x) − C(x).
Find the revenue function,
R(x) = px.
R(x) =

Answers

Answer:

[tex]R(x) = -0.00051x^2 + 5x[/tex]

[tex]P(x) = -0.00049x^2 + 3x-600[/tex]

Step-by-step explanation:

Given

[tex]p = -0.00051x + 5[/tex] [tex]\to[/tex] [tex](0 \le x \le 12,000)[/tex]

[tex]C(x) = 600 + 2x - 0.00002x^2[/tex] [tex]\to[/tex] [tex](0 \le x \le 20,000)[/tex]

Solving (a): The revenue function

We have:

[tex]R(x) = x * p[/tex]

Substitute [tex]p = -0.00051x + 5[/tex]

[tex]R(x) = x * (-0.00051x + 5)[/tex]

Open bracket

[tex]R(x) = -0.00051x^2 + 5x[/tex]

Solving (b): The profit function

This is calculated as:

We have:

[tex]P(x) = R(x) - C(x)[/tex]

So, we have:

[tex]P(x) =-0.00051x^2 + 5x - (600 + 2x - 0.00002x^2)[/tex]

Open bracket

[tex]P(x) =-0.00051x^2 + 5x -600 - 2x +0.00002x^2[/tex]

Collect like terms

[tex]P(x) = 0.00002x^2-0.00051x^2 + 5x - 2x-600[/tex]

[tex]P(x) = -0.00049x^2 + 3x-600[/tex]

What is this fraction converted by a decimal?

Answers

Convert the fraction by dividing the numerator by the denominator
Answer: 0.25

Answer:

2

Step-by-step explanation:

Which expression is equivalent to the area of square A, in square inches?
1. 1/2(10)(24)
2. 10(24)
3. (10+24)^2
4. 10^2 + 24^2

Answers

Answer:

4.) 10^2 + 24^2

Step-by-step explanation:

From the attached diagram, the area of a square A is given by the measure of the square of its hypotenus :

The hypotenus is given by :

Hypotenus² = opposite² + Adjacent²

Hypotenus² = 10² + 24²

The square of hypotenus =  10^2 + 24^2

Sam is making a table of values and a graph for the equation 16x + y = −48. He says that when x = 3, y = 0. Is Sam correct?

Answers

Answer:

No

Step-by-step explanation:

16x + y = −48

Substitute the point into the equation and see if it is true

16(3) +0 = -48

48 = -48

This is not true so the point is not a solution

"when reading a cd-rom disk 2.8 cm from its center the rotational speed is 726 rpm what is the rpm at 5.2cm

Answers

9514 1404 393

Answer:

  726 rpm

Step-by-step explanation:

The angular speed is not dependent upon the radius. The rotational speed is 726 rpm at any radius.

2 squared plus b squared equal 256

Answers

Answer:

[tex]2^2+b=256[/tex]

b=252

Step-by-step explanation:

[tex]2^2+b=256[/tex]

4+b=256

b=252

I wasn't very sure about what you are asking, but I hope this helps!

B= 252
Hopes this helps

t^2 +11t+30/t^2+5t-24 ÷ t^2+4t-21/t^2+10t+25

Answers

Answer:

t^2 + 30t - 15/t^2 + 25

Step-by-step explanation:

a) __m=10km 25m =___km

b) __m=__km__m=1.5 km

Answers

Answer:

0.01m=10km

25m=25000km

1m=1000km

0.0015m=1.5km

If this is incorrect forgive me plz

I hope this will help you

establish this identity

Answers

Answer:

see explanation

Step-by-step explanation:

Using the identities

tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x

sin2x = 2sinxcosx

Consider left side

cosθ × sin2θ

= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )

= 2sin²θ

= 2(1 - cos²θ)

= 2 - 2cos²θ

= right side , then established

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A game involves rolling a number cube. You get one point if you roll an even number and negative one point if you roll an odd number.A 7-column table has 3 labeled rows. The first row is labeled Roll with entries 1, 2, 3, 4, 5, 6. The second row is labeled Probability with entries one-sixth, one-sixth, one-sixth, one-sixth, one-sixth, one-sixth. The third row is labeled Point(s) with entries negative 1, 1, negative 1, 1, negative 1, 1.Which statements are true regarding this scenario? Check all that apply.The sample space is {1, 2, 3, 4, 5, 6}.The expected value for the game is 0.The expected value for the game is One-half.The game is fair because the expected value is equal to 0.The game is unfair because the expected value does not equal 0. Bi 7: Khoanh trn p n ng.1.My mother told me to (put/ get) on warm clothes before I went out2. Jim really (got/ put) me down when he forgot my birthday.3. My father never (tells/ drops) me off but my mother is always shouting at me.4. I couldnt believe she (turned/ got) down my invitation for the second time.5. My mother often lets me (look/ take) after my younger brother.6. Why did she (break/ stay) up with you?She said I didnt care much about her.7. Please (drop/ tell) me off in front of the theater.8. Weve been (saving/ looking) up to travel to New York this summer.9. Have you (take/ put) out clean towels for the guests?10. (Take/ Dress) off your rain coat before you come in.11. I remember (paying/ looking) Jim back but he kept asking me for his money.12. Jims poor test results (got/ looked) his parents down.13. grandmother (died/ passed) away before I was born.14. I have many tasks to (attend/ took) to.15. Who does this bag (belong/ own) to? Bi 8: Hon thnh cc cu di y bng cch in tiu tthch hp vo ch trng.1.We will set _________for Tokyo in the next few hours.2. Everyone says that Jim takes _________his father but I think he is more like his mother.3. Who will take _________your position when you are on parental leave?4. There are four of us so Peter cuts the cake _________four pieces.5. I am going to buy a new bike, so I put my old one _________.6. Remember to put the trash _________before the garbage truck comes.7. You must take _________yourhat before you come intoa temple.8. I hate the way my manager shuts me _________when she disagrees with me.9. What are you looking _________ ? My car keys.10. Watch _________for the dog. Everyone says that it is a fierce dog. (a) This is a new English grammar book. (What) AA population growth has emerged as "the complex problems in the world for both developed and developing countries". Justify. Which is most applicable when continuous inspection is used? I-chart, P-chart, c-chart C-bar chart Suppose that 25% of people own dogs If you pick three people at random, whatis the probability that they all three own a dog? (Let me add that we dont know thepopulations size so calculate the probability as if the population is infinite.) Which of the following counteracts the movement of bicarbonate ions from the RBC?A) chloride shiftingB) the Haldane effectC) release of hydrogen ionD) the Bohr effect who much the velocity of a body when it travels 600m in 5 min Ludwig borrowed $700,000 for aperiod of 2 years. His interest rate is10%. How much interest willLudwig pay in all?$[?] WILL GIVE BRAINLIEST!Rewrite each sentence using correct capitalization, end punctuation and adding commas where needed.1. we send food medicine and supplies to many countries overseas such as ethiopia and thailand2. janice michael henry and denise often go skating at the oldtown skating rink on monday nights3. "john played saxophone for the band" said ms. smith4. "let's go swimming in the pond" paul said, "and then we can warm up by the fire Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next schoolyear are given in the following table:Grade Geometry Algebra II Pre-Calculus AP Statistics Total10th1507525525511th50100752024512th105010065225Total 21022520090725Part A: What is the probability that a student will take AP Statistics? (2 points)Part B: What is the probability that a 12th-grader will take either Pre-Calculus or AP Statistics? (2 points)Part C: What is the probability that a student will take Algebra II given that he or she is in the 11th grade? (2 points)Part D: Consider the events "A student takes Algebra II and "A student is a 10th-grader. Are these events independent? Justify your answer. (4 points)