Find the equation of a parabola with a focus at (3,1) and a directrix at y = 3.
Question 5 options:

A)

y = 1∕4(x – 3)2 + 2


B)

y = –1∕4 (x – 3)2 + 3


C)

y = –1∕4 (x – 3)2 + 2


D)

y = 1∕4(x – 3)2 + 3

Answer:

The answer is letter D.

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

Typically you would want to solve this equation by dividing both sides by 3 but we need to find an equivalent equation that gives the same answer. 3 divided by 3 is the same as 3 times 1/3. Thus;

3x * 1/3 = 9 * 1/3

x = 3

Best of Luck!

Answer:

3

Step-by-step explanation:

3x = 9

= 3x/3 = 9/3

= 3

Answer:

265.1

Step-by-step explanation:

10% = 0.1

15% = 0.15

0.1(42)(8) + 0.15(14)(15) + 200 = 33.6 + 31.5 + 200 = 265.1 - total amount  Adam earned last week.

Answer:

2.14?

Step-by-step explanation:

(I'm not good at explaining, but I THINK its 2.14)

Answer:

Because when your finding a point on the x line going left goes towards the negative side, like a number line. So for the y line think of it like the number line but going up is positive and going down is negative.

so if we wanted to go right 6 units and down 3 units it would written as:

(x+6,y-3) Because going right on the x line is like adding 6 units and going down on the y line is like subtracting 3 units for this example

Step-by-step explanation:

Answer:

Solving the equation [tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex] we get: [tex]\mathbf{a=-\frac{1}{15} }[/tex]

Step-by-step explanation:

We need to solve the equation:

[tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex]

And find the value of a

Solving the equation: [tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex]

First we will be Switching sides

[tex]\frac{3a}{4}-\frac{13}{20}=-\frac{7}{10}[/tex]

Now, for finding value of a we will be adding 13/20 on both sides

[tex]\frac{3a}{4}-\frac{13}{20}+\frac{13}{20}=-\frac{7}{10}+\frac{13}{20}[/tex]

[tex]\frac{3a}{4}=-\frac{7}{10}+\frac{13}{20}[/tex]

Now, on right hand side, Taking LCM of denominators i.e 10 and 20, we get 20 and simplifying:

[tex]\frac{3a}{4}=\frac{-7*2+13}{20}\\\frac{3a}{4}=\frac{-14+13}{20}\\\frac{3a}{4}=\frac{-1}{20}[/tex]

Now, multiply both sides by 4/3

[tex]\frac{3a}{4}\times \frac{4}{3} =\frac{-1}{20}\times \frac{4}{3}\\a=\frac{-1}{5}\times \frac{1}{3}\\a= \frac{-1}{15}[/tex]

So, solving the equation [tex]-\frac{7}{10}=\frac{3a}{4}-\frac{13}{20}[/tex] we get: [tex]\mathbf{a=-\frac{1}{15} }[/tex]

Answer:

Yes.  There can be 56 games (92%) of Exploding Snap every evening throughout September and October that can be played without having the same three Gry ndors play a game twice.

Step-by-step explanation:

This is a combination game without repetition.

The formula for combination without repetition is:

n! /r! (n - r)!

where n = 8 and r = 3

Therefore, n! /r! (n - r)!

= 8! / 3! (8 -3)!

= 40,320 / 6 (120)

= 40,320 / 720

= 56

There are 30 nights in September and 31 nights in October, totaling 61 nights

This implies that 56/61 games can be played in these two months without repeating the same three gamers.

56/61 = 0.918

= 92%

Answer:

The answers to the questions are well numbered below.

Step-by-step explanation:

We have arrival rate

λ = 7 in every 10 minutes = 0.7

Service time u = 7 minutes

1. Average time a car is in system

W = 1/u - λ

= 1/7-0.7

= 0.1587

= 0.16 to 2 decimal places

2. Average number of cars in system

= λ/u-λ

= 0.7/7-0.7

= 0.1111

= 0.11 to 2 decimal places

3. Average time that cars spend to receive service

= λ/u(u-λ)

= 0.7/7(7-0.7)

= 0.01587

= 0.016 to 2 decimal places

4. Average number of cars in line behind customer receiving service

= λ²/u(u-λ)

= 0.7²/7(7-0.7)

= 0.49/44.1

= 0.011 to 2 decimal places

5. Probability no cats at window

1-λ/u

= 1-0.7/7

= 0.9 = 9%

6. Percentage of time postal clerk is busy

= λ/u = 0.7/7 = 0.1 = 10%

7. Probability of exactly 2 cars

= λ²e^-λ/2!

= 0.7²e^-0.7/2!

= 0.1217

= 12.17%

Answer:

A= –5x2 + 4x – 7y + 14 = 0

C= 9x2 – 12xy + 4y2 + 4x – y + 5 = 0

D= 12x + 6y – 5y2 + 14 = 0

Step-by-step explanation:

I finished the assignment from Edge2020

The equation which would produce a parabola from the provided options are equation first and forth,

[tex]-5x^2 + 4x - 7y + 14 = 0[/tex]

[tex]12x + 6y -5y^2 + 14 = 0[/tex]

To of identify the type of conic section from an equation whether it is parabola, or not, let suppose the equation as,

[tex]Ax^2+By^2+Cx+Dy+E=0[/tex]

If In this equation,

Either [tex]A=0[/tex] or [tex]B=0[/tex], but not both. Then it is the equation of parabola.

The first equation is,

[tex]-5x^2 + 4x - 7y + 14 = 0[/tex]

There is no square term of y. Thus, this is the equation of parabola.

The second equation is,

[tex]-x^2 + 6x + y^2 - 8 = 0[/tex]

This is not the equation of parabola, as there is two square terms of variable x and y.

The third equation is,

[tex]9x^2 - 12xy + 4y^2 + 4x - y + 5 = 0[/tex]

Similar to the second equation, here is also two square terms of different variable. Thus, it is not a equation of parabola.              

The fourth equation is,

[tex]12x + 6y -5y^2 + 14 = 0[/tex]

This equation is the equation of parabola, as there is only a single square term.

The fifth equation is,

[tex]20x^2 + 10xy - y^2 + 3x - 6y + 5 = 0[/tex]

This is now the equation of parabola because of two square terms.

Hence, the equation which would produce a parabola from the provided options are equation first and forth,

[tex]-5x^2 + 4x - 7y + 14 = 0[/tex]

[tex]12x + 6y -5y^2 + 14 = 0[/tex]

Learn more about the conic section here;

https://brainly.com/question/8320698

Step-by-step explanation:

18/hour life guarding and 9/hour clearing tables. so 9 divided by 144 gives you ur hours then u just divide by 2 to get life guarding hours pls tell me if u need help

Answer:

220 = B + 30

Step-by-step explanation:

This can be rearranged many ways

B= 190

B= 220 - 30

ETC...

Answer:

Okay!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The answer is 14

Step-by-step explanation:

Folow order of operations and when doing multipactiona or subtraction or division and addition, make sure to go from left to right

Answer:

14

Step-by-step explanation:

I hope this helps!

Answer:

4 glasses

Step-by-step explanation:

im sorry if im wrong

Answer:

4 glasses

Step-by-step explanation:

ur welcome

Since the leading degree of the resulting expression is 2, hence the  polynomial simplifies to an expression that is a quadratic

Polynomial expressions are expressions that has a leading degree of 3 and above.

Given the expression

(-5x² - 2x + 4) + (8x² - x - 1) - (x+2)(x-5)

Expand the polynomial

(-5x² - 2x + 4) + (8x² - x - 1) - (x² -3x - 10)

Collect the like terms

-5x² + 8x² - x² - 2x - x + 3x + 4 - 1 + 10

2x²  + 13

Since the leading degree of the resulting expression is 2, hence the  polynomial simplifies to an expression that is a quadratic

Learn more on polynomial here: https://brainly.com/question/2833285

#SPJ1

Answer:

w = 10π

w ≈ 31.4159

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

4π = w - 6π

Step 2: Solve for w

Answer and Step-by-step explanation:

4[tex]\pi[/tex] = w -6[tex]\pi[/tex]

Add 6[tex]\pi[/tex] to both sides.

10[tex]\pi[/tex] = w

(10 pi equals variable w)

This is your answer.

#teamtrees #WAP (Water And Plant)

Answer:- Things look 250 larger.

Answer:

2,500x.

Step-by-step explanation:

Answer:

2) no

3) yes

Step-by-step explanation:

i think. sorry if im wrong

Answer:

2 No

3 Yes

Step-by-step explanation:

x = ky

Substitute the values of x and y to check if it's proportional. Then solve for k. If k is the same for all 4 equations, then 2 is proportional.

6 = -2k, k = 6/-2, k = -3

7 = -1k, k = 7 / -1, k = -7

8 = 0k, k = 8 / 0, k = 0

9 = k, k = 9

2 is not proportional.

Substitute the values of x and y to check if it's proportional. Then solve for k. If k is the same for all 4 equations, then 3 is proportional.

-70 = -10k, k = -70 / -10, k = 7

-56 = -8k, k = -56 / -8, k = 7

-14 = -2k, k = -14 / -2, k = 7

-7 = -k,  k = -7 / -1, k = 7

3 is proportional.

Answer:

2%

Step-by-step explanation:

so the point [tex](\sqrt{3},\sqrt{7})[/tex] is in the circumference so the distance from (0,0) to this point will be the radius of the bullseye

[tex]x=\sqrt{(\sqrt{3}-0)^2+(\sqrt{7}-0)^2}\\\\x=\sqrt{3+7}\\\\x=\sqrt{10}[/tex]

so that's the radius

so the area will be

[tex]A=\pi x^2\\\\A=\pi (\sqrt{10})^2\\\\A=10\pi[/tex]

so the percentage is

[tex]P=\frac{A}{1600}\\\\=\frac{10\pi}{1600}\\\\=\frac{\pi}{160}\\\\P\approx 0.02[/tex]

so it's 2%

Answer:

Her meal was $26 and 62 cents

Step-by-step explanation:

Answer:

[tex]1. x=27\\2. x=30[/tex]

Step-by-step explanation:

[tex]1.\ We\ are\ given\ that,\\Point\ W\ belongs\ to\ line\ VX\ or\ Point\ W\ lies\ in\ the\ line\ VX.\\Point\ Y\ belongs\ to\ line\ XZ\ or\ Point\ Y\ lies\ in\ the\ line\ XZ.\\\angle WXY=90\\Now\ let's\ consider\ \triangle XYW.\\We\ observe\ that,\\\angle XWY\ and\ \angle VWY\ form\ a\ linear\ pair\ and\ hence\ are\ supplementary.\\Hence,\\\angle XWY\ + \angle VWY\ =180\\\angle XWY=180- \angle VWY\\Substituting\ \angle VWY=6x\ in\ the\ equation\ (\angle XWY=180- \angle VWY),\\[/tex][tex]\angle XWY=180-6x\\Now\ \ \angle XWY\ and\ \angle WXY\ are\ interior\ angles\ opposite\ to\ \angle WYZ.\\\\Hence,\ from\ the\ 'Exterior\ Angle\ Property',\ we\ know\ that,\ the\\ measure of\ the\ \exterior\ angle\ is\ equal\ to\ the\ sum\ of\ the\ interior\ opposite\\ angles.\\Hence,\\\angle XWY + \angle WXY= \angle WYX\\Substituting\ \angle XWY=(180-6x),\ \angle WXY=90,\ \angle WYX=4x,\\(180-6x)+90=4x\\-6x-4x=-90-180 \\-10x=-270\\x=\frac{-270}{-10}\\x=27[/tex]

[tex]2. We\ are\ given\ that,\\Point\ N\ belongs\ to\ the\ line\ KO\ or\ Point\ N\ lies\ on\ the\ line\ KO.\\\angle LNM=45, \angle ONM=105, \angle NLM=90\\Hence,\\As\ we\ observe\ that,\\\angle LNM,\angle ONM\ and\ \angle KNL\ lie\ on\ the\ line\ KO\ and\ are\ hence,\\ supplementary.\\Hence,\\\angle LNM + \angle ONM\ + \angle KNL =180\\Substituting\ \angle LNM=45, \angle ONM=105,\\45+105+ \angle KNL=180\\150+ \angle KNL=180\\\angle KNL=180-150\\\angle KNL=30[/tex]

[tex]Hence\ by\ considering\ \triangle NML,\\\angle LNM + \angle NLM + \angle NML=180\ [Angle\ Sum\ Property\ Of\ A\ Triangle]\\Hence\ by\ substituting\ \angle LNM=45, \angle NLM=90,\\45+90+\angle NML=180\\135+\angle NML=180\\\angle NML=180-135\\\angle NML=45\\Now,\ as\ we\ observe\ that\ \angle KNM= \angle KNL+ \angle LNM\\Hence\ by\ substituting\ \angle KNL=30, \angle LNM=45,\\\angle KNM=30+45\\\angle\ KNM=75\\[/tex]

[tex]Now,\ consider\ \triangle\ KNM,\\\angle NKM+ \angle KNM + \angle NMK=180 [Angle\ Sum\ Property\ Of\ A\ Triangle]\\Hence\ substituting\ \angle NKM=45, \angle KNM=75 , \angle NMK=2x,\\45+ 75 + 2x=180\\120+2x=180\\2x=180-120\\2x=60\\x=\frac{60}{2}\\x=30[/tex]

Answer:

a. [tex]f(a) = -0.03a +1.53[/tex]

b. See Explanation

c. The slope is reasonable but the p intercept is not

d. [tex]f(20) = 93\%[/tex]     [tex]f(30) = 63\%[/tex]    [tex]f(40) = 33\%[/tex]   [tex]f(50) = 3\%[/tex]

Step-by-step explanation:

Given

[tex]a = age[/tex]

[tex]p = probability\ of\ marriage[/tex]

[tex]a = 45[/tex] when [tex]p = 18\%[/tex]

[tex]a = 25[/tex] when [tex]p = 78\%[/tex]

Solving (a): The linear function

We start by calculating the slope, m

[tex]m = \frac{p_2 - p_1}{a_2 - a_1}[/tex]

[tex]m = \frac{78\% - 18\%}{25- 45}[/tex]

[tex]m = \frac{60\%}{-20}[/tex]

[tex]m = -3\%[/tex]

[tex]m = -0.03[/tex]

The function is then calculated as follows

[tex]p - p_1 = m(a - a_1)[/tex]

This gives:

[tex]p - 18\% = -0.03(a - 45)[/tex]

[tex]p - 0.18 = -0.03(a - 45)[/tex]

[tex]p - 0.18 = -0.03a +1.35[/tex]

Solve for p

[tex]p= -0.03a +1.35+0.18[/tex]

[tex]p= -0.03a +1.53[/tex]

Hence,

[tex]f(a) = -0.03a +1.53[/tex]

Solving (b): Interpret the slope and the p intercept

The slope is calculated as:

[tex]m = -0.03[/tex]

And it implies that, there is a 3% reduction in change of getting older as women get older

The p intercept implies that, there is a 1.53 chance for 0 years old female child to get married.

Solving (c): Is (b) reasonable

The slope is reasonable.

However, the p intercept is not because of the age of the woman

Solving (d): Determine f(20), f(30), f(40), f(50)

We have that:

[tex]f(a) = -0.03a +1.53[/tex]

[tex]f(20) = -0.03 * 20 + 1.53[/tex]

[tex]f(20) = -0.6 + 1.53[/tex]

[tex]f(20) = 0.93[/tex]

[tex]f(20) = 93\%[/tex]

[tex]f(30) = -0.03 * 30 + 1.53[/tex]

[tex]f(30) = -0.9 + 1.53[/tex]

[tex]f(30) = 0.63[/tex]

[tex]f(30) = 63\%[/tex]

[tex]f(40) = -0.03 * 40 + 1.53[/tex]

[tex]f(40) = -1.2 + 1.53[/tex]

[tex]f(40) = 0.33[/tex]

[tex]f(40) = 33\%[/tex]

[tex]f(50) = -0.03 * 50 + 1.53[/tex]

[tex]f(50) = -1.5 + 1.53[/tex]

[tex]f(50) = 0.03[/tex]

[tex]f(50) = 3\%[/tex]

Answer:

the smallest number of equally sized pieces is 20

Step-by-step explanation:

The computation of the smallest number of equally sized pieces is as follows:

Given that

The sum of 1 by 5 and 3/4

Now

if we sum it

= 1 ÷ 5 + 3 ÷ 4

= 4 + 15 ÷ 20

= 19 ÷ 20

Now as if we do the lcm so the denominator sum be 20

Therefore the smallest number of equally sized pieces is 20

Step-by-step explanation:

A(-4, 5) => A'(-4+2, -5) = A'(-2, -5)

B(-6, -4) => B'(-6+2, -(-4)) = B'(-4, 4)

C(4, -4) => C'(4+2, -(-4)) = C'(6, 4)

Hence the new coordinates are A'(-2, -5), B'(-4, 4) and C'(6, 4).

Answer:

D. 0.981

Step-by-step explanation:

Given :

Rainfall (in inches) X

8.3

6.6

11.2

10.3

16.6

8.1

4.8

13.4

13.8

Yield (bushels per acre). y

55.5

512

63.8

64

87.4

54.2

36.9

81

83.8

Using the Pearson regression Coefficient calculator :

The Regression Coefficient (R) value obtained is 0.9808 = 0.981 wgi h sig ifues a strong positive relationship between inches of Rainfall and bushel yield.

Answer:

Step-by-step explanation:

Answer:

I replaced x with y because, If it was x there would be no graph

Step-by-step explanation:

Answer:

I cant tell what u mean but if the angles are equal the answer is 10

Step-by-step explanation:

Based on the calculations, the value of x is equal to 42.5.

Given the following data:

To determine the value of x:

A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.

Mathematically, a supplementary angle is calculated as follows:

[tex]Angle\;2+Angle\;4 =180\\\\3x-5 +x+15=180\\\\4x+10=180\\\\4x=180-10\\\\4x=170\\\\x=\frac{170}{4}[/tex]

x = 42.5.

Read more on supplementary angle here: brainly.com/question/10335289

Answer:

12x+10

Step-by-step explanation:

9x+3x=12x

and

4+6=10