Derive the equation of the parabola with a focus at (2, -1) and a directrix of y = - =
2
f(x) = -(x + 2)2 - 3
4
7
3
f(x) = (x + 2)2 +
4
3
f(x) = -(x - 2)2 +
4
3
f(x) = -(x - 2)2 -
4

Answer:

Step-by-step explanation:

1] 6x + 10 = 28  {subtract 10 from both sides}

6x + 10 -10 = 28 - 10

6x = 18  {Divide both sides by 6}

6x/6 = 18/6

x = 3

2]  -2m - 4 = 8 {Add 4 to both side}

 -2m - 4 + 4 = 8 + 4

-2m = 12  {Divide both sides by -2}

-2m/-2 = 12/-2

m = -6

3] x + x + 2x = 48  {add the like terms}

  4x = 48  {divide both sides by 4}

4x/4 = 48/4

x = 12

4] 3y +4 +3y  - 6 = 34 {add the like terms}

   6y - 2 = 34  {Add 2 to both side}

6y - 2 + 2 = 34 +2

6y = 36 {divide both sides by 6}

6y/6 = 36/6

y = 6

5]9(w - 6) = 36 {divide both sides by 9}

[9(w - 6)]/9 = 36/9

w - 6 = 4  {Add 6 to both sides}

w - 6 + 6 = 4 + 6

w = 10

Answer:

w = 10

Step-by-step explanation:

You first mutlply like terms and then add it up

Answer:

Step-by-step explanation:

a) Total number of people surveyed, n = 2500

Let X denote the number in the sample that say they support the increase. If 30% of all adults in Ohio support the increase, it means that the percentage of all adults in Ohio that did not support the increase is

100 - 30 = 70%

This is a binomial probability because there are only two possible outcomes. Therefore,

Probability of success, p = 30/100 = 0.3

Probability of failure, q = 1 - p = 1 - 0.3

q = 0.7

Standard deviation = √npq

Standard deviation = √(2500 × 0.3 × 0.7) = 22.91

b) The probability that x is at least 800 is expressed as

P(x ≥ 800)

We would determine the probability by using the binomial probability calculator. Therefore,

P(x ≥ 800) = 0.01577

b. about 0.015.

Answer:

= 3 3/5 yards

Step-by-step explanation:

If 1 piece = 3/5 yard

What about 6 pieces = ?

= (6 x 3/5) ÷ 1

= 18/5 ÷ 1

= 18/5

= 3 3/5 yards

Answer:

Answer: D) equal rights for African Americans

Step-by-step explanation:

Answer:

Since you are given ALL three sides, then you will ALWAYS be able to make ONLY unique triangles.   ^‿^

Answer:

28/50

Step-by-step explanation:

You look at the total amount of men there are, (50)

then amount of dog in the column of men, (28)

So (dog|man) = 28/50

ask questions if u need anything else

Answer:

answer is A.

Step-by-step explanation:

divide price by amount of kg to see how much it cost per kg. Find the lowest answer by doing this to all answers. Don't forget to round to the nearest cent!

Answer:

A

Step-by-step explanation:

Factor the numerators/ denominators where possible, that is

[tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] ÷ [tex]\frac{(x-5)(x+3)}{(x+4)(x+1)}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down.

= [tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] × [tex]\frac{(x+4)(x+1)}{(x-5)(x+3)}[/tex]

Cancel the factors (x - 5) and (x + 4) from numerator/denominator

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

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

Answer:

x=4

Step-by-step explanation:

Answer:d

Step-by-step explanation:

Answer:

HELP

Step-by-step explanation:

Answer:

f(x)=(x-3)/4

Step-by-step explanation:

To find the inverse of a function, I like to flip the x and the y, and then try to isolate the y. In this case:

x=4y+3

x-3=4y

y=(x-3)/4

Hope this helps!

Answer:

x = 2

Step-by-step explanation:

-12 = -2x - 4x

-12 = - 6x

x = -12/(-6) = 2

Answer:

Step-by-step explanation:

Answer:

y = (3/2)x + 3

Step-by-step explanation:

slope is rise over run so 3 up and, 2 right

y-intercept is at (3,0)

Answer:

551.7

Step-by-step explanation:

it is the square + the circle

15*25+πr²

375+π(15/2)²

375+π225/4

375+176.625=551.625

Answer:

E) 551.7 ft Squared

Step-by-step explanation:

First find the area of the rectangle. 15 x 25 = 375. Then remove the rectangle so your left with a circle with a diameter of 15. Find the area of the circle.            Pi x R squared. Pi x 7.5 squared = 176.7 . Then add the areas together.                         375 + 176.7 = 551.7

Answer:

328

Step-by-step explanation:

Answer:

9 4/5

Step-by-step explanation:

You can rewrite them into decimal. It would be 3.5 times 2.8 and you get 9.8 or 9 4/5

Answer:

49 /5  = 9.8

Step-by-step explanation:

The correct answer is a translation.

A rotation would change the direction, a reflection would change the direction, and a dilation would change the size.

I hope this helps :)

Answer:

translation

Step-by-step explanation:

Answer:

B I think

Step-by-step explanation:

Answer: The solution is (4,99) which means for in 4 months the total cost of each health club will be the same.

Step-by-step explanation:

Club A can be represented by the equation    y = 23x + 7  where x is the number of months  and y is the cost.

Club B can be represented by the equation   y = 16x + 35  where x is the number of months and y is the cost.

23x + 7 = 16x + 35     set the equation equal each other to solve for x

        -7               -7

23x  = 16x + 28

-16x     -16x

7x= 28

x= 4   now we know the value of  x is 4 so we will put it into the equation and solve for y

y= 16(4) + 35

y= 99

Step-by-step explanation:

the answer is

A,72

B,739

D,-11

Answer:

A) -3/2 and 7

Step-by-step explanation:

this equation factors to (2x+3)(x-7)

the goal is to solve for 0

if 2x+3=0 then x=-3/2

if x-7=0 then x=7

Answer:

=18.38cm

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment .

Look at the attached picture. The longest segment we can draw is AG (or any of its equivalent: BH, CE, DF). Let's focus on AG for example.

We can think of AG as the hypotenuse of triangle ACG. So, we need AC first. AC is itself the hypotenuse of triangle ABC,

so we have,

[tex]AC^2 = AB^2+BC^2=8^2+7^2=113[/tex]

Now we can resume where we stopped with triangle AGC, and we have

[tex]AG=\sqrt{AC^2+CG^2}=\sqrt{113+225}=\sqrt{338}[/tex]

=18.38cm

Answer:

B)

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors.

Answer:

A= 36π mm²

Step-by-step explanation:

Area of circle = πr² where radius= 6mm

A = π(6)²

A= 36π mm²

Answer:

5,040 different passwords are possible

Step-by-step explanation:

Assuming that 4-digit means using only numeric values.

This is a permutations problem.

n = number of values used with number values only this is 10

r = the number used in each case without repeating in this case 4

nPr = n! / (n - r)!

nPr = 10! / (10-4)!

nPr = 10! / 6!

The ! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24

A quick hack for dividing factorials is to use cancelling.

10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)

= 5040

Answer:

216

Step-by-step explanation:

Hope this helps.

Answer:

Side of cube = 6 cm

Volume = side ^3 = 6^3 = 216 cm^2

Answer:

Standard Form

Step-by-step explanation:

Answer:

Rate of change refers to the change in one variable (i.e. independent variable) as a result of a change in another (i.e. dependant variable). A very common example is speed as it refers to the change in distance per a change in time. Graphically representing the relationship between two variables, the rate of change will be the gradient or slope of the graph.

Answer:

The answer is -2

Step-by-step explanation:

start at 4 and go to the left six times

4+(-6)=4-6=-2