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3 years ago

Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8

1 answer:

8 0

The best thing to do when finding conic equations from the focus and directrix is to sketch a little graph. When you do this, you can easily identify the vertex right in the middle and can determine if the parabola is vertical or horizontal since it must wrap around the focus. This way you know whether the x or the y is squared. When you sketch the focus and directrix, you will see the vertex is at (0,0) and the parabola is sideways, so the y is squared. now remember your formula is y^2=4px where p is the distance from the vertex to the focus, or you could write x=1/(4p)y^2. Now from 0 to -8 is -8 so that means 4p=-32. This gives you y^2=-32x or x=-1/32y^2. Thsi type of question will also be on your module exam and then the final exam so be sure to practice some:)

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2. Write the probability of each event when choosing one card at random from a standard

xeze [42]

Answer:

Step-by-step explanation:

(King of Diamonds) = 1/52

(A Heart) = 1/4

(Red Three) = 1/26

(Red Card) = 1/2

3 0

2 years ago

A + b·c = a + c·b is an example of the associative property.

muminat

Answer:

yes , This is an example of the associative property.

Step-by-step explanation:

8 0

2 years ago

I need some help with this, I am supposed to solve for x

liq [111]

They are the same measurements, because:

from 10x + 5, first do vertical angle.

then, alternate interior angle,

then vertical angle again,

and another alternate interior angle.

For each vertical and alternate interior angles, the measurements stay the same.

Set them equal to each other, isolate and solve for x.

10x + 5 = 11x - 1

First, isolate the x. Subtract 10x from both sides, and add 1 to both sides

10x (-10x) + 5 (+1) = 11x (-10x) -1 (+1)

Simplify

5 + 1 = 11x - 10x

6 = x

x = 6

6 is your answer for x.

hope this helps

3 0

3 years ago

The area of Terry's room at the old house was 96 ft.2. The area of Terry's room at the new house is 108 ft.2

Finger [1]

Answer:

12.5%

Step-by-step explanation:

First we need to calculate the change in the area of Terry's room this is

108 ft2 - 96 ft2 = 12 ft2

Then we use a direct proportion in order to find the percentage

96 ft2 ----- 100%

12 ft2 ----- p?

Solvin for p we have that

$p=\frac{12\times 100}{96}$

p=12.5

3 0

3 years ago

Read 2 more answers

Liam is making barbecue ribs over a fire. The internal temperature of the ribs when he starts cooking is 40°F. During each hour

Soloha48 [4]

Answer: You need to wait at least 6.4 hours to eat the ribs.

t ≥ 6.4 hours.

Step-by-step explanation:

The initial temperature is 40°F, and it increases by 25% each hour.

This means that during hour 0 the temperature is 40° F

after the first hour, at h = 1h we have an increase of 25%, this means that the new temperature is:

T = 40° F + 0.25*40° F = 1.25*40° F

after another hour we have another increase of 25%, the temperature now is:

T = (1.25*40° F) + 0.25*(1.25*40° F) = (40° F)*(1.25)^2

Now, we can model the temperature at the hour h as:

T(h) = (40°f)*1.25^h

now we want to find the number of hours needed to get the temperature equal to 165°F. which is the minimum temperature that the ribs need to reach in order to be safe to eaten.

So we have:

(40°f)*1.25^h = 165° F

1.25^h = 165/40 = 4.125

h = ln(4.125)/ln(1.25) = 6.4 hours.

then the inequality is:

t ≥ 6.4 hours.

4 0

2 years ago