What is the directrix of a parabola with equation x^2 = 4y

Answer:

-5n + 8

Step-by-step explanation:

1. What is the difference?

  The sequence goes down by 5. This means that the formula will have -5n in it.

2. Work out the term before the first term.

    The first term is 3, and we know that the sequence goes up by 5. So, to get the term before 3 we would add 5.

3 + 5 = 8   Remember, this is positive 8. (+8)

3. Put that term at the end of the equation.

   We have -5n already and we just worked out the term before the first one which is positive 8 - so put that at the end of the equation.

-5n + 8  This is our answer!

Just to prove it works:

Substitute:   n = term

Lets see if we can get the 3rd term which is -7. (n = 3)

-5(3) + 8

-15 + 8 = -7

See, it works!

x = -1

x = 2

x = -2

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Checking for a perfect cube :

1.1    x3+x2-4x-4  is not a perfect cube

Trying to factor by pulling out :

1.2      Factoring:  x3+x2-4x-4  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x3+x2  

Group 2:  -4x-4  

Pull out from each group separately :

Group 1:   (x+1) • (x2)

Group 2:   (x+1) • (-4)

              -------------------

Add up the two groups :

              (x+1)  •  (x2-4)

Answer:

The statement true about the results of the survey is:

Step-by-step explanation:

To identify if the D option is right, you only must use a simple rule of three, where you use the total of the members surveyed in the club (150), and the number of members that preferred the seacoast (72), by the last the operation must confirm that this value (72) is equal to the 48% (how says in the D option). First, you must establish the rule of three:

And operate:

How you can see, the value obtained in the simple rule of three is exactly the percentage of the D option, for this reason, this is the true statement.

Answer:

Ax+By=C

Step-by-step explanation:

Answer:

an equation

Step-by-step explanation:

just did it

Answer:

56 times

Step-by-step explanation:

To find the probability of both spinners landing on red, we need to multiply the probability of the spinner A landing on red (0.5) by the probability of the spinner B landing on red (0.6):

P(redA and redB) = 0.5 * 0.6 = 0.3

Then, to find the probability of both landing on blue, we do the same:

P(blueA and blueB) = 0.5 * 0.4 = 0.2

Now, if the number of times that both spinners land on red is 84, to estimate the number of times that both land blue, we just need to multiply this number of times by the ratio of P(blueA and blueB) over P(redA and redB):

84 * 0.2 / 0.3 = 56 times

Answer:

y=0.5x-4

Step-by-step explanation:

y+3=0.5(x-2)

y+3=0.5x-1

y=0.5x-4

Answer:

the ball takes 3.1944 sec

Step-by-step explanation:

Answer:

It takes 3.498 seconds.

Step-by-step explanation:

To calculate free fall you must use the formula: h=1/2gt^2

Answer:

Positive Coterminal Angles = 60°,780°

Negative Coterminal Angles = -300°, -660°

Step-by-step explanation:

To find nearest two coterminal angle of 420°:

1) Subtract 360° from 420°:

420°- 360° = 60° (First Positive Coterminal Angle)

2)Add 360° to 420°:

420°+ 360° =780° (Second Positive Coterminal Angle)

To find nearest two negative coterminal angles of 420°. We' lave to take the value below 0.

1) Substract 360° from 420°

420°- 360° = 60°

Which is still a positive value.

2) Again Substract 360° from 60°

60°- 360° = -300° (First Negative Coterminal Angle)

3)Subtract 360° from -300°

-300°- 360° = -660° (Second Negative Coterminal Angle)

Answer:

f(3) = 30

Step-by-step explanation:

f(3) = 3^(3) + 3

f(3) = 27 + 3

f(3) = 30

Answer:The area is [tex]A=\frac{YZ+XW}{2}h=\frac{7+3}{2}(4)=20[/tex]

YZ  = 5-2=3

XW = 8-1 = 7

h = 5-1=4 (height)

Answer:

20

Step-by-step explanation:

Split it up so it would be like this.

Small right triangle with dimensions of 1 x 4 = 2

Square 4 x 3 = 12

Other right triangle (the one on the right) 3 x 4 = 6

2 + 12 + 6 = 20

Hope this helps!

Answer:

670 cans of fruit

Step-by-step explanation:

sorry if this answer is wrong

Answer:

1450

Step-by-step explanation:

Take the amount of people times the dollar amount

5800 * .25 =1450

Answer:

I  depends on P, R, and T describes the relationship between the variables of the simple interest formula

Step-by-step explanation:

We are given that The simple interest on a principal amount, P, borrowed for T years at R% annual interest is given by the following :

Formula: [tex]I = \frac{P \times T \times R}{100}[/tex]

So,[tex]I \propto P[/tex]

[tex]I \propto T[/tex]

[tex]I \propto R[/tex]

So, I depends on P , T and R

So, Option C is true .

Hence I  depends on P, R, and T describes the relationship between the variables of the simple interest formula

Answer:

I depends on P, R, and T

Step-by-step explanation:

Answer:

Unit rate in grams of drink mix per ounce of water = 11 gram / ounces

Step-by-step explanation:

Given:

Amount of drink mix = 19 (1 /4) gram = 19.25 gram

Amount of water = 1 (3 /4) ounces = 1.75 ounces

Find:

Unit rate in grams of drink mix per ounce of water = ?

Computation:

⇒  Unit rate in grams of drink mix per ounce of water = Amount of drink mix / Amount of water

⇒  Unit rate in grams of drink mix per ounce of water = 19.25 / 1.75

⇒  Unit rate in grams of drink mix per ounce of water = 11 gram / ounces

Answer:

8 degrees

Step-by-step explanation:

Hope this helps!

Answer:

8 Degrees

Have a nice day!

Answer: A line is the undefined geometric term is described as a two-dimensional set of points that has no beginning or end.

Answer:

B (3,6)

Step-by-step explanation:

y = x + 3

then we will use this y to substitute the other y

4x + y = 18

4x + (x +3) = 18

4x + x + 3 = 18

5x = 18 - 3

5x = 15

x = 15/5 = 3

then we can find the value of y

y = x + 3 = 3 + 3 = 6

so the (x,y) is (3,6)

Answer:

Step-by-step explanation:

(4x + 3)(4x+3) is the factor

the third one is the solution

Answer:

-4

Step-by-step explanation:

-16 + 12

When the signs are different we subtract the smaller from the larger and take the sign of the larger

16-12 = 4

The larger number has a sign of negative

-4

Answer:

b

Step-by-step explanation:

ur mom

Answer: number 16 is d

number 20 is d

Step-by-step explanation:

Answer:

The answer for 16 is A,  the answer for 20 is D, and the answer for 25 is A

Step-by-step explanation:

For 16, the equation is 6a = 72. 6a is also equal to 6*a. To get a one side by itself, you have to divide both sides by 6.

For 20, it only makes sense for it to be a triangular prism because it has 2 triangles as the base and 3 faces

For 25, you can subtract what was the leftovers from the total number of pizzas. 8 - 1 3/4 - 5/6 is about 5.41, which is closer to 5 so the answer is 5.

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is

h² = 3² + 7² = 9 + 49 = 58 ( take the square root of both sides )

h = [tex]\sqrt{58}[/tex] → B

Answer:

It's probably B

Step-by-step explanation:

you use the pythagorean theorm

a^2+b^2=c^2

3^2+7^2=c^2

9+49+=c^2

[tex]\sqrt{58}[/tex]=[tex]\sqrt{c^2}[/tex]

[tex]\sqrt{58}\\[/tex]=c

Answer:

[tex]x=15^\circ[/tex]

Step-by-step explanation:

In a right triangle:

[tex]\sin \theta =cos(90^\circ-\theta) $ (Complementary angles)[/tex]

Therefore, given:

[tex]Sin (30 + x) \º = Cos (3x) \º\\30+x+3x=90^\circ\\30+4x=90^\circ\\4x=90^\circ-30^\circ\\4x=60^\circ\\$Divide both sides by 4\\x=15^\circ[/tex]

Answer:

The final answer is [tex]\frac{8}{27}[/tex] .

Step-by-step explanation:

Solve the following equation:

[tex](2^{2} \cdot 3^{-1} \cdot 4^{-1})^{-1} \over 2^{-3} \cdot 3^{4}[/tex]

-Simplify [tex]2^{2}[/tex] :

[tex](2^{2} \cdot 3^{-1} \cdot 4^{-1})^{-1} \over 2^{-3} \cdot 3^{4}[/tex]

[tex](4 \times 3^{-1} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]

-Simplify [tex]3^{-1}[/tex] :

[tex](4 \times 3^{-1} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]

[tex](4 \times( \frac{1}{3}) \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]

-Multiply both [tex]4[/tex] and [tex]\frac{1}{3}[/tex] :

[tex](4 \times( \frac{1}{3}) \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]

[tex](\frac{4}{3} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]

-Simplify [tex]4^{-1}[/tex] :

[tex](\frac{4}{3} \times 4^{-1})^{-1} \over 2^{-3} \times 3^{4}[/tex]

[tex](\frac{4}{3} \times (\frac{1}{4}) )^{-1} \over 2^{-3} \times 3^{4}[/tex]

-Multiply both [tex]\frac{4}{3}[/tex] and [tex]\frac{1}{4}[/tex] together:

[tex](\frac{4}{3} \times (\frac{1}{4}) )^{-1} \over 2^{-3} \times 3^{4}[/tex]

[tex](\frac{1}{3})^{-1} \over 2^{-3} \times 3^{4}[/tex]

-Simplify [tex]\frac{1}{3}^{-1}[/tex] :

[tex](\frac{1}{3})^{-1} \over 2^{-3} \times 3^{4}[/tex]

[tex]3 \over 2^{-3} \times 3^{4}[/tex]

-Then, on the denominator,  simplify [tex]2^{-3}[/tex] :

[tex]3 \over 2^{-3} \times 3^{4}[/tex]

[tex]3 \over \frac{1}{8} \times 3^{4}[/tex]

Simplify [tex]3^{4}[/tex] :

[tex]3 \over \frac{1}{8} \times 3^{4}[/tex]

[tex]3 \over \frac{1}{8} \times 81[/tex]

Multiply both [tex]\frac{1}{8}[/tex] and [tex]81[/tex] together:

[tex]3 \over \frac{1}{8} \times 81[/tex]

[tex]3 \over \frac{81}{8}[/tex]

Divide [tex]3[/tex] and [tex]\frac{81}{8}[/tex] by multiplying [tex]3[/tex] by the reciprocal of [tex]\frac{81}{8}[/tex] :

[tex]3 \over \frac{81}{8}[/tex]

[tex]3 \times (\frac{81}{8})[/tex]

-And you multiply [tex]3[/tex] and [tex]\frac{81}{8}[/tex] together:

[tex]3 \times (\frac{81}{8})[/tex]

[tex]\frac{8}{27}[/tex]

So, the final answer would be [tex]\frac{8}{27}[/tex] .

Answer:

1) the football already reached the ground

2) t = 0.625 seconds

3) t = 1.46 seconds

Step-by-step explanation:

Data

1) time, t = 2.25 s

To relate these variables we need to use the next equation:

H = Hi + Vi*t - 1/2*g*t²

H = 5 + 20*2.25 - 1/2*32*2.25²

H = -31 ft

that is, 31 ft under the line of reference. This means that the football already reached the ground

2) At the highest point the final velocity (Vf) is zero.

To relate these variables we need to use the next equation:

Vf = Vi - g*t = 0

Vi = g*t

t = Vi/g

t = 20/32

t = 0.625 s

3) When the football hits the ground, ΔH = -5 ft. Then:

ΔH = Vi*t - 1/2*g*t²

-5 = 20*t - 1/2*32*t²

0 = -16t² + 20t + 5

Using quadratic formula:

[tex] t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]

[tex] t = \frac{-20 \pm \sqrt{20^2 - 4(-16)(5)}}{2(-16)} [/tex]

[tex]t = \frac{-20 \pm 26.83}{-32}[/tex]

[tex]t_1 = \frac{-20 + 26.83}{-32}[/tex]

[tex] t_1 = -0.21 [/tex]

[tex]t_2 = \frac{-20 - 26.83}{-32}[/tex]

[tex] t_2 =1.46 [/tex]

The first result is discarded because it doesn't have physical sense. So, the football hit the ground after 1.46 seconds

Answer:

Answer is 67%

Step-by-step explanation:

If you want to get the number four from 4 rolls the chances would be

1st roll = 1/6 (16.667%)

2nd roll = 2/6 (33.333%)

3rd roll = 3/6 (50.000%)

4th roll = 4/6 (66.667%)

So the answer is 67%

Answer:

21. 98 cents

Gabby placed in 4th.

Step-by-step explanation:

Assuming Steven is paying, 51+45+2=98 cents.

Answer:

21. 98 cents

Gabby placed in 4th.

Step-by-step explanation:

oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo have a great day

Answer:

Step-by-step explanation:

[tex]\frac{8x}{7}=8[/tex]

Multiply both sides by 7

[tex]7*\frac{8x}{7}=8*7\\\\8x=8*7\\[/tex]

Divide both sides by 8

[tex]\frac{8x}{8}=\frac{8*7}{8}\\[/tex]

x = 7

Answer:

-The value of [tex]x[/tex]:

[tex]x = 7[/tex]

Step-by-step explanation:

-Solve for the value of [tex]x[/tex]:

[tex]\frac{8x}{7} = 8[/tex]

-Multiply both sides by the denominator, which is [tex]7[/tex]:

[tex]7\cdot \frac{8x}{7} = 8 \cdot 7[/tex]

[tex]8x = 56[/tex]

-Divide both sides by 8:

[tex]\frac{8x}{8} = \frac{56}{8}[/tex]

[tex]x = 7[/tex]

So, the value of [tex]x[/tex], would be [tex]x = 7[/tex].

Answer:

29

Step-by-step explanation:

If you mean the exterior angle at the same vertex as the interior,

(9+k)+(5k-3)=180

9+k+5k-3=180

6k+6=180

6k=174

k=29 degrees

Answer:

29

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Just multiply the 1 times 4