Answer:
y = - [tex]\frac{1}{32}[/tex] x²
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-0)^2+(y+8)^2}[/tex] = | y - 8 |
Square both sides
x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides
x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )
x² + 32y = 0 ( subtract x² from both sides )
32y = - x² ( divide both sides by 32 )
y = - [tex]\frac{1}{32}[/tex]x²
The standard form of the equation of the parabola is y = -x²/32
What is parabola?The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.
here, we have,
The general form of a parabola is
(x-h)^2 = 4p(y-k)
Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
√(x-0)² + (y-8)² = | y - 8 |
Square both sides
x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides
x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )
x² + 32y = 0 ( subtract x² from both sides )
32y = - x² ( divide both sides by 32 )
y = - x²/32
Hence, The standard form of the equation of the parabola is y = -x²/32
learn more on parabola:
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SIMPLE GRAPHING EQUATION (CORRECT ANSWER = BRAINLIEST, THANKS, 5 STAR, AND A COMMENT + THE POINTS
Find the value of “b” so that the slope of the line passing through the points A(5, –8) and B(–1, b) is –2.
Answer:
b=4
Step-by-step explanation:
For this question we need to know the formula of slope that is m which is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where [tex](x_1,y_1) , (x_2,y_2)[/tex] are the points [tex](5,-8),(-1,b)[/tex] respectively
and hence we have the value of m= -2 which is the slope we simply plug in all the values.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\-2=\frac{b-(-8)}{-1-5} \\\\-2=\frac{b+8}{-6} \\\\12=b+8\\12-8=b\\4=b[/tex]
So the value of b=4
Answer:
b is 4
Step-by-step explanation:
Several steps are required to find this answer. You need to use the information you are given as well as the formula y=mx+b. You are given the slope and one of the coordinates. Plug the information into the formula to find b, which is the constant.
The point given is (5,-8)
The slope given is -2
Plug the x and y into y=mx+b
-8=-2(5)+b
-8=-10+b
-8+10=b
b=2
Now that you have the full equation, y=-2x+2 , you can plug in the x-coordinate of the other coordinate to find the missing y-value.
y=-2(-1)+2
y=2+2
y=4
Therefore, the b you are solving for is 4.
Find the missing value using the slope and points m=2/3 and (8, 4) (x, 8)
(I’ll give brainlest answer too whoever answers quick and it’s right I’ll be checking)
Answer:
the missing value should be 14
Step-by-step explanation:
Describe what the ! means in n!
Answer:
Usually n stands for a (positive) integer. The exclamation point used after an integer usually means “factorial.”
Step-by-step explanation:
Bam scored 12 points per game last year. This year he scores 19 points per game. By what percent did his point production change?
Answer:
[tex]\%Change = 58.33\%[/tex]
Step-by-step explanation:
Given
[tex]Initial = 12[/tex]
[tex]Final = 19[/tex]
Required
Determine the percentage change
Percentage change is calculated as thus:
[tex]\%Change = \frac{|FInal - Initial|}{Initial} * 100\%[/tex]
[tex]\%Change = \frac{|19 - 12|}{12} * 100\%[/tex]
[tex]\%Change = \frac{|7|}{12} * 100\%[/tex]
[tex]\%Change = \frac{7}{12} * 100\%[/tex]
[tex]\%Change = \frac{7* 100\%}{12}[/tex]
[tex]\%Change = \frac{700\%}{12}[/tex]
[tex]\%Change = 58.33\%[/tex]
Simplify -|-5+2|
-7
3
7
-3
Match the numbers with the correct label.
Answer:
I'm assuming A is -3/7 B is -0.4 and c is -1/5
a square had a side length of 9cm. what is the area?
Answer:
81cm^2
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
Let's do a quick refresher on how to find area.
l = length
w = width
a = area
a = l(w)
Since one side is 9cm, and all the sides are equal, you multiply 9x9.
Nine times nine is 81.
Hope it helped!
Jim earned $20 of interest on a $4000 deposit that was left in the bank for 9 months. What was the interest rate?
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using ? nothing nothing The original pulse rates are measure with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below. A. The z scores are measured with units of "minutes per beat." B. The z scores are measured with units of "beats per minute." C. The z scores are measured with units of "beats." D. The z scores are numbers without units of measurement.
Answer:
(1) 0 and 1
(2) Correct option D
Step-by-step explanation:
It is provided that pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
Let X denote the pulse rates of women.
(1)
Let us consider a random variable, X that follows N (µ, σ²), then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and variance V (Z) = 1.
That is, Z follows N (0, 1).
In statistics, a standardized score is the number of standard deviations an observation or data point is from the mean.
Thus, z-scores are a type of standardized scores.
The values of the mean and standard deviation after converting all pulse rates of women to z scores are 0 and 1 respectively.
(2)
The z scores are numbers without units of measurement.
SOULJA BOY CREATED THE INTERNET!!!!!!!!!!!!!
Answer:
wait what???
Step-by-step explanation:
I don't get it
Answer:
NO WAY
Step-by-step explanation:
Which decimal number is equal to 1/8?
A. 0.125
B. 0.(125)
C. 0.1(25)
D. 0.12(5)
Answer:
A. 0.125
Step-by-step explanation:
a 141 inch is cut into two pieces one piece is two times the length of the other . find the length of the shorter piece
Answer:
The second length of the piece because 141 times 2 which is two times the amount of the second piece is 282.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer is 47.
01:41:3
What value of x is in the solution set of 8x - 6 > 12 + 2x?
Answer:
x > 3
Step-by-step explanation:
Answer:
x > 3
Step-by-step explanation:
Step 1:
8x - 6 > 12 + 2x Equation
Step 2:
6x - 6 > 12 Subtract 2x on both sides
Step 3:
6x > 18 Add 6 on both sides
Step 4:
x > 18 ÷ 6 Divide 6 on both sides
Answer:
x > 3
Hope This Helps :)
Jimmy wants to serve iced tea at his birthday party. He purchases 14 containers filled with 1.5 liters of tea. Approximately how many gallons of tea did he purchase? (1 gallon is about 3.8 liters)
Answer:
5.5 gallons
Step-by-step explanation:
The answer is 5.5 gallons.
Number of containers = 14
Amount in each container = 1.5 liter
1 gallon = 3.8 liter
Find:Total amount of tea in gallon
Computation:Total amount of tea in gallon = Number of containers × Amount in each container / 3.8
Total amount of tea in gallon = 14 × 1.5 / 3.8
Total amount of tea in gallon = 21 / 3.8
Total amount of tea in gallon = 5.5 liter (Approx.)
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justin has 3/4 quart of cranberry juice. If he divides the juice into glasses that hold 1/8 quart, how many glasses can Justin fill
Answer:
6 glasses
Step-by-step explanation:
3/4 = 6/8
¿Cual es el area de un circulo de r=5cm?
Porfavor urgente
Answer:
En este caso, área de un círculo de diámetro 5 cm es de 19,63 cm2
What is the value of x? *
(7x - 15)
(x+28)
(4x - 3)
Mrs. Peterson makes ceramic figurines. She recently made 25 figurines. Of those figurines, 16 are animals. What percent of the figurines are NOT animals?
An account is opened with an initial deposit of $700 and earns 3.3% interest compounded semi annually. What will the account be worth in 3 years
Answer:
772.22
Step-by-step explanation:
A=$700(1+0.0332)2(3). Simplify using the order of operations: A=$700(1.0165)6=$700(1.103174712)≈$772.22.
Clarence is 42 inches tall. His brother Charlie is 37 inches tall. How much taller is Clarence?
Answer:
Clarence is 5 inches taller.
42-37=5
Answer:
Clarence is 5 inches taller.
Step-by-step explanation:
You are using subtraction by doing 42-37
42-37 cross out the 4 to be a 3, make the 2 a 12 and subtract 12-7=5
3-3 is 0 so it would be 5.
5(3.4k - 7) + (3k + 21)
Answer:
20k - 4
Step-by-step explanation:
Step 1: Write expression
5(3.4k - 7) + (3k + 21)
Step 2: Simplify
Distribute 5: 17k - 35 + 3k + 21Combine like terms (k): 20k - 35 + 21Combine like terms (integers): 20k - 14Multiple by 10 and 100 8*10
Answer:
800, 8000
Step-by-step explanation:
8*10=80*10=800, 8*10=80*100=8000
Im not exactly sure as to what the question you are asking or what lesson this is from but I hope this helped being the closest and only way I could answer this, terribly sorry if this wasn't the correct solution
15.4x7=
Show your work
Answer:
107.8
Step-by-step explanation:
−7x+y
3
+7x
3
+6x−3y
3
−2x
3
+3x
Answer:
-7 is less than -2 is less than 3 is equal to 3 is equal to 3 is equal to 3 is equal to 3 is less than 6 is less than 7
Step-by-step explanation:
Add. Write the answer in standard form.
(9 + 5i) + (11 + 21) =
Answer:
45
Step-by-step explanation:
just add them but why is there a I
Answer:
41+5i
Step-by-step explanation:
Combine like terms; 9+11+21.
Which 2 expressions are equivalent to 647 × 39
Answer:
25233
Step-by-step explanation:
What expressions, please complete your answer!
647 × 39 = 25233
Pls consider marking my answer as Brainliest! It would mean a lot!
A jury pool has 15 people that are married and 20 people that are not married, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.)
Answer:
a
[tex]P(K) = 0[/tex]
b
[tex]P(Z) = 0[/tex]
c
[tex]P(W) = 0.1016[/tex]
d
[tex]P(R) = 0.29[/tex]
Step-by-step explanation:
From the question we are told that
The number of married people is k = 15
The number of people that are not married is u = 15
The number of people selected is e = 12
The total number of people is n = 30
Generally the number of ways of selecting 12 people from the married people is mathematically represented as
[tex]B = ^k C_e[/tex]
Here C stands for combination hence we will be making use of the combination functionality in our calculators
[tex]B = ^{15} C_{12}[/tex]
=> [tex]B = 455[/tex]
Generally the number of ways of selecting 0 people from the not married people is mathematically represented as
[tex]A = ^u C_0[/tex]
=> [tex]A = ^{15} C_0[/tex]
=> [tex]A = 1[/tex]
Generally the number of ways of selecting 12 people from the total number of people is mathematically represented as
[tex]D = ^{n} C_{12}[/tex]
=> [tex]D = ^{30} C_{12}[/tex]
=> [tex]D = 8.6493225 *10^{7}[/tex]
Generally the number of ways of selecting 12 people from the married people is equal to the number of ways of selecting 12 people from not married, also the number of ways of selecting 0 people from the not married is equal to the number of ways of selecting 0 people from the married people, all this is because the number of married people is equal to the number of not married people
Generally the number of ways of selecting 8 people from the married people is
[tex]E = ^{k} C_{8}[/tex]
=> [tex]E = ^{15} C_{8}[/tex]
=> [tex]E =6435[/tex]
Generally the number of ways of selecting 4 people from the not married people is
[tex]F = ^{u} C_{4}[/tex]
=> [tex]F= ^{15} C_{4}[/tex]
=> [tex]F=1365[/tex]
Generally the number of ways of selecting 6 people from the married people is
[tex]G = ^{k} C_{6[/tex]
=> [tex]G= ^{15} C_{6}[/tex]
=> [tex]G=5005[/tex]
Generally the number of ways of electing 6 people from the married people is equal to the number of ways of selecting 6 people from the not married people
Generally the probability that the jury consists of all married people is mathematically represented as
[tex]P(K) = \frac{455 * 1 }{8.6493225 *10^{7}}[/tex]
=> [tex]P(K) = \frac{455 * 1 }{8.6493225 *10^{7}}[/tex]
=> [tex]P(K) = 0.000005[/tex]
=> [tex]P(K) = 0[/tex]
Generally the probability that the jury consists of all not married people is mathematically represented as
[tex]P(Z) = \frac{455 * 1 }{8.6493225 *10^{7}}[/tex]
=> [tex]P(Z) = \frac{455 * 1 }{8.6493225 *10^{7}}[/tex]
=> [tex]P(Z) = 0.000005[/tex]
=> [tex]P(Z) = 0[/tex]
Generally the probability that the jury consists of 8 married and 4 that are not married is mathematically represented as
[tex]P(W) = \frac{ E * F}{D}[/tex]
=> [tex]P(W) = \frac{ 6435 * 1365}{8.6493225 *10^{7}}[/tex]
=> [tex]P(W) = 0.1016[/tex]
Generally the probability that the jury consists of 6 married and 6 that are not married. is mathematically represented as
[tex]P(R) = \frac{G * G}{D}[/tex]
[tex]P(R) = \frac{5005 * 5005}{8.6493225 *10^{7}}[/tex]
=> [tex]P(R) = 0.29[/tex]
Hello please help I will give brainliest!
Answer:
D
Step-by-step explanation:
Scores of high school seniors taking the English Regents examination in New York State are normally distributed with a mean of 70 and a standard deviation of 10.
Required:
a. Find the probability that a randomly selected high school senior will have a score between 70 and 75.
b. Find the probability that a randomly selected high school senior will have a score higher than 85.
Answer:
0.19146
0.066807
Step-by-step explanation:
Given that :
Mean (m) = 70
Standard deviation (s) = 10
a. Find the probability that a randomly selected high school senior will have a score between 70 and 75.
X ≤ 70 :
Using : z = (x - m) / s
Z = (70 - 70) / 10
Z = 0 / 10
Z = 0
P( Z < 70) = 0.500
X ≤ 75
z = (x - m) / s
Z = (75 - 70) / 10
Z = 5 / 10
Z = 0. 5
P(z < 0.5) = 0.69146
0.69146 - 0.5000
= 0.19146
b. Find the probability that a randomly selected high school senior will have a score higher than 85.
X ≥ 85
z = (x - m) / s
Z = (85 - 70) / 10
Z = 15 / 10
Z = 1.5
P(z > 1.5) = 0.066807 ( Z probability calculator)
How do I do this? I am so confused...
1. 12
2. 28
3. 44
This is because when you multiply 4. It also increases the number when you multiply 7.
Answer:
Multiply the first numbers by three and then keep multiplying :)
Step-by-step explanation: