Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin
The standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin and directrix is y² = 16x.
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
Given that the parabola's vertex is located at the origin and that the directrix is at x = -4, the focus is at (4,0).
Then the equation can be written as
[tex]\rm \sqrt{(x-4)^2 +(y-0)^2} = \sqrt{(x+4)^2 + (y-y)^2}\\\\\sqrt{(x-4)^2 +(y-0)^2} = \sqrt{(x+4)^2}[/tex]
On squaring both sides, we have
[tex]\begin{aligned} (x-4)^2 +(y-0)^2 &= (x+4)^2 \\\\x^2 + 16 - 8x +y^2 &= x^2 + 16 + 8x\\\\y^2 &= 16x \end{aligned}[/tex]
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Beatrice has $0.28 in her pocket. what is the percent that she has
Answer:
she has 28% of a dolar in her pocket
Step-by-step explanation:
Please hurry!A flagpole casts a shadow that is 28 fery long. At the same time,a stick that is 2 feet tall casts a shadow that is 3.5 feet long how tall is the flagpole?
Answer - The flagpole is 16 feet tall.
Explanation -
2/3.5 =1.75
1.75x16 =28
A solid is cut by a plane that is parallel to its base, forming a two-dimensional cross section in the shape of a square. Which of the following solids could have resulted in that cross section?
Answer:
It's A.
Step-by-step explanation:
This is because the cross section of the shape is a square, which is why it is A.
Help me find the media, mode and the mean look at the photo and solve the puzzle
Answer: See below.
Good Luck! I hope this helps!
Step-by-step explanation:
1) Find the Mean of 7 18 9 22 4.
7 + 18 + 9 + 22 + 4 = 50
50 ÷ 5 = 10
2) Find the Median of 7 18 9 22 4.
4 7 9 18 22
The Median is 9.
3) Find the Mean of 7 3 7 4 8 9 2.
7 + 3 + 7 + 4 + 8 + 9 + 2 = 40
40 ÷ 7 = 5.7
4) Find the Median of 7 3 7 4 8 9 2.
2 3 4 7 7 8 9
The Median is 7.
5) Find the Mode of 7 3 7 4 8 9 2.
Mode is the number that occurs the most.
2 3 4 7 7 8 9
The Mode is 7.
6) Find the Median of 6 10 23 24 13 9 23 12.
6 9 10 12 13 22 23 24
There are 8 numbers in this set of numbers, so the Median is the average of the two numbers in the middle. So, [tex]\frac{(12+13)}{2} = \frac{25}{2} = 12.5[/tex]
The Median is 12.5.
7) Find the Mean of 6 10 23 24 13 9 23 12.
6 + 10 + 23 + 24 + 13 + 9 + 23 + 12 = 120
120 ÷ 8 = 15
The Mean is 15.
8) Find the Median of 120 113 101 101 112.
101 101 112 113 120
The Median is 112.
9) Find the Mean of 73 72 72 98 99 96 98 98 73.
73 + 72 + 72 + 98 + 99 + 96 + 98 + 98 + 73 = 779
779 ÷ 9 = 86.6.
10) Find the Mode of 73 72 72 98 99 96 98 98 73.
72 72 73 73 96 98 98 98 99
The Mode is 98.
11) Find the Mode of 6 10 23 24 22 9 23 13.
6 9 10 13 22 23 23 24
The Mode is 23.
12) Find the Median of 73 72 72 98 99 96 98 98 73.
72 72 73 73 96 98 98 98 99
The Median is 96.
13) Find the Median of 12 22 26 15 18 22 29 11 22 18.
11 12 15 18 18 22 22 22 26 29
There are 10 numbers in this set of numbers, so the Median is the average of the two numbers in the middle. So, [tex]\frac{(18+22)}{2} = \frac{40}{2} = 20[/tex]
The Median is 20.
THE END! Yay!What Is The Volume? Show Your Work Please
Answer:
406[tex]ft^{2}[/tex]
Step-by-step explanation:
State the equation of a line perpendicular to y = -3 going through (-5, -3).
Answer:
x=-5
Step-by-step explanation:
Answer:
Equation of the perpendicular line is x = -5
Step-by-step explanation:
The equation of the given line is y =-3
This means that the given line is parallel to the x axis. Imagine a horizontal line and for all values of x, the y value is constant -3. So the line perpendicular to this line would be one that is parallel to the Y axis. Imagine a vertical line. This line would have the same x value for all values of Y. Equation would be of the form
x = constant.
It is given that the line passes through (-5, -3), from which we get that constant value as -5.
Equation of the perpendicular line is x = -5
3. Write the polynomial function with the given degree and zeros. Degree: 8 zeros: 7 multiplicity 2
Step-by-step explanation:
I think answer is 14 please give me a brain list
The length of one side of an ice cube is 2.5 cm. Calculate the volume of the ice cube.
Answer:
15.63 cm^3
Step-by-step explanation:
Assuming that the ice cube is a perfect cube, then all of the sides are equal. There for, each side is 2.5 cm.
v = l*w*h
v = 2.5 * 2.5 * 2.5
v = 6.25 * 2.5
v = 15.625 cm^3
A statement and portions of the flowchart proof of the statement are shown.
Which reason should appear in the box labeled 1?
Angle Addition Postulate
Angle Congruence Postulate
Ruler Postulate
Linear Pair Postulate
Flow chart proof. Given measure of angle B A C is 20 degrees and measure of angle C A D is 15 degrees. Prove the measure of angle B A D is 35 degrees. Given image shows acute triangle A B D. Point C is on side B D with point C slightly closer to point D. Segment A C drawn. Flow chart consisting of 4 rows of horizontal text boxes. A horizontal line segment joins the midpoints of each of the vertical sides of each of the text boxes effectively subdividing each text box into an upper box and lower box. In row 1 there is 1 textbox. In the upper half of the box is the equation the measure of angle B A D equals the measure of angle B A C plus the measure of angle C A D. In the lower half of the box is the number 1 in a smaller box. In row 2 there are 2 text boxes. In the upper half of the box on the left is the equation the measure of angle B A C equals 20 degrees. In the lower half of the box is the word Given. In the upper half of the box on the right is the equation the measure of angle C A D is 15 degrees. In the lower half of the box is the word Given. In row 3 there is 1 text box. In the upper half of the box is the equation the measure of angle B A D equals 20 degrees plus 15 degrees. In the lower half of the box is the phrase Substitution Property of Equality. In row 4 there is 1 text box. In the upper half of the box is the equation the measure of angle B A D equals 35 degrees. In the lower half of the box is the word Simplify. A ray is drawn from the text box in row 1 to the text box in row 3. A ray is drawn from each of the text boxes in row 2 to the text box in row 3. A ray is drawn from the text box in row 3 to the text box in row 4.
Answer:
Ruler Postulate
Step-by-step explanation:
In box 1, the reason that justifies the statement, m∠BAD = m∠BAC + m∠CAD, is: angle addition postulate.
What is the Angle Addition Postulate?The angle addition postulate states that the measure of a larger angle equals the sum of smaller angles that make up the larger angle.
∠BAD comprises of ∠BAC and ∠CAD.
Therefore, based on the angle addition postulate, m∠BAD = m∠BAC + m∠CAD.
The missing reason in box 1 would be: angle addition postulate.
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so i have this question this math problem is: James works in a factory and wraps 8 packages every hour. How many hours will it take James to wrap 3,736 packages THIS IS CONFUSING someone help
Answer:
467 hours.
Step-by-step explanation:
3736 / 8
= 467.
The width of a rectangle measures (36 + 5) centimeters, and its length measures
(86 + 6) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
Answer:
Step-by-step explanation:
36+5=41
86+6=92
41*2=82
92*2=184
82+184=266
I NEED HELP ASAP
Identify the x value of the solution to the system of equations.
x – 4y = 1
6x + 4y = 20
Answer:
1x + 4y = 4 ⇒ 6x + 24y = 24
6x - 8y = 0 ⇒ 6x - 8y = 0
32y = 24
32 32
y = 3/4
x + 4(3/4) = 4
x + 3 = 4
-3 -3
x = 1
(x, y) = (1, 3/4)
Step-by-step explanation:
up there :D
Which picture shows a distance of 2/6 from point A to point B?
The correct choice for this question is Option B
Which statements are true for the given geometric sequence? Check all that apply.
The domain is the set of natural numbers.
The range is the set of natural numbers.
The recursive formula representing the sequence is f(x + 1) = Three-halves(f(x )) when f(1) = 4.
An explicit formula representing the sequence is
f(x) = 4(three-halves) Superscript x
The sequence shows exponential growth.
The statements are true for the given geometric sequence.
The domain is the set of natural numbers.
The recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.
The sequence shows exponential growth.
We have given the graph.
What is the geometric sequence?
A geometric sequence is a sequence in which the ratio of every two successive terms is a constant.
The graph is given below we can see that
The domain is the set of natural numbers.
The recursive formula representing the sequence is
f(x + 1) = 3/2(f(x )) when f(1) = 4.
The given graph grows exponentially.
The sequence shows exponential growth
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Answer:
a, c, e
The domain is the set of natural numbers.
The recursive formula representing the sequence is f(x+1) = Three-halves(f(x)) when f(1) = 4
The sequence shows exponential growth.
Step-by-step explanation:
What fraction of 2.4 litres is 400 ml?
Answer:
1\5 of 2 litres is 400 ml.
Step-by-step explanation:
Hope this helps!!!
A person has 7 songs to choose from and will perform 3. How many different ways can they do this?
Answer:
They can chose the best song out or used others opinion.
Step-by-step explanation:
This is easy answer this and you will get points!!love you guys
Answer:
4. 56 is 8 times as many as 7.
56 = 8 x 7
5. 6, 12, 18, 24, and 30
6. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Hope this helps!
Hey there!
SIMPLIFYING #4
Question reads….
“56 is _____ times as many as _____”
~ The factors of 56 is/are
• 1, 2, 4, 7, 8, 14, 28, & 56
~ The factor pairs of 56 is/are
• 1 × 56 = 56
• 2 × 28 = 56
• 4 × 14 = 56
• 7 × 8 = 56
~ So, for the FIRST portion we can day
“56 is _2_ times as many as _28_”
(or you could choose any numbers from your factoring pair !)
SIMPLIFYING #5
Question reads….
“List the first five multiples of 6”
~ Meaning of multiples
• Multiples is any number that can be divided EVENLY without any remainders.
~So, the first five multiples are….
• 6, 12, 18, 24, & 30
SIMPLIFYING #6
Question reads….
“Name all the factors of 72”
~ Meaning of factoring/factor
• Factoring is another name for factorizing/factorization. It is basically a number that when you’re multiplying with another number that produces a number or expression
~ So, the factors of 72 is/are….
• 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 , & 72
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
help me please please please i need it
Answer:
Step-by-step explanation:
Remark
If you take one radius whose length is r and start it at (0,0) on one end and (r,0) at the other, and sweep it around so the (r,0) hits every point on the circumference of the circle, the radius will go through 360°.
You have only gone through 120°. That's no problem. All you have to do now is add a fraction that adjusts for the 120°.
Formula
Arc length = fraction * 2*pi * r
2*pi * r is the circumference
Arc Length = 2* (120/360) * pi * r
Givens
r = 13
pi = 3.14
Solution
Arc Length = (120/360) * 2 * pi * 13
Arc Length = 27.21
Answer
Arc Length = 27.21
Help me please
Trina invests $ 16000 at a rate of 5% per year interest. Work out the value of her investment at the end of a year.
Answer:
$ 16800
Step-by-step explanation:
Simple Interest Value = Principal × Interest Rate × Time
0.05 × 16000 × 1 = $ 800
(Money invested + Interest = Total money in the account)
16000 + 800 = 16800
Trivia's Bank account will have $16800 at the end of one year.
what is the projected population for 2015
Answer:
the answer is b
Step-by-step explanation:
ive did it before
A line passes through the points (3,0) and (4,2). What is its equation in slope-intercept form?
Answer:
y = 2x - 6
Step-by-step explanation:
Slope intercept form:Equation of the line:
[tex]\sf \boxed{ y = mx +b}[/tex]
Here m is the slope and b is the y-intercept.
Step 1: Find the slope
(3 , 0) ⇒ x₁ = 3 & y₁ = 0
(4 , 2) ⇒ x₂ = 4 & y₂ = 2
[tex]\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{2 -0}{4-3}\\\\= \dfrac{2}{1}\\\\=2[/tex]
m = 2Step2: Now, substitute the value of 'm' in the equation.
y = 2x + b
Step3: In the above equation plug in any point. Here, (3 ,0) is chosed.
0 = 2*3 + b
0 = 6 + b
-6 = b
b = -6Step4: Equation of the line:
y = 2x - 6
What best describes arc ZMF? ARC TFM and ARC TZ? I have no clue which is which.
1. Major Arc
2. Semicircle
3. Minor Arc
What is minor arc?An arc whose measure is less than 180 degrees is called a minor arc.
What is major arc?An arc whose measure is greater than 180 degrees is called a major arc.
What is semicircle?An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.
1. The arc ZMF defines a major arc as the measure is more than 180.
2. Arc TFM defines semicircle as it measure 180 degrees.
2. Arc TZ defines a minor arc as the measure is less than 180.
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The integer succeeding -9 is
The integer succeeding -9 is - 8.
Answer:
-8 is the answer as it goes like -10,-9,-8 etc
Goblin gryh can count the coins in a bag in 10 minutes. of goblin Birt counts with him, they can count all the coins in 6 minutes. How long would it take goblin Birt to count the coins in the bag by himself?
Answer:
pagpalit og pandesal og kopiko didto sa bakery
Goblin Birt can take 15 minutes to count the coins in the bag by himself.
What is unitary mehtod?The unitary method is a process for solving a problem by first finding the value of a unit, and then finding the necessary value by multiplying the single unit value.
How to calculate how long would it take goblin Birt to count the coins in the bag by himself ?In this problem, unitary method is to be applied three times.Here, counting all the coins is considered as the entire work which is considered as 1.According to the problem,
Goblin gryh can count the coins in a bag in 10 minutes.∴ In 10 minutes Goblin gryh can count the coins in the bag.
∴ In 1 minute Goblin gryh can count [tex]\frac{1}{10}[/tex] th part of the coins in the bag.
Again, according to the problem,
Goblin gryh and Goblin Birt both can count all the coins in 6 minutes.∴ In 6 minutes, Goblin gryh and Goblin Birt both can count all the coins in the bag
∴ In 1 minute, Goblin gryh and goblin Birt both can count [tex]\frac{1}{6}[/tex] th part of the coins in the bag.
∴ In 1 minute, Goblin Birt can count [tex](\frac{1}{6} - \frac{1}{10})[/tex] th part of the coins in the bag.
= [tex]\frac{5-3}{30} = \frac{2}{30} = \frac{1}{15}[/tex] th part of the coins.
∴ We can say,
Goblin Birt can count [tex]\frac{1}{15}[/tex] th part of the coins in the bag in 1 minute.
∴ Goblin Birt himself can count all the coins in the bag in 15 minutes.
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A square table has a perimeter of 20 feet. What is its area?
Answer:
25 feet squared :)
Step-by-step explanation:
20/4 = 5
5^2 = 25
What is the sum of the numbers in the series below? 15 11 7 . . . (–129)
Using Gauss's method, the sum of the numbers in the given series [ 15 11 7 . . . . ( –129 ) ] is -2664.
What is an arithmetic sequence?An arithmetic sequence is simply a sequence of numbers in which the difference between the consecutive terms is constant.
From Gauss's method nth term is an arithmetic sequence is expressed as;
n = (( first term - last term )/d) + 1
d is the common difference between terms.
Given the series in the question;
15 11 7 . . . (–129)
d = 15 - 11 = 4
Next, we find n
n = (( first term - last term )/d) + 1
n = (( 15 - (-129))/4) + 1
n = ( 144/4 ) + 1
n = 36 + 1
n = 37
Now, using the common difference between terms the sun will be;
S = 15 + 11 + 7 . . . -125 -129
Also
S = -129 -125 . . . + 7 + 11 + 15
We add
2S = -114, 114, 114 . . . . n
Hence, the sum will be;
2S = ( -114 ) × n
2S = ( -114 ) × 37
2S = -5328
S = -5328 / 2
S = -2664
Therefore, using Gauss's method, the sum of the numbers in the series [ 15 11 7 . . . (–129) ] is -2664.
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7. Solve the equation 2x + 4 = 9. Explain the
and properties you used.
The surface area of a cube is 96 square units. What is the volume of the cube?
Answer:
volume=64
Step-by-step explanation:
surface area of cube =96
6l²=96
l²=16
l=4
now, by the question
volume of cube =l³
=(4)³
=64
can you pls help me, i need it
according to the topic
5000+1400+1700+2200-5000×80%+1200
=55300-4000+1200
=$52500
Thus we choose option B
B.$52,500
