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]
More about the parabola link is given below.
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Can i get some help? Points P, Q, R, and S represent -3, -1, 0 and 2, respectively, on a number line. How many units is the midpoint of PQ from the midpoint of RS?
Answer:
3 units
Step-by-step explanation:
The midpoint of P and Q is -2, the midpoint of R and S is 1, the total distance between -2 and 1 is three
|-2| + |1| = 3
What is the fraction in its simplest for of a recuring decimal 0. 1
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
x= 0.1111...
10x = 1.11111111
10x - x = 1
9x = 1
x = [tex]\frac{1}{9}[/tex]
Hey guys! Sorry to bother but I need help with these. 5th grade math, will give brainliest! (If you see multiple questions by me that look the same, they are all different.)
Answer:
1/36 and 1/28
Step-by-step explanation:
i believe this is the answer as you should divide the denomonator by the answer as you cannot divide the numerator.
5
Alvin, Simon and Theo all collect marbles.
Alvin has k marbles.
Simon has 3 more marbles than Alvin.
Theo has twice as many marbles as Alvin.
Complete the table by writing an expression in for Simon and Theo.
Answer:
[tex] \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\sf { \rightarrow \: \red{i \: dont \: know \: anymore\:\color{green}☘}}\end{array}}\end{gathered} \end{gathered}[/tex]
[tex] \color {blue} \rule {1pt} {100000pt} [/tex]
The student council sets up a booth to sell bracelets for $2.50 each and a booth to sell necklaces for $5 each. A $50 donation is made at the booth selling bracelets. The student council decides to close the booths when the amount of money collected is the same.
The students council sold 20 bracelets and 10 necklesses.
What is division?The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic,
here the number of the bracelets sold will be
[tex]N_{B}=\dfrac{50}{2.5}=20[/tex]
Number of the necklesses sold will be
[tex]N_{N}=\dfrac{50}{5}=10[/tex]
Hence the students council sold 20 bracelets and 10 necklesses.
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lengths
Find the value of x in the triangle shown below.
Choose 1 answer:
x = 6
® X = 13
X = V 65
Answer:
C
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 4² = 9²
x² + 16 = 81 ( subtract 16 from both sides )
x² = 65 ( take square root of both sides )
x = [tex]\sqrt{65}[/tex]
Help!!! Find the slope and y-intercept
Answer:
To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).
Step-by-step explanation:
what is f(x)=x^2 transformed 3 units to the left
Answer:
Equation:
f(x) = (x + 3)^2
Graph: see image
Step-by-step explanation:
Translation just means shift or slide. To show a LEFT shift in the equation, go in close to the x, inside the parenthesis with the x, for LEFT shift, insert +3.
Left and right shifts might be the opposite of what you may think. Minus a number shifts right and plus a number shifts left.
For the graph, see image. The answer is the green curve.
what is 2y + 3 + 5x + 6 simplified and justified
2y + 3 + 5x + 6
2y + 5x + 9 = 0
hope it helps...!!!
If f(x)= 2^8-x+3, what is the value of f(5), to the nearest tenth (if necessary)
Answer:
Step-by-step explanation:
f(5) = 2^8 - 5 +3
f(5) = 256-5+3
f(5) = 254
a) What is the definition of the square root of a number k?
b) what is the definition of the cube root of a number k?
c) what is the definition of the n^th root of a number k?
d) What are the limitations of working with roots and real numbers?
#a
Square root of k is a factor of the number k that when it is multiplied with itself yields the result as k
#b
Cube root of k is a factor of the number k that when it is multiplied thrice with itself yields the result as k
#c
n th root of k is a factor of the number k that when it is multiplied n times with itself yields the result as k
#d
For even value of root it should be positive to be realFor odd value it can be both positive and negative(a) How long did it take you to set up your building materials? How do you
(b) How long did it take to build each shelf
Before his shopping spree,hall owned 31 phones. He bought 70 more phones. What is the ratio of phones purchase to the resulting total number of phones?
Answer:
70:101 70 is 69% of 101
Step-by-step explanation:
Since he had 30 phones and bought 70, he totals with 101 phones. Since 70/101 is 69, 70 is 69% of 101
Ok well good luck! Have a good day!
Beniah sells hats and umbrellas. He charges 57.75 per hat and $9.50 per umbrella. Last week he sold 90 items for a total
of $757
The area of a rectangular ink pad is 28 square centimeters. It is 7 centimeters wide. How tall is it?
Answer:
4 cm
Step-by-step explanation:
The area is found by the length times width. You already know that the area is 28 and the width is 7. All you have to do is divided 28 by 7 to get 4.
Answer:
4 cm
Step-by-step explanation:
28=7*W
W=28/7
W=4 inches
Which coordinates identify a location north of a city that has a latitude of 38. 0°n and a longitude of 25. 0°w?.
Using translation concepts, y-coordinates greater than 38 identify a location north of the city.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Considering latitude and longitude, the coordinates of a city are given as follows:
(LON, LAT).
Hence, the given city has coordinates given by:
(25, 38)
As we move north, the latitude increases, hence, y-coordinates greater than 38 identify a location north of the city.
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Jia needs 3/4 cups of blueberries to make scones. How many cups of blueberries does she need to make 3 times as many scones? I think it's either C or A, i'm not sure
A. 1/4 cups
B. 1 1/2 cups
C. 2 1/4 cups
D. 3 3/4 cups
Independent and Dependent events
There are 3 cards and only 1 card is off.
If you pick the odd card first and do not replace it there is no chance of picking a second odd card.
The probability would be 0
The amount of money on account it makes M for working H hours can be represented by the equation m = 29.4H what is the constant of proportionality of the equation
6 raised to the third power plus 4
Answer:
6^3+4 equals 220.
Step-by-step explanation:
6^3 equals 216.
Plus 4 equals 220.
Answer:
Step-by-step explanation:
6004
6 to the third power is 6000 and 6000+4 is 6004
I need help round pleae
Answer:
Mean=49 pounds
Median=11pounds
Step-by-step explanation:
If all the cats got weighted (5, 11,11,12,10) for each cat you need to add, multiply and divide to get all the answers (P.S. you don't need to round for your answers!)
For solving the Mean you need to add up all the numbers and then divide by how many numbers there are (5+11+11+12+10÷ 5=49)
For solving the Median you need to put the numbers in smallest to biggest order to solve for this (5,10,11,11,12) and then kept crossing them out (left to right) until you get the two middle numbers (11,11) then add them both right and then divide 22 by 2 then you have your answer!
You're going to rock this:)
Kenz
help asap check picture
The value of the P(2 < X ≤ 4) is 0.14 if the probability of P(x =3) is 0.10 and P(x = 4) is 0.04.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have a probability distribution shown in the table:
P(2 < X ≤ 4)
We have to find the probability between 2 and 4
P(2 < X ≤ 4) = P(x =3) + P(x = 4)
From the table
P(x =3) = 0.10
P(x = 4) = 0.04
P(2 < X ≤ 4) = 0.10 + 0.04 = 0.14
Thus, the value of the P(2 < X ≤ 4) is 0.14 if the probability of P(x =3) is 0.10 and P(x = 4) is 0.04.
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i need help with this question
Answer:
express 33362imstandard form
If m varies directly with t, and m = 4 when t = 12, what is the value of t when m = 12?
O4
O20
O24
O36
Answer:
t = 36
Step-by-step explanation:
given that m varies directly with t then the equation relating them is
m = kt ← k is the constant of variation
to find k use the condition m = 4 when t = 12 , then
4 = 12k ( divide both sides by 12 )
[tex]\frac{4}{12}[/tex] = k , that is
k = [tex]\frac{1}{3}[/tex]
m = [tex]\frac{1}{3}[/tex] t ← equation of variation
when m = 12 , then
12 = [tex]\frac{1}{3}[/tex] t ( multiply both sides by 3 to clear the fraction )
36 = t
Calculate the line of best fit using m= y2-y1/x2-x1 using your brain not a calculator
Take two points
(1,940)(2,950)Slope
m=950-940/2-1=10Equation in point slope form
y-y1=m(x-x1)y-940=10(x-1)y-940=10x-10y=10x-10+940y=10x+930Answer:
[tex]y=-\dfrac{300}{7}x+1000[/tex]
Step-by-step explanation:
Method 1 (see attachment 1 with red line)
Plots the points on a graph and draw a line of best fit, remembering to ensure the same number of points are above and below the line.
Use the two end-points of the line of best fit to find the slope:
[tex]\textsf{let}\:(x_1,y_1)=(0,1000)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(7,700)[/tex]
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{700-1000}{7-0}=-\dfrac{300}{7}[/tex]
Input the found slope and point (0, 1000) into point-slope form of a linear equation to determine the equation of the line of best fit:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1000=-\dfrac{300}{7}(x-0)[/tex]
[tex]\implies y=-\dfrac{300}{7}x+1000[/tex]
Method 2 (see attachment 2 with blue line)
If you aren't able to plot the points, you should be able to see that the general trend is that as x increases, y decreases. Therefore, take the first and last points in the table and use these to find the slope:
[tex]\textsf{let}\:(x_1,y_1)=(1,940)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(7,710)[/tex]
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{710-940}{7-1}=-\dfrac{115}{3}[/tex]
Input the found slope and point (1, 940) into point-slope form of a linear equation to determine the equation of the line of best fit:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-940=-\dfrac{115}{3}(x-1)[/tex]
[tex]\implies y=-\dfrac{115}{3}x+\dfrac{2935}{3}[/tex]
helppppppppppppppppp
5 STARS ON YOUR AND ANSWER AND A THANK YOU.
Answer:
It's the fourth answer, D.
Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
Answer:
y=4/-2x+4
Step-by-step explanation:
Formula (y=mx+b)
m= 4/-2 (rise over run)
b= 4 (y-axis intercept point)
y=mx+b
y=4/-2x+4
A theater has 33 seats in the first row, 37 seats in the second row. 41 seats in the third row, and so on. How many seats are there in row 19?
Answer:
90 seats are in row 19
Step-by-step explanation:
The pattern is adding 4 seats so 3 x 19 is 57 so 33 + 57 is 90 seats
Hope this helps
triangle ABC has a perimiter of 22cm
ab=8cm
bc=5cm
by claculation deduce whether triangle abc is a right angle triangle
Answer:
ABC is not a right angled triangle.
Step-by-step explanation:
Step 1: Given the perimeter of ΔABC = 22 cm, sides AB = 8 cm and BC = 5 cm. Find the side AC.
Perimeter = AB + BC + AC
⇒ AC = 22 - (8 + 5) = 22 - 13 = 9 cm
Step 2: Find whether the triangle is right angled using Pythagoras Theorem which is Hypotenuse² = Side² + Base²
AC² = AB² + BC²
⇒ AC² = 9² = 81
⇒ AB² + BC² = 8² + 5² = 64 + 25 = 89
∴ AC² ≠ AB² + BC²
⇒ ΔABC is not a right angled triangle.
