The equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.
What is the Equation of a parabola?y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
As it is given that the focus of the parabola is at F(3,0) and its directrix is the line x=−3, therefore, we can write that
x=-3
x+3=0
Now, Let A(x,y) be any point in the plane of the directrix and focus, and MA be the perpendicular distance from A to the directrix, therefore, A lies on parabola if FA=MA,
[tex]FA=MA\\\\\sqrt{(x-3)^2 +(y-0)^2}=\dfrac{|x+3|}{1}\\\\{(x-3)^2 +(y-0)^2}={(x+3)^2}\\\\-6x^2+y=6x\\\\y=6x^2+6x[/tex]
Hence, the equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.
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10 is to the power of one hundred because it is a factor of itself true or false?
True.
[tex]10^{10}[/tex] = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
Its a factor which can be written in short and simplified form.
Given the functions k(x) = 2x2 − 7 and p(x) = x − 4, find (k ∘ p)(x). (k ∘ p)(x) = 2x2 − 8x 16 (k ∘ p)(x) = 2x2 − 16x 32 (k ∘ p)(x) = 2x2 − 16x 25 (k ∘ p)(x) = 2x2 − 11.
Function represents a relationship between variables. The product of the two given functions (k·p)(x) is 2x³-8x²-7x+28.
What is Function?A function assigns the value of each element of one set to the other specific element of another set.
Given to us
k(x) = 2x² − 7
p(x) = x − 4
As the two equations are given to us, k(x) and p(x), and we need to find (k ∘ p)(x), And we know the product of two functions can be written as,
[tex](k \cdot p)(x) = k(x) \cdot p(x)[/tex]
therefore,
[tex]k(x) \cdot p(x)\\\\= (2x^2-7)(x -4)\\\\= 2x^3 - 8x^2 - 7x +28[/tex]
Hence, the product of the two given functions (k·p)(x) is 2x³-8x²-7x+28.
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Please someone help me !!
Answer:
hope this helps...
answer in the diagram
Bennie swims 6 laps in 4 1/2 minutes.What is this rate in minutes per lap?
A. 2/3 minutes per lap
B. 3/4 minutes per lap
C. 1 1/3 minutes per lap
D. 1 1/2 minutes per lap
S is located at (9 -3) point T is located at (4 -3)
what is the distance from point S to point T
Answer:
5
Step-by-step explanation:
The distance formula is:
[tex]d = \sqrt {\left( {x_2 - x_1} \right)^2 + \left( {y_2 - y_1} \right)^2 }[/tex]
We can plug in the given coordinates into the equation:
[tex]d = \sqrt {\left( {4 - 9} \right)^2 + \left( {-3 - (-3)} \right)^2 }\\d = \sqrt {\left( {-5} \right)^2 + \left( {-3+3} \right)^2 }\\d = \sqrt{25 + \left( {0} \right)^2 }\\d=\sqrt{25+0}\\d=\sqrt{25}\\d=5[/tex]
A carpenter lays 18 square feet of tiles in 2/3 of an hour. How many square feet of tile does the carpenter lay per hour?
How would I do this problem if the options are the following choices:
A: 12 Square Feet Per Hour
B: 17 1/3 Square Feet Per Hour
C: 18 2/3 Square Feet Per Hour
D: 27 Square Feet Per Hour.
Answer:
D. 27 square feet per hour
Step-by-step explanation:
Step 1:
Find the unit rate. Since 18 tiles are per 2/3 of an hour, we can divide 18 by 2 to get 9 tiles layed per third hour.
Step 2:
Multiply the 9 per third of an hour by 3 to find how many are per hour,
[tex]9*3=27[/tex] square feet per hour
This is called finding the unit rate of a scenario.
Brainly pls help me this is k12
Answer:
228
Explain your answer:
Answer:
A = 228 ft²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height and b₁, b₂ the parallel bases
here h = 12 and b₁ = 14, b₂ = 24 , then
A = [tex]\frac{1}{2}[/tex] × 12 × (14 + 24) = 6 × 38 = 228 ft²
can anyone help with this
c)29.75
Step-by-step explanation:
sin 24° =12.1/x
x= 12.1/sin24
x=29.75
The functions f(x) and g(x) are described using the following equation and table: f(x) = −2(1.07)x x g(x) −4 −10 −2 −7 0 −4 2 1 Which equation best compares the y-intercepts of f(x) and g(x)? The y-intercept of f(x) is equal to the y-intercept of g(x). The y-intercept of f(x) is equal to 2 times the y-intercept of g(x). The y-intercept of g(x) is equal to 2 times the y-intercept of f(x). The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).
The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).
How to compare the y-intercepts?The functions are given as:
f(x) = -2(1.07)^x
Table of values for g(x)
x g(x)
−4 −10
−2 − 7
0 −4
2 1
The y-intercept is when x = 0.
So, we have:
g(0) = -4
Also, we have:
f(0) = -2(1.07)^0
f(0) = -2
-2 is greater than -4 by 2
Hence, the y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).
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what the anwser fast !!!!!!
Answer:
The initial height is the y-intercept of the graph
slope of the graph = -2
Jordon interprets the only the slope correctly.
Aral interprets the only the initial height correctly.
Step-by-step explanation:
Slope = change in y ÷ change in x = (0 - 12) ÷ (6 - 0) = -12 ÷ 6 = -2
So the slope of the graph = -2
by inspection, the y-intercept = 12
Therefore, the equation for the line is y = -2x + 12
Jordon interprets the only the slope correctly.
Aral interprets the only the initial height correctly
Anna baked 333 batches of cookies with ccc cookies in each batch. She then ate 888 cookies!
How many cookies does Anna have left?
Write your answer as an expression.
Answer:
okay so anna bakes 333 batches of whatever amount of cookies but she be bakin a ton of cookies. Like we got a whole walmart filled with anna cookies.
so we are going to make this into an expression by saying 333n-888
okay so because anna is chronically obese, she eats 888 cookies. this means we subtract 888 cookies from 333(some number) amount of cookies.
your answer?
333n - 888
you can thank me later. Good luck.
Answer:
3c-8
Step-by-step explanation:
khan
how can i find percent %
A car requires 9 liters of gasoline to cover a distance of 108 km. If the car
spent 12.5 liters of gasoline, how far did the car travel?
Answer: 150km
Step-by-step explanation:
The question says that the car required 9 litres of gasoline to cover 108km which means we and then derive that:
9L = 108km
And we are trying to find out how much distance can cover:
12.5L =?
Therefore, in order to find out the distance, we need to figure out how much distance can 1L take the car
therefore:
1L = [tex]\frac{108km}{9L}[/tex] = 12km
So if we know how far 1L can take us, we can just multiply 12.5 litres by the 12km to find out the distance:
12.5L × 12km = 150km
So, therefore, 12.5 litres can cover 150km.
Find the distance between the points (-4,1) and ( – 4, -8).
Answer: 9 units
Step-by-step explanation:
If you draw this one out, you should be able to notice that it is only a vertical distance it travels, which means that the difference in y-units should give you the distance.
Find m angle BCD. Geometry math questions
Sum of two interiors=exterior
[tex]\\ \tt\longrightarrow 69+3x+12=6x+27[/tex]
[tex]\\ \tt\longrightarrow 3x+81=6x+27[/tex]
[tex]\\ \tt\longrightarrow 3x=54[/tex]
[tex]\\ \tt\longrightarrow x=18[/tex]
m<BCD=6(18)+27=108+27=135can you help me with this please 9u+6u+9u–7u
Answer: 17u
Step-by-step explanation:
(9+9+6-7)u=17u
Answer:
17u
Step-by-step explanation:
9u+6u+9u =24u
24u-7u=17u
4 whole numbers that have median of 11 and range of 3
Answer:
What is the question?
Step-by-step explanation:
∠ and ∠ are complementary angles. If ∠ = (12x - 3)° and ∠ = (7x - 2)°, find the
∠.
Answer:
57 °
Step-by-step explanation:
Complementary angles = 90 °
Since, Your angle don't have ∠ [ ] Then Let let "C" and "y"
Thurs, C = 12x- 3 and y = 7x - 2
It is given that angles r and s are complementary angles. Two angles are complementary if they add up to 90 degrees. This means the sum of measures of angle r and angle s must be 90 degrees. So,
c + y = 90
12x - 3 + 7x - 2 = 90
19x - 5 = 90
19x = 95
x = 95/19
x = 5
Using the value of x in expression or r, we get:
c = 12x - 3 = 12(5) - 3 = 60 -3 = 57 degrees.
So measure of angle c is 57 degrees.
Hence, the ∠ is 57 °
[RevyBreeze]
Marco puts his coins into stacks. Each stack has 10 coins.
He makes 17 stacks of quarters.
He makes 11 stacks of dimes.
He makes 8 stacks of nickels.
How much money does Marco have in his stacks of coins?
Answer:
Marco has $57.50 in total.
Step-by-step explanation:
17 x 10 = 170 quarters
170 x 0.25 = $42.50
11 x 10 = 110 dimes
110 x 0.10 = $11.00
8 x 10 = 80 nickels
80 x 0.05 = $4.00
a __________ is a collection of numbers gathered to give some meaningful information
a data is a collection of numbers gathered to give some meaningful information
Answer:
[tex]data[/tex]
is the correct answer and have a great day bye
Step-by-step explanation:
[tex]kai6417[/tex]
Will cooked for 45 people on Friday, 62 people on Saturday, and 43 people on Sunday. What is the mean (average)? *
Answer:
50
Step-by-step explanation:
45+62+43= 150
150/3= 50
Please, I need an answer to this question urgently.
Answer:
156
Step-by-step explanation:
While solving we will have to use the area formula of the rectangle, which is :A=w*l ; length*width=A.
Steps:
1)let’s consider that the shape is a full rectangle. => 16*12=192.
2)9*2=18 -> 18*2=36
3)192-36=156.
Area of the shape is 156 cm².
For explanation, please check the attached image.
7) An umpire at a little league baseball game has 14 baseballs in his pockets. Five of the baseballs are brand A, 6 are brand B, and 3 are brand C. What is the probability that the next ball he throws to the pitcher is a brand C baseball? Record your answer as a fraction, decimal, and a percent.
Answer:
3/14
Step-by-step explanation:
if he has 14 baseballs 5 of them are a so:
14-5=9
if he has 6 the are b then:
9-6=3
so 3 divided 14= 3/14
Ms. Wang wants to make equal groups of iPads and computers without mixing iPads and computers. She has 36 iPad and 40 computers, and she wants to make equal-sized groups. What is the largest number of iPad and computers that she can put in each group?
Answer:
6
Step-by-step explanation:
6 is the highest factor that will go into both 36 & 40. Leaving 6 groups of 6 for both ipads and laptops.
Luna drew a scale drawing of the high school. The parking lot, which is 54 meters wide in real life, is 102 centimeters wide in the drawing. What scale did Luna use? 17 centimeters:___meters
Scale drawings are used to draw shapes in a different proportional size
The scale used in the drawing is 17 centimeters : 9 meters
How to determine the scale of the drawingFrom the question, we have:
Real length = 54 metersScale length = 102 centimetersSo, the scale is:
Scale = Scale length : Real length
This gives
Scale = 102 centimeters : 54 meters
Reduce the scale
Scale = 17 centimeters : 9 meters
Hence, the scale used in the drawing is 17 centimeters : 9 meters
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Answer: The answer is 9 meters.
Explain how to get the variable alone in the following equation a / 13=4
Answer:
52
Step-by-step explanation:
a/13=4
a=13x4
So, a = 52
The mean weight of NINE players on a Basketball team is 177 POUNDS. Find the total weight of the nine players.
show working please
Answer:
The total weight is 1593 lbs.
Step-by-step explanation:
177*9 = 1593
Find the inverse matrix or type
"none". (Use decimals)
3
2
4
1
? ]
Enter
Answer:
[tex]\left[\begin{array}{cc}-0.2&0.4\\0.8&-0.6\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}3&2\\4&1\end{array}\right] ^{-1} =\frac{1}{3*1-2*4} \left[\begin{array}{cc}1&-2\\-4&3\end{array}\right]=(-0.2)*\left[\begin{array}{cc}1&-2\\-4&3\end{array}\right]=\left[\begin{array}{cc}-0.2&0.4\\0.8&-0.6\end{array}\right]\\[/tex]
Will give brainliest
Answer:
B
Step-by-step explanation:
q and u are the only congruent angles
Dean ran 5 miles this week and wants to know how many kilometers he ran. His work is below.
StartFraction 5 miles Over 1 EndFraction times StartFraction 1.61 kilometers Over 1 mile EndFraction = 80.5 miles
A 2-column table with 1 row titled Units of Length. Column 1 is labeled Customary System Units with entry 1 mile. Column 2 is labeled Metric System Units with entry 1.61 kilometers.
What are Dean’s errors? Select all that apply.
He has the wrong units in his answer.
Dean should have used two conversion factors.
Dean should have kilometers in the denominator of the conversion factor.
The decimal point in his answer is in the wrong place.