C
X
A parabola has a focus at ( 1.5, 0) and a directrix of x= -1.5. Which of the following equations represent the parabola?
Answers
Step-by-step explanation:
Since the focus lies on the x axis, and the diretcrtirx is a vertical line, we have a sideways parabola so we have the equation
[tex](y - k) {}^{2} = 4p(x - h)[/tex]
where h,k is the vertex and
p is the distance from the vertex to the focus or the distance fromcthe vertex to the directrix.
Since the focus is 1.5, and the directrix is -1.5 the vertex is (0,0) so we have
[tex]y {}^{2} = 4px[/tex]
We know p is 1.5 so we have
[tex] {y}^{2} = 6x[/tex]
[tex] \frac{1}{6 } {y}^{2} = x[/tex]
Related Questions
Define the algebraic terms by counting how many terms given on the expression below.
4x + 3n + 5
Answers
Answer:
Two terms ( [tex] x [/tex] and [tex] n [/tex])
Step-by-step explanation:
If simplified it gives 3n+4x+5
And cannot be factored
=======================================================
We're given the following expression:
[tex]\bigstar{\boxed{4x+3n+5}[/tex]
Here,
4x is a term
3n is a term
5 is a term
4 is the coefficient of x
x is a variable
3 is the coefficient of n
n is a variable
5 is a constant
Details:-
A coefficient is a number before a variable
A variable is a letter
A constant is a number without any variables next to it
=========================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
What equation results from completing the square and then factoring?
x^2 + 4x = 5
A. (x + 2)^2 = 3
B. (x + 2)^2 = 7
C. (x + 2)^2 = 1
D. (x + 2)^2 = 9
Answers
Answer:
(x+2)^2 = 9
Step-by-step explanation:
To complete the square we need to add 4 to both sides of the equation,
Why we add 4 to both sides? Because if we add it to one side only, the equation will turn into an inequation
x^2 + 4x + 4 = 5 + 4
x^2 + 4x + 4 = 9 and the factor of the expression is (x+2)*(x+2) = 9
(x+2)^2 = 9
•Pls help•
Describe the Order of Operations. Create an example and explain each step using the order of
operations.
Answers
Answer:
The order of operations says that operations must be done in the following order: parentheses, exponents, multiplication, division, addition, and subtraction. You can also create a little phrase to go along with this, like "Please Excuse My Dear Aunt Sally." Whatever you choose, make sure that you know all six steps of the order of operations very well. The order of operations tells us the order to solve steps in expressions with more than one operation. First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.
Step-by-step explanation:
hope this helps :)
(This is a multiple choice question)Suppose you are rehearsing for a dance competition and you fall and hurt your shoulder. At the hospital, they take X-rays, consult a shoulder specialist, and give you a stabilizer brace. You pay a $50 co-pay at the time of service, and the ER bills your insurance company for the rest. The total hospital bill is $3,720. The table below shows the payment structure for your health insurance policy. If the injury happened in July, what is your total paid in monthly premiums?
A. 1,050$
B. 150$
C. 900$
Answers
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Answers
Dilation is the change in size of of object. The length of the side OB' will be 3 units
Dilation of coordinateFrom the given diagram, we can see that there is a change in the side of the triangle OAB to OA'B'
Given the following parameters
OB = 3/4 units
Scale factor = 4 units
The measure of OB' = 4 * 3/4 = 3 units
Hence the length of the side OB' will be 3 units
Learn more on dilation here: https://brainly.com/question/10253650
Answer:
3
Step-by-step explanation:
edg 2022
The volume of a right cone is 252pi units^3. If its height is 21 units, find its radius.
Answers
Based on the calculations, the radius of this right cone is equal to 6 units.
Given the following data:
Volume of cone = [tex]252\pi \;units^3[/tex]Height of cone = 21 units.How to calculate the volume of a cone.Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where:
h is the height.r is the radius.Making r the subject of formula, we have:
[tex]r=\sqrt{\frac{3V}{\pi h} } \\\\[/tex]
Substituting the given parameters into the formula, we have;
[tex]r=\sqrt{\frac{3\times 252\pi}{\pi \times 21} } \\\\r=\sqrt{\frac{756}{21} }\\\\r=\sqrt{36}[/tex]
r = 6 units.
Read more on radius here: brainly.com/question/21367171
Help picture below problem 17
Answers
Answer:
40
Step-by-step explanation:
Angle KPJ is going to have the same measure as Angle DPE. This problem is a bit tricky, but I'll try my best to explain it. A straight angle is basically just a straight line, and it equals 180 degrees. Angle FPG is a straight angle.
To find the measure of Angle KPJ, we first have to find the measure of angle DPE, and the way we're gonna do that is add together the other angles in the straight angle (which would be Angle FPD and Angle EPG) and then subtract that from 180 (measure of a straight angle).
That might have sounded a bit confusing, but that's the best way I could explain it. Now, let's add Angle FPD and Angle EPG.
105 + 35 = 140
Now, let's subtract that from 180.
180 - 140 = 40
We now know that the measure of Angle DPE is 40, and since it's equivalent to Angle KPJ, our answer is 40!
I know that was confusing, but I hope it helped a little bit! Have a lovely day!! :)
The diameter of a circular placemat is 42 centimeters. What is the approximate area of the circular placemat
Answers
[tex] area \: of \: a \: circle \: or \: circular \: object \: = \pir^{2} \\ \: [/tex]
Answer:
1386cm^2.
Step-by-step explanation:
Radius of a circle = diameter / 2
= 42cm /2
= 21cm.
Area = (3.142 *21*21)cm^2
= 1386cm^2
To convert into metres:
=1386/100
=13.86m^2
A fair die is rolled twice. Let X denote the sum of the values. What is E[X|A] where A is the event that the first roll was a 6.
Answers
We will see that the expected value for X given that the first number is a 6, is:
E[X|A] = 9.5
How to get the expected value?
We know that X represents the sum of both values. The first value is already 6, so we have that fixed:
X = 6 + p
Now, remember that all the numbers in the dice have the same probability of rolling up, then the expected value of p is:
E(p) = (1 + 2 + 3 + 4 + 5 + 6)*(1/6) = 3.5
Then the expected value of X, given the event A.
E[X|A] = 6 + p = 6 + 3.5 = 9.5
So the expected value for X is 9.5
If you want to learn more about expected values, you can read:
https://brainly.com/question/15858152
Alexandra drew the logo shown on half-inch graph paper. Enter a rule that describes the translation
Alexandra used to create the shadow on the letter A
Answers
Answer:
(x+1, y-1)
Step-by-step explanation:
the original logo starts at 1in on the x-axis, the shadow is on 1.5in on the x-axis. menaing it moved 1 square to the right.
which means x+1
while the shadow went down 1 square on the y-axis
this means y-1
A rectangular table cloth measures 150cm by 200cm.the area of the table cloth in square meters is ?
Answers
Answer:
30,000
Step-by-step explanation:
150 x 200
Explanation:
To find the area you need to multiply the two numbers. Therefore, giving you your correct awswer.
Sayeed is buying a crate for his puppy. The crate is 20 inches long, 13 inches wide, and 16 inches high. What is the volume of the crate?
Answers
V = 4,160 cu in
Sorry if this was confusing, this was my first time answering a question, if I got it wrong I apologize, have a nice day/night!
Using the digits 1, 3, and 5 only once, write the greatest
and least three-digit numbers you can.
Answers
Answer:
Greatest: 531
Least: 135
Step-by-step explanation:
In order to make the greatest number, you want the highest number to be in the highest digits place.
In this case, 5 is the largest number
This is because having a number that is 500 is greater than a number that is 300 or 100.
Then, the next biggest number will be used for the next digit, which is 3, so 3 will be in the 10s place
Then the left over 1 will be in the single digits place, so the greatest number is
531
This is the same process as before, just instead of big numbers, you want little numbers
For the least number, you want the lowest number to be in the 100s place, which is 1
Then 3 is the next lowest number
and the left over is 5
So the least number you can make is:
135
Suppose you have a data set that includes the values 20, 30, and 50. If you add a fourth value to this data set, and after doing that the mean of the data set is 50, what was the value that you added? a. -10 c. 50 b. 40 d. 100 Please select the best answer from the choices provided A B C D
Answers
Answer:
D. 100
Step-by-step explanation:
Mean = Sum of all numbers divided by the count of all numbers
Mean = 50
Let say that the sum of all numbers = X
50 = X / 4
200 = X
X = (20+30+50) + The 4th Value
200 = 100 + 4th Value
The 4th Value = 100
Find the product. (6y - 2)2
A. 36y2 - 24y + 4
B. 36y2 + 24y = 4
C. 36y2 + 4
D. 12y2 - 16y + 4
Answers
Answer:
A. 36y² - 24y + 4Step-by-step explanation:
Use identity
(a ± b)² = a² ± 2ab + b²Here we have a = 6y, b = 2
(6y - 2)² = (6y)² - 2(6y)(2) + 2² = 36y² - 24y + 4Correct choice is A
15 POINTS ANSWER FAST!
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 14 inches, and the width QR is labeled as 7 inches. The side LM of the square is labeled as 7 inches.
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answers
Diagonal of the rectangle PQRS:
7^2 + 14^2 = SQ^2
SQ = 7 root 5
Diagonal of the square LMNO:
7^7 + 7^7 = OM^2
OM = 7 root 2
When dividing SQ or multiplying OM by 2, you don’t get the exact answer so she’s wrong
What the line measures
Answers
Can you please help
Answers
Answer:
used formula to find Area of parallelogram
area of parallelogram =b× h
Step-by-step explanation:
solution :
given ,
h = 7cm
b = 9 cm
we know ,
Area of parallelogram = b× h
=63cm²
The equation is :
Answer x =
Answers
Answer:
4x-11=73,
x=21
Step-by-step explanation:
11 subtracted from means -11
four times a number means 4(x) because x is the number
is = equals
so
4x-11=73
+11 +11
4x=84
/4 /4
x=4
I have a question whats 2+2
Answers
Answer:
22
Step-by-step explanation:
You add the to numbers together and the answer will be 22
I hope it helps! Have a great day!
Muffin ^^
Mike is buying a car for $24,300. He wants to make a maximum down payment of $3.000. TWo. deals are available, both for 48-month loans. In the first deal, with a factory rebate his down payment will be $1,000. His monthly loan payments would be $573 21 at 8.4% interest. In the second deal, he gets no rebate and makes a $3,000 down payment but his interest rate is 0.9% resulting in a $451.95 loan payment. a) What total amount will Mike pay with the first deal? b) What total amount will Mike pay with the second deal?
Answers
Answer:
1,000
Step-by-step explanation:
Rectangular rug has a perimeter of 3320 inches the length is 25 inches more than twice the width find the length and width of the rug
Answers
Answer:
length= 1115 inches
width= 545 inches
Step-by-step explanation:
The perimeter of the rectangular rug is the sum of the lengths of all its sides.
Start by defining the variables that we are going to use throughout our working.
Let the length and the width of the rug be L and W inches respectively.
Perimeter= 2(L +W)
Given that the length is 25 inches more than twice the width,
L= 2W +25 -----(1)
3320= 2(2W +25 +W)
Divide both sides by 2:
1660= 2W +W +25
1660= 3W +25
3W= 1660 -25
3W= 1635
Divide both sides by 3:
W= 1635 ÷3
W= 545
Substitute W= 545 into (1):
L= 2(545) +25
L= 1115
Thus, the length and width of the rug is 1115 and 545 inches respectively.
4 and 1/3 times 4 and 1/5
Answers
Answer:
The answer is 18.2 OR 18 1/5
Step-by-step explanation:
Hope it helps
a student sketched some art on an 8 inch x 10 inch piece if paper he wants to resize it to fit an 4 inch x 6 inch frame. What percent of the original sketch was still able to be included?
(someone asked this question but all the answers were wrong, so I am letting you know that the correct answer is 83.3%)
Answers
Answer:
83.3%
Step-by-step explanation:
can you please help me
Answers
Answer:
Angle ABC = 6x
Step-by-step explanation:
this is an isosceles triangle so the values of angle ACB and angle ABC are the same.
Factor 5x2y + 22xy – 15y.
Answers
Answer:
5y(x^2 - 3)
Step-by-step explanation:
Hope this helps :)
Jonathan wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift boxIf all the triangles are equilateral, how much wrapping paper did he use, in square meters
Answers
Jonathan will need a warping paper of 420.78m^2
Data;
slant height = 12mlength of sides = 10.39mSurface Area of an Equilateral TriangleTo find the amount of warping paper used, we can use the formula of surface area of an equilateral triangle since the triangle used here is an equilateral triangle.
[tex]Surface Area = base area + \frac{1}{2}(perimeter * slant height)[/tex]
Let's calculate the base area and perimeter of the triangle.
base area of an equilateral triangle is given as
[tex]B.A = \frac{\sqrt{3} }{4} a^2[/tex]
a = length of the sideLet's substitute the value and solve
[tex]B.A = \frac{\sqrt{3} }{4} a^2\\B.A = \frac{\sqrt{3} }{4}*10.39^2\\B.A = 46.74m^2[/tex]
The base area is 46.74m^2
Let's calculate the perimeter of the triangle
[tex]P = 3a\\[/tex]
Substitute the value into the equation and solve
[tex]P = 3a \\P = 3 * 10.39\\P = 31.17m^2[/tex]
We can proceed to substitute the values of the base area and perimeter of the triangle into the formula of the surface area of an equilateral triangle.
[tex]S.A = base area + \frac{1}{2}(perimeter * slant height)\\S.A = 46.74 + \frac{1}{2}(31.17*12)\\S.A = 46.74 + 374.04\\S.A = 420.78m^2[/tex]
The surface area of the equilateral triangle is 420.78m^2
Jonathan will need a warping paper of 420.78m^2
Learn more on surface area of an equilateral triangle here;
https://brainly.com/question/14886715
Answer:c
Step-by-step explanation:
X^2 - 2x = 8
Find the value of X
Answers
To find the solutions to the quadratic equations
⇒ factor the equation
[tex]x^2-2x = 8\\x^2-2x-8=0\\(x-4)(x+2) = 0[/tex]
Now to find the exact solutions, we have to set 'x - 4' and 'x + 2' equal to 0
[tex]x - 4 = 0\\x = 4\\\\x + 2 = 0\\x = -2[/tex]
Thus the solution to this problem is -2 and 4
Hope that helps!
Answer:
4 and - 2
Step-by-step explanation:
x² - 2x = 8
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x ( x + 2 ) - 4 ( x + 2 ) = 0
( x + 2 ) ( x - 4 ) = 0
x + 2 = 0
x = - 2
x - 4 = 0
x = 4
The values of x are - 2 and 4.
How do you solve this?
Answers
Answer:
22
Step-by-step explanation:
5x + 8 = 118
5x = 110
x = 22
A pencil has a mass of 25 grams of there are 8 pencils what is the total mass of all the pencils
Answers
Answer:
200g/0.2kg
Step-by-step explanation:
8 × 25g = 200g
The total mass of the pencil is 200 grams.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
A pencil has a mass of 25 grams.
there are 8 pencils.
Total number of pencils = 8
Mass of each pencil = 25 grams
Total mass of the pencils = 8 × 25 = 200 grams
Hence the total mass is 200 grams.
Learn more about Multiplication here :
https://brainly.com/question/29153616
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