Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(0, −8) and line y = 8.
Answers
Answer:
-1/32 × x
Step-by-step explanation:
let's define and identify the correct markers of the correct parabola.
so, we have the focus point F (0, -8).
we have the directrix y = 8.
that means the the vertex point (the middle between the focus and the directrix) is (0, 0).
a parabola is turning away from the directrix. the vertex here is below the directrix, so the parabola is opening downwards and has therefore a negative factor of x.
so, we can rule out the 2 positive answer options.
to decide between the other 2, let's use a value of x and see, if the point is equidistant to the focus and the directrix.
e.g. x = 1
so,
y = -1/8 × x²
gives us y = -1/8 for x = 1
that means the point is (1, -1/8).
the distance to the focus (0, -8) is
(1 - 0)² + (-1/8 - - 8)² = 1 + (7 7/8)² = 1 + (63/8)² =
= 64/64 + 3969/64 = 4033/64
the distance to the directrix is the distance to the point (1, 8) as the point on the directrix must have the same x value.
so, the distance (1, -1/8) to (1, 8) is
(1 - 1)² + (-1/8 - 8)² = 0 + (-65/8)² = 4225/64
that is not equal to the distance to the focus.
so, let's try
y = -1/32 × x
the point for x = 1 is (1, -1/32)
distance to focus
(1, -1/32) to (0, -8) = (1-0)² + (-1/32 - -8)² = 1 + (255/32)² =
= 1024/1024 + 65025/1024 = 66049/1024
distance to directrix
(1, -1/32) to (1, 8) = (1-1)² + (-257/32)² = 66049/1024
which is the same distance as to the focus.
so, y = -1/32 × x is the right answer.
FYI - for an actual distance I would have to create the square roots of the numbers used here.
but since we only needed to see, if distances are equal or not, it was sufficient to check if the squares of the distances are equal or not.
Related Questions
Solve for x.
x−8=−518
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
The value of x in the equation, as a mixed number in simplest form is solved as: x = 2 2/9.
How to Solve an Equation?To solve for a variable, say x, in an equation, it means to find the value of x that will make the equation true. Do this by isolating x in the equation.
Given the equation:
x/−8 = −5/18
Cross multiply
18x = (-5)(-8)
18x = 40
Divide both sides by 18
x = 40/18
x = 2 2/9.
Therefore, the value of x in the equation, as a mixed number in simplest form is solved as: x = 2 2/9.
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what is the definition of an average?
Answers
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Answer:
Average: a calculated "central" value of a set of numbers
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How to find it in the average:
Add all of the numbers given, then divide by the number of digits.
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Example:
Question 1. ) Find the average of the digits.
10, 12, 7, 9, 14, 8, 5, 19
Step 1. Add all of the numbers - 70
Step 2. Count how many different numbers there are - 8
Step 3. Take your first answer and your second and divide them
Step 4. 70 ÷ 8 = 8.75 So 8.75 would be the average
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The equation y=19x relates proportional quantities x and y. What is the value of y when x is 4?
Answers
Answer:
y = 76
Step-by-step explanation:
Since x = 4
Substitute:
y = 19(4)
Multiply the numbers
y = 76
~Lenvy~
What is the range of this data set? 12.5, 10.1, 11.4, 17.3, 17.9, 12.1, 14.1, 14.4, 20.4, 19.1, 12.4, 18.9
Answers
The range of a dataset is the distance between the maximum value and the minimum value. The range is found by subtracting the minimum value from the maximum value: maximum - minimum = range.
Maximum value of this dataset = 20.4
Minimum value of this dataset = 10.1
20.4 - 10.1 = 10.3
Range = 10.3
Hope this helps!
Answer:
10.3
Step-by-step explanation:
Given set of values
12.5, 10.1, 11.4, 17.3, 17.9, 12.1, 14.1, 14.4, 20.4, 19.1, 12.4, 18.9Maximum value
The number with the greatest value in the data set⇒ 20.4Minimum value
The number with the least value in the data set⇒ 10.1Range
Maximum value - Minimum value20.4 - 10.110.3The aspect ratio of the television screen is 16:9 and it is 63cm High. What is its width?
Answers
Leo is testing different types of greenhouse material to determine which type is most effective for growing strawberry bushes. He purchases two different brands of tarps from a local store. Leo applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial shade. He waters both areas daily. At the end of the study, Leo concludes brand A is more effective in growing strawberry bushes. Is Leo's conclusion valid? please explain how and why so I can understand
Answers
For Leo conclusion to be valid, he should apply both brand A and B to area receiving same amount of sunlight.
What is bias?Bias is an error due to sampling or testing by selecting or preferring one outcome over others.
Leo applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial shade. This shows that Leo is bias.
For Leo conclusion to be valid, he should apply both brand A and B to area receiving same amount of sunlight.
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Answer:
His conclusion is not valid.
He should have put both tarps over the area of the yard that receives full sunlight. So that the experiment can be valid.
Step-by-step explanation:
Write this ratio as a fraction in simplest form without any units six weeks to 18 days
Answers
Answer:
7/3
Step-by-step explanation:
To write the ratio with no units. we need to have both parts of the ratio in the same units. That way the units cancel.
__
6 weeks : 18 days = (6×7) days : (6×3) days = 7 : 3
The ratio as a fraction is ...
(6 weeks)/(18 days) = 7/3
529 as a desmil number
Answers
Answer:
529.000
Step-by-step explanation:
A decimal number is a number whose whole number and fraction part are separated by a decimal point.
529 represented as a decimal is 529.000
Also, you can add as many zeros as you want behind the decimal point.
Please pick as brainliest!
Aja made a 20% down payment on a house and was approved for a $185,000 mortgage. Therefore, she should expect her closing costs to be about $3,700 to $12,950.
O A True
O B. False
Answers
If Aja was approved for a $185,000 mortgage is true Aja's closing costs are between $3,700 and $12,950.
What are closing costs?This is the amount of money paid for the mortgage settlement or closing.
How to calculate the closing costs?The closing costs are equal to 2-7% of the cost of the loan.
What are Aja's closing costs?185,000 x 0.02 = $3700 (2%)
185,000 x 0.07 = $12,950 (7%)
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3/4x+1/3=1/2x+5
2
3
6
12
Answers
Answer:
12 because it is a common factor of the denominators
Answer:
178
Step-by-step explanation:
18. Find the present value of a deferred annuity of ₱ 30,000.00 at the end of every year for 10 years. The first payment of a mother will be done at the end of the second year, and the money is compounded at 3% annually. a. ₱ 244,354.12 b. ₱ 248,452.51 c. ₱ 278,520.14 d. ₱ 291,245.18
Answers
Answer:
₱ 248,452.51
Step-by-step explanation:
₱ 248,452.51
40 feet in one hour = what speed in inches per second
Answers
Answer:
1728000
Step-by-step explanation:
40 feet is 480, then convert hour tom minute (times 60) then times 60 again to convert minute to second (times 60)
Hope this helps!
jan saw 9 full moons in 252 days write each statement as a rate
Answers
Question 2 of 10
Classify the following triangle. Check all that apply.
9
11.4
I A. Right
B. Obtuse
C. Isosceles
DD. Acute
O E. Scalene
OF Equilateral
SUBMIT
Answers
Hello, it seems your questions didn't upload correctly. Are you able to resend it?
help The area of a square
Answers
Answer:
[tex]2551\dfrac{1}{2}[/tex]
Step-by-step explanation:
[tex]\bf l = 20\dfrac{\sf 1}{4} \ in = \dfrac{81}{4} \ in[/tex]
[tex]\bf w = 10\dfrac{1}{2} = \dfrac{21}{2} \ in\\\\\\h = 12 \ in[/tex]
Volume of rectangular prism = l*w*h
[tex]= \dfrac{81}{4}*\dfrac{21}{2}*12\\\\\\= 81 *\dfrac{21}{2}*3\\\\\\= \dfrac{5103}{2}\\\\\\= 2551 \dfrac{1}{2} \ cubic \ inches[/tex]
Answer:
[tex]\sf 2551\frac12 \ cubic \ inches[/tex]
Step-by-step explanation:
volume of a cuboid = width × length × height
Given:
[tex]\sf width=10\frac12 \ in[/tex][tex]\sf length=20\frac14 \ in[/tex][tex]\sf height=12 \ in[/tex]Substituting given values into the formula for volume:
[tex]\sf \implies volume=10\frac12 \times 20\frac14 \times 12[/tex]
[tex]\sf =\dfrac{21}{2} \times \dfrac{81}{4} \times \dfrac{12}{1}[/tex]
[tex]\sf =\dfrac{21 \times 81 \times 12}{2 \times 4 \times 1}[/tex]
[tex]\sf =\dfrac{20412}{8}[/tex]
[tex]\sf =2551\frac12 \ in^3[/tex]
The diameter of a circle is 8 miles. What is the angle measure of an arc 3 miles long?
Answers
Answer:
[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]
Step-by-step explanation:
Formulae
[tex]\sf radius (r)=\dfrac12 d[/tex]
(where d is the diameter of a circle)
[tex]\sf arc \ length =r\theta[/tex]
(where r is the radius and [tex]\theta[/tex] is measured in radians)
Calculation
Given:
[tex]\sf radius (r)=\dfrac12 \cdot 8=4 \ mi[/tex]arc length = 3 miSubstituting these values into the formula for arc length:
[tex]\implies \sf 3 =4\theta[/tex]
[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]
To convert radians to degrees use
[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]
[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]
Now
[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]
[tex]\\ \rm\rightarrowtail l=r\theta[/tex]
[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]
[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]
A grocer wants to mix two kinds of candy. One kind sells for $1.15 per pound, and the other sells for
$2.75 per pound. He wants to mix a total of 24 pounds and sell it for $1.30 per pound. How many
pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
Answers
Hey there!
This grocer is mixing two kinds of coffee. I always love the smell of coffee!
We will say that x sells for $1.15 per pound and y sells for $2.75 per pound.
Altogether there are 24 pounds of coffee he is selling.
The algebraic equation would be x + y = 24
At $1.30 per pound, he will make 24 * $1.30 = $31.2
So, how many of the x and y kinds of coffee should he use to make the $1.30 per pound mixture which will net him $31.2?
The algebraic equation would be 1.15x + 2.75y = 31.2
We now have two equations :
x+y = 24
1.15x + 2.75y = 31.2
Substituting x= 24 -y in the second equation gives us
1.15(24-y) + 2.75y = 31.2
27.6 - 1.15y + 2.75y = 31.2
27.6 + 1.6y = 31.2
1.6y = 31.2 - 27.6
0.3y= 3.6
y= 2.25
x + y = 24
x + 2.25 = 24
x = 24 -2.25
x = 21.75
If y=2.25, then x= 21.75 as well.
So, he will use 21.75 pounds of the $1.15 per/lb one and another 2.25 pounds of the $2.75per/lb one.
~Done~
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answers
Answer:
143
Step-by-step explanation:
I'm not sure if this is correct but this is what I came up with:
all angles combined must add to 360
125+55+37= 217
360-217=143
As you move to the
on a number line the values of the numbers
Which choice best completes the sentence?
right; increase
right; decrease
left; increase
left; remain the same
Help please I’m stuck on this question!
Answers
Answer:
Based on the argument behind the correctness of the assumption is impossible, so we rule that the assumption is correct, now is the answer
The second answer from above
Which of the following is NOT an integer? A. 8/2 B. 1/4 C. 0 D. -5
Answers
Answer:
B. 1/4
Step-by-step explanation:
Even though A is a fraction it is also an integer (4)
Help help help help help
Answers
[tex]\mathbf{m}=-\frac{1}{2}[/tex]
Step-by-step explanation:⇒ Find the slope of the line that is perpendicular to y = 2x + 7 :
↓
[tex]\mathbf{m}=-\frac{1}{2}[/tex]
I hope this helps you
:)
slope intercept form:
y = mx + b (where m is slope)
since the slope of the first line is 2
the perpendicular line’s slope must be -1/2
I hope this helps and is the BRAINLIEST!
Good luck with your studies!
F(x)=4x^2 and g(x)=x+1, find (f x g)(x)
Answers
Answer:
option b
Step-by-step explanation:
It is option b
Your answer is 4(x+1)²
Answer:
B
Step-by-step explanation:
Given functions:
[tex]f(x)=4x^2[/tex][tex]g(x)=x+1[/tex][tex](f \circ g)(x) & =f[g(x)][/tex]
This means substitute the x of f(x) with the function g(x).
[tex]\implies f[g(x)]=4(x+1)^2[/tex]
Jerry poured water to a height of 1 feet into a
new aquarium with dimensions shown below.
2 ft.
1 ft.
Water
2
3 ft.
One cubic foot of water weighs approximately
62 pounds. What is the weight of the water that
Jerry put in the aquarium?
B. 465 pounds
A. 403 pounds
C. 558 pounds
D. 744 pounds
Answers
Since 1 cubic feet = 62 pounds, the weight of the water that Jerry put in the aquarium is 558 pounds
How to calculate the volume/weight of waterWe have to find the volume of water in the aquarium.
Recall the shape of the aquarium is a rectangular prism. Therefore,
volume = lwh
where
l = lengthw = widthh = heightTherefore,
l = 3 ft
w = 2 ft
h = 1.5 ft
volume = 3 × 2 × 1.5
volume of water = 9 ft³
Therefore,
1 ft³= 62 pounds
9 ft³ = ?
cross multiply
weight of water = 9 × 62
weight of water = 558 pounds
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SECTION (A) (Answer ALL questions) a) Iff:R → R is defined by f(x) = x2 +3, find the function g such that (fog)(x) =9x2 – 12x+7.
Answers
Answer:
g(x)=3x--2
Step-by-step explanation:
please mark me as brainlest
I really need Help if u give right answer u get brainliest
Answers
Answer:
Step-by-step explanation:
The measure of an angle is 74.4°. What is the measure of its complementary angle?
Answers
Answer:
15.6
Step-by-step explanation:
complementary angles sum up to 90
90-74.4=15.6
therefore the measure of it's complementary angle is 15.6
Tomas used 3 and one-third cups of flour and now has 1 and two-thirds cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f + 3 and one-third = 1 and two-thirds
f minus 3 and one-third = 1 and two-thirds
3 and one-third f = 1 and two-thirds
f divided by 3 and one-third = 1 and two-thirds
Answers
Answer : B
Explanation :
f - 3 and one third = 1 and two thirds goes with the word problem.
Answer: B
f - 3 and one third = 1 and two thirds
In how many ways can you spell the word FOOT in the grid below? You can start on any letter F, then on each step you can step one letter in any direction (up, down, left, right, or diagonal).
Answers
There are six ways in which the word FOOT may be spelt starting at any letter.
What is combination?The term combianntion offers a plausible way to carry out a selection as long as we do not give preference to the order in which the selection is made. In this case, we are told that we can start from any letter therefore order is not important.
There are four letters in FOOT and one letter is repeated twice therefore;
4C2 = 4!/(4-2)! 2!
4C2 = 4 * 3 * 2!/2! * 2 * 1
4C2 = 12/2
4C2 = 6
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When asked to factor the trinomial 6x^2 - 18 + 12, a student gives the answer (x - 2)(x - 1). What is the one thing wrong with this answer?
A. 6 is also a factor of this trinomial
B. The minus signs should always be plus signs
C. There is nothing wrong with the answer
D. The factors are not simplified
Answers
Answer:
the answer is C which one is this
What is 1 * 2 = + * 1 = + + 2 2 + 1 8 5 / 9
Whoever answers it gets grevious
Answers
Answer:
Can you use a specific question please
Step-by-step explanation:
Answer: = 17 7/
Step-by-step explanation:
8 1/5 + 9 1/2 = 177/
10
= 17 7/