Find the equation of the parabola with its focus at (–7,6) and its directrix at y = 4
Answers
The equation of the parabola with its focus at (–7,6) and its directrix at y = 4 will be (x + 7)² + 5.
How to illustrate the equation?By drawing the graph, it's can be depicted that the equation in this scenario is x² + 14x + 54.
Complete the square on the expression. This will be done by adding 49. This will be:
= x² + 14x + 7² + 54 - 49
= (x + 7)² + 5
Therefore, the equation of the parabola with its focus at (–7,6) and its directrix at y = 4 will be (x + 7)² + 5.
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Related Questions
PLEASE HELP!!! LOOK AT PIC PLEASE!!
Answers
Answer: C, D
Step-by-step explanation:
Acute angles of right triangles are complementary, and the sine of an angle is equal to the cosine of its complement.
what is the slope of (4, −6) and (0, 2)
Answers
Step-by-step explanation:
please mark me as brainlest
Please help me, I have more
Answers
Answer:
i dont have it the answer ofvthis
20 divided by tann(45°)
Answers
Answer:
20
Step-by-step explanation:
as we know
[tex] \tan {45}^{0} = 1 \\ [/tex]
20/ 1=20
is correct answer
Jennifer starts a new investment account that grows exponentially. Her financial advisor tells her
the initial investment of $50,000 grows at a rate of about 15% annually.
1. Determine a function, I(t), that determines Jennifer’s investment account balance after t years. For the exponential growth function, what are the “a” and “b” values? What do those values represent? (5 points for the explanation of “a” and “b” and 5 points for the function)
Answers
The exponential function is given by [tex]I(t) = 50000(1.15)^t[/tex]. The initial investment of $50,000 grows at a rate of about 15% annually.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the rate of increase per period.
Let I(t) represent Jennifer’s investment account balance after t years, hence:
a = 50000, b = 100% + 15% = 115% = 1.15
[tex]I(t) = 50000(1.15)^t[/tex]
The exponential function is given by [tex]I(t) = 50000(1.15)^t[/tex]. The initial investment of $50,000 grows at a rate of about 15% annually.
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1. How many ways can Grant arrange 3 of his 10 plants on a window ledge?
2. A parade organizer received 8 entries for floats. How many ways can he arrange 4 floats out of the 8 entries?
3. Express 4! in expanded form.
4. The number of ways 15 members of a 24-member club can be arranged. ( use permutation notation). PLEASE HELP ME!! and thankyou
Answers
The number of ways that Grant can arrange 3 of his 10 plants on a window ledge is 120 ways
How to solve the combination problem?The number of ways that Grant can arrange 3 of his 10 plants on a window ledge will be:
= 10!/(10! - 3!)3!
= 10!/7!3!
= (10 × 9 × 8)/(3 × 2)
= 120
When the parade organizer received 8 entries for floats, the number of ways that he can arrange 4 floats out of the 8 entries will be:
= 8!/(8! - 4!)4!.
= 8!/4!4!
= (8 × 7 × 6 × 5)/(4 × 3 × 2)
= 70
4! in expanded form will be:
= 4 × 3 × 2
= 24
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A typewriter types 750 words per hour. If she works for 8 hours a day, find the number of words she type
in a day.
Answers
Answer:
8,000 words
Step-by-step explanation:
If a typewriter types 750 words per hour and she types 8 hours a day she would write 8,000 words a day because 750 x 8 = 8,000.
Pineapples were packed in three large crates. for each crate, the weight of every pineapple in the crate was recorded. here are three box plots that summarize the weights in each crate. select all of the statements that are true, according to the box plots. (select all that apply. ) the weights of the pineapples in crate 1 were the most variable. the heaviest pineapple was in crate 1. the lightest pineapple was in crate 1. crate 3 had the greatest median weight and the greatest iqr. more than half the pineapples in crate 1 and crate 3 were heavier than the heaviest pineapple in crate 2
Answers
the weights of the pineapples in crate 1 were the most variable.The heaviest pineapple was in crate 1.More than half the pineapples in crate 1 and crate 3 were heavier than the heaviest pineapple in crate 2.What are the correct statements?
A box plot is used to study the distribution and level of a set of scores. The box plot consists of whiskers which measure the minimum and maximum numbers. The difference between these numbers is the range which measures variability.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the first quartile and the third quartile is the interquartile range.
For the first box plot:
Maximum number = 6Minimum number = 1.5Range = 6 - 1.5 = 4.5Median = 4First quartile = 3Third quartile = 4.5IQR = 4.5 - 3 = 1.5For the second box plot:
Maximum number = 3.5Minimum number = 1 Range = 3.5 - 1 = 2.5Median = 2First quartile = 1Third quartile = 2.5IQR = 2.5 - 1 = 1.5For the third box plot:
Maximum number = 5Minimum number =2.5Range = 5 - 2.5 = 2.5Median = 4First quartile = 3.5Third quartile = 4.5IQR = 4.5 - 3.5 = 1Please find attached the box plots. To learn more about box plots, please check: https://brainly.com/question/27215146
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Does anyone know the answer to this ?
Answers
Answer:
5182
Step-by-step explanation:
To figure out the mean of a number, you must add all of the numbers together and divide by the amount of numbers you added up.
To find the total sum, we just need to reverse this process.
We are already given the final number so all we have to do is multiply the mean by 100 and we have our answer of 5182.
Hope this helps :D
Anna and Brian share £24.50
in the ratio 2:5. How much
does each person get?
Answers
Brian gets £17.50
2+5=7
24.50 divide 7= 3.50
3.50 x 2 = 7
3.50 x 5 = 17.60
And to check if it’s correct do 17.50 + 7 = 24.50
what letter and the answer
Answers
The average amount of milk used for an orders of pancakes can be found by taking the total number of cups used for the 10 pancakes and take the answer divided by 10 (the amount of total pancakes)
We have 6 of 1/2 cups, 2 of 1/4 cups and 2 of 3/4 cups
So there are a total of [6•(1/2)]+[2•(1/4)]+[2•3/4]=5 cups for the total of 10 pancakes
Therefore, the average amount of milk used for an order of pancakes is 5/10=1/2 cups.
Mike buys a large goldfish for $22 and food for his new friend
that costs $3. He receives a birthday with $5 in the afternoon.
Then Mike had $7. How much money did he start the day off
with
Answers
Answer:
Mike started off the day with $27.
Step-by-step explanation:
Using the information given to us, we can set up an equation. Knowing that Mike ended the day with $7, and the amount of money that he spent and received can help us set up an equation. The amount of money that he started the day off with, is unknown, and recognized as x. [tex]7=x-22-3+5[/tex]
To solve this, we can simply solve the numbers that we know on the right hand side, to get this:
[tex]7=x-20[/tex]
Now, to get our final answer we must isolate x. We can do this by simply adding 20 to both sides. This cancels out the -20 on the right, and makes the 7 on the left become 27.
[tex]27=x[/tex]
Therefore, Mike started the day off with $27.
Find the value of k (k,3) and (2,3) is 5
A: 5
B: 6
C: 7
D: 8
Answers
Answer:
its option c (7)
Step-by-step explanation:
trust your bro
Answer:
[tex]C)~ 7[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~~ (x_1,y_1) = (k,3)~ \text{and}~ (x_2 ,y_2) = (2,3)\\\\\text{Distance,}~ \\\\~~~~~~~~d= \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\\\\\implies 5=\sqrt{(2-k)^2 + (3-3)^2}\\\\\implies 5=\sqrt{(2-k)^2 +0}\\\\\implies 5 = \sqrt{(2-k)^2}\\\\\implies 5=|2-k|\\\\\implies \pm 5=2-k \\\\\implies 2-k =5~~~~~~\text{or}~~~~~~~~2-k = -5\\\\\implies k = 2-5~~~~~~\text{or}~~~~~~~~k = 2+5\\\\\implies k = -3~~~~~~~~~\text{or}~~~~~~~~k = 7[/tex]
Select the elements in A.
A = {x: 10 < x < 30}
= {x:x is a square number}
Answers
Answer:
A= 4,5
Step-by-step explanation:
the required ans is above
Answer:
[tex]\{ 16, 25\}[/tex]
Step-by-step explanation:
[tex]x~ \text{is a perfect square and}~ 10 < x < 30 \\\\\text{The possible values of x are}:\\\\4^2 = 16\\\\5^2 = 25[/tex]
kelly recorded the amount of money she earned y for hours worked x in the table shown
Answers
Answer:
10
Step-by-step explanation:
4 overtime hours - regular pay + $40
Total $ earned - $160
Total hours - 12 hours (8 reg + 4 overtime)
$160 - $40 = $120
$120/12 = $10
Her regular pay is $10 per hour.
The vertices of an isosceles triangle are a(3, 6), b(7, 2), and c(4, 3). what is the equation of the triangle's line of symmetry?
y = x + 1
y = x - 1
y = x
y = -x + 1
Answers
Based on the calculations, the equation of the triangle's line of symmetry is equal to: B. y = x - 1.
How to determine the equation of the triangle's line of symmetry?First of all, we would determine the midpoint where the line of symmetry passes through points A and B:
Midpoint at point A = (3 + 7)/2 = 10/2 = 5.
Midpoint at point B = (6 + 2)/2 = 8/2 = 4.
Point D = (5, 4)
Mathematically, the standard equation of a line is given by y = ax + b.
D(5, 4); 4 = 5a + b ....equation 1.
C(4, 3); 3 = 4a + b ....equation 2.
Subtracting eqn. 2 from eqn. 1, we have:
1 = a
Next, we would find the value of b:
4 = 5a + b
4 = 5(1) + b
b = 4 - 5
b = -1.
Therefore, the equation of the triangle's line of symmetry is given by:
y = ax + b
y = x(1) + (-1)
y = x - 1.
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Which two details support the key idea that pollution is threatening marine life?
Marine Debris
Source: The National Oceanic and Atmospheric Association
Marine debris is a persistent pollution problem that reaches throughout the entire ocean and Great Lakes. Our ocean and waterways are polluted with a wide variety of marine debris, ranging from tiny microplastics, smaller than 5 mm, to derelict fishing gear and abandoned vessels. Worldwide, hundreds of marine species have been negatively impacted by marine debris, which can harm or kill an animal when it is ingested or they become entangled, and can threaten the habitats they depend on. Marine debris can also interfere with navigation safety and potentially pose a threat to human health.
All marine debris comes from people with a majority of it originating on land and entering the ocean and Great Lakes through littering, poor waste management practices, storm water discharge, and extreme natural events such as tsunamis and hurricanes. Some debris, such as derelict fishing gear, can also come from ocean-based sources. This lost or abandoned gear is a major problem because it can continue to capture and kill wildlife, damage sensitive habitats, and even compete with and damage active fishing gear.
Answers
Answer:
Worldwide, hundreds of marine species have been negatively impacted by marine debris, which can harm or kill an animal when ingested or they become entangled, and can threaten the habitats they depend on.
This lost or abandoned gear is a major problem because it can continue to capture and kill wildlife, damage sensitive habitats, and even compete with and damage active fishing gear.
Step-by-step explanation:
The key idea is that pollution is threatening marine life impact of marine life and the source of marine debris.
Marine debris is risky to a wide variety of marine animals. Animals can ingest debris, which can cause health problems or death, or they may get caught in debris, which can be equally harmful. In addition, marine debris harms the environments in which many species rely on being alive.
The greater part of marine garbage is caused by human activity on land. Marine debris is produced by poor waste management methods, dumping waste, stormwater discharge, and natural disasters such as tsunamis and hurricanes. Furthermore, ocean-based sources, such as wasted fishing gear, contribute to the problem.
The key idea is that pollution is threatening marine life impact of marine life and the source of marine debris.
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In a coin box there are 20-cent, 50-cent and $1 coins. The number of 20-cent coins is 2x, the number of 50-cent coins is y and the number of $1 coins is 4x. If the total value of the coins is $58.80, what is the total number of coins?
Answers
13 coins (50 cent)
24 coins (20 cent)
Select the correct answer.
Consider the function given below.
f(x)= |x-51 +2
Which of the following statements about the y-values of the graph of the function is true?
OA. The y-values are all less than or equal to 5.
B.
The y-values are all greater than or equal to 5.
OC.
The y-values are all less than or equal to 2.
D.
The y-values are all greater than or equal to 2.
Answers
Answer: The correct answer is D.
Step-by-step explanation: A and B are incorrect because you can plug in 5 for x to get 2, and there are multiple values that can be greater than 5. C is incorrect because you cannot reach lower than 2. Therefore, the correct answer is D.
The y values are all greater than or equal to 2.
The correct option is D.
Given,
Function : f(x) = |x − 5| + 2
Here,
A function is a law that relates a dependent and independent variable.
The function is
f(x) = |x − 5| + 2
The domain of the function is all negative and positive integers.
The range is all the possible function values, the function value will always be greater than or equal to 2.
At x = 5 , f(x) = 2
Therefore, the y values are all greater than or equal to 2. The correct option is D.
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Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750n. What is the percentage change in volume between cylinders A and B? Cylinder B is 50% smaller than cylinder A. Cylinder B is 75% smaller than cylinder A Cylinder B is 50% bigger than cylinder A Cylinder B is 200% bigger than cylinder A
Answers
Answer: Cylinder B is 50% bigger than cylinder A
Cylinder A volume:
= πr²h
= π(10)²(5)
= 500π
Cylinder B volume:
= 750π
Cylinder B bigger than Cylinder A by:
= (750π - 500π)/500π × 100 = 50%
[tex]\hrulefill[/tex]
Hence, cylinder B is bigger than cylinder A by 50%
Answer:
Cylinder B is 50% bigger than Cylinder A
Step-by-step explanation:
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Cylinder A
Given:
r = 10 inh = 5 inSubstituting the given values into the formula:
[tex]\implies \sf Volume_A=\pi (10)^2(5)=500\pi \:in^3[/tex]
Cylinder B
Given:
volume = 750 in³[tex]\implies \sf Volume_B=750\pi \:in^3[/tex]
Percentage Change
[tex]\begin{aligned}\sf percentage\:change & =\sf \dfrac{final\:value-initial\:value}{initial\:value} \times 100\\\\& = \sf \dfrac{Volume_B-Volume_A}{Volume_A} \times 100\\\\& = \sf \dfrac{750\pi-500\pi}{500\pi} \times 100\\\\& = \sf \dfrac{1}{2} \times 100\\\\& = \sf 50\%\end{aligned}[/tex]
Therefore, Cylinder B is 50% bigger than Cylinder A
Order these numbers from least to greatest. 6.2052, 6.2, 6.75, 6.705
Answers
Answer:
6.2 , 6.2052 , 6.705 , 6.75
Step-by-step explanation:
Least to Greatest!
A triangle has a base of 53 and a height of 21. What is the hypotenuse?
Answers
Answer:
Approximately 57
Step-by-step explanation:
The Pythagorean theorem says that a^2+b^2=c^2, where a and b are the base and height, while c is the hypotenuse. 53^2+21^2=2809+441=3250. The square root of 3250 is 57.008771255, which rounded to the nearest tenth is 57. Hope this helped!
Answer:
57.008771255 or 57
Step-by-step explanation:
53^2+21^2=57.008771255^2
In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?
Answers
Therefore, 110 calories are in 1 serving of milk.
Given, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda.
Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk.
Marian consumes 510 calories by drinking 3 servings of milk and 1 soda.
What are Linear Programming problems?Linear programming, commonly known as LP, is a straightforward technique for representing complex real-world interactions by means of a linear function.
Now,
Let the calories in one serving of milk be x
Let the calories in one serving of juice be y
Let the calories in one serving of soda be z
For Joe, the equation to show the amount of calories is
2x + y + z = 530 -----(1)
For Darius, the equation to show the amount of calories is
x + 2y = 370 ------(2)
For Marian, the equation to show the amount of calories is
3x + z = 510 ------(3)
Now, y=370/2-x/2 and z=510-3x substitute in the equation 2x + y + z = 530.
2x+185-0.5x+510-3x=530
⇒695-1.5x=530
⇒1.5x=165
⇒x=110 calories
Hence, 110 calories are in 1 serving of milk.
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Which expression is equivalent to -6.50 -5.1 + 2.3c - 1.8?
Answers
Answer:
-13.4+2.3c
Step-by-step explanation:
Add the like terms.
-6.5-5.1-1.8=-13.4
-13.4+2.3c
Hope this helps!
If not, I am sorry.
What is 4 ( x − 1 ) ≥ 2 x + 6 as an improper fraction?
Answers
Answer:
18/5
Step-by-step explanation:
you have to times then divide
-4.625,-5.2,-4 4/5, -4 8/11 order least to greatest
Answers
Answer:
-4.625, -4 8/11, -4 4/5, -5.2
Step-by-step explanation:
-4 8/11 = -4.72727272723
-4 4/5 = -4.8
Make c the subject:
A=b+cd
Answers
All you have to do is this! Please mark me as brainliest
Answer:
C = A/d - b/d or C = (A - b)/d
Step-by-step explanation:
A = b + cd
A - b = cd
A/d - b/d = c
A motorbike was discounted by 10% and sold for $5220. What was the cost of the motorbike before the discount was applied?
Answers
So the motorbike was discounted by 10% and sold for $5220, that means $5220 is 90% of x. Let x be the original value. Now, set up a proportional equation. 5220/90=x/100. Multiply 5220 by 100, that will give you 522,000. Now let’s divide that by 90, and the answer will be $5800.
Simplify to create an equivalent expression. 2(-n-3)-7(5+2n)
Answers
Answer:
-16n-41
Step-by-step explanation:
Answer:
-16n - 41
Step-by-step explanation:
(2 • (-n - 3)) - 7 • (2n + 5)
-n - 3 = -1 • (n + 3)
-2 • (n + 3) - 7 • (2n + 5)
-16n - 41 = -1 • (16n + 41)
Use the leading term for your answer
-16n - 41
Given limit of f (x) = 4 as x approaches 0. what is limit of one-fourth left-bracket f (x) right-bracket superscript 4 baseline as x approaches 0? 0 4 64 128
Answers
The limit of the given function if [tex]\lim_{x \to 0} f(x)=4[/tex] is 64
Limit of a functionGiven the following limit of a function expressed as;
[tex]\lim_{x \to 0} f(x)=4[/tex]
We are to determine the value of the function
[tex]\frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]
This can also be expressed as
[tex]\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64[/tex]
Hence the limit of the given function if [tex]\lim_{x \to 0} f(x)=4[/tex] is 64
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