The equation of the ellipse in standard form with vertices along the major axis at (0, 1) and (0, -9) and the foci of the ellipse at (0, -1) and (0, -7) is (y+4)²/16 + x²/25 = 1.
How to derive an equation of the ellipse based on the information of the major axis and foci
The location of the center of the ellipse is the midpoint of the line segment between the ends of the major axis, that is:
(h, k) = 0.5 · (0, 1) + 0.5 · (0, -9)
(h, k) = (0, -4)
The length of the major semiaxis (b) is 5 and the distance between the center and any of the foci (c) is 3. Then, the length of the minor semiaxis is:
[tex]a = \sqrt{b^{2}-c^{2}}[/tex] (1)
a = 4
Lastly, we substitute all the variables and conclude that the equation of the ellipse is (y+4)²/16 + x²/25 = 1. [tex]\blacksquare[/tex]
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Answer:
A=10
Step-by-step explanation:
Got it right on Edge2022
10 points need this answer ASAP
Answer:
C
Step-by-step explanation:
Y=2(-1)+3
y=-2+3
y=1
true
Where do 2x - y = 4 and 4x + y = 9 intersect?
Answer: They intersect at [tex](2\frac{1}{6}, \frac{1}{3} )[/tex]
Step-by-step explanation:
We can solve this system of equations through elimination
Add (4x+y=9) with (2x-y=4)
[tex]4x+y=9\\+2x-y=4\\=\\6x+0=13[/tex]
Now that y is canceled out we can solve for x
[tex]6x=13\\\frac{6x}{6}=\frac{13}{6} \\x=2\frac{1}{6}[/tex]
Now sub back x into one of the original equations to find the value of y
[tex]4(2\frac{1}{6} )+y=9\\8\frac{2}{3} +y=9\\8\frac{2}{3}-8\frac{2}{3}+y=9-8\frac{2}{3}\\y=\frac{1}{3}[/tex]
22. The population, P, of the city of Hazelton has grown according to the mathematical model
P = 65,000(1.075)', where t is the number of years since 2005.
a) At what percentage is the population growing? [1 mark]
Answer:
7.5%
Step-by-step explanation:
The exponent 't' is applied to 1.0751.075 is the rate at which it increasesDecimal → % = x 1001.075 × 100 = 107.5%107.5% - 100% = 7.5%The line plot shows the heights of the players on a basketball team, in inches.
Part B
he next year, a player who is
71
inches tall is replaced by a player who is
73
inches tall. Otherwise the team remains the same. Is
74
an outlier the next year? Explain.
A: based on the given dot plot are: statements B, D, and E.
B: A. No. 74 is not an outlier because it is not different from the other heights in the dot plot.
What is a Dot Plot?In a dot plot, frequencies of each data point is represented as dots.
Part A:
Thus, in the dot plot given:
Players of 70 1/2 in. tall and above are 7 in number. This is half of the number of the total players. (option B is true).
Players with height of 69 1/2 in. (3 players) are more than those that are 70 in. tall (1). (option A is not true).
One of the player is 68 1/2. (option C is not true).
Four of the players are 74 in. tall (option D is true).
The team has 6 different heights as shown in the dot plot given (option E is correct).
Therefore, the statements that are correct based on the given dot plot are: statements B, D, and E.
Part B:
If a player of 73 in. tall replaces a player of 71 in, tall, 73 is close to 74.
Therefore, we can conclude that: A. No. 74 is not an outlier because it is not different from the otehr heights in the dot plot.
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Origami paper is always in the shape of a square. If you take the top corner of either side of a 9 x 11-inch piece of paper and fold it to the lower opposite side and trim off the excess paper, this creates the square that we need. Then fold the top corner to the opposite corner to create a diagonal, which is a typical first step to most origami designs. What are the dimensions of your square? What is the length of the diagonal? Write your answer in exact and decimal form.
Answer:
Dimensions are nine by nine, the diagonal is the square root of 162.
Step-by-step explanation:
The resulting square will have the same width as before, with a height to match, (9,9) The diagonal can be found using the pathagyreon theorom.
9^2 + 9^2 = x^2.
The dimensions of the square would be nine by nine, the diagonal is the square root of 162.
The square will have the same width as before, with a height to match, (9,9)
The diagonal can be found using the Pythagorean theory.
9^2 + 9^2 = x^2.
What is the Pythagorean theorem?This theorem states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
What is the Pythagorean theorem and what is it used for?The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle.
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Your food costs are $2,000.
Your total food sales are $8,500. What percent of your food sales do the food costs represent?
Answer:
23.53%
Step-by-step explanation:
Given :
food costs = $2,000total food sales = $8,500Solving :
Food costs / Total Food Sales2000/85004/170.235323.53%Please help asap!
Which of the graphs has the greatest rate of change?
A) Graph A
B) Graph B
C) Graph C
D) Graph D
Answer:
B) Graph B
Step-by-step explanation:
find the missing length of a rectangle with a width of 7b^3 and an area of 77a^8b^8
Answer:
Step-by-step explanation:
Use the volume formula to find the volume of the prism.
help!!
20 points!!
Answer:
B. 9 cubic units
Length×width×height
What does 5 in = how many feet/foot?
Answer:
5/12
Step-by-step explanation:
Since 12 inches is one foot, the number has to be a fraction number. The answer is 5/12 feet.
What number can be divided into 2 equal groups whit out a reminder
all even numbers
hope it really helps...!!!
Answer:
all even numbers. because when divisible by two there is no reminder
Help help ASAP math math
Answer:
-25
Step-by-step explanation:
f(-12) means x = -12
so you just plug it in the equation and solve for x
[tex]f(x) = 3(-12)+11\\f(x) = -36+11\\f(x) = -25[/tex]
answer? i give vrainlist
Answer:
3 I think
Step-by-step explanation:
1/3 opposite is 3/1 or 3
At a dance school, 18 students attend class on Tuesday. Six of those students are boys. What is the ratio of girls
to total students attending class on Tuesday?
Answer:
= 12 : 18
Step-by-step explanation:
• 18 - 6 = 12
• girls = 12
• total students = 18
• girls to total students
= 12 : 18
Answer:
12:18
Step-by-step explanation:
HELP QUICKLY PLEASE
31. Tony is borrowing $10 from his mom every week for buying more toy cars for his Hot Wheels collection. How much money does he owe at the end of 7 weeks?
33. Linda borrowed $7 a day until she had borrowed a total of $56. For how many days did she borrow money?
34. The temperature increased 2o per hour for six hours. How many degrees did the temperature raise after six hours?
35. Max lost 24 pounds in 8 weeks on his new weight-loss plan. What was his average change in weight per week?
Answer:
the answer to 33 is 8 7×8=56 or 56÷7
What is the solution to 3x/4 =7/3
Answer:
[tex]x=\frac{28}{9}[/tex]
Step-by-step explanation:
[tex]\frac{3x}{4} =\frac{7}{4}[/tex]
[tex]\Longleftrightarrow \left( 3x\right) \times 3=7\times 4[/tex]
[tex]\Longleftrightarrow 9x=28[/tex]
[tex]\Longleftrightarrow x=\frac{28}{9}[/tex]
f(x) =2x^3 + 3x^2 - 7x + 2 g(x) = 2x-5 find (f+g)(x)
Answer:
Step-by-step explanation:
Remark
The way this is written, the notation is directing you to add the right hand sides of the two given polynomials.
Givens
f(x) = 2x^3 + 3x^2 + 7x + 2
g(x) = 2x - 5 Add
Solution and Answer
Answer: (f + g)(x) = 2x^3 + 3x^2 + 9x -3
Be careful with that - 5. The result is -5 + 2 = - 3
Answer: It's (f+g)(x)=2x^3+3x^2-5x+3
Step-by-step explanation: I just did it.
Which expression correctly shows the difference between the product of 8 and 5 and the sum of 8 and 7?
O 8 x (5-8) +7
O (8 x 5) + (8 + 7)
O 8x (5+8)+7
O (8 x 5) - (8 + 7)
feel
Wacom
aer
Answer:
D. (8 x 5) - (8 + 7)
Step-by-step explanation:
Evaluate the word problem.
The difference (we will be subtracting.) between the product of 8 and 5 (8 * 5) and the sum of 8 and 7 (8 + 7)?
So set it up.
(8 * 5) - (8 + 7)
This is the correct answer because we are taking the difference of the product of 8 and 5 and the sum of 8 and 7.
how is 0.136 written as a fraction in simpilist form. is my answer correct?
Answer:
Yes you are
Step-by-step explanation:
case as) the repeating decimal is 36
Multiply x by a power of , one that keeps the decimal part of the number the same:
Subtract from
The repeating decimals should cancel out
solve for x
Divide by both sides
Simplify
Divide by both numerator and denominator
therefore
the answer case a) is
The fraction in easyiest form is
case b) the repeating decimal is 136
Let
Multiply x by a power of, one that keeps the decimal part of the number the same:
Subtract from
The repeating decimals should cancel out
solve for x
Divide by both sides
-----> irreducible
therefore
the answer case b) is
The fraction in simplest form is
136/999
Which of the following statements is not true?
- the median is not affected by outliers as much as the mean.
- the mode is the most frequently occurring value(s) in a data set.
- the best measure of central tendency depends on the data set.
- the mean is the middle value of a data set.
Answer:
the mean is the middle value of the data set.
Step-by-step explanation:
the mean is the average of all the data, so i would say the last statement is incorrect.
Answer:
the mean is the middle value of a data set
1. you make a deposits of a 467,00 into an ordinary annuity earning 5.75.7. compounded moyenthly, how many deposits must you make so that you will have atleast & 196.000?
Which expression is equivalent to StartFraction 5 y cubed Over (5 y) Superscript negative 2 Baseline EndFraction?
y5
y6
125y3
125y5
Answer:
125y3
Step-by-step explanation:
12x5=y
y3/2 = y26 - 5 =y
Answer:
D should be right
Step-by-step explanation:
3. If a = 2, b = -5 and c = 3, determine the value of b(a)+c
How to calculate percentage profit?
Answer:
Profit/Cost Price*100
Step-by-step explanation
Calculated by working out the difference between the cost price and the selling price, which is then divided by the original price and multiplied by 100, giving you a percentage. Cost price is the original price for good which the retailer has bought for.
Maya is building a model of her city's downtown area. She is constructing part of an office building, as shown below. Each cube has an edge length of 1/6 foot.
The volume of the model building is cubic foot?
A.2/3
B.1/36
C.1/4
D.1/9
E.1/2
Answer:
B I think my bad if its wrong
Answer: the answer is e
Step-by-step explanation: 1 over 6 multiplied by 9 cubes will give 1.5 which is 1 over 2 . 4 cubes are the length and 2 the width and 3 height s o equal 9 . 9 times 1 over 6 equals 1.5 which is the last one. hope it helps buddy .
Please please give brainliest !!! Thanks .
What is the equation to this graph using Y=MX+B. Show Work.
Answer:
y = 2x + 9
Step-by-step explanation:
Y = mx + b indicates slope-intercept equation.
"b" represents y -intercept/beginning.
"mx" represent slope/constant of variation/rate of change
x-intercept represents the end of the graph. (in stories using money its the ending amount).
The y-intercept is always when the x-value is 0. The point of the y-intercept is on the y-axis. The line on the graph starts at the point (0,9). It can be located on the point right above the number labeled under the 9 which is 8. Since the x-value is 0,
The y-intercept is 9.
To find the slope, we have to find two points on the graph to use.
Two points on the graph are:
(1.5, 13) , (2, 14)
Using the slope formula:
y2-y1/x2-x1
Plug in:
14-13/2-1.5
Complete:
1/0.5
divide:
The numbers in 1 divided by 1/2 are labeled below:
1 = whole number
1 = numerator
2 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
1 x 2/1 = 2/1
Thus, the answer to 1 divided by 1/2 in fraction form is:
2/1
To make the answer to 1 divided by 1/2 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
2 / 1 = 2
The answer is rounded to the nearest two decimal points if necessary.
2/1 is an improper fraction and should be written as 2.
So now that we have the y-intercept and slope:
Y-intercept: 9
Slope: 2
Equation: y = 2x + 9
Terms: Linear Equations 8th Grade
What is the perimeter of a rectangle 5cm by 8cm?
Answer:26
Step-by-step explanation:
Let's Apply Solve for the surface area of the following figures.
Answer:
1. 864in^2
2. 331.2581cm^2
3. 201.0619m^2
4. 516.548m^2
5. 2827.4334mm^2
The data set below shows the weights of some puppies, in pounds, at a kennel:
10, 11, 12, 12, 13, 13, 14, 15, 15
Which histogram represents the data set?
Answer:
The second histogram. and this is because of the arrangement of data which is the puppies
Answer:
I think its A)
Step-by-step explanation:
What’s the following sum?
[tex] \huge{ \orange{ \boxed{ \bold{6 \sqrt{5} }}}}[/tex]
EXPLAINATION :
By following the rule in finding the sum or difference of similar radicals
[tex] \green{a \sqrt{c} \: + \: b \sqrt{c} \: = (a + b) \sqrt{c} }[/tex]
Answer:
3.73
Step-by-step explanation: