An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
Which equation represents this ellipse?
Answers
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex] is the equation of the ellipse.
What is the equation of an Ellipse ?The equation of an ellipse is given by
[tex]\rm \dfrac{ (x-h)^2 }{a^2} + \dfrac{ (y-k)^2}{b^2} = 1[/tex]
here
(h,k) is the center
c = is the distance between center to focus
c = [tex]\rm \sqrt{a ^2 - b^2}[/tex]
as the a = 10 , component length
and c = 8
8 = [tex]\rm \sqrt{10 ^2 - b^2}[/tex]
8² = 10² -b²
b² = 36
b = 6
h = 0 ,k = 0
Substituting the values given
[tex]\rm \dfrac{ (x-0)^2 }{10^2} + \dfrac{ (y-0)^2}{6^2} = 1[/tex]
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex]
Therefore the equation of the ellipse has been determined.
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Related Questions
Which expression is equal to the equation?
Answers
Answer: [tex]-11\sqrt{7}[/tex]
Step-by-step explanation:
To find the expression equal to the given, we will simplify the original.
Given:
[tex]\displaystyle 2\sqrt{28} -5\sqrt{63}[/tex]
Simplify:
[tex]-11\sqrt{7}[/tex]
Answer: [tex]-11\sqrt{7}[/tex]
Answer: [tex]-11\sqrt{7}[/tex]
Step-by-step explanation:
[tex]2\sqrt{28}-5\sqrt{63}[/tex]
= [tex]2\sqrt{4*7}-5\sqrt{7*9}[/tex]
= [tex]2*\sqrt{4}*\sqrt{7} - 5*\sqrt{7} *\sqrt{9}[/tex]
= [tex]2*2*\sqrt{7} - 5*\sqrt{7}*3[/tex]
= [tex]4\sqrt{7} - 15\sqrt{7}[/tex]
= [tex]-11\sqrt{7}[/tex]
A bank employee is filling an empty cash machine with bundles of $100.00,$500.00 and $1000.00 bills each bundle has 100bills in it and the machine hold 10 bundles of each type. What amount of money is required to fill the machines?
Answers
Answer:
65fghxtt
Step-by-step explanation:
ΔABC has the following angle measures: A = 40 degrees, B = 60 degrees, and C = 80 degrees. The triangle is reflected across the x-axis to obtain ΔA’B’C’. What is the measure, in degrees, of angle B' ?
Answers
Answer:
60 degrees.
Step-by-step explanation:
A reflection does not alter the size of the angles of the triangle so B = 60 degrees.
9-5(x+4) = 3(2-x) - 1
Answers
Answer: x=-8
Step-by-step explanation:
For the graph, which are possible functions f and g?
Answers
The possible functions for f and g are f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]
What is an exponential function?An exponential function is a mathematical function of the following form: f ( x ) = [tex]p^{x}[/tex] where x is a variable, and p is a constant called the base of the function. The most commonly encountered exponential function base is the transcendental number e.
Analysis:
If for every value of x being positive and y is a positive whole number and for every x being negative y is a positive fraction, then that exponential function has a whole number base, Other wise it would have a fractional base. From the above explanation, f has (1,3) (positive x and whole number y) and (-1, 1/3) (negative x and positive fraction y). so therefore f has a whole number base and g has a fraction base.
Therefore f(x) = [tex]3^{x}[/tex] and g(x) = [tex](\frac{1}{3} )^{x}[/tex]
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In a small town in the Himalayas, the average snowfall each month is 6 inches. July is the month with the lowest average snowfall, of 1 inch. Construct a function that models this behavior. During what period is there more than 10 inches of snowfall?
Answers
The function that models the above behavior is given as:
f(x) = ACos(B(x + C)) + 6 ..... .......i
where x = 1 (that is January)
D (Average Snowfall) = 6.
Hence, the amplitude (A) is given as:
A = 6-1
= 5
What is a mathematical function?A mathematical function is a function comprising of different variables that represent different factors or events and the relationships between them.
During what period is there more than 10 inches of snowfall?
Recall that in a year we have 12 months. Hence, P = 12
→ P = (2π) /.B → (2π)/B = 12 → B = π/6
Taking the values of A and B and plugging them in, we ahve:
F(x) = 5 cos (π/6(x + C)) + 6................ii
This means that in July, we'll have
x = 7 and f(x) = 1
Therefore,
1 = 5cos ((π/6) (7 + C) + 6 → 5 Cos ((π/6) (7 + C) → -5cos ((π/6) (7 + C)
= -1
→ ((π/6) (7 + C) = π
→ 7 + C = 6
→ C = -1
Taking equation ii, we have
F(x) = 5cos ((π6) (x -1)) + 6
F (x) > 10
Therefore
5cos ((π/6) (x-1) + 6 > 10
→ cos ((π/6) (x-1) + 6 > 4/5
→ (π/6) (x-1) > Cos⁻¹ (4/5)
(π/6) (x-1) < 0.6435 and
(π/6) (x-1) > 5.6397
→ x < 2.23 and x > 11.77
The interpretation is that upwards of ten inches of snow fall in January, February, November, and December.
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How do you solve this?
Answers
Answer:
No solutions
Step-by-step explanation:
First ADD 4 /(X+4) to both sides of the equation to get
( x+4)/ (x+ 4) = 3
1 = 3 ???? There are no solutions
[tex]\dfrac{x}{x+4}=3-\dfrac{4}{x+4}\qquad(x\not=-4)\\\\x=3(x+4)-4\\x=3x+12-4\\2x=-8\\x=-4[/tex]
Which contradicts initial assumption, therefore [tex]x\in\emptyset[/tex].
Which of the following represents the unlike terms? 8m and 12a,2x and 3x,3m and 6m,6a and 9a.
Answers
8m and 12a
Step-by-step explanation:Like terms are terms that can be combined to condense a mathematical expression or equation.
Unlike Terms
Unlike terms are defined as terms that have different variables or powers.
This means that for terms to be unlike they must either be multiplied by a different variable, like x and y, or have different exponents.If terms meet either of these requirements, they are unlike. On the other hand, for terms to be like they must have both the same variable and power. The coefficients for the terms are not important.
Final Answer
All of the answer choices are to the first power, so the exponents are not important for this question. However, the last 3 answer choices all share the same variable. This means that they are all like terms.
The first answer choice, 8m and 12a, have different variables. This means that they cannot be combined and are unlike terms.
what’s the answer to this?
Answers
The solution set of the compound inequality is (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.
What is a solution set of a compound inequality?The solution set of a compound inequality is the set of values that intersect between the two inequalities and they satisfy the solution to each individual inequality.
The graph of a compound inequality can be illustrated on the number line.
From the given information, we have:
[tex]\mathbf{-\dfrac{1}{3}x+10 \geq 7}[/tex]---- (1)
x - 10 ≥ 7 ----- (2)
From equation (1), the solution to the inequality is:
x ≤ 9 and the interval notation can be represented as (-∞, 9]The solution to the second inequality is:
x ≥ 17 and the interval notation is [17, ∞)The solution set of the compound inequality is (-∞, 9] ∪ [17, ∞) and the correct graphical representation on the number line can be seen in the first option.
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the the value of x, if the perimeter of the rectangle is 98ft
Answers
Answer:
98/22 or 4.4545
Step-by-step explanation:
Perimeter of a rectangle: 2*width+2*length
4x*2+7x*2 = 98
8x+14x = 98
22x = 98
x = 98/22 or 4.4545
Ryan has $3$ red lava lamps and $3$ blue lava lamps. He arranges them in a row on a shelf randomly, then turns $3$ random lamps on. What is the probability that the leftmost lamp on the shelf is red, and the leftmost lamp which is turned on is also red
Answers
There are 6! = 720 ways of arranging the lamps.
If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.
Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.
Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.
Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So
P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4
NEED HELP LAST DAY TO SUMMIT
Answers
Answer:
A 3.5
Step-by-step explanation:
To Break it down there 1 3/4 so to put in halve it would be 1/2 1/2 1/2 1/4 so u have 3 feet because 1/2 in is 3 feet then u have a 1/4 inch so that is half of a feet 1 + 1 + 1 + 1/2 is 3 1/2 converted to decimal is 3.5.
Reperesent 1.235 as P/q.
Answers
Answer:
[tex]\frac{247}{200}[/tex]
Step-by-step explanation:
1.235
= 1 + 0.235 ( the place value of the 5 is thousandths ) , then
= [tex]\frac{1000}{1000}[/tex] + [tex]\frac{235}{1000}[/tex]
= [tex]\frac{1235}{1000}[/tex] ( divide numerator/denominator by 5 )
= [tex]\frac{247}{200}[/tex] ← in simplest form
16 The perimeter of the pentagon is equal to the perimeter of the square.
Not to scale
5X tỉ 3
2x + 3
11
7x + 4
5x + 8
9x10
Find an expression for the length of one side of the square.
Give your answer in terms of x in its simplest form.
Answers
7x+2
Step-by-step explanation:
add all the sides of the pentagon and make it equal to the perimeter of the square which is 4y
sides of the pentagon are
5x+3
2x+3
7x+4
9x-10
5x+8
28x+8=4y
7x+2 = y
7x+2 = answer
gathmath
gathmathier6961
another way :
in a standardized test you may want to use real numbers
make x equal a prime number like 3
so then the sides are
18
9
25
17
23
=
92
then divide by 4
23
then divide by 3
which is 7 remainder of 2
which is
7x+2
36.18 litres = _____ litres ______millilitres
Answers
36 litres 180 millilitres
Hope this helps!
Listen
If 2/3 is the fraction representing the ratio of corresponding sides of two similar
triangles, the ratio of the areas of the triangles would be:
2/3
3/2
1.41/1.73
4/9
Question 3 (1 point)
6
Answers
Reason
The theorem of areas of similar triangles "When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides".
The square root of 4 is 2
The square root of 9 is 3
Giving two similar triangles
If two expressions have the same factor and base , what happens to the exponents when the expressions are multiplied
Answers
Rectangle A and Rectangle B are similar. Rectangle A has side lengths of 20 and 15. Rectangle B has a side length of 60. What are the possible values for the length of the other side of Rectangle B? Select all that apply.
- 40
- 45
- 80
- 100
Answers
20 / 15 = 60 / x
What is the length of PR?
Answers
Answer:
D
Step-by-step explanation:
By observation we just know that one of the angles of two triangles is the same.
There are two sides that are not equal in ability to determine similarity.
HELP
Given: ABCD is a parallelogram and AC bisects BD.
Prove: AC bisects
Answers
2) [tex]ABCD[/tex] is a rhombus (a parallelogram with perpendicular diagonals is a rhombus)
3) [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex] (diagonals of a rhombus bisect the angles from which they are drawn)
A department store placed 144 suits on sale. By
the end of the day 108 suits had been sold. What
percent of the suits were sold on the day?
Answers
Answer:
75%
Step-by-step explanation:
[tex]\frac{108 }{144} = 0.75[/tex]
0.75 * 100 = 75%
1. If the ratio of AB to BC is 4:9, what is the area of Parallelogram ABCD?
Answers
Answer:
not determinable
Step-by-step explanation:
you can't determine--think of it like this: let's say I figure out a combination of two lengths that work, I could always scale it up (or down)
Let's say AB = 4, and BC = 9, then the area would be 36
but let's say AB = 8, and BC = 18, then the area would be 144
so, from this information alone, we cannot find the answer
hope this helps! have a lovely day :)
The area of the given parallelogram is that: It cannot be determined from the information given
How to find the area of the parallelogram?The formula for the area of a parallelogram is:
Area = Base * Height
Now, we are told that the ratio of AB to BC is 4:9.
The most important point here is that we do not know the altitude of the parallelogram; the area of a parallelogram is altitude times base.
A secondary point would be that we do not know the lengths of AB and BC; we only know the ratio of the two sides.
The actual lengths of the sides could be, for example, 8 and 18
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Complete question is:
If the ratio of AB to BC is 4:9, what is the area of Parallelogram ABCD attached?
Given a decile cut point value of 10.4, where the tenth sequential value is 32 and the eleventh value is 42, what is the actual decile value
Answers
The actual decile value is 126.6
To get the actual decile value, the decile formula is used. The formula used is:
Di = I (n+1) / 10 multiplied by (n - n+1)/10
This implies that the decreased fee, which in this case is 32 + 1, is delivered to the entire multiplication of the cut point 10.4, and the difference among the more tremendous value whilst organized in the ascending fee and the newly brought decreased value.
This gives:
33 + 10.4 * (42 - 33)
= 126.6
The actual decile value is 126.6
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helpppp!!!!!!!!!!!!!
Answers
Answer:
D is the right answer.
Perimeter is the distance around an objectArea represents space inside a 2-D objectVolume represents space inside a 3-D objectHope it helps!
Charnika has $599 in saving account at the beginning of the summer. She wants to save atleast $200 in the account by the end of the summer. She withdraws $25 every week for food,clothes, and the movie tickets. How many week can withdraw money from her account
Answers
Answer:
12
Step-by-step explanation:
we can setup an equation and solve for x: 500-25x = 200, where x stands for the number of weeks she withdraws money.
subtract 500 from both sides to get -25x = -300.
multiply each side by -1 to get 25x = 300
divide each side by 25 to get that x = 12
Question 2 of 5
Drag each tile to the correct box. Not all tiles will be used.
A scientist conducted an experiment to determine how effective an organic cleaner is at killing bacteria. To conduct the experiment, the
scientist randomly selected 50 doorknobs in an office building. She cleaned 25 of the doorknobs with the organic cleaner
(subject group 1). She did not clean the remaining 25 doorknobs (subject group 2).
After applying the treatments to each group, the scientist tested each doorknob to measure bacterial growth.
Which description matches each term?
bacterial growth
subject group 2
the scientist
water
control group
explanatory variable
response variable
subject group 1
Submit
-C
organic cleaner
Reset
Thanks y’all for helping :)
Answers
Based on the terms given on the population type and the variables, the correct matches are:
Population - all 108 restaurant locations in the chain. Frame - the list of all restaurant locations in the chain. Sample - the 10 randomly selected locations. Control group - subject group 2.explanatory variable - organic cleaner.response variable - bacterial growth.What are some terms in research?The population is total set of items that a sample is drawn from and in this case it all the restaurants. The sample would be the selected items from the population.
The control group is the group that is not manipulated by the explanatory variable which is the organic cleaner. The response variable is what changes as a result of the explanatory variable so it is bacterial growth.
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Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions. (2 points) Equation 1 Equation 2 |5x + 6| = 41 |2x + 13| = 28 Equation 1 has more solutions than equation 2. Equation 1 and Equation 2 have the same number of solutions. Equation 2 has more solutions than Equation 1. The number of solutions cannot be determined.
Answers
Answer:
Step-by-step explanation
5+5
The expression x-y equals 0.7 if x and y have certain values. Evaluate the following expression with the same values of x and y
1/x-y
Answers
The expression with the same values of (1/x – y) in x and y will be 10 / 7.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The expression x-y equals 0.7.
x - y = 0.7 …1
If x and y have certain values.
Then the expression with the same values of (1/x – y) in x and y will be
Take the reciprocal of equation 1, then we have
1 / (x – y) = 1 / 0.7
1 / (x – y) = 10 / 7.
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Solve Proportions In the following exercises, solve.
403. A golden retriever weighing 85 pounds has diarrhea. His medicine is prescribed as 1 teaspoon per 5 pounds. How much medicine should he be given?
Answers
Answer:
Thus, a golden retriever should be given 19 teaspoon of medicine.
Step-by-step explanation:
Given that a golden retriever weighing 85 pounds has diarrhea. His medicine is prescribed as 1 teaspoon per 5 pounds.To find how much medicine should he be given.Assign a variable. Write a sentence that gives the information to find it.Translate into a proportion be careful of the units.Multiply both sides by the Least Common Denominator and simplify. Check the answer.Step 1 of 3
Write the data in mathematical form and simplify.
Let x=the number of teaspoon
If 1 teaspoon medicine is 5 pounds then 85 pounds is how many teaspoon of medicine.
Translate the statement into proportion.
[tex]\begin{aligned}\frac{\text { pounds }}{\text { teaspoon }} &=\frac{\text { pounds }}{\text { teaspoon }} \\\frac{5}{1} &=\frac{85}{x}\end{aligned}[/tex]
Step 2 of 3
Multiply both sides by x and simplify
[tex]$x(5)=\frac{85}{\bcancel{x}}(\bcancel{x})[/tex]
5x=85
Divide by 5,
[tex]x=\frac{85}{5}[/tex]
Simplify, x=19
Step 3 of 3
Check the answer.
Substitute x=19 in original proportion and simplify.
[tex]$$\begin{aligned}\frac{5}{1} &=\frac{85}{x} \\5 &=\frac{85}{19}\end{aligned}$\\ \\ Hence, $5=5$, True[/tex]
help me please, anwser me fast please
Answers
Answer:
Yes, it is a function
Step-by-step explanation:
A function has only one output for each input. So a function can have the same output for different input, but one input can only have one output. In this case none of the inputs output more than one output, so it is a function.