Answers
For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.
The standard equation of an ellipse is given below:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.
The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:
[tex]\begin{gathered} \frac{(x+2)^2}{3^2}+\frac{(y-2)^2}{2^2}=1 \\ \frac{(x+2)^2}{9}+\frac{(y-2)^2}{4}=1 \end{gathered}[/tex]In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:
[tex]\begin{gathered} e=\sqrt{a^2-b^2} \\ e=\sqrt{3^2-2^2} \\ e=\sqrt{9-4}=\sqrt{5} \end{gathered}[/tex]The coordinates of the foci are given by:
[tex]\begin{gathered} F(h+e,k)=(-2-\sqrt{5},2) \\ F^{\prime}(h-e,k)=(-2+\sqrt{5},2) \end{gathered}[/tex]The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).
Related Questions
Hello! I need some assistance with this homework question, pleaseQ2
Answers
Recall that:
[tex](f\cdot g)(x)=f(x)g(x)\text{.}[/tex]Then, if:
[tex]\begin{gathered} x\in\text{Dom(f)}\cap Dom(g) \\ \text{then} \\ x\in\text{Dom(f}\cdot g)\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\begin{gathered} x\in\text{Dom(f}\cdot g)\text{ if } \\ f(x)\text{ and g(x) exists,} \\ \text{then} \\ x\in\text{Dom(f)}\cap Dom(g). \end{gathered}[/tex]Therefore:
[tex]\text{Dom(f}\cdot g)=\text{Dom(f)}\cap Dom(g).[/tex]Answer: True.
3. Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps.
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We can find the percentage of increase in the number of Magikarps that Jose captured in the lake by taking the initial number of them and subtracting it from the number that he had by the end of the day, like this:
16 - 8 = 8
Now, we just have to divide 8 by 16 and then multiply by 100, like this:
[tex]\frac{8}{16}\times100=50[/tex]Then, his number of Magikarps increased a 50%
3. What is the value of k whena. 2b. -14c. -10d. 14e. 10x² - x + 24= x - 2?x - 12TEXT=PL-=
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We will have the following:
[tex]\begin{gathered} \frac{x^2-kx+24}{x-12}=x-2\Rightarrow x^2-kx+24=(x-2)(x-12) \\ \\ \Rightarrow x^2-kx+24=x^2-12x-2x+24 \\ \\ \Rightarrow x^2-kx+24=x^2-14x+24 \\ \\ \Rightarrow-kx=-14x\Rightarrow k=14 \end{gathered}[/tex]So, the value of k will be 14.
Find the volume of a cone with a height of 9 cm and a base diameter of 6 cm. Use the value 3.14 for , and do not do any rounding. Be sure to include the correct unit in your answer. Explanation Check cm 6 cm 0 A cm X cm² cm³ ?
Answers
Given:
Required:
We need to find the volume of given cone
Explanation:
Take
[tex]\begin{gathered} r=\frac{6}{2}=3\text{ cm} \\ \\ h=9\text{ cm} \\ \pi=3.14 \end{gathered}[/tex]The volume of cone is
[tex]V_c=\frac{1}{3}\pi r^2h[/tex]Plug the values
[tex]V_c=3.14*\frac{1}{3}*3*3*9=84.78\text{ cm}^3[/tex]Final answer:
Volume of cone is 84.78 cubic cm
Determine if the triangles are similar. If similar, state how and complete the similarity statement.
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Answer:
SAS (Both sides share common angle n, and the sides, 40 : 65 and 32 : 52 have the same ratio)
▲LMN ~ ▲GHN
Drag each number to the correct location on the image.
Classify the real numbers below as rational or irrational numbers.
Please actually help and if its right ill give brainliest
Answers
Rational number will be 1/4, 2/3, √4 and Irrational number will be √8, √90, π/2, π as "Any whole number, fraction, or decimal that ends or repeats is a rational number. Any number that cannot be divided into a fraction and thus does not meet the definition of a rational number is considered to be irrational."
What is rational number?If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).
What is irrational number?Any real number that cannot be expressed as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number. For instance, the square root of 2 cannot be expressed as an integer or a fraction. A real number that cannot be expressed as a straightforward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to p/q if N is irrational. Example: The numbers 2, 3, 5, 11, 21, and (Pi) are all illogical.
Here,
Rational number=1/4, 2/3, √4
Irrational number=√8, √90, π/2, π
As "Any whole number, fraction, or decimal that ends or repeats is a rational number. Any number that cannot be divided into a fraction and thus does not meet the definition of a rational number is considered to be irrational." so Rational number will be 1/4, 2/3, √4 and Irrational number will be √8, √90, π/2, π.
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What is the sufragerie area of this shape?
1cm
5cm
4cm
6cm
3cm
2cm
Answers
Answer:
I think the answer would be 88
Which technique is most appropriate to use to solve each equation? Drag the name of the technique into the box to match each equation. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. (x+3)(x+2)=0 x² + 6 = 31
Answers
In (x+3)(x+2)=0, we use zero product property
And in [tex]x^{2}[/tex]+6=31, we use square root property
What is square root property and zero product property?
It is a property that can be used to solve the quadratic equations. It is used to solve an equation that can be put into one of the following two forms.
zero product property states the product of two non-zero elements is non-zero. The principle of zero-product property states that if there is any product of two numbers, that is equivalent to zero.
(x + 3) (x + 2) = 0
The most appropriate technique used to solve this equation is,
1.) zero product property
The solutions are:
(x + 3) = 0
x = -3
(x + 2) = 0
x = -2
x² + 6 = 31
The most appropriate technique used to solve this equation is,
2.) square root property
x² = 31-6
x² = 25
x = +/- root (25)
x = +/- 5
The solutions are:
x = 5, x=-5
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14x + 7 + 4 I need help asap
Answers
Answer:
Step-by-step explanation:
14x + 11
Write the sentence as an equation. 238 is 84 more than p Type a slash (/) if you want to use a division sign.
Answers
238 = 84 + p
definition of more than is to add.
definition of "is" is total
Q
R
85°
6.7 cm
8.0 cm
38°
S
6.7 cm
38°
8.0 cm
What is the measure, in degrees, of
U
Answers
Answer:
VB.
Step-by-step explanation:
between which two numbers is = 1.5 located on a number line -4 and 3
Answers
EXPLANATION
Given the number 1.5, is located between 1 and 2.
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.
What is a rectangle?A rectangle is a kind of parallelogram that has equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
The dimensions of the given rectangle is (650 - 2x) and x.
Then, the area of the given rectangle is A(x) = x(650 - 2x)
In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,
(660 - 2x) - 2x = 0
=> 4x = 660
=> x = 660 / 4
=> x = 115
Now, the maximum area is the value of A(x) at x = 115 as below,
= 115 × (650 - 2×115)
= 115 × 320
= 36800
The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.
Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.
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Find the value of csc (13π/6) using the unit circle.
Answers
The meaning of 13*pi/6 is as if you made 13 complete revolutions around the point pi/6.
therefore, is the same calculate the sin of 13pi/6 than the sin of pi/6.
[tex]\begin{gathered} sin(\frac{\pi}{6})=\frac{1}{2} \\ sin(\frac{13\pi}{6})=\frac{1}{2} \end{gathered}[/tex]Substituing:
[tex]csc(\frac{13\pi}{6})=\frac{1}{sin(\frac{13\pi}{6})}=\frac{1}{\frac{1}{2}}=2[/tex]The answer is: csc(13pi/6)=2.
Please help! I need explanation on why the answer is what it is.
Answers
The graph that matches the given linear inequality is (B) .
In the question ,
it is given that
the linear inequality is y [tex]>[/tex] -x + 4
on rewriting the inequality
we get
x + y [tex]>[/tex] 4
to plot the inequality , we need points to plot .
So ,when x = 0 , we have y = 4
and when y = 0 , we have x = 4
so the two points are (0,4) and (4,0) .
For shading the inequality , we put x = 0 and y = 0 ,
and get 0+0 > 4
0>4 , the result is False , So , the shaded region will be away from the origin which is shown in option (b) .
Therefore , The graph that matches the given linear inequality is (B) .
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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it. (10 points)
f(x) h(x)
f(x) = −4(x − 8)^2 + 3 graph of negative 1 times the quantity of x minus 3 squared, plus 2
I have attached a picture of the graph below.
Please do not answer if you don't know or are not sure. Thank you.
Answers
Answer:
x = 8 for f(x) and x = 3 for h(x)
Step-by-step explanation:
the axis of symmetry is a vertical line which passes through the vertex of the graph with equation
x = c ( c is the value of the x- coordinate of the vertex )
the equation of a parabola in vertex form is
f(x) = a(x - h )² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = - 4(x - 8)² + 3 ← is in vertex form
with vertex (h, k ) = (8, 3 )
equation of axis of symmetry of f(x) is x = 8
given the graph of h(x) with vertex = (3, 2 ) , then
equation of axis of symmetry of h(x) is x = 3
If the length of EG is 22, find the length of EQ
Answers
Given that:
Diameter of the circle, EG = 22
To find EQ, take the half of the diameter.
[tex]\begin{gathered} EQ=\frac{EQ}{2} \\ =\frac{22}{2} \\ =11 \end{gathered}[/tex]The third option is correct.
The map shows air travel distances from Minneapolis to four other cities. Use the triangle
inequality to find the range of possible distances between:
Minneapolis
1584
San Francisco
355
1056
1018
Chicago
Houston
New York
a.
b.
C.
d.
Chicago and Houston
San Francisco and Chicago
New York and San Francisco
Houston and New York
Answers
Answer:7
Step-by-step explanation:
Mrs Nunez brought person receive? 2 1/2 cakes to school for her class. If there are 15 people in the class including Mrs. Nunez, how much cake will each person receive?
Answers
Write it on the venn diagram:-School starts may include your expectations ; School ends include your experience. -The Center/middle area may include your experience from the start until this day.
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It is a pictorial representation that shows a logical relations between sets.
The centre portion of the set is the intersection between the two sets. This will represent your experience from the start until this day.
The other portion of school starts will represent expectation while for school emds will represents your experience as shown
28. Find four consecutive integers with the sum of 54.
Answers
The four consecutive integers with the sum of 54 is 12, 13, 14, 15
Let the four consecutive integers be x, x+1 , x+2, x + 3
x + x + 1 + x + 2 + x + 3 = 54
4x + 6 = 54
4x = 48
x = 12
The consecutive integers are
x = 12
x + 1 = 12 + 1 = 13
x + 2 = 12 + 2 = 14
x + 3 = 12 + 3 = 15
Therefore, the four consecutive integers with the sum of 54 is 12, 13, 14, 15
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A city has a population of 260,000 people. Suppose that each year the population Grows by 6%. What will the population be after 5 years?
Answers
Answer:
3343621.39918 or rounding would be 3343621.40
Step-by-step explanation:
this is because taking 260,000 divided by .6 then dividing that answer by .6 so on till you done that five times
If I drive 250 miles on Tuesday and 180 miles on Wednesday. How many miles did I drive in all? (Multiply)
Answers
The miles drive on Tuesday is , 250 miles.
The miles drive on Wednesday is , 180 miles.
The total miles drive on Tuesday and Wednesday is, the sum of drive on Tuesday and Wednesday.
[tex]S=250+180[/tex][tex]S=430.[/tex]Thus, the total miles drive on Tuesday and Wednesday is, 430 miles.
x/5 = 15
please quick now now now faults hurry
Answers
Answer:
x=75
Step-by-step explanation:
Answer:
x = 75
Step-by-step explanation:
x/5 = 15
Multiply 5 on both sides
x = 75
This the photo and I need you to answer this question
Answers
Given:
The graph shows the prices of the current year for the number of bushels.
And the table shows the prices of the previous year.
Part A: We will find the rate of change of bushels of corn in the current year.
As the graph shows a line, so, the rate of change will be the slope of the line
We will find the slope using two points.
As shown the line passes through the points (0,0) and (3,24)
So, the slope will be as follows:
[tex]slope=\frac{24-0}{3-0}=\frac{24}{3}=8[/tex]So, the rate of change = $8 per Bushel.
Part B: How many dollars more in the price of a bushel of corn in the current year than the previous year.
From the table: the price of the previous year = 21/3 = $7
And form the graph, the price of the current year = $8
So, the differnce = 8 - 7 = $1
So, the answer will be:
$1 more is the price of the current year than the price of the previous year.
Alpha Company sells their product for $ 1 each. The variable costs are $ 7 per unit and the fixed costs are $ 30,000 per year. How much should we sell the unit to: 1- Reach the break-even point 2- Achieve a net profit of $ 21,000 3- Achieve a net profit equal to $ 21,000.
Answers
we have that
Part 1
Remember that breakpoint is when the revenue (R) is equal to the cost (C)
so
C=7x+30,000
R=10x
equate both equations
10x=7x+30,000
solve for x
10x-7x=30,000
3x=30,000
x=10,000 units
the answer Part 1 is 10,000 unitsPart 2
net profit of $ 21,000
so
R-C=21,000
10x-(7x+30,000)=21,000
10x-7x-30,000=21,000
3x=21,000+30,000
3x=51,000
x=17,000 unitsPart 3
net profit equal to $ 60,000
so
R-C=60,000
10x-(7x+30,000)=60,000
10x-7x-30,000=60,000
3x=60,000+30,000
3x=90,000
x=30,000 unitsa. In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. Thereare enough tables to fit 200 students. Write an inequality whose solution is the possiblenumber of 4-seat tables in the cafeteria.b. 5 barrels catch rainwater in the schoolyard. Four barrels are the same size, and theAfth barrel holds 10 liters of water. Combined, the 5 barrels can hold at least 200 litersof water. Write an inequality whose solution is the possible size of each of the 4barrels.c. How are these two problems similar? How are they different? Solve ach problem.
Answers
According to the statement given in Part a, there is one table for 10 people and many tables for 4 and in total there are tables for 200 people. Taking x as the number of tables for 4 people, the inequality that represents this situation is:
[tex]\begin{gathered} 4x+10\leq200 \\ 4x\leq190 \\ x\leq47.5 \end{gathered}[/tex]It means that there must be less than or 47.5 tables in the cafeteria.
According to the statement given in Part b, there are 4 barrels that are the same size, and one that is 10 liters, in total they can hold 200 liters. Taking x as the volume hold by the 4 barrels , the inequality that represents this situation is:
[tex]\begin{gathered} 4x+10\leq200 \\ 4x\leq190 \\ x\leq47.5 \end{gathered}[/tex]It means that each barrel must hold less than or 47.5 liters of water.
These problems are similar because of the inequality used to find the solution is the same, they are different because of the variable that is found is completely different, the first one is the number of tables and the second one is the volume that can be hold by the barrels.
A longitudinal wave produced on a toy slinky travels at a speed of 30 m/s with a frequency of 20 Hz. Find the minimum separation between the consecutive compressions of the slinky.
Answers
Answer:
pagal
Step-by-step explanation:
pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagalwhat is the meaning of a mad person
Use the following function rule to find f(–3a + 7). Simplify your answer.
f(b) = – 8b
f (–3a + 7) = ?
Answers
The functional value of f(-3a + 7) is 24a - 56
What is a function?
A rule that assigns a specific element of B to each element of A is known as a function from A to B. Both A and B are referred to as the function's domain and codomain, respectively. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
There are different operations on functions like addition, subtraction, multiplication, division, and composition of functions.
Here we have,
the given function is
f(b) = -8b
f(-3a + 7) = -8(-3a + 7)
= 24a - 56
Hence, the functional value of f(-3a + 7) is 24a - 56
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9. The graph shows a proportional relationship between the variables x and y. a. Write an equation to model the relationship. b. Reasoning Explain how you know if an equation or a graph represents a proportional relationship. у 96 72 48 24 X 2 4 6 8
Answers
Answer:12x
Step-by-step explanation: