A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is 40 feet, and the maximum horizontal width is 18 feet. Which of the following equations represents the pool?
x squared over 400 plus y squared over 81 equals 1
y squared over 400 plus x squared over 81 equals 1
x squared over 1600 plus y squared over 324 equals 1
y squared over 1600 plus x squared over 324 equals 1
Answers
The correct option; y squared over 1600 plus x squared over 324 equals 1, represents the equation of the elliptical pool.
What is defined as the ellipse?An ellipse is indeed the locus of all the points in a plane whose distances from two specific locations in the plane are constant. The fixed points, which are encircled by the curve, are known as foci (singular focus). The constant ratio is the eccentricity of the ellipse and the fixed line is directrix.When the ellipse's center is at the origin (0,0) as well as the foci are on the x- and y-axes, we can suitable examples the ellipse equation.The ellipse equation is given by;
x²/a² + y²/b² = 1
Where,
The major axis is the ellipse's longest diameter (usually denoted by 'a'), which runs through center through one end to the other at the broadest part of the ellipse. The minor axis is the ellipse's shortest diameter (denoted by 'b'), passing through to the center at its narrowest point.For the given question;
The maximum vertical length is 40 feet, and the maximum horizontal width is 18 feet.
Thus, a = 18 ; a² = 324
b = 40; b² = 1600
Put the value in equation of ellipse.
x²/324 + y²/1600 = 1
Thus, the equation of the ellipse is given by equation; y squared over 1600 plus x squared over 324 equals 1.
To know more about the ellipse, here
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Answer:
option B / y^2/400+x^2/81=1
Step-by-step explanation:
got it right on the test
Related Questions
f={(-2,-1),(2,-2),(-1,4)} and g={(4,-3),(-5,1),(-2,-4)} Find (f+g)(-2)
Answers
Given:
f={(-2,-1),(2,-2),(-1,4)}
g={(4,-3),(-5,1),(-2,-4)}
[tex](f-g)(-2)=f(-2)-g(-2)[/tex][tex](f-g)(-2)=-1+4[/tex][tex](f-g)(-2)=3[/tex]U = {a, b, c, d, e, f, g}A = {a, c, e, g)B = {a, b, c, d]Find A U B'
Answers
Answer:
{a,c,e,f,g}
Explanation:
Given that the Universal Set is:
[tex]U=\left\{ a,b,c,d,e,f,g\right\} [/tex]Sets A and B are given as:
[tex]\begin{gathered} A=\left\lbrace a,c,e,g\right\rbrace \\ B=\left\lbrace a,b,c,d\right\rbrace \end{gathered}[/tex]The complement of B (B') is the set of all elements that are in the universal set but not in B. Thus:
[tex]B^{\prime}=\left\lbrace e,f,g\right\rbrace [/tex]The union of A and B' is, therefore:
[tex]\begin{gathered} A\cup B^{\prime}=\left\lbrace a,c,e,g\}\cup\left\lbrace e,f,g\right\rbrace \right? \\ =\left\lbrace a,c,e,f,g\}\right? \end{gathered}[/tex]8) Describe the appearance of the graph of the equation given as compared to the parent function. Discuss the similarities and/or differences of the slope and y-intercept .. y=1/2x
Answers
As the equation represents a linear equation, the parent function must be
y=x. So, the intercept is the same for both y=1/2x and y=x, since the intercept is zero. And the slope of the parent function is 1 and the slope of the other function y=1/2x is 1/2, they are different.
The equation 4x-3 = 5 has been modeled below.If inverse operations is used to solve for x, what will be the second step in solving this equation?a. Add 3 negatives to the left.b. Add 3 positives to the right.c. Add 5 negatives to the left.d. Add 3 positives to the left.
Answers
we have the equation
4x-3 = 5
solve for x
adds 3 both sides
4x-3+3=5+3
4x=5+3
so
the answer is
b. Add 3 positives to the right
where can I find the volume and cross section of this shape?
Answers
The first step is to subject the solid into two parts. We have
cuboid at the base and triangular prism at the top. Thus,
Volume = volume of cuboid + volume of triangular prism
The formula for calculating the volume of a cuboid is expressed as
V = length x width x height
From the diagram,
width = 9
height = 8
length = 12
Thus,
V = 12 x 9 x 8 = 864 cm^3
The formula for calculating the volume of a triangular base prism is expressed as
V = base area x height
base area = area of triangle = 1/2 x base x height
For the triangle,
base = 9
height = 15 - 8 = 7
Area of triangle = 1/2 x 9 x 7 = 31.5
Height of prism = 12
Volume of prism = 31.5 x 12 = 378 cm^2
Volume of shape = 864 + 378 = 1242 cm^3
help!!! !!!!!!!!!!!!!!!!!!
Answers
Answer:
A,C,E
Step-by-step explanation:
note: first answer is wrong.
question 2: A, C, E
Solve each system by graphing. Check your solution. (I'll send the image)
Answers
To graph each line we need two points of each of them. To find them we give values to the variable x.
Equation y=-2/5x-2:
If x=0 then y=-2, then we have the point (0,-2).
If x=-5 then y= 0, then we have the point (-5,0).
Now we plot this point and join them with a line:
Equation y=-x-5:
If x=0 then y=-5, then we have the point (0,-5).
If x=-5 then y= 0, then we have the point (-5,0).
Now we plot this point and join them with a line:
The solution of the system is where the lines intersect. Therefore the solution is the point (-5,0).
QuestionGraph the line passing through (-1,4) whose slope is m=1/4Provide your answer below:
Answers
To find the equation for the line, we have to use the slope, the point, and the point-slope formula.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=\frac{1}{4}(x-(-1)) \\ y-4=\frac{1}{4}(x+1) \\ y-4=\frac{1}{4}x+\frac{1}{4} \\ y=\frac{1}{4}x+\frac{1}{4}+4 \\ y=\frac{1}{4}x+\frac{1+16}{4} \\ y=\frac{1}{4}x+\frac{17}{4} \end{gathered}[/tex]Once we get the equation, we graph. The image below shows the graph of the line.
In words, the lines must pass through the points (-17,0) and (0, 4.25).(b) In the diagram below, ABC is an isos-celes triangle. /AB/=/AC/= 5 cm and/BC/= 8 cm. Calculate correct to thenearest degree, ZBAC.AB5 cm8 cmX 5 cmC
Answers
Step 1
Given;
Step 2
From the triangle;
Using cosine rule;
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex][tex]\begin{gathered} 8^2=5^2+5^2-2(5)(5)cos(y) \\ m\angle BAC=y \\ 64-50=-50(cos(y)) \\ \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{14}{-50}=cosy \\ y\approx106^o \end{gathered}[/tex]Answer;
[tex]m\angle BAC\approx106^o\text{ to the nearest degree}[/tex]Exponential from Two Points Level 1
Answers
First write the equation
[tex]\begin{gathered} y=ab^x \\ (0,4)\text{ and (3,500)} \\ \text{when x = 0, y = 4} \\ 4=ab^0 \\ b^0\text{ = 1} \\ \text{Therefore} \\ 4\text{ = a x 1} \\ a\text{ = 4} \\ \text{when x = 3, y = 500} \\ 500=ab^3 \\ 500=4b^3 \\ \text{divide through by 4} \\ \frac{500}{4}=\frac{4b^3}{4}^{} \\ 125=b^3 \\ \text{Take cube root of both sides} \\ b\text{ = }\sqrt[3]{125} \\ b\text{ = 5} \end{gathered}[/tex]Therefore, the exponential equation
[tex]\begin{gathered} is\text{ } \\ y=4(5^x) \end{gathered}[/tex]Which situation can be considered a binomial experiment?A. Tossing a coin 20 times and recording the number of times itlands on headsB. Rolling a single number cube until you get a 2C. Asking 25 students how tall they are and recording their answersOD. Drawing one marble from a bag containing 10 red and 7 bluemarbles (replacing after each draw) until you have drawn 5 blue marbles
Answers
Remember that by definition, a binomial distribution (experiment) is defined as follows:
A random variable X has the binomial distribution with parameters n and p if X has a discrete distribution for which the probability function is as follows:
In this distribution, n must be a positive integer, and p must lie in the interval
0 ≤ p ≤ 1.
In other words, binomial distribution summarizes the number of trials when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.
Thus, we can conclude that the correct answer is:
Answer:Tossing a coin 20 times and recording the number of times it lands on heads
Find the length of the segment AB.A. √50B. √19C. √144D. √169
Answers
Answer:
To figure out the length of AB, we will calculate the length of BC first
Step 1:
Calculate length BC
Using the Pythagoras theorem, we will have that
[tex]\begin{gathered} BC^2=BD^2+CD^2 \\ BC^2=3^2+4^2 \\ BC^2==9+16 \\ BC^2=25 \\ BC=\sqrt{25} \\ BC=5 \end{gathered}[/tex]Step 2:
Calculate the length of segment AB
Using the Pythagoras theorem, we will have
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ AB^2=12^2+5^2 \\ AB^2=122+25 \\ AB^2=169 \\ AB=\sqrt{169} \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow\sqrt{169}[/tex]OPTION D is the right answer
How do you find slope?
Answers
The slope of a line is a value that indicates both the direction and the steepness of the line. In a linear function graph in a cartesian grid the slope tells us how much does the value of y increases or decreases when the value of x increases in one unit. The slope appears in the equation of a line when this is written in the slope-intercept form:
[tex]y=mx+b[/tex]And in the point-slope form:
[tex]y-k=m\cdot(x-h)[/tex]In both cases the letter m expresses the slope, b is the y-intercept and (h,k) is a point in the line. Any point (x,y) that is part of the line is a solution to this equations. When you are given a table of values or the graph of the line and you need to find the slope you just need to take two points and use them to build two equation (you can use the point-slope or the slope-intercept form). For example, let's assume that you are given the graph of a line that passes through (1,2) and (3,8). We can take the general equation in slope-intercept form and build two equations replacing x and y:
[tex]\begin{gathered} 2=m\cdot1+b \\ 8=m\cdot3+b \end{gathered}[/tex]By solving this system of equations you can find the slope. For example we can substract m from the first equation:
[tex]\begin{gathered} 2=m+b \\ 2-m=m-m+b \\ 2-m=b \end{gathered}[/tex]And replace this in place of b in the second equation:
[tex]\begin{gathered} 8=3m+b \\ 8=3m+2-m \\ 8=2m+2 \end{gathered}[/tex]We substract 2 from both sides and then we divide both side by 2:
[tex]\begin{gathered} 8=2m+2 \\ 8-2=2m+2-2 \\ 6=2m \\ \frac{6}{2}=\frac{2m}{2} \\ 3=m \end{gathered}[/tex]Then for this case the slope is 3. You can do something similar using the equation in point-slope form remembering that (h,k) is a point of the line. We use one of the two points we have, for example (1,2) and we get:
[tex]\begin{gathered} y-k=m\cdot(x-h) \\ y-2=m\cdot(x-1) \end{gathered}[/tex]Then we use the other point taking (x,y)=(3,8) and we have an equation for m:
[tex]\begin{gathered} (x,y)=(3,8) \\ 8-2=m\cdot(3-1) \\ 6=2m \end{gathered}[/tex]If we divide by two we get:
[tex]\begin{gathered} \frac{6}{2}=\frac{2m}{2} \\ 3=m \end{gathered}[/tex]And we arrived at the same result. That's how you can find the slope of a line using two of its points. These points can be given by the question, found in a table of values or in a graph.
I need help solving a math problem(a) millimeters/ centimeters/ meters/ kilometers(b) grams/kilograms(c) milliliter/liter
Answers
ANSWERS
(a) kilometers
(b) grams
(c) liter
EXPLANATION
(a) In this question, the measure is the distance from Tammy's house to the school. These kinds of distances are longer than centimeters or millimeters and, usually, also longer than meters.
Hence, we can conclude that Tammy's house is about 5 kilometers from school.
(b) Here we are talking about the weight of a candy bar, which is 60 [unit]. If its weight was 60 kilograms, we wouldn't be able to hold it with just one hand and eat it. Therefore, the mass must be 60 grams.
(c) Finally, it is said that Juan drank some amount of water. 1 milliliter of water is less than the volume of one drop of water, so it is almost impossible to say that he drank 1 milliliter of water.
Hence, we can conclude that Juan drank about 1 liter of water.
Find tan A and tan B for the following triangles. Enter answers as fractions in simplest form not decimals.
Answers
First, we must find the dimension of the missing side, for this, we use the Pythagoras theorem
[tex]c^2=a^2+b^2[/tex]Now, we replace these values an solve
[tex]\begin{gathered} (3\sqrt[]{3})^2=a^2+3^2 \\ a^2=(3\sqrt[]{3})^2-3^2 \\ a^2=(9\cdot3)-9 \\ a^2=27-9 \\ a^2=18 \\ a=\sqrt[]{18}=\sqrt[]{9\cdot2}=3\sqrt[]{2} \end{gathered}[/tex]The magnitude of the missing side is
[tex]a=3\sqrt[]{2}[/tex]Second, since we have all the sides defined we use the trigonometric tangent identity.
[tex]\tan (x)=\frac{O}{A}[/tex]Where O is opposite and A is adjacent, now we can find tan A and B
Tan A
[tex]\tan (A)=\frac{3}{3\sqrt[]{3}}[/tex]Tan B
[tex]\begin{gathered} \tan (B)=\frac{3\sqrt[]{2}}{3\sqrt[]{3}} \\ \tan (B)=\frac{\sqrt[]{2}}{\sqrt[]{3}} \end{gathered}[/tex]If h(x)= 5x +3 and h(a)= 33, what is the value of a?
Answers
We are told that h(a) = 33, which means when you put an into the function the output is 33. In other words,
[tex]h(a)=5(a)+3=33[/tex]This gives us the equation
[tex]5a+3=33[/tex]Subtracting 3 from both sides gives
[tex]5a=30[/tex]Finally, dividing both sides by 5 gives
[tex]a=6.[/tex]Which is choice A,
Find the fraction equal to 3.408 forever.
Answers
If we take 0.408 and convert it to fraction, then we have:
408/1,000 because we have three places after the dot or period.
But that result would be 3.408 but not forever.
For doing it forever, we will replace a nine in the denominator of the fraction for every decimal place we have, this way:
0.408 forever = 408/999 (three decimal places) and now we add the 3.
So, we have 3 408/999
The answer is 3 408/999
in the diagram, triangle JKL is inscribe in the circle and mJL=62°. What is the m
Answers
Given: triangle JKL is inscribed in the circle
So, the measure of angle J = 90
The measure of arc JL = 62
so, the measure of the angle K = 0.5 * 62 = 31
The sum of the angles of the triangle = 180
so,
[tex]m\angle L=180-(90+31)=59[/tex]So, the answer is option C. 59
Graph each lineY + 3 = 1/4(x - 4)X = 3
Answers
We have two expressions to graph, we'll start with the easiest one this is x = 3
x = 3 represents a continuous line that passes through all points when x has a value of 3, i.e. a vertical line through the point when x is 3
For the other equation to be graphed, let's first solve this one by simplifying it
[tex]\begin{gathered} y+3=\frac{1}{4}(x-4) \\ y+3=\frac{1}{4}x-\frac{4}{4} \\ y=\frac{1}{4}x-1-3 \\ y=\frac{1}{4}x-4 \end{gathered}[/tex]In conclusion, the equation of the simplified line is:
[tex]y=\frac{1}{4}x-4[/tex]To determine the values and graph this equation we must take values of "x" and replace them, the result when replacing these values will form the coordinates that we must locate in the Cartesian plane
Next, we will make a few points
[tex]\begin{gathered} x=8 \\ y=\frac{1}{4}\cdot(8)-4 \\ y=2-4 \\ y=-2 \end{gathered}[/tex][tex]\begin{gathered} x=-8 \\ y=\frac{1}{4}\cdot(-8)-4 \\ y=-2-4 \\ y=-6 \end{gathered}[/tex]Therefore, the line passed for (-8,-6) and (8,-2)
Below is a graph that shows how both equations are plotted and that the equation of the line passes through these two points
You have the following data set: 10, 14, 12, 16, 13, 15, 20, 16, 10, 14. Based on the values in the given data set, which of the following values is not included in the frequency distribution? 15 14 11 10
Answers
Trequency distribution table:
10.....2
14.....2
12.....1
16.....2
13.....1
15.....1
20....1
Answer:
The number 11 is NOT INCLUDED in the frequency distribution
3(-n + 3)Use the Distributive Property towrite an equivalent expression.
Answers
Given the expression
[tex]3(-n+3)[/tex]Using the distributive property to deduce an equivalent expression,
By using the distributive property of multiplication over addition
[tex]3(-n+3)=3(-n)+3(3)[/tex]The equivalent of the expression is
[tex]3(-n+3)=-3n+9[/tex]Hence, the answer is -3n + 9
Luis made an error when he used the distributive property to solve the problem shown. In which step did he make the error?Evaluate 60 • x-60 • 15, when x=8.Step 1 60• x - 60 • 15 = 60(x-15)Step 2 = 60 • 8 - 15Step 3 = 480 - 15Step 4 = 456
Answers
Given:
The steps are shown in the question.
There is a mistake in step 3 that can be corrected as:
Step 1:
[tex]60.x-60.15=60(x-15)[/tex]Step 2: x=8:
[tex]=60(8-15)[/tex]Step 3:
[tex]undefined[/tex]Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that randy are related by theequation 10x +1250 = y.Answer the questions below.Note that a change can be an increase or a decreaseFor an increase use a positive number. For a decrease use a negative numberwhat is the change in the total cost for each book printedwhat is te cost to get started before any books are printedsoCheckSave For LaterSubtAssetTe bere to search***SM
Answers
The equation desbribing the total cost is:
[tex]y=10x+1250[/tex]This equation has the form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept. Comparing both equations we conclude that in this case we have m=10 and b=1250.
The slope represents the change in cost for each book while the y-intercept represents the intial cost, therefore:
The change in the total cost for eah boog printed is 10.
The cost to get started before any books are printed is 1250.
Joe worked 12 hours and packed 32 cartons. Bob worked 25 hours and packed 64 cartons. Did Joe and Bobwork at the same rate?O YES, Joe and Bob worked at the same rateO NO, Joe and Bob did not work at the same rate
Answers
To be able to compare the rates, we will write them in fraction form.
The fraction that represents Joe's rate is:
[tex]\frac{32}{12},[/tex]and the fraction that represents Bob's rate is:
[tex]\frac{64}{25}\text{.}[/tex]Simplifying the above fractions, we get:
[tex]\begin{gathered} \frac{32}{12}=\frac{8}{3}, \\ \frac{64}{25}=\frac{64}{25}\text{.} \end{gathered}[/tex]Since:
[tex]\frac{8}{3}\ne\frac{64}{25}[/tex]then Bob and Joe did not work at the same rate.
Answer:
No, Bob and Joe did not work at the same rate.
Az-scores are a conversion of individual scores into astandard form. The conversion allows us to more easilycompare different data. We can find a Z-score for avalue to see it's Nistance in standard deviations from themean.(x – u)-score =where xis our given data, u ("mu")0is the population mean, and o ("sigma") is thepopulation standard deviation.Is Paul tall? According to the National Center for HealthStatistics, the distribution of heights for 15-year-oldmales has a mean of 170 centimeters (cm) and astandard deviation of 7.5 cm. Paul is 15 years old and179 cm tall.Find the Z-score corresponding to Paul's height. Explainwhat this value means.
Answers
ANSWER
EXPLANATION
We want to find the z score corresponding to Paul's height.
We have been given the formula for finding the z score of a data point. That is:
[tex]z\text{ = }\frac{x\text{ - u}}{\sigma}[/tex]x = mean
which values are solutions to the inequality below. check all that apply. x^2<81 49A. 6B.9C.7D.11E.4
Answers
All the value less than 9 applies
The answer is A, C, E
State whether the equation has one solution, no solution, or definitely many solution.
Answers
Given:
[tex]5j=5j-6[/tex]Simplify:
[tex]\begin{gathered} 5j-5j=5j-6-5j \\ 0=-6 \end{gathered}[/tex]The sides are not equal so the equation has no solution.
Answer: no solution
I need help with this practice *please read below*I am BRAND new to this type of mathematics, so please explain how to solve this step by step(Act as if your tutoring someone new to this, on how to solve this type of equation) Thanks in advance !
Answers
Solve the equation:
[tex]4x+3x+2(x+5)=28[/tex]Apply the distributive property to remove the brackets:
[tex]4x+3x+2x+10=28[/tex]Collect like terms on the left side:
[tex]9x+10=28[/tex]Subtract 10 on both sides of the equation:
[tex]9x=18[/tex]Divide by 9 and operate:
[tex]x=\frac{18}{9}=2[/tex]Answer: E. x = 2
Create a real world situation that demonstrates the following statement: -5> -9
Answers
Example: If you are Bob a sum of $5 and your brother is owing Bob a sum of $9
If you both hold equal amount of $10 to settle your debts with Bob
Hence, you will be left with $5 and your brother will be left with $1
This implies that -5 > -9
Find the length of the hypotenuse of a right triangle whose legs are each 13 inches long
Answers
Use Pythagorean theorem:
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]According to question
base = 13
perpendicular = 13
[tex]\begin{gathered} \text{hypotenuse}^2=\text{base}^2+\text{perpendicular}^2 \\ h^2=13^2+13^2 \\ h^2=169+169 \\ h^2=338 \\ h=\sqrt[]{338} \\ h=18.38 \end{gathered}[/tex]So the hypotenuse is 18.38 inches