Answers
Answer: [tex]\frac{x^2}{16}+\frac{y^2}{49} = 1\\\\[/tex]
This is the same as writing (x^2)/16 + (y^2)/49 = 1
===========================================================
Explanation:
The general equation for an ellipse is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\\\\[/tex]
where
(h,k) is the center'a' is half the total width (along the x axis)'b' is half the total height (along the y axis)Notice how 'a' pairs with the x term, so that's why 'a' describes the horizontal width along the x axis. The horizontal width is 8 ft, which cuts in half to 4 ft. So a = 4.
The vertical length is 14 ft, which cuts in half to 7 ft. So b = 7.
The center isn't mentioned (other than the fact that the actor is located here), but I'm assuming by default it's at the origin (0,0).
With that all in mind, we then get the following:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{7^2} = 1\\\\\frac{x^2}{16}+\frac{y^2}{49} = 1\\\\[/tex]
The graph is below. I used GeoGebra to make the graph.
From the graph, we can see that the horizontal width spans from x = -4 to x = 4. This is a total distance of |-4-4| = 8 feet. Similarly, the vertical length spans from y = -7 to y = 7 which is a distance of 14 feet.
Related Questions
I need help please anyone ?????!!!
Answers
answer:
2 on the picture is the amplitude
find the value of x, circles and angles
Answers
Answer:
x = 50
Step-by-step explanation:
When two secants intersect in the interior of a circle, the angles formed are the average of the arc an angle and its vertical intercept. In this case, our angle, 73, should be the average of x and 96. We can translate this to an equation and solve:
[tex]\frac{x+96}{2} = 73[/tex]
x + 96 = 146
x = 50
Graph the equation
y = 5x
Use the graphing tool to graph the line.
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
You want a line that goes through (0, 0) and has a slope of 5. That means it will also go through (1, 5) and (2, 10), for example. I like the attached graphing tool because it will draw the graph directly from the equation.
what is the volume of a hempisphere with a radius of 9.7 cm rounded to the nearest 10th of a cubic centimeter
Answers
Answer:
volume of hemisphere =1912.26cm^3
Step-by-step explanation:
through how many degrees does the hour hand of a clock move in 10 hours
Answers
Answer:
120 degrees move in 10 hours
PLS HELP! VERY URGENT PICTURE INCLUDED!!
Answers
Answer:
y = 6x ^2 - 6x + 9
Step-by-step explanation:
hopefully it's visible
:)
Graphs of the following equations are straight lines except :
A. 3x+2y=8
B. y=x/2-5
C. x=4y
D. y=x^2+3
Answers
Answer:
D.
Step-by-step explanation:
D. This contains an x^2 and is called a parabola ( curved line like a U).
Answer:D
Step-by-step explanation: d is the correct answer
Radicals and Exponents. Tutorial Use the properties of exponents to simplify the expression. (y 3/2 x-1/2)4 =
Answers
(x
3
+y
3
)(xy
4
+7)
Answers
Answer:
question is not proper
Step-by-step explanation:
question is
Angelique travels 75 miles. Jamila travels 115 kilometres. Show that Angelique has travelled futher than Jamila.
Answers
Answer:
Angelique has traveled further than Jamila by about 6 km.
Step-by-step explanation:
Make them the same unit (I will make them both kilometers)
There is about 1.609 km in 1 mile
75 miles * 1.609 km/1 mile = 120.675
120.675 km>115 km
Which point on the number line shows the graph
Answers
Answer:
B
Step-by-step explanation:
State two similarities and one difference between the graphs of f(x)= 3^x and g (x)= (1/3) ^x
Answers
look at the image below plz !!!!!!!!!!!!!! U R G E N T PLZ
Answers
Answer: Volume is 4.19
Step-by-step explanation:
The equation for the volume of a cone is πr^2(h/3)
r = 1
h = 4
Fill in values into the equation
π(1)^2(4/3) = 4.19
The ray EG is the angle bisector of DEF and m DEF = 84º.
Find mDEG.
mDEG =
degrees
Answers
Jua Kali Products Ltd has been in operation for the last 10 years. Its annual revenue and cost functions take form of quadratic functions. The following data was obtained from the records of the company. Year 2017 2018 2019 Units produced and sold (000) 5 10 15 Revenue (sh000) 1900 3600 5100 Cost (sh000) 7525 7100 6725 Required: The revenue and cost functions (10 marks) The breakeven number of units (5 marks)
Answers
Answer:
Step-by-step explanation:
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The revenue function is y₁ = –4x² + 400x, the cost function is y₁ = x² – 100x + 8000, and the break-even number of units is 20 or 80.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Jua Kali Products Ltd has been in operation for the last 10 years.
Its annual revenue and cost functions take the form of quadratic functions.
The following data was obtained from the records of the company.
Year Unit Sold Revenue Cost
2017 5 1900 7525
2018 10 3600 7100
2019 15 5100 6725
We know that the quadratic equation is given as
[tex]\rm y = ax^2 + bx + c[/tex]
Let y₁ be the revenue function, y₂ be the cost function and x be the unis sold.
Then the revenue function will be
1900 = 25a + 5b + c ...i
3600 = 100a + 10b + c ...ii
5100 = 225a + 15b + c ...iii
From equations (i), (ii), and (iii), we have
a = –4, b = 400, and c = 0
Then the revenue function will be
y₁ = –4x² + 400x
Similarly, the cost function will be
7525 = 25a + 5b + c ...1
7100 = 100a + 10b + c ...2
6725 = 225a + 15b + c ...3
From equations 1, 2, and 3, we have
a = 1, b = –100, and c = 8000
Then the cost function will be
y₁ = x² – 100x + 8000
For the break-even units, the cost function and the revenue function will be equal. Then we have
[tex]\begin{aligned} x^2 -100x + 8000 &= -4x^2 + 400x\\\\5x^2 -500x + 8000 &= 0\\\\x^2 - 100x + 1600 &= 0\\\\x^2 - 80 x - 20x + 1600 &= 0\\\\x(x-80) - 20 (x-80) &= 0\\\\(x-80)(x-20) &= 0\\\\x &= 20, 80 \end{aligned}[/tex]
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
Find the greatest common factor of 65a3b4 and 39a4b5.
Answers
Step-by-step explanation: Let's begin by finding the
greatest common factor for the numbers 65 and 39.
I would make a factor tree and break up 65 and 39.
So 65 is 13 x 5 and 39 is 13 x 3.
Since the 13's match up, the greatest
common factor between 65 and 39 is 13.
For the variables, we use the smallest power on each of them.
So we use a^3 and b^4 to get 13a^3b^4 as our GCF.
Please help brainliest will be given
Complete the equation describing how
x and y are related.
x
-1
5
0 1 2 3 4
3 8
V 2
13
18
23
28
y = 5x + [?]
Enter the answer that belongs in [?].
Answers
y = 5x + 3
Step-by-step explanation:
When x = 0 y = 3 so the y-intercept will be 3
And the equation is y = 5x + 3 where the slope is 5
Evaluate each expression if r = 3,q = 1, and W =-2
Answers
Answer:
2) - 12
3) - 1
4)y = 8
5)r = 4
6)x= -7/29
Hope it helps you
Find the product: 12 x 3/5 =
Answers
Answer:
12 x 3/5 = 7 1/5
Step-by-step explanation:
12 x 3/5
Add 1 below 12 as a denominator to make it an improper fraction
= 12/1 x 3/5
Multiply numerators from both fractions as long as the denominators:
12 x 3 = 36
1 x 5 = 5
12/1 x 3/5 = 36/5
36/5 SIMPLIFIED IS 7 1/5
Hope this helps!
Answer:
36/5 = 7.2 = 7 1/5
Step-by-step explanation:
12 x 3/5
Change 12 into fraction form to make it easier.
12/1 x 3/5
Now multiply the numerators and the denominators.
12 x 3 = 36
1 x 5 = 5
12/1 x 3/5 = 36/5
If you don't want the answer as an improper fraction, 36/5 = 7.2 which is also equal to 7 1/5
Consider the function f(x) = square root of x+3
a. In your own words, explain the meaning of f'(2).
b. Now using mathematical notation, write f'(2) as a limit.
(Plz hurry and help meee)
Answers
Step-by-step explanation:
f'(x) is usually used in calculus to denote the first derivative of f(x) so f'(2) will simply be the first derivative of f(2).
f(x)=x+3
f'(x)=1
thus x does affect the first derivative and your answer for f'(x)=1
Which expression is equivalent to the following complex fraction?
Answers
Answer:
The correct choice is option B. y+1/y-1
Step-by-step explanation:
Any number that CAN be divided by 2 without having remainder is considered an _______ number
Answers
Step-by-step explanation:
Any number that can be divided by 2 without having remainder is considered an even number.
I hope it helped U
stay safe stay happy
is f(x)=sqrt{x}+3x an exponential function?
Answers
Simplify the equation
(X 2/5) 10
Answers
Answer:
x^4
Step-by-step explanation:
x^(2/5) ^10
We know that a^b^c = a^(b*c)
x^(2/5*10)
x^4
Answer:
[tex]{x}^{4} [/tex]
Step-by-step explanation:
[tex] ({x}^{ \frac{2}{5} } ) ^{10} \\ {x}^{ \frac{2}{5} \times 10} \\ {x}^{ \frac{20}{5} } \\ {x}^{4} [/tex]
7. When running you discover you are only in second place. You were initially running at a speed of 18 km/h and
increase your speed to 21 km/h. It takes you 3 seconds to speed up to your new rate. What is your
acceleration
Answers
Step-by-step explanation:
check it out.
Hope it helps.
What is the 21st term of the sequence with a1 = -6 and d = 4?
a) 70
b) 74
c) -40
d) 78
Answers
Answer:
74
Step-by-step explanation:
for this question you have to use the formula of the nth term which is Tn=a+(n-1)d,
T21=-6+(21-1)4
=-6+(20)4
=-6+80
=74
I hope this helps
Simplify (6z-4y+2x)+(3z-5x+2y)
Answers
Answer:
9z-2y-3x
Step-by-step explanation:
(6z-4y+2x)+(3z-5x+2y)
Combine like terms
6z+3z-4y+2y+2x-5x
9z-2y-3x
Answer:
-3x - 2y + 9z
Step-by-step explanation:
Since you are adding two polynomials, the parentheses are unnecessary, so you can just drop them. Then combine like terms. Like terms are terms that have the same variable part such as 6z and 3z.
(6z - 4y + 2x) + (3z - 5x + 2y) = Original problem.
= 6z - 4y + 2x + 3z - 5x + 2y Drop unnecessary parentheses.
= 2x - 5x - 4y + 2y + 6z + 3z Rearrange terms to group like terms.
= -3x - 2y + 9z Combine each set of like terms.
Answer: -3x - 2y + 9z
Change the following to percentages:
a) 83 out of 100
b) 24 out of 50
c) 9 out of 25
d) 7 out of 20
e) 6 out of 10
f)72 out of 200
g)12 out of 40
h)36 out of 60
Answers
Answer:
a.83%
b. 48%
c.36%
d.35%
e.69%
f.36%
g.30%
h.69%
HELP!!!!! ASAP I'm getting confused and It's to long to solve it online!
Answers
Answer:
Step-by-step explanation:
What is the wavelength of light with 5.53 x 10-19 J of energy? (The speed of
light in a vacuum is 3.00 x 10 m/s, and Planck's constant is 6.626 10-34
J•s.)
A. 399 nm
B. 278 nm
C. 250 nm
D. 359 nm
Answers
Answer:
D. 359 nm
[tex]{ \boxed{ \bf{ energy = \frac{hc}{ \lambda} }}} [/tex]
lambda is the wavelength
c is the speed of light
h is the Planck's constant
[tex]{ \sf{5.53 \times {10}^{ - 19} = \frac{(6.626 \times {10}^{ - 34}) \times (3.00 \times { {10}^{8} }) }{ \lambda} }} \\ \\ { \sf{\lambda = 3.59 \times {10}^{ - 7} }} \\ { \sf{\lambda = 359 \: nm}}[/tex]
