Answer:
Step-by-step explanation:
The question doesn't seem complete, but the question is likely to ask for 2 things: the equation of the ellipse and it's foci. So I'll respond to that. Also, the ellipse will be at the center since the artist wants the largest.
Firstly, the equation of an ellipse at the center is given by:
(x²/a²) + (y²/b²) = 1 where a > b.
Since the artist wants to make the largest ellipse, then the length of the rectangle will be the length of the ellipse, same applies to the width.
Since the length is 60, then a = 60/2 = 30
Since the width is 40, then b = 40/2 = 20
Therefore, the equation of the ellipse is:
(x²/30²) + (y²/20²) = 1
To find the foci we need to know the center and this can be gotten by
c² = a² – b²
c² = 30² – 20² = (30 + 20)(30 – 20) = (50)(10) = 500
c = √(500) = 10√(5).
The foci, since it's at th center would be:
(–10√(5), 0) and (+10√(5), 0)
The largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: [tex]\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\[/tex](assuming its major and minor axes lie on x and y axis respectively)
What is the equation of ellipse if its major and minor axis are given?Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, then if major axis is on x-axis and minor axis is on y-axis, then the equation of that ellipse would be:
[tex]\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1[/tex]
For this case, as we have rectangular piece of board the maximum ellipse will have it's major axis of length 60 inches, and of minor axis as 40 inches.
Thus, we have:
[tex]a = 60/2 = 30\: \rm inches\\b = 40/2 = 20 \: inches[/tex]
Thus, if the rectangle is placed such that the major axis is on x-axis, and minor axis is on y-axis, then the equation of that ellipse would be:
[tex]\dfrac{x^2}{30^2} + \dfrac{y^2}{20^2} = 1\\\\\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\[/tex]
Thus, the largest ellipse that the artist can make on the considered rectangular wooden piece will have area as: [tex]\dfrac{x^2}{900} + \dfrac{y^2}{400} = 1\\[/tex](assuming its major and minor axes lie on x and y axis respectively)
Learn more about ellipse here:
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The golden ratio is a solution to a quadratic equation.
a. Find the precise value for Φ by solving Φ2 − Φ − 1 = 0.
b. Which method of solving a quadratic equation did you use? Explain your reasoning.
c. What type of number is Φ? Why can it only be approximated by a decimal value?
Answer:
Below.
Step-by-step explanation:
a. Φ^2 − Φ − 1 = 0
Φ2 − Φ = 1
(Φ - 0.5)^2 - 0.25 = 1
(Φ - 0.5)^2 = 1.25
Φ - 0.5 = √(1.25) (We only take the positive root).
Φ = 0.5 + √(1.25)
b. I used Completing the square.
c. Φ is irrational That is it cannot be represented as a fraction a/b and because of this it can only be approximated by a decimal.
WILL MARK BRAINLIEST !!!
find the indicated value for each of the figures shown or described
Answer:
10. 9
In the first question we can solve using the Pythagorean theorem. It states that the hypotenuse in a right triangle or the longest side of the triangle, squared is equal to the other 2 sides, squared. Its expressed as so: C^2 = A^2 + b^2 where c is the hypotenuse and a and b are the other sides oft eh triangle.
Therefore,
15^2 = 12^2+x^2
225=144+x^2
81=x^2
x=9
__________________________________________________________
11. x=12
In this figure, there are 2 right triangles on the sides of the square. If we can find the lengths of the base of both triangles then we can find x using the Pythagorean theorem. the total base is 21 and the square is 11. 11+a+b=21. We can assume that both triangles are congruent and therefore we can solve this equation:
11+a+b=21
a+b=10
5+5=10
b=5
a=5
The bases of the two triangles are 5 and the hypotenuse is 13. Now we can solve using the Pythagorean theorem:
c^2 = a^2+b^2
13^2=5^2+x^2
169=25+x^2
144=x^2
144= 12 x 12
x=12
__________________________________________________________
12.
The diagnol of a triangle is the hypotenuse and since the length is the square root of 3, we have all the information we need.
c^2 = a^2+b^2
2^2 = (square root of 3)^2+b^2
4=3+b^2
1=b^2
b=1
Step-by-step explanation:
what is Alternate interior angles give an example
Hey there!
Basically, the alternate interior angles is/are the inside of the given lines but it’s unlikeable sides of your transversal
Basically, ∠1 & ∠2 are alternative interior angles
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Answer:
in the above pic you can see 12345678 marked angles
the alternate interior angles are angle3,5,4and6
they are pairs of alternat interior angles
Step-by-step explanation:
I hope it helps mate
i will always help you understanding your assingments
have a great day
#Captainpower#
a girl was asked about her age and she said she is half her mothers age and she was asked how old was her mother and she said i dont know but my mom is 5 years younger than my dad and we asked how old is your dad and she said i dont know but the sum of our ages is equal to 100years.how old is the dad ,the mom and the girl?
Answer: girl- 19yr old mom- 38yr old dad- 43 yr old
Step-by-step explanation:
5x+5=100
5x-5=100-5
5/5x=95/5
x=19
2(19)=38
38+5=43
hi, pls help me! :((
Answer:
the y-intercept is (0,4) because it's the point that's sitting on the y-axis (the one going up and down)
Step-by-step explanation:
Find the reference angle of 155o. –25o 25o –65o 65o
Answer:
The reference angle for 155° is 25°
Step-by-step explanation:
The reference angle is the angle that the angle arm makes with the x-axis be it clock wise or anti-clock wise.
The reference angles are obtained by the following reference
0 - 90° => Angle
90° - 180° => 180 - angle
Our given angle is: 155° so we will use the second rule
The reference angle will be:
180° - 155° = 25°
Hence,
The reference angle for 155° is 25°
Latoya needs to make a total of deliveries this week. So far she has completed of them. What percentage of her total deliveries has Latoya completed?
Answer: 35%
Step-by-step explanation:
You did not give the numbers. Let me help out by giving some figures and explain with that.
Latoya needs to make a total of 60 deliveries this week. So far she has completed 21 of them. What percentage of her total deliveries has Latoya completed?
To solve this, we divide 21 by 60 and then multiply by 100. This will be:
= (21 / 60) × 100
= 7/20 × 100
= 35%
What is an equation in point line slope form of the line that passes through the point (4,-1) and had slope 6
Answer:
y+1=6(x-4)
This is if you want it in point slope for,.
Step-by-step explanation:
Then, if you simplify it.
y+1=6x-24
y=6x-25
Now, it is in slope intercept form.
a reindeer leaves the north pole flying east at 20mph. Another reindeer leaves the north pole at the same time flying west at 15mph. How long will it take them to be 700miles apart?
Answer: well if they leave at the same time and one leaves 5mph faster than the other then...
Step-by-step explanation: ... it will take 15 hours for them to be 700 miles apart
8x − 4y = −16
3x + 15y = −6
Answer:
good job that is correct
Step-by-step explanation:
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Blake is working two summer jobs, making $9 per hour washing cars and making $22 per hour tutoring. In a given week, he can work no more than 16 total hours and must earn no less than $220. If x represents the number of hours washing cars and y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
9x + 22y ≥ 220
x + y ≤ 16
Step-by-step explanation:
First x is number of hours washing cars and y is number of hours tutoring.
He makes $9 per hour on cars, $22 per hour tutoring. So we use variables as substitutes for actual values.
That is 9x + 22y. He can't make less than 220, so use the sign greater or equal to 220.
He also must work no more than 16 hours. Total hours is x+y, and no more than 16 means use the sign less than or equal to.
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The number of hours washing cars and number of hours tutoring, if Blake is working two summer jobs, making $9 per hour washing cars, making $22 per hour tutoring, are 10.2 and 5.85 respectively. The graph is also attached below.
What is equation?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in, 3x + 5 Equals 15, instances.
Given:
Blake is working two summer jobs, making $9 per hour washing cars, making $22 per hour tutoring,
Total working hour = 16
Total money to be earned = $220
Write the equation of the above statement as shown below,
x + y = 16
9x + 22y = 220
Solve the above equation using a graph,
y = 5.85 and x = 16 - 5.85 = 10.2
To know more about equation:
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Write as a mixed number.
4/3
Answer:
1 1/3
Step-by-step explanation:
hope this helps!! : D
1 1/3 sorry if this is wrong!
CAN ANYONE HELP ME THAT IS GOOD IN MATH
find the slope of the line y = -2x + 3
Answer:
Step-by-step explanation:
Triangles LMN and FGH are shown. True or False questions
1.MN/NL=GH/HF
2.LM+MN+NL=FG+GH+HF
3.Triangle LMN is similar to triangle FGH.
Answer:
yeah they are very similar to each other
Answer:
questions
1.MN/NL=GH/HF=true
2.LM+MN+NL=FG+GH+HF=false
3.Triangle LMN is similar to triangle FGH.=true
What is the molar mass of the element gold?
help
Answer:
Molar Mass Molar mass is defined as the mass of one mole of representative particles of a substance. By looking at a periodic table, we can conclude that the molar mass of lithium is 6.94g, the molar mass of zinc is 65.38g, and the molar mass of gold is 196.97g. Each of these quantities contains 6.02 × 1023 atoms of that particular element.
Step-by-step explanation:
Hope this helps!!!
-BB
please mark me brainly
A car travels 2/5 mile in 1/2 minute . What is the car’s speed in miles per hour? Explain how you determined your answer
Answer:
48%28mil%2Fh%29
Step-by-step explanation:
if car travels %282%2F5%29mil%2F%281%2F2%29min =>2%282%2F5%29%28mil%2Fmin%29=%284%2F5%29%28mil%2Fmin%29
since 1h=60min multiply %284%2F5%29mil by 60 to get the number of miles per hour %284%2Fcross%285%29%29cross%2860%2912%28mil%2Fh%29=4%2A12%28mil%2Fh%29=48%28mil%2Fh%29
Answer:
48 miles
Step-by-step explanation:
1h = 60m
[tex]\frac{1}{2}[/tex]m --- [tex]\frac{2}{5}[/tex]miles
0.5m --- [tex]\frac{2}{5}[/tex]miles
60m --- [tex]\frac{60}{0.5}[/tex] × [tex]\frac{2}{5}[/tex]miles
= 48 miles
Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes Which printer prints the fastest?
Answer:
printer A- 36/1.5
printer B- 114/3
printer C- 115/5
first, multiply 1.5 x 10, 3 x 5, and 5 x3
you should get 15 for each.
once you have the denominators all done, multiply the numerators by the value you multiplied the denominator by and you should have your answer.
so all in all, printer B prints the fastest
please mark brainliest
Write the slope perpendicular to y=-5/4x+1
Answer:
the slope is -4/5
Step-by-step explanation:
to find a perpendicular slope, you take the opposite of the reciprocal of the slope, if I remember correctly.
Edward deposited $10,000 into a savings account 2 years ago. The simple interest rate is 2%. How much money did Edward earn in interest?
Step-by-step explanation:
Simple interest = PRT/100
S I = $10000 x 2 x 2
_____________
100
SI = $400
Answer:
$ 10,400
Step-by-step explanation:
Interest = P( 1 + rt)
10000 { 1 + ( 0.02 x 2 )
= 10000 * 1.04
= 10, 400
Helppppppp circle theorems
Answer:
m=14°, n=28°
Step-by-step explanation:
Angles in a Circle
The central angle is formed between two radii and its vertex at the center of the circle.
An inscribed angle is formed between two chords whose vertex lies on the circumference of a circle.
The measure of the central angle a formed by the same lines that form an inscribed angle b is:
a = 2b
This means the angle of a = 98° is double of the inscribed angle of 35°+m:
98 = 2(35 + m)
Dividing by 2:
49 = 35 + m
Solving for m:
m = 49 - 35 = 14
m = 14°
Angles m and n are also formed by the same lines, and:
n = 2m
Thus:
n = 28°
Answer: m=14°, n=28°
Parallel lines and transversals
20 POINTS and BRAINLIEST
Solve the simultaneous equation!
Answer:
x=7 y=-2
Step-by-step explanation:
Which set of ordered pairs represents a function?
(0, 0), (1, 2), (2, 4), (3, 4)
(0, 1), (1, 2), (2, 3), (2, 4)
{0, 0), (0, 2), (2, 2), (2, 4)
(O0, 1), (1, 3), (1, 5), (2, 6)
Step-by-step explanation:
на я был в bbs я был в душе
plsss help no spam.
.....................
Answer:
Third one.
x=6 y=12
Ok!
Answer:
fourth option
Step-by-step explanation:
Given the 2 equations
y = 2x - 3 → (1)
x + y = 18 → (2)
Substitute y = 2x - 3 into (2)
x + 2x - 3 = 18
3x - 3 = 18 ( add 3 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Substitute x = 7 into (1) for corresponding value of y
y = 2(7) - 3 = 14 - 3 = 11
Solution is x = 7, y = 11
Sam typed 420 words in 10 minutes. If he continues to type at this rate, how many words will he have typed in 3 hours? Group of answer choices
Answer:
7,560 words were typed in 3 hours.
Write an equation of the line that goes through the point (6, 12) and has a slope of 2 3 .
Answer:
3y = 2x + 24
Step-by-step explanation:
The correct question is as follows;
Write an equation of the line that goes through the point (6, 12) and has a slope of 2/3
Solution
Here, we have a point and a slope, and we want to write the equation of the line
The method we shall use here is the point slope method
Mathematically, that will be;
y-y1 = m(x-x1)
(x1,y1) = (6,12)
m = 2/3
y-12 = 2/3(x-6)
3(y-12) = 2(x-6)
3y-36 = 2x - 12
3y = 2x -12 + 36
3y = 2x + 24
I need help with this question
Answer:
51 degrees
Step-by-step explanation:
angle 1 is 104 and angle 3 is 25
add those and u get 129
it has to all equal 180 so...
180-129 is 51
Simplify completely: 220 - 2,5
O 65
O /15
O 25
O 2/15
Answer: Okay, the answer is [tex]2\sqrt{5}[/tex], the decimal form is 4.4, please mark me as brainliest! :)
Step-by-step explanation: You'll need to pull terms out from under the radical, assuming positive real numbers. I hope you using Math-way to simplify the square root expression correctly to find this helpful for you, have a wonderful day! :D
please help me !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
20
Step-by-step explanation:
15 is the mid so +5 is 20 thus 20 is the anser
