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:
https://brainly.com/question/16868628
Does the table below show a linear relationship between total cost of
balloons in dollars and the number of balloons purchased?
Answer:
A yes
Step-by-step explanation:
Answer:
YES, because the points fall in a straight line when plotted on a graph.
Step-by-step explanation:
To graph these numbers we can take two of the points and put them into two point form and then convert that to slope intercept form.
(2,6) and (4,12)
(y-y1) = [(y2-y1)/(x2-x1)]*(x-x1)
y-6 = [(12-6)/(4-2)]*(x-2)
y = 3x+4
pls help, MARK BRAINLEST with correct answer. Work out the surface area of this solid prism.
Answer:
Where's the prism? ＞︿＜
Step-by-step explanation:
7. You are ordering sweaters from American Eagle. Each sweater costs $25. They also charge a shipping fee of $7. You spent. $132 How many sweaters?
Answer:
Step-by-step explanation:
Alright, after reading this problem, let’s highlight some key points. Each sweater costs $25, we can write that down as 25x because will represent the amount of sweaters we buy. But we have a shipping fee of $7, so we will +7 to our highlights. And the total money spent was $132.
So far, we have: 25x + 7 = 132
Let’s subtract the 7 from the 132. Now we have: 25x = 125
Then we can divide by 25 on each side, and get x by itself.
X = 5 sweaters.
BONUS: Let’s replace 5 for our x to prove our answer
25(5) + 7 = 132 >>> 125 + 7 = 132 >>> 132 = 132 :D
There you go!! We buy 5 sweaters from American Eagle..!
12. A bag contains a total of
100 black and white marbles.
Without looking a marble is
chosen, recorded, and placed
back in the bag. The student
records 8 black marbles and 2
white marbles. Predict the
number of black marbles in
the bag.
Answer:
The answer would be 80 black marbles.
Step-by-step explanation:
The student chose 10 marbles. 8 of those were black. There are 100 marbles total. Going at this rate, picking 10 at a time, 10x10 is 100. So we would do this 10 times. 8x10 is 80. 2x10 is 20. There are 80 black marbles.
3 pounds cost $15. How many pounds can you buy for $45?
Answer:
you can buy 9 poundssss
The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠CDA.
Answer:
< CDA = 140 degrees
Step-by-step explanation:
For a rhombus, the sum of the interior angles is 360 degrees and also the opposite angles are equal i.e <ABC = <CDA and <BAD = <BCD
Given
<CAD = 20 degrees
<BCE = 20 degrees (based on geometry)
<BAD = <CAD + <BCE
<BAD = 20 + 20
<BAD = 40 degrees
Since <BAD = <BCD, then <BCD = 40 degrees
Get <CDA
<CDA + <ABC + <BAD + <BCD = 360
<CDA + <CDA + <BAD + <BCD = 360
2 < CDA + 40 + 40 = 360
2< CDA + 80 = 360
2< CDA = 360-80
2< CDA = 280
< CDA = 280/2
< CDA = 140 degrees
PLZ HELP ILL MARK U BRAINLEIST
Answer:
Step-by-step explanation:
OK so i think triangle c
Answer:
F And C
Step-by-step explanation:
congruent means identical in form
WILL GIVE 100 POINTS AND BRAINLIEST TO FIRST TO ANSWER CORRECT
RQ = TQ
1 2
RS _____ ST
Choose the relationship symbol to make a true statement.
Answer:
>
Step-by-step explanation:
In the lesson, we learned that the side opposite the larger angle was larger. In this case; angle 1 is larger than angle 2. This makes line segment RS > ST. Hope this helps!
Also I did this question myself and this was correct. :D.
Given the following functions, find the indicated values.
f(x) = 2 -5x
(a) f(-6) (b) f(0) (c) f(9)
(a) f(- 6) = 2
(b) f(0) =
(c) f(9) =
Answer:
f(-6) = 32
f(0) = 2
f(9) = -43
Step-by-step explanation:
Since in this question we are given a function all we have to do is to plug in the values that were indicated in the question and find out what value are we going to get as an output of this function. So we just do the following.....
a)
f(-6) = 2 - 5(-6)
f(-6) = 2 - (-30)
f(-6) = 2 + 30
f(-6) = 32
b)
f(0) = 2 - 5(0)
f(0) = 2 - 0
f(0) = 2
c)
f(9) = 2 - 5(9)
f(9) = 2 - 45
f(9) = -43
The wholesale price of a flower arrangement was $60 and the flowers were marked up 30%.
Finish the diagram to find the retail price.
100 percent is a 60 dollars wholesale price, 30 percent markup is a, and retail price is b.
a =
b =
Answer:
A=18
B=78
Step-by-step explanation:
Answer:
A: $18.00
B: $78.00
Step-by-step explanation:
I did the assignment and got it right
edge 2021
Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS
Triangles R M S and R Q S share side R S. Point N is on line R S. Lines are drawn from point M to point N and from point Q to point N. Angles M R S and S R Q are congruent.
Which relationship in the diagram is true?
ΔMNR ≅ ΔMNS by ASA
ΔRMS ≅ ΔRQS by AAS
ΔSNQ ≅ ΔSNM by SSS
ΔQNR ≅ ΔMNR by HL
Answer:
B. ΔRMS ≅ ΔRQS by AAS
I just took the test :)
Answer:B
Step-by-step explanation:just took the test
Solve: 6 -x= 4(5 + x)- 4
OA. x=-2
O B. There are infinitely many solutions.
O C. a =-
OD. X=-5
Answer:
x = - 2
Step-by-step explanation:
Given
6 - x = 4(5 + x) - 4 ← distribute and simplify right side
6 - x = 20 + 4x - 4
6 - x = 16 + 4x ( subtract 4x from both sides )
6 - 5x = 16 ( subtract 6 from both sides )
- 5x = 10 ( divide both sides by - 5 )
x = - 2
Please help as soon as possible! I need to get this done now! Thank you so much
Answer: SSS and CMW=FPY
Step-by-step explanation:
The lines on each side of the triangle show which sides match. So it is just a case of matching sides with sides.
What is the answer to this question? (pls help)
Answer:
D
Step-by-step explanation:
if you divide the money by the ounce, D is the cheapest with 0.24 per ounce
Answer:
Step-by-step explanation:
My guess is that it is not A. And A is not the answer.
You have to try each one to see.
3.20 / 8 = .40 cents/ounce.
6.25/25 = .25 dollars per ounce
3.84/16 = .24
The last one is the better buy.
(Plzzzzz help) (15 points)The group of points {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function, but the group of points {(1, 4), (2, 7), (3, 1), (5, 7)} is a function. What do you notice about the two groups of points? What do you think it means to be a function?
Answer:
21
Step-by-step explanation: You have to first put all the numbers in order and divided it by the amount of numbers that are in ur set and boom ur done.
Find the equation of the straight line which is perpendicular to the straight line 3x+4y=12 such that perpendicular distance from the origin is equal to the perpendicular distance from (3,2) on the given line
Answer:
3y-4x = -6Step-by-step explanation:
First get the slope of the given line;
Given the equation of the line 3x+4y=12
Rewrite in standard form y = mx+c where m is the slope;
3x+4y=12
4y = -3x + 12
y = -3x/4 + 12/4
y = -3x/4 + 3
Hence the slope of the given line is -3/4
Since the required line is perpendicular to this line, the slope of the required line will be M = -1/(-3/4) = 4/3
Get the equation:
Substitute M = 4/3 and the point (3,2) into the point slope equation of a line as shown;
y-y0 = m(x-x0)
y - 2 = 4/3(x-3)
Cross multiply
3(y-2) = 4(x-3)
3y - 6 = 4x - 12
3y - 4x = -12 + 6
3y-4x = -6
Hence the required equation of the line is 3y-4x = -6
Identify the method that will be used to solve for x for each equation. 4r = 20 x-11 = 9 5x + 6x = 22 5(x - 2) = 30
Answer:
for 4x = 20 you have to use the division property of equality divide 20 by 4
for x - 11 = 9 you have to use the addition property of equality add 9 to 11
for 5x + 6x = 22 you have to combine like terms add 5x and 6x to make 11x
for 5(x – 2) = 30 you have to use the distributive property multiply 5 and x; 5 and -2
4x = 20; x = 5
x - 11 = 9; x = 20
5x + 6x = 22; 11x = 22; x = 2
5(x – 2) = 30; 5x - 10 = 30; x = 8
Step-by-step explanation:
hope this helps
Find the area of the shaded region.
help immediately please
Answer:
1
Step-by-step explanation:
you just divide 6/4 and it will equal one
What are the coordinates of the image D0.5(3,5)?
Answer:
There isn't an image attached .
Step-by-step explanation:
Answer:
The answer is 5.-3
Step-by-step explanation:
3y (x + x^2 - y)
i need help :(((
Answer:
3yx+3yx^2-3y^2
Step-by-step explanation:
What does 7/2h(-15h + 1 1/2) equal to? x doesn’t equal anything.
Answer: -7 (30h - 11) / 4h
Step-by-step explanation:
Answer:
Step-by-step explanation:
All you can do is remove the brackets.
7/2 h * -15h = -52.5 h^2
7/2 h * 1 1/2= 7/2h * 3/2 = 21/4 h =5.25 h
7/2h(-15h + 21/4) = - 52.5 h^2 + 5.25 h = -52 1/2 h^2 + 5 1/4 h
Find the value of x. Give reasons to justify your solution. D ∈ AC
Answer:
x = 13
Step-by-step explanation:
Find the diagram attached
From the diagram, the sum of angle of the straight line BCD is 180°. Hence;
<BCE+<ECF<90 = 180
<BCE+64+90=180
<BCE+154 = 180
<BCE = 180-154
<BCE = 26°
Next is to get x.
The sum of interior angles <BCE and <BEC is equal to exterior angle <ABE
<BCE + <BEC = <ABE
26+x = 3x
Collect like terms
26 =3x-x
26=2x
x = 26/2
x = 13
Hence the value of x is 13
A man is trying to fit a washing machine into a corner of a four-sided room. He knows that all the walls are perfectly straight, but he is not sure if the corner is an exact right angle. If the other three corners are all 90° angles, what is the measure of the missing corner?
pls helpppppppppppppp
Answer/Step-by-step explanation:
The following steps to solve equation given by join are shown below including the property of numbers applied for each reasons:
4(2a + 3) = -3(a - 1) + 31 - 11a ----› Given
Apply the distributive property to open the parentheses
4*2a + 4*3 = -3*a -3*-1 + 31 - 11a
8a + 12 = -3a + 3 + 31 - 11a ----› Distributive property
Combine like terms together
8a + 12 = 3 + 31 -3a - 11a
8a + 12 = 34 - 14a ---› Combining like terms
Add 14a to both sides
8a + 12 + 14a = 34 - 14a + 14a
22a + 12 = 34 ----› Addition property
Subtract 12 from both sides
22a + 12 - 12 = 34 - 12
22a = 22 ----› subtraction property of equality
Divide both sides by 22
22a/22 = 22/22
a = 1 ----› Division property of Equality
I'll love you forever if you help me with this
which expression is equivalent to (1+cos(x))2(tan(x/2))?
a. sin(x)
b. 1-cos(x)
c. 1-cos2(x)
d. (1+cos(x))(sin(x))
Answer:
It's d
Step-by-step explanation:
(1+cos(x))(sin(x))
The trigonometric expression (1+cos(x))2(tan(x/2)) is equivalent to (1+cos(x))(sin(x)) option (d) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The trigonometric expression is:
= (1+cos(x))²(tan(x/2))
As we know,
1 + cos(x) = 2cos²(x/2)
Use the above trigonometric identity:
= (2cos²(x/2))²(tan(x/2))
= 2 cos⁴(x/2) sin(x/2)/cos(x/2)
= 2 sin(x/2) cos³(x/2)
2sin A cos B = sin2A
Use the above trigonometric identity and after simplification we get:
= (1+cos(x))(sin(x))
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Thus, the trigonometric expression (1+cos(x))2(tan(x/2)) is equivalent to (1+cos(x))(sin(x)) option (d) is correct.
Learn more about trigonometry here:
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3. Write 7 thousandths as a decimal.
Comments
Answer:
7 thousandths as a decimal is 0.007
Step-by-step explanation:
The part where "ths" means a decimal. So we put 3 zeros, because a thousand also has 3 zeroes. 7 thousandths as a decimal is 0.007
Hope this helps
Mark me brainliest please :D
The diagram represents a reduction of a triangle by using a scale factor of 0.8.
What is the height of the reduced triangle?
A) 4.0 inches
B) 4.8 inches
C) 5.2 inches
D) 7.5 inches
Answer:
B 4.8 inches
Step-by-step explanation:
The scale factors are used to convert a figure into another one with similar characteristics but different lengths, in this example is a triangle, and in order to calculate the measure of the height you just have to multiply the original height by the scale factor:
If b=24 and c=10 what is for the missing side a= ? by Use the Pythagorean Theorem to find
Answer:
a = 21.82 if and only if b=10 and c=24
if you meant b=24 c=10
there can't be such a triangle because the hypotenuse is the longest side
Step-by-step explanation:
[tex]a^2+b^2=c^2\\\\a=?\\\\b=24\\\\c=10\\\\\\a^2+(24)^2=(10)^2\\\\a^2=(10)^2-(24)^2\\\\a^2=(10-24)(10+24)\\\\a^2=-14(34)[/tex]
which doesn't work because something squared can't be a negative
if you meant
c=24 and b=10
[tex]a^2+(10)^2=(24)^2\\\\a^2=(24)^2-(10)^2\\\\a^2=(24-10)(24+10)\\\\a^2=(14)(34)\\\\a\approx 21.82[/tex]
9514 1404 393
Answer:
a = 26 or 21.82
Step-by-step explanation:
If 'a' is the hypotenuse, then ...
a² = b² +c²
a² = 24² +10² = 576 +100 = 676
a = √676 = 26 . . . if 'a' is the hypotenuse
__
If 'a' is the long side, then ...
b² = c² + a²
b² -c² = a² = 24² -10² = 576 -100 = 476
a = √476 ≈ 21.82 . . . if 'a' is the long leg
__
Comment on the question
The problem statement doesn't tell us what side of the triangle is labeled 'a'. There are two possibilities. An answer has been provided for each. Use the one that applies to the figure you are given.