A geometry student wants to draw a rectangle inscribed in the ellipse x² + 4y2 = 49.
What is the area of the largest rectangle that the student can draw?

Answers

Answer 1

Maximum area = 2ab

from ellipse eqn

x^2 + 4y^2 = 49

(x+4y)^2= 49

underoot both sides

x + 4y = 7 ---eqn1

from

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{{b}^{2} } = 1[/tex]

(ab)^2 = (ax + by)^2

ab= ax + by

compare to eqn1

ab=7

then, area of the largest triangle will be 14 units.

i hope it's ryt


Related Questions

slope intercept form,
4x-2y=18

Answers

Answer:

x=9/2+y/2

Hope this helped

Write an
equation in point-slope form of the line
through point J(-2, 2) with slope -8.

Answers

Answer: y=-8x-14

Step-by-step explanation:

See attached picture

Tom's's garden has 9 tomato plants, 5 pepper plants, 3 squash plants, and 6 pumpkin plants.
For every 3 tomato plants in Sunny's garden, there is 1 ____ plant.

Answers

Answer:

Squash plant.

Step-by-step explanation:

I'm not sure how to explain, but if you divide 9 by 3, you get 3. There are 3 squash plants, so that's the answer. You could also write it as a ratio...

9:3

3:1

I'm not exactly sure how to explain the ratio part either, but I hope it helped at least a little bit...have an amazing day :3

Sanjay, Colby, and Arpitha are training to run a marathon. On Saturday, Sanjay ran StartRoot 125 EndRoot miles, Colby ran 13 miles, and Arpitha ran the shortest route from the library to her house, as shown in the diagram.

A right triangle. The distance from the angle with measure 90 degrees to Arpitha's Home is 9 miles, and the distance to the Library is 6 miles.

Which list shows the names in order from the person who ran the shortest distance to the one who ran the greatest distance?
Colby, Sanjay, Arpitha
Sanjay, Arpitha, Colby
Sanjay, Colby, Arpitha
Arpitha, Sanjay, Colby

Answers

Answer:

D

Step-by-step explanation:

Cuz it is right. -_-

Answer: D. Arpitha, Sanjay, Colby

Step-by-step explanation:

got it right on egde. brainlyest please im stuck on ambitious :-(

And this one help pleaseee

Answers

54 degrees
• you would do 180 degrees minus 126 to find angle 1, and angle 1 is the same as angle 5

Answer:

m∠5 = 54

Step-by-step explanation:

m∠1 + 126 = 180

m∠1 = 54

m∠1 = m∠5

m∠5 = 54

daily reminder that you are beautiful INSIDE & OUT! You got this!

Comment one thing you’re most proud of!

Answers

I’m proud of Everything

Answer:

i am proud of how large the meat between my legs is

Step-by-step explanation:

marco is 6ft and 3 inches tall.there are 2.54 cenimeters in 1 inch what is marco's hight in inches

Answers

Answer:

190.5 centimeters.

Step-by-step explanation:

First you need to convert 6ft 3 inches into just inches. There are 12 inches in a foot. 12 x 6 is 72. 72 inches + 3 = 75 inches. 75 inches x 2.54 = 190.5 centimeters.

Which of these numbers round to 6.81 nearest hundredth

Answers

Answer:

6.81

Step-by-step explanation:

If the last digit in the fractional part of 6.810 is less than 5, then simply remove the last the digit of the fractional part.

Answer:

6.81 stays the same you can't round it because there is a 1 behind the 8 so u givee it a rest so stays the same

14=3y
This is DPOE and MPOE . 7th Grade honors ( 8th grade math)

Answers

Answer:

I dont know what dpoe and mpoe means but to get 14=3y I would assume you would divide 14 by 3 and 3y by 3 to get 14/3=y. and then you have to figure out what 14 divided by 3 is because I want to go to bed

Not sure to be honest

Write the algebraic expression for the following word phrase: the product of 9 and 4 less than p

Answers

Answer:

36 < p

Step-by-step explanation:

Product means multiplication, therefore,

9 × 4 = 36

The symbol of "less than" in mathematics is < , hence:

36 < p

Sylvia buys a case of water that contains 24 bottles and sells x number of bottles to her co- workers. Sam buys a case of water that contains 36 bottles and sells three times as man bottles as Sylvia sold to his co-workers. How many bottles of water did Sylvia sell if they ended up with the same number of bottles of water left over?

Answers

Answer:

6 bottles

Step-by-step explanation:

Given the following :

SYLVIA:

Case of water = 24 bottles

Number of bottles sold = x

SAM:

case of water = 36 bottles

Number of bottles sold = 3x

Number of bottles left after sales are the same ;

Number of bottles left :

24 - x = 36 - 3x

Then solve for x

-x + 3x = 36 - 24

2x = 12

x = 12/2

x = 6

Hence, Sylvia sold 6 bottles of water.

2/5 divided by 1/6 this is dividing fractions

Answers

Answer:

exact form: 12/5

decimal form: 2.4

mixed number: 2 2/5

hope this helps :)

Step-by-step explanation:

The required solution of the given fraction divide 2/5 by 1/6 is equal to 12/5.

Given that the fraction is divide 2/5 by 1/6.

When dividing fractions, multiply the first fraction by the reciprocal of the second fraction.

To divide 2/5 by 1/6, write it as:

(2/5) ÷ (1/6)

To find the reciprocal of 1/6, flip the fraction:

Reciprocal of 1/6 = 6/1

Now, rewrite the expression as:

(2/5) × (6/1)

Multiplying the numerators and denominators gives us:

(2 × 6) / (5 × 1) = 12/5

Therefore, 2/5 divided by 1/6 is equal to 12/5.

Learn more about Fractions here:

brainly.com/question/10354322

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What is another way to select (5-x)

Answers

Answer:

x-5

Step-by-step explanation:

Because the opposite of (5-x )is (x-5)

Answer:

x-5 or -5x

Step-by-step explanation:

Solve for X please help !!
A) 6
C) 9
B) -4
D) 7

Answers

The answer is 6 which is a

I need help on this math question

Answers

Answer:

5

Step-by-step explanation:

Marco takes 12 mins to drive his car down the hill to the movies and 24 mins to drive up the hill from the movies he goes to the movies Monday through Friday.How many mins does he spend driving his car to and from the movies in two weeks ?Wrote an equation to model your work

Answers

Answer:

360 minutes

Step-by-step explanation:

Given that:

Driving down the hill (d) = 12 minutes

Driving up the hill (u) = 24 minutes

Days = Monday - Friday = 5days

For 2 weeks : 2 * 5 = 10

Total time taken to drive up and down daily (T) : (12 + 24) minutes = 36 minutes

For the two weeks :

10(T)

= 10(36)

= 360 minutes

Model:

Let number of days = n

Number of minutes :

n(u + d)

Write an equation that represents the relationship between the distance the car has traveled in miles, , and the amount of gas left in the tank in gallons x

Answers

Answer: y= Y/x = ?

Step-by-step explanation: write the equation like said, and use the numbers you get to fill in. So say you traveled 500 miles , and you had 540 miles till empty yku would have 40 miles left , so you traveled 500 miles per gallon of gas :) hope this helps

is 2 1/6 a irrational?

Answers

Answer:

it is rational

Step-by-step explanation:

hope i help? :DD

all of the classifications for the number -8

Answers

Answer:

:)

Step-by-step explanation:

-8 is rational, and an integer.

It is a rational number because -8 is an integer or decimal from above, and not equal to 0.

It is a integer because it is a whole number, even if it is a negative!

Marie needs 2 1/4 yards of fabric
She already has 1 3/8 yards.
How many yards of fabric does she need
a
1/8 yard
b
3/4 yard
c
7/8 yard
d
1/4 yard

Answers

The answer is c because if you subtract the smaller fraction from the bigger one you will get 7/8 yards of fabric left!

MATH QUESTIONS FOR>>> jimthompson5910 >> jimthompson5910 >> jimthompson5910 >> jimthompson5910 >> jimthompson5910 >> jimthompson5910 >> jimthompson5910<<<
2.
Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x+9) ?

The graph of g(x) is the graph of​​​ f(x) translated 9 units right.
The graph of g(x) is the graph of f(x) translated 9 units left.
The graph of g(x) is the graph of​ f(x)​ vertically stretched by a factor of 9.
The graph of g(x) is the graph of​​ f(x)​ vertically compressed by a factor of 9.
3.
The linear parent function, f(x)=x ,was transformed to create a graph g(x) =f(x)−1.

Which statement about the graphs is true?

The graph of f is shifted 1 unit to the left to create the graph of g.
The graph of f is shifted 1 unit down to create the graph of g.
The graph of f is reflected over the x-axis to create the graph of g.
The graph of f is reflected over the y-axis to create the graph of g.
4.
The graph of function g(x) is a vertical stretch of the graph of function f(x)=x ​​by a factor of 2.

Which equation describes function g(x)?

​​g(x)=f(x)−2
​g(x)=12f(x)
g(x)=2f(x)
​​g(x)=f(x)+2
5.
The function f(x)=x was transformed to create a graph g(x)=f(x−3)+1.

Which statement describes how the graphs of f and g are related?

The graph of f is shifted to the right 3 units and down 1 unit to create the graph of g.
The graph of f is shifted to the right 3 units and up 1 unit to create the graph of g.
The graph of f is shifted to the left 3 units and up 1 unit to create the graph of g.
The graph of f is shifted to the left 3 units and down 1 unit to create the graph of g.

Answers

Answer:

I'm not sure with the answer cuz it's s graphic question it can't be explained

Problem 2

Answer: B) Shift 9 units to the left

If we replace every x with x+9, then the inputs are now 9 units larger. This moves the xy axis 9 spaces to the right. If we keep the f(x) curve fixed in place while the xy axis moves, then it gives the illusion f(x) moves 9 units to the left.

====================================================

Problem 3

Answer: B) Shift 1 unit down

Think of f(x) as y. So f(x)-1 means y-1 to show that we subtract 1 from each y coordinate of each (x,y) point on f(x).

====================================================

Problem 4

Answer: C) g(x) = 2f(x)

We multiply each y value by 2. So g(x) = 2y = 2*f(x). This makes f(x) twice as tall as before.

====================================================

Problem 5

Answer: B) shifted to the right 3 units and up 1 unit

The replacement of x with x-3 means we shift 3 units to the right. It's the similar idea to problem 2, but we're working in reverse now.

The +1 at the end means we shift 1 unit up.

Brandon has 32 pieces of paper. Sophia has 2 times as many pieces of paper as Brandon. How many pieces of paper does Sophia have?

Answers

Answer:

64 pieces of paper

Step-by-step explanation:

32 × 2 = 64

So 2x32 is 64 write down 32 then write x 2 now make a line  your answer is 64

- A credit card company charges 12% interest
on the unpaid balance. If Mona has an unpaid
balance of $220, how much interest will she be
charged for one month?
a. $2.75
b. $14.40
C. $24.00
d. $26.95

Answers

The answer is C. $24



30 POINTS AND I WILL MARK BRAINLYEST

What are the x intercept and the y intercept of the graph 9x-7y=-63 identify the x and y intercepts then choose the graph of the equation

Answers

Answer:

x intercept -7,0

y intercept 0,9

Find the measure of each marked angle. Assume the lines are parallel.
(2x - 30)° =
(x+3)° =

Answers

Answer:

Measure of each angle = 36°

Step-by-step explanation:

[tex](2x - 30) \degree = (x + 3) \degree \\ (alternate \: \angle \: s) \\ \\ 2x - 30 = x + 3 \\ \\ 2x - x = 30 + 3 \\ \\ x = 33 \\ \\ (2x - 30) \degree \\ = (2 \times 33 - 30)\degree \\ = (66 - 30)\degree \\ = 36 \degree \\ \\ (x + 3) \degree \\ = (33 + 3) \degree \\ = 36\degree[/tex]

The value of x will be equal to 33.

What are alternate exterior angles?

According to the alternate exterior angle theorem, the exterior angles created on either side of a transversal when two parallel lines intersect are equal. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given angles (2x - 30)°  and (x+3)° are alternate exterior angles so these two angles will be equal to equal to each other.

(2x - 30)° = (x+3)°

Separate all the like terms and calculate the value of x:-

(2x - 30)° = (x+3)°

2x - x = 33 + 3

x = 33

Therefore, the value of x will be equal to 33.

To know more about alternate exterior angles follow

https://brainly.com/question/23134598

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what is latoyas error

Answers

Answer:

there are two threes. Latoya only included one of them.

!!! HELP PLS will mark brainliest:

Answers

Answer: domain would be clearest

Step-by-step explanation: range is all about you

how do i know if this is parallel, perpendicular, or neither?

Answers

Answer:

It's perpendicular

Step-by-step explanation:

Well, normally you would have two equations. But in this case it is perpendicular to the x-axis. You must first solve for y and you'll get the answer:

y=3/4x+8

Then you plug numbers into the equation and graph them onto a graph. It'll be perpendicular to the x-axis.

GIVING BRAINLIEST TO WHOEVER ANSWERS FIRST!!!

Select all of the transformations or series of transformations that support his claim.
a translation of 12 units right and 2 units down
a translation of 2 units down followed by a 180° rotation about the point (1, 2)
a reflection over the line x = 0 followed by a reflection over the line y = 4
ОООООО
a translation of 6 units right
a reflection over the line x = 1 followed by a translation of 2 units down
a rotation of 180° about the point (1,4)
Previous

Answers

translation of 12 units right and 2 units down

A reflection over the line x=1 followed by a translation of 2 units down

Solve the linear equation 39-4t= 24+ t for t

Answers

Answer:

T is 3 because you could of asked google

Answer:

t = 3

Step-by-step explanation:

39-24=t+4t

15 = 5t

5t = 15

t = 15 divided by 5

t = 3

hope this helps!

pls marks as brainliest!!

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