11. Which of the following points is on the
line 3x - 5y = 1
A. (1, 2)
B. (2,1)
C. (3/5,1)
D. (2,3)

Answer:

The answer is below

Step-by-step explanation:

Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16

Solution:

Given that the ellipse has the equation: 4x² + 16y² = 16

let us make x the subject of the formula, hence:

4x² + 16y² = 16

4x² = 16 - 16y²

Dividing through by 4:

x² = (16 - 16y²)/4

x² = 4 - 4y²

Taking square root of both sides:

[tex]x=\sqrt{4-4y^2 }\\[/tex]

The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4xy

[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]

Therefore the length = 2x = 2√2, the width = 2y = 2/√2

Answer:

don't know what you need

Step-by-step explanation:

9514 1404 393

Answer:

  1)  c, f

  2) a, e

  3) b, d

Step-by-step explanation:

If you think about the units associated with a coordinate (feet, for example), then you may recognize the following

a) each difference is of "feet", so each difference will have units of "feet". The ratio of "feet" to "feet" cancels the units, leaving a pure number. In this case, it is called "steepness" in selection e. Steepness is given by the slope formula (2).

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b) The difference in parentheses has units of "feet" (as in (a)), so the square will be "square feet". The sum of two of those will still be "square feet" and the square root of that will be "feet". The units of the formula are those of distance, or length, matching selection d. Distance is given by the distance formula (3).

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c) The form shown is an ordered pair. That is the same as the representation of a coordinate point, selection f. Coordinates of a point are given by the midpoint formula (1).

Answer:

apples cost a total of 2.16

cherrys cost a total of 9.05

Step-by-step explanation:

1.35*1.6=2.16

3.62*2.5=9.05

Answer:

It will read the same at F = -40.

Step-by-step explanation:

The relation between fahrenheit and celsius is given by the following equation:

[tex]C = \frac{5(F-32)}{9}[/tex]

At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer?

This is F for C = F. So

[tex]C = \frac{5(F-32)}{9}[/tex]

[tex]F = \frac{5(F-32)}{9}[/tex]

[tex]9F = 5F - 160[/tex]

[tex]4F = -160[/tex]

[tex]F = -\frac{160}{4}[/tex]

[tex]F = -40[/tex]

It will read the same at F = -40.

Answer:

9

Step-by-step explanation:

Move the variable to the other side of the equation

144 ÷ 16 = a

9 = a

Check:

144 ÷ a = 16 (Correct)

Answer:

The value of the test statistic is t = 2.19.

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Sample of 1300 voters:

This means that [tex]n = 1300[/tex]

Found that 45% of the residents favored construction.

This means that [tex]X = 0.45[/tex]

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.

This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:

[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]

So, the test statistic is:

[tex]t = \frac{X - \mu}{s}[/tex]

[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]

[tex]t = 2.19[/tex]

The value of the test statistic is t = 2.19.

Answer:

4.24

Step-by-step explanation:

the calculator says otherwise (but yea its 4.24

Answer:

C

Step-by-step explanation:

Answer:

126 degrees

Step-by-step explanation:

The sum of adjacent side of the rectangle is 180 degrees

Hence <1 + <4 = 180 degrees

Given

<4 = 54 degrees

<1 = 180 - <4

<1 = 180 - 54

<1 = 126degrees

Hence the value of <1 is 126 degrees

Answer:

Its oka linden

Step-by-step explanation:

Just cause

Answer:

Hey

Step-by-step explanation:

Where is the question

Answer:

$12.49

Step-by-step explanation:

cost of two purses = $57.97 - cost of dress = $57.97 - $32.99 = $24.98

cost of one purse = $24.98 ÷ 2 = $12.49

Answer:

B

Step-by-step explanation:

(x+4)(3x^2-7)

multiply and get 3x^3 +12x^2 -7x -28 which is anwser choice b

Answer:

x=9

Step-by-step explanation:

13+14=3x

27=3x

27/3=x

9=x

Answer:

it's 78<C. < means less than

Answer:

50°

Step-by-step explanation:

the angles should add up to 180. there is a 90° angle abd a 40° angle which adds up to 130. 180-130 gives you rour missing angle if 50°.

Answer:

4.5 (j + m) + 27

Step-by-step explanation:

Answer:

- AB is similar to YZ because all the sides from triangle ABC got multiplied by 3/4, and 40 times 3/4 = 30.

- AC is similar to YX because 50 times 3/4 = 37.5.

- CB is similar to XZ because 60 times 3/4 = 45.

hope this helps!

Answer:

attached below is the solution

Step-by-step explanation:

|x| < 7

= -7 < x < 7

| y | < 3

= -3< y < 3

attached below is the shaded region in the xy-plane

Answer:

C) n=5

Step-by-step explanation:

6n+13=43

6n+13-13=43-13

6n=30

6n/6=30/6

n=5

Answer:

Your answer is c

Step-by-step explanation:

Here you go mate

Step 1

6n+13=43  Equation/Question

Step 2

6n+13=43  Simplify

6n+13=43

Step 3

6n+13=43  Subtract 13 from sides

6n=30

Step 4

6n=30  Divide sides by 6

5

Answer

n=5

Hope this helps

Answer:

300 feet

Step-by-step explanation:

Answer: the initial number of water lily’s

Step-by-step explanation:

the value 1.106 represents the population increase rate

edge 2021

The value 3.915 represents the initial population of water lilies

The standard exponential equation is given as y = ab^x

where;

Given the exponential equation y = 3.915(1.106^x

On comparison, we can see that;

a  = 3. 915

This shows that the value 3.915 represents the initial population of water lilies

Learn more on exponential equation here: https://brainly.com/question/2456547

Answer:

15lb chicken 30 oz. soy sauce 5lb. green peppers

2 1/2 lb. scallions 10 oz. ginger

10 cups Water

To make 60 proportions of Stir Fried Chicken requires 15lbs of chicken,

30 oz of soy sauce, 3 lb. green peppers, 5/2 lb scallions, 10 oz ginger, and 10 cups Water.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given  12 portions of  Stir-Fried Chicken requires 3 lb chicken 6 oz.

soy sauce 1 lb. green peppers

1/2 lb scallions

2 oz ginger

2 cups Water.

∴ To make 60 proportion or (12×5) proportion we have to multiply each ingredient by a factor of 5.

So,  60 proportions of  Stir-Fried Chicken requires (3×5) = 15lbs of chicken,

(6×5) = 30 oz of soy sauce,  (1×3) = 3 lb. green peppers, (1/2×5) = 5/2 lb scallions, (2×5) = 10 oz ginger and (2×5) = 10 cups Water.

learn more about ratios and proportions here :

https://brainly.com/question/26974513

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