Convert the rectangular equation to polar form and sketch its graph.
(x^2 +y^2)^2 - 9 (x^2-y^2) = 0

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

31x³-60x²+7x-75

Step-by-step explanation:

(30x³-49x³+7x)+(50x³-60x²-75)

(-19x³+7x)+(50x³-60x²-75)

-19x³+50x³+7x-60x²-75

31x³-60x²+7x-75

Answer:

Please refer to the attached diagram for answer.

Step-by-step explanation:

Upper-left coordinates on a rectangle are (-1, 4)

Upper-right coordinates are (3, 4)

Perimeter of rectangle = 24 units

To find:

To draw the rectangle on the coordinate plane.

Solution:

Let the rectangle be ABCD.

So, sides AB  = CD and BC = DA

Let Point A has coordinates (-1, 4).

And upper right coordinates will be adjacent to A.

So, let Point B (3, 4).

Let us find the distance between A and B by distance formula:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Where,

\(x_2 = 3\\x_1 = -1\\y_2 = 4\\y_1 = 4\)

\(AB = \sqrt{(3-(-1))^2+(4-4)^2}\\\Rightarrow AB = \sqrt{(4)^2+(0)^2}\\\Rightarrow AB = 4\)

AB = 4 = CD

Perimeter of rectangle = Sum of all four sides = 2 (AB+DA) = 24

\(2 \times 4 + 2DA = 24\\\Rightarrow 2DA=24-8\\\Rightarrow 2DA=16\\\Rightarrow DA =8\ units\)

As it is a rectangle, its adjacent sides will be perpendicular to each other.

When we move from A to B only x coordinate is changing and it has changed by  4 (3- (-1) ) units. (Found by subtracting the x coordinates of the two points.)

Similarly, when we will move from D to A, only y coordinate will change by 8 units. (D is lower left coordinate so add 8 to y)

\(\Rightarrow y + 8 = 4 \Rightarrow y =-4\)

\(x\) coordinate will be same as that of A i.e. -1.

So, D will be (-1, -4)

Similarly, when we will move from C to B, only y coordinate will change by 8 units. (C is lower right coordinate so add 8 to y)

\(\Rightarrow y + 8 = 4 \Rightarrow y =-4\)

\(x\) coordinate will be same as that of B i.e. 3.

So, C will be (3, -4).

Now, let us draw

A(-1, 4)

B(3, 4)

C (3, -4)

D(-1, -4)

Please refer to the attached diagram for answer.

Answer:

A(-1, 4) B(3, 4)C (3, -4)D(-1, -4)

Step-by-step explanation: Brainliest plus-size

Answer:

a) x=4

b) y=3

c) 3m-2n

Answer:

A) x = 12

Step-by-step explanation:

4x-6 = 42

4 = 48

x = 12

7x+10 = 94

7x = 82

x = 12

Answer:

1) -13/8

Step-by-step explanation:

decimal form is -1.625

Answer:

(x+12)^2=84

Step-by-step explanation:

x^2+24x+60=0

x^2+24x=-60

x^2+24x+(24/2)^2=-60+(24/2)^2

(x+24/2)^2=84

(x+12)^2=84 (ans)

The safe load, l, of a wooden beam of width w, height h, and length l, then the nearest integer is, L = 4607.7 pounds.

Based on the given conditions,

The safe load = L

A wooden beam of width = w

Height = h

Length = l

The safe load L, of the beam varies directly as the product of the width and the square of the height.

L∝ (w × h²)

And varies inversely as the length of the wooden beam.

L∝ (w × h²)/l

L = \(\frac{k*w*h^{2} }{l}\)       (Equation-1)

Where k = proportionality constant

If w = 4 inches, h = 7  inches, l = 240 inches and L = 2540 pounds

Then,

We can substitute values in equation-1,

L = \(\frac{k*w*h^{2} }{l}\)  

2540 = (k*4*\(7^{2}\))/240

2540 = (k*4*49)/240

2540 = (k*196)/240

2540*240 = k*196

609600 = k*196

609600/196 = k

3110.20 = k

If w = 5 inches, h = 8 inches and l = 216 inches

L = \(\frac{k*w*h^{2} }{l}\)  

L = ( 3110.20 * 5 * \(8^{2}\) )/216

L = ( 3110.20 * 5 *64 )/216

L = 995264/216

L = 4607.7 pounds

Therefore,

The safe load, l, of a wooden beam of width w, height h, and length l, then the nearest integer is, L = 4607.7 pounds.

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Explanation:

The two angles shown are vertical angles. This occurs whenever you have an X shape like this, and whenever the angles are opposite one another. Vertical angles are always congruent.

6x+7 = 8x-17

6x-8x = -17-7

-2x = -24

x = -24/(-2)

x = 12

The another endpoint of a line is (13, -3).

What is Straight line?

A line with no curve is called a straight line.

Given that;

One endpoint of a line = (-3, 7)

Midpoint of a line = (5, 2).

Now, Let the other endpoint of a line = (x, y)

Then, Other endpoint is solve by the definition of midpoint of two points as;

(x + (-3) / 2 , y + 7 / 2 ) = (5, 2)

(x - 3 / 2 , y + 7 / 2) = (5, 2)

By compare we get;

x - 3/ 2 = 5

x - 3 = 2 * 5

x - 3 = 10

x = 10 + 3

x = 13

And,  

y + 7 / 2 = 2

y + 7 = 2 * 2

y + 7 = 4

y = 4 - 7

y = -3

Hence, The another endpoint of a line is (13, -3).

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Answer:

msdnvqkyfhcjavnyoqrudfn fn,bq2yor78DHCBN

Here some examples of math by using Mr. Maxs life outside the classroom.

One example of math in Mr. Max's life outside the classroom could be calculating the amount of gas needed to fill up his car's tank before a road trip. This involves using basic arithmetic operations such as addition, subtraction, multiplication, and division to calculate the total distance he intends to travel, the fuel efficiency of his car, and the capacity of the fuel tank. By doing so, he can estimate the amount of gas needed for the trip and plan accordingly. Additionally, he may also use math to calculate the cost of the gas based on the current price per gallon or liter, and decide on the most cost-effective way to fill up his tank.

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complete question is:

What is one example of math in Mr. Max's life outside the classroom? 10. Is math everywhere, as Bobby believes? Support your answer with evidence.

Answer:

it says download docx so download it first and start typing

Step-by-step explanation:

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

277.46

Step-by-step explanation:

a. This sample can be classified as a convenience sample because it was taken from a specific group of students enrolled in a psychology class at a particular college.

b. Reason: The researchers did not use any randomization technique to choose the students; rather, they selected those who were readily available to them.

The estimate of the proportion of students who reported using illegal stimulants based on data from this survey in a psychology should not be generalized to all U.S. college students because of the following reasons: the sample was taken from a small, competitive college, which may not represent all U.S. colleges.

Students at other colleges may have different characteristics and behaviors that could affect their use of illegal stimulants. The study used self-report measures, which may not be entirely accurate. Students may not have been truthful about their use of illegal stimulants, intentionally or unintentionally, which could have led to an underestimation of the proportion of students who use these substances.

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Answer:

GRAPH OF 3x + y = 3 (written on attachment)

GRAPH OF 2y = 10 - 6x (written on attachment)

Answer:

f ÷ 10

Step-by-step explanation:

We  want to write an expression

divided by means the number or variable before comes first, then the divided by symbol, then what comes after

f ÷ 10

Hello!

F divided by 10 is written like this:

\(\sf{\cfrac{f}{10} \ or \ f\div10}\).

\(\triangleright\)This expression is read "f divided by 10"

Hope that helps!

-art lover

Answer:

18000 of it was her salary.

that leaves 3000 commission.

3000/.12 = 25000.

she made sales of 25000.

the formula for her pay would be pay = 18000 + .12 * sales

if sales is 25000, then formula for pay becomes:

pay = 18000 + .12 * 25000

simplify to get:

pay = 18000 + 3000

combine like terms to get:

pay = 21000

Step-by-step explanation:

hope this helps you

Mark my answer as brainalist please

Answer:

a

Step-by-step explanation:

sum of all 3 angles in a triangle is 180 degrees and a straight line is also 180 degrees, so the angle is basically equal to 65+30

Answer:

∠ ADC = 122°

Step-by-step explanation:

ABCD is a cyclic quadrilateral.

opposite angles in a cyclic quadrilateral sum to 180° , that is

∠ ADC + ∠ ABC = 180∠

∠ ADC + 58° = 180° ( subtract 58° from both sides )

∠ ADC = 122°

Answer:

the answer will be a because its on top of it

Answer:

E, I hope this helps :D

Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

Answer:

0.1s + 125 < 180

The independent variable in either a before/after t-test or a within-subjects ANOVA is always measured on a nominal or categorical scale.

This is because these statistical tests are used to compare means of two or more related groups, where the independent variable represents the different conditions or time points in which the dependent variable is measured.

For example, in a before/after t-test comparing the effectiveness of a medication, the independent variable would be the two time points (before and after), which are categorical in nature. Similarly, in a within-subjects ANOVA comparing three different treatment conditions, the independent variable would be the three treatment conditions, which are nominal in nature.

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The correct answer of the operation is option B: 4x^2 - 9.

To perform the operation (2x-3)(2x+3), we can use the FOIL method, which stands for First, Outer, Inner, Last. Let's go through the steps:

First: Multiply the first terms of each binomial.

(2x)(2x) = 4x^2

Outer: Multiply the outer terms of each binomial.

(2x)(3) = 6x

Inner: Multiply the inner terms of each binomial.

(-3)(2x) = -6x

Last: Multiply the last terms of each binomial.

(-3)(3) = -9

A binomial is a two-term algebraic expression that contains variable, coefficient, exponents and constant, a binomial is an expression that has two unlike terms connected through an addition or subtraction operator in between.  

Now, let's combine the like terms:

4x^2 + 6x - 6x - 9

Notice that the terms 6x and -6x cancel each other out.

Simplifying further, we have:

4x^2 - 9

The correct answer is option B: 4x^2 - 9.

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The percentage of tires that will have a life of 45,000 to 55,000 miles is  68.27%. So the correct option is 68.27%.

To find the percentage of tires that will have a life of 45,000 to 55,000 miles, we can use the concept of the normal distribution.

First, we calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation

For 45,000 miles:
z1 = (45,000 - 50,000) / 5,000 = -1

For 55,000 miles:
z2 = (55,000 - 50,000) / 5,000 = 1

Next, we look up the corresponding values in the standard normal distribution table. The table will provide the proportion of data within a certain range of z-scores.

The percentage of tires with a life between 45,000 and 55,000 miles is the difference between the cumulative probabilities for z2 and z1.

Looking at the standard normal distribution table, the cumulative probability for z = -1 is 0.1587, and the cumulative probability for z = 1 is 0.8413.

Therefore, the percentage of tires that will have a life of 45,000 to 55,000 miles is:
0.8413 - 0.1587 = 0.6826

Converting this to a percentage, we get:
0.6826 * 100 = 68.26%

So the correct answer is 68.27%.

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We have demonstrated that x² ≥ x for all integers x. Therefore, the statement x² ≥ x for all x ∈ Z is true.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

To prove that x² ≥ x for all x ∈ Z, we need to show that the inequality holds true for any arbitrary integer value of x.

We can prove this by considering two cases:

Case 1: x ≥ 0

If x ≥ 0, then x² ≥ 0 and x ≥ 0. Therefore, x² ≥ x.

Case 2: x < 0

If x < 0, then x² ≥ 0 and x < 0. Therefore, x² > x.

In either case, we have shown that x² ≥ x for all integers x. Therefore, the statement x² ≥ x for all x ∈ Z is true.

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Answer:

2+2=4

Step-by-step explanation:

Step-By-Step Explanation:

1hour = 52×1= 52miles

2hours = 52×2= 104miles

5hours = 52×5= 260miles

8hours = 52×8= 416miles

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