The annual revenue and cost functions for a manufacturer of zip drives are approximately R(x)=520x-0.02x² and C(x) = 160x+100,000, where x denotes the number of drives made. What is the maximum annual profit? A. $1,620,000 B. $1,720,000 C. $1,520,000 D. $1,820,000

To get the simplified form of the algebraic expression x²+ y², we need to subtract -2xy from the expression x² +y²-2xy.

To subtract 2xy from the expression x² + y² - 2xy and get x² + y², you can simply remove the -2xy term. This is because subtracting 2xy is the same as adding -2xy, which is the same as negating 2xy and keeping it in the same position.

The reason for this is that subtracting a number is the same as adding its opposite. In this case, -2xy is the opposite of 2xy, so when you subtract 2xy, you are effectively adding -2xy.

Therefore, x² + y² - 2xy and x² + y² are equivalent expressions, since they both represent the same mathematical value.

In mathematical terms:

x² +y²-2xy = x²+ y² +2xy

In other words, the subtraction of 2xy is a commutative operation and the order of the terms does not matter. If you add or subtract the same value, it does not change the final result.

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What should be subtracted from x² +y²-2xy to get x²+ y² algebraic expressions?

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Since FE bisects <DFG, then the value of x and measure of <DFG are:

a. x = 24

b. m<DFG = 106^o

An angle bisector is a straight line constructed in such a way that it divides a given angle into two equal measures.

Thus given that FE bisects <DFG, this implies that;

i. m<DFE ≅ m<EFG

So that,

3x - 19 = 2x + 5

collect like terms to have;

3x - 2x = 19 + 5

x = 24

To solve for x, the value of x is 24^o.

ii. To determine the measure of DFG;

m<DFG = (3x - 19) + (2x + 5)

             = (3(24) - 19) + (2(24) + 5)

             = 53 + 53

             = 106

m<DFG = 106^o

The measure of <DFG is 106^o.

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The requried equation used to find the total cost of care of dogs is given as, 1. y = 35x  for 0 ≤ x ≤3 2. y = 35 + 25x for 3 < x. None of the op[tions are correct.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Emma takes care of dogs while their owners are on vacation. She charges $35 for each of the first 3 days she takes care of a dog and $25 for each day thereafter.

Two equations will be formed,
1. y = 35x  for 0 ≤ x ≤3
2. y = 35 + 25x for 3 < x

Thus, the requried equation used to find the total cost of care of dogs is given as, 1. y = 35x  for 0 ≤ x ≤3 2. y = 35 + 25x for 3 < x. None of the op[tions are correct.

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The distance between points (7, 4) and (3, 4) is 4 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, Are two points (7, 4) and (3, 4).

Therefore, By the distance formula the distance between the two points

(7, 4) and (3, 4) would be,

[tex]D = \sqrt{(3 - 7)^2 + (4 - 4)^2[/tex].

[tex]D = \sqrt{(-4)^2 + (0)^2[/tex].

[tex]D = \sqrt{(16[/tex].

D = 4.     (negative 4 is inadmissible).

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The equation is true when putting parentheses. The equation becomes:

(5 - 3)(-1 + 6)² = 50.

What is an equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

The given equation is 5 - 3 - 1 + 6² = 50.

Here we need two parentheses.

Since 50 can be written as 50 = 25 × 2 = 5² × 2

Now 2 can be written as (5-3) and 5 can be written as (-1+6).

Now put the parentheses:

(5 - 3)(- 1 + 6)²

= 50

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Answer:

x = 3

y = 4
Step-by-step explanation:

The opposite sides of a parallelogram are always equal.

From the above statement, we get two equations-

[tex]4x+6 = 7x-3[/tex] and [tex]4y-3=3y+1[/tex]

Solving for x:

[tex]4x+6=7x-3\\6=3x-3\\9=3x\\3=x[/tex]

Solving for y:

[tex]4y-3=3y+1\\y-3=1\\y=4[/tex]

On solving the provided question, we can say that multiplication of polynomial  3(8 + ) is 24+3

A polynomial is an algebraic expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of variables and coefficients.

For example, in the expression , x is the variable and coefficients of  and  are 1 and 2 respectively.

When we are asked to do multiplication of polynomials, we multiply term by term in the brackets until every term is multiplies with another in different bracket.

Like in 3(8 + ), we first multiply 3 with the first term inside the bracket, which is 8 and then we multiply 3 with the second term, which is b and maintaining the plus sign as it is.

So the answer is

(3)(8)+(3)()

=24+3

Hence, the answer is 24+3.

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The third one will represent a linear relationship between x and y.

What is a linear relationship?

A linear relationship is any relationship between two variables that creates a line when graphed in the xy-plane.

Linear equations can be used to represent the relationship between two variables, most commonly x and y. To form the simplest linear relationship, we can make our two variables equal:

y=x

By plugging numbers into the equation, we can find some relative values of

x and y.

0        0

1         1

2        2

3        3

If we plot those points in the xy-plane, we create a line.

Now,

For the given graphs only the third one shows a straight line made from equations.

Hence, It represents the linear relationship between x and y.

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Que knows that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem.

The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.

So, we have:

Height of 6 and bas of 9 units of the right triangle.

Pythagorean formula:

c=√a²+b²

Now, insert values and calculate as follows:

c = √a²+b²

c = √9²+16²

c = 18.35 units

Therefore, we know that the required hypotenuse of the given right triangle is 18.35 units from the Pythagorean theorem.

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Complete question:

A right triangle has a base of 9 and a height of 16. Calculate hypotenuse.

we can find out the domain of a given function by looking at the values of real number where the function f(x) i defined

range can be find out by putting the values of x and find out the values of y and y will be your range of a given function f(x)

let us take an example

suppose f(x)= x+1

here function is defined for all real values

therefore domain is real number

and range is also real number because if we take the value of x whatever we will take we get the value of y

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Answer: 34

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

Answer: No, the correct answer is 125/100

Step-by-step explanation:

When adding fractions together the denominator must always be the same and stay the same when added together.

Answer:

Dimensions are 12 , 6

Step-by-step explanation:

      Let the length be 'x' miles.

                   width = (x - 6) miles

 Area of a rectangle = length * width

       x *(x -6) = 72 square miles

       x*x - x *6 = 72

     x² - 6x -72 = 0

Sum = -6

Product = -72

Factors = -12 , 6   { -12 * 6 = -72  & -12 + 6 = -6}

x² - 12x + 6x - 72 = 0       {Rewrite the middle term using the factors}

x(x - 12) +6(x - 12)=0

(x -12)(x + 6) =0

x - 12 = 0 ;

    x = 12

{x + 6= 0 is ignored, as dimensions will not have negative value}

length = 12 miles

widht = 12 - 6 = 6 miles

Answer:

1 1/2 cups of flour.

Step-by-step explanation:

You can work this as a proportion:

1/4 cup → 1/6 of a cake

x cups  → 1 cake

Cross-multiply.

(1/4 cup)(1 cake) = (x cups)(1/6 cake)

Solve for x.

x = 6(1/4) = 1 1/2 cups

[tex]\displaystyle n\hat A[/tex] is the number of squares of arrays present.

An arrangement of objects, images, or numbers in rows and columns is called an array. Arrays are a convenient representation of the concept of multiplication. This array has 4 rows and 3 columns. This can also be described as a 4 x 3 array. Arrays are a way of representing multiplication and division using rows and columns. Rows represent the number of groups. The columns represent the number of each group or the size of each group. The number 24 can be represented as a 6-by-4 array (6-by-4) because 6-by-4 = 24. It can also be represented as a 2 by 12 array, since 2 by 12 = 24.

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Answer:

4x-10=3x+12

4x+3x= 12+10

7x= 32

x= 32÷7

x=4.571

Each measure of the angle when the total measure of the angles is (n−2)·180° and n is 8 will be 235°.

From the information, the total measure of the angles is (n−2)·180°, where n=8. The term regular means all interior angle measures are the same.

It should be noted that in Mathematics, the value of the sum of angles is Illustrated in this case. We can determine each angle measure from the total angle measure thus:

(n - 2) × 180

n = 8

It should be noted that n in this case simply means the number of sides

= (n - 2) × 180

= (8 - 2) × 180

= 1080°

Each measure of the angle will be:

= 1080° / 8

= 135°

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3x² is a second-degree polynomial, also known as a quadratic equation.

A polynomial is a mathematical expression that consists of constants, variables, and exponents. This polynomial can be represented as an equation in the form of ax^2 + bx + c, where a, b, and c are constants, and x is an unknown. In this case, a = 3, b = 0, and c = 0. In this case, the polynomial is 3x², which contains one constant (3) and one variable (x) with an exponent of 2. To calculate the value of this polynomial, we can substitute a value for x and then solve. For example, if x=2, then 3x² = 3x2 = 3(2)2 = 3(4) = 12.

Therefore, when x=2, 3x² = 12.

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Answer: look it up

Step-by-step explanation:

The absolute value (Modulus) of a number is the distance of the number from zero.

Absolute value is always acting for in the modulus(|z|) and its value is always positive.

So, the absolute value of the complex number is Z = a + ib is |z| = √ (a2 + b2).

Now, the absolute value of the complex number is the positive square root of the sum of the square of the real part and the square of the unreal part, i.e.,

The complex number is defined as the number in the form a+ib, where a is the real part while ib is the unreal part of the complex number in which i is known as iota and b is a real number.

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The rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

One way to think of a function is as a rule that assigns or maps each member of a set, x, to the same value, y, known as its image.

x → Function → y

Functions are frequently denoted by a letter, such as f, g, or h. F(x) = x2+ 5 is the formula for the function that squares a number and adds a 3. A function's impact on specific values can be demonstrated using the same idea.

Given that  f(x) =  √(x² - 2)

And g(x) = -2f(x+5)

Substitute the function f(x) =  √(x² - 2) in g(x) = -2f(x+5)

g(x) = -2(√(x² - 2))(x+5)

g(x) = (-2x - 10)(√(x² - 2))

Thus, the rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

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The expression of an exponential function f that has a slope of 12 of a line from the point (0, f(0)) to the point (2, f(2)) is the exponential function;

An exponential function is a function that includes the argument as an exponent, index or power of a constant.

The points on the function are; (0, f(0)), and (2, f(2))

The required slope between the points x = 0, and x = 2 is 12

Therefore;

(f(2) - f(0))/(2 - 0) = 12

f(2) - f(0) = 12 × (2 - 0) = 24

The

The exponential function can be presented in the form;  f(x) = a·bˣ

When x = 0, we get; f(0) = a·b⁰ = a

When x = 2, we get; f(2) = a·b²

f(2) - f(0) = a·b² - a = 24

a·(b² - 1) = 24

Let a = 3, and b = 3, we get;

3 × (3² - 1) = 24

Therefore, possible values of a and b are; a = 3, and b = 3

The exponential function is therefore;

The slope of the line that extends from the point (0, f(0)), to the point (2, f(2), is therefore;

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 y = 4x - 8 is linear equation .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and x + y = 2. Another example is 3x - y + z = 3.

(0,-8) and (2,0)

 m = 0 - (-8)/2 - 0

      = 8/2 = 4

y - (-8) = 4 ( x - 0)

 y + 8 = 4x

  y = 4x - 8

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So on solving the provided question we can say that here all angles of of a quadrilateral = 30, so, each will be 90

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here all angles of of a quadrilateral = 30

so, each will be 90

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Prime multiples of number 3 is number 3 itself as other multiples of three are representing composite numbers.

As given in the question,

Given number is equal to :

3

Multiples are those numbers which we get when we multiply the given number by any other integer.

Multiples of three are equal to :

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

............... so on.

When we multiple 'n' by three we get 3n.

All other multiples have more than two factors that is one , three , and at least number itself.

So other multiples of three are composite numbers.

Prime multiples has only two factors one and number itself.

3 represents the prime multiple.

Therefore, three is the only number which is the prime multiple of 3.

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The amount of money you must pay at the gas station could be represented using the variables y = price in dollars, x = gas in gallons, and a proportionality constant, k: y = kx.

Mrs. Tenon has spent $5 on 25 party favours.

Equation form of proportional relationships is written as y=kx.

If you substitute $5 for y and $25 for x in the formula for the proportional relationship above, you can find the value of the proportionality constant, or k.

$5=k(25)\sk=$5/25\s=0.2

0.2 is the proportionality constant. Thus, each party favour costs $0.20.

Let's say there are r party favours and the cost is c. c=0.2r

In the equation above, 40 should be substituted for r to get the price of 40 party favours: c=0.2 (60) = 12.00.

As a result, the cost for 40 guests is $ 8.00, and the cost for 60 party favours is $ 12.00.

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No, These both expressions are not equal to each other.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expressions are,

⇒ 12(8y - 16k) and 16(2y - 4k)

Now, We can check both expressions as;

⇒ 12 (8y - 16k)

⇒ 12 × 8 (y - 2k)

⇒ 96 (y - 2k)

⇒ 16 (2y - 4k)

⇒ 16 × 2 (y - 2k)

⇒ 32 (y - 2k)

Thus, We get;

⇒ 96 (y - 2k) ≠ 32 (y - 2k)

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The rule for any number raised to the power of 1 is that the number remains unchanged.

Mathematically, this can be written as: a^1 = a where "a" is the base number. The rule for a number raised to the power of 1, is also known as the exponent.

For example, if we take the number 2, and raise it to the power of 1, we would get:

Key points:

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