You decide to form a partnership with another business. Your business determines that the demand x for your product is inversely proportional to the square of the price for x ≥ 5.(a) The price is $1000 and the demand is 16 units. Find the demand function.(b) Your partner determines that the product costs $250 per unit and the fixed cost is $10,000. Find the cost function.(c) Find the profit function and use a graphing utility to graph it. From the graph, what price would you negotiate with your partner for this product? Explain your reasoning.

Yes, the sides 5 cm, 12 cm, and 13 cm form a right-angled triangle.

This is because of the Pythagorean Theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, 13 cm is the hypotenuse, and 5 cm and 12 cm are the other two sides.

5^2 + 12^2 = 25 + 144 = 169

13^2 = 169

Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, this means that the triangle is indeed a right-angled triangle.

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one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.

An obtuse triangle is a triangle that has one angle which measures greater than 90 degrees. In order to determine if a triangle is an obtuse triangle, we need to calculate its angles.

To calculate the angles of the triangle, we can use the following formula:

Angle 1 = arccos ( (b2 + c2 - a2) / 2bc )

Angle 2 = arccos ( (a2 + c2 - b2) / 2ac )

Angle 3 = arccos ( (a2 + b2 - c2) / 2ab )

In this case, a = 6cm, b = 10cm, and c = 13cm. Substituting these values into the formula, we get:

Angle 1 = arccos ( (102 + 132 - 62) / 2 x 10 x 13 ) = 89.99 degrees

Angle 2 = arccos ( (62 + 132 - 102) / 2 x 6 x 13 ) = 110.01 degrees

Angle 3 = arccos ( (62 + 102 - 132) / 2 x 6 x 10 ) = 89.99 degrees

Since one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.

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Answer: x = 2

Step-by-step explanation:

8 = 2x + 4

2x = 8-4

    = 4

x = 4 ÷ 2

  = 2

x = 2

What it would look like if it was an actual equation :

8 = 2₂ + 4

Answer:

x = 2

Terminology

Variable: Any letter than stands for a value than can be solved and change value.

Coefficient: The number right before a variable (without being separated by an operator). It is a multiplication factor for a variable. Basically, it's just a way to express what you are multiplying a variable by,

If the coefficient is 1, it means [variable] * 1. 1[variable]

If the coefficient is 3, it means [variable]  * x.  3[variable]

etc.

Constant: A fixed value (i.e. 3, 8, 1928). A variable is not a constant because if you were to add a coefficient (not including 0) to the start of a variable, the result would change depending on the value of the variable.

How to Solve

To solve, you must isolate the variable. It means moving the variable and it's coefficient to the other side of the equation with only the same variable on the same side with all the constants on the other side.

Do this with this rule that is extremely important in ALL of math beyond per-algebra and algebra.

Rule

If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same. That is how you solve for it.

Subtract 4 on both sides to isolate the variable.

8 - 4 = 2x + 4 - 4

Simplify by combining like terms.

4 = 2x

Divide 2 on both sides to solve for x as the coefficient is currently 2.

[tex]\frac{4}{2} =\frac{2x}{2}[/tex]

Simplify.

x = 2

The function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.

A function called exponential growth depicts population growth that happens consistently over time. You can assume that data increases exponentially when populations double or triple in size.

Exponential decay, which occurs when data contracts rather than expands, is the opposite of exponential growth.

A function of the form [tex]y=a(1 - r)^t[/tex], where a > 0and 0 < r < 1, is an exponential decay function.

A function of the form [tex]y=a(1 +r)^t[/tex], where a > 0 and r > 0, is an exponential growth function.

As 1.06 > 1,

y = 0.4(1.06)^t is an exponential growth function and the

growth factor = 1 + r

                       = 1 + 0.06

Percent rate of change = 0.06

                                        = 6/100 × 100%

                                         = 6%

Thus, the function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.

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Yes, there is possibility to construct a triangle whose sides are 2 cm, 3 cm and 5 cm.

According to the SSS or side-side-side rule of triangle, the sum of any two sides of triangle should be greater than third side of triangle. Assuming the side a to be 2 cm, side b to be 3 cm and side c to be 5 cm.

Side a + side b > side c

2 + 3 > 5

Performing addition on Left Hand Side of the equation

5 = 5

Side b + side c > side a

3 + 5 > 2

Performing addition on Left Hand Side of the equation

8 > 2

side c + side a > side b

5 + 2 > 3

Performing addition on Left Hand Side of the equation

7 > 3

Thus, we see the sum to be greater in two situations. Hence, the triangle is possible.

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The rocket’s height to the nearest hundredth when the distance between you and the rocket is 100 feet is equal to 96.83 feet.

Based on the information provided, the height h (in feet), of this rocket during its launching with respect to distance d between you and the rocket can be modeled by this quadratic function:

d(h) = √(625 + h²)

Substituting the given parameters into the quadratic function d(h), we have the following;

d(h) = √(625 + h²)

100 = √(625 + h²)

Taking the square of both sides of the quadratic function, we have the following:

100² = [√(625 + h²)]²

10,000 = 625 + h²

Rocket’s height, h² = 10,000 - 625

Rocket’s height, h² = 9,375

Rocket’s height, h = √9,375

Rocket’s height, h = 96.83 feet.

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Answer: 29/18 or 1  11/18  

Step-by-step explanation:  When adding fractions, you need the fractions to have a common denominator. In order to get the common denominator, find the lowest common number between 9 and 6. That number is 18.

7/9 times 18 = 14/18         5/6 times 18 = 15/18     14/18 + 15/18 = 29/18

Improper fraction: 29/18        Mixed number:  1   11/18

The perimeter of a square with an area of 100 square meters is calculated to be 40 m

The perimeter of a square is calculated using the formula 4 * length

Some necessary properties of a square

A square is a four sided polygon otherwise known as quadrilateral

All the sides are equal hence Length =  width or breadth

The angles at which each side intersect is at 90 degrees

The area of a square is Length² hence

Length² = 100

Length = √100

Length = 10

plugging in Length = 10 to the perimeter

P = 4 * length

P = 4 *10

P = 40 m

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Yes, The ordered pair (-1,- 3) is a solution to the inequality y > -5x⁴ + 7x³ + 8.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ y > -5x⁴ + 7x³ + 8.

And, The point is (- 1, - 3).

Now, We can substitute the value of (x, y) = (- 1, - 3) in given inequality and check as;

⇒ y > -5x⁴ + 7x³ + 8.

⇒ -3 > -5(-1)⁴ + 7(-1)³ + 8

⇒ -3 > -5 + 7 × - 1 + 8

⇒ - 3 > - 5 - 7 + 8

⇒ - 3 > - 4

This is true.

Thus, The ordered pair (-1,- 3) is a solution to the inequality

y > -5x⁴ + 7x³+ 8.

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The complete question is this,

The ordered pair (-1,- 3) is a solution to the inequality y >-5x⁴ + 7x³ + 8.

1) True

2) False

The range:{-8, 4, 10} and the function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}

A pair of numbers in a certain order is called an ordered pair. Ordered pairs include, for instance, (1, 2) and (-4, 12). The two numbers' relative placement is crucial: (2) is not equal to (1, 1) (2, 1) — (1, 2)≠(2, 1). (2, 1).

When displaying two variables, ordered pairs are frequently used. By writing (x, y) = (7, - 2), we indicate that x = 7 and y = -2. The terms "x-coordinate" and "y-coordinate" refer to the number that relates to the value of x and the value of y, respectively.

The, function is given as y = 3x - 2

Lets put this in graph

Domain: {-2, 2, 4}

put the x values in function

y = 3(-2) - 2

y = −8

y = 3(2) - 2

y = 4

y = 3(4) - 2

y = 10

Range: {-8, 4, 10}

The function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}

Thus, the range:{-8, 4, 10} and the function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}

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The value of the expression:  [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex] will be: [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]

We have to determine the value of the expression:  [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex]

First solving the expression without using the values of Limits:

As we can write the above as:

[tex]\int {( x^2 + 9)^{0.5}} \, dx \\\frac{1}{0.5+1}[( x^2 + 9)^{0.5+1}] \times \frac{x^3}{3} +9x[/tex]

As we know, [tex]\int{x^n} \, dx =\frac{1}{n+1}x^{n+1}[/tex], where, n is any number.

So we can write the above as:

[tex]\\\frac{1}{1.5}[( x^2 + 9)^{1.5} \times \frac{x^3}{3} +9x][/tex]

Now we will put the value of limits in the above expression:

First putting the lower limit, i.e. the value of x = 3

We will get it as:

[tex]\frac{1}{1.5}[( 3^2 + 9)^{1.5} \times (\frac{3^3}{3} +9\times 3)]\\\frac{1}{1.5} [18^{1.5}\times (9+27)]\\\frac{1}{1.5} [18^{1.5}\times 36][/tex]

Now putting the value of lower limit, i.e the value of x = 3,

We will get it as:

[tex]\frac{1}{1.5}[( 0^2 + 9)^{1.5} \times ({\frac{0^3}{3} +9\times 0)}]\\\frac{1}{1.5} [9^{1.5}\times ({0+0})]\\\frac{1}{1.5} [9^{1.5}\times 0]=0[/tex]

Now, for detemining the value of the expression,

We will subtract the value of lower limit from upper limit

We will get it as; [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]

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The number of times we will pick an orange or blue marbles = 1/768

The term probability refers to the possibility of happening an event. It is the ratio of favorable outcome to the total possible outcome.

Available marbles = 8

purple marbles = 5

orange marble = 2

blue marble = 1

probability of picking an orange marble = 2/48 = 1/16

as the marble is put back each time after picking up so

the probability of picking a blue marble = 1/48

Now we multiply the probabilities of each individual events = 1/16 × 1/48

                                  the proportion = 1/768            

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Answer:

hw could make 200 dollars in 4 weeks

Answer: Yes and no?

Step-by-step explanation: Yes, because since it is one single number, it would be considered a "linear" polynomial. But no, because since there is only one term, it wouldn't be considered a polynomial.

I only just learned about linear polynomials, so I think the safe answer would just be no, since there is only one term.

The complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

What is the congruent triangle?

The triangles are congruent regardless of how they are rotated or flipped. The symbol “≅” is frequently used to express the congruence of two items. In the diagram given, ΔABC ≅  ΔXYZ.

The corresponding angles and the sides of the triangles are also congruent with each other.

We have given,

all the corresponding congruent angles and sides. Then the triangle congruence statement.

a)

∠A ≅ ∠Y

∠B ≅ ∠Z

∠C ≅ ∠X

b)

AB ≅ YZ

AC ≅ XY

BC ≅ XZ

c)

ΔABC ≅  ΔXYZ.

Therefore, the complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

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For weeks before labor starts, the cervix can dilate to 1 centimeter. The cervix is only beginning to prepare for labor at this stage of dilatation.

Every woman experiences a different amount of time between dilation to 1 cm and delivery. While another woman maybe 1-2 cm dilated for days or weeks, one woman may move from having a closed cervix to giving birth in a matter of hours.

Some women don't start dilating until they start laboring actively. This indicates that the cervix is initially fully closed, but as labor goes on, it opens to a diameter of 10 cm. First pregnancies are where it occurs most frequently. Other women, particularly those who have already given birth, may begin dilating days or weeks before the commencement of labor.

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Number 4 is the correct answer

Solution:

Using law of exponent:
x^2*x^2*x^2*x^2 is the same as x^(2+2+2+2)= x^8

It took 19 minutes for each to read 115 pages.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents.

Let x be the number of minutes

And y be the number of pages.

y = 96 + x  --equation1 (for danielle )

y=39+4x --equation2 (for lorenzo)

By substituting equation 1 in equation 2.

we get,

96+x = 39 + 4x

96-39+x = 39-39+4x

57+x = 4x

4x-x = 57

3x = 57

x = 57/3

x = 19 .

Substitute x = 19 in equation 1 we get y = 96 + 19 and y=115

in equation 2 we get , y = 39 + 4*19

y = 39+76

y = 115

Hence , it took 19 minutes for each to read 115 pages.

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As per the combination method, if we take 5 vases, then we can put 11 flowers on each of them then we have the given combinations.

Here we have given that the florist has 55 flower and then he want to put the them in the same number of flower in each vase without a leftover.

Here we need to find the number of ways to put them as 2,3 or 5 flower in each vase.

If we take 2 vase, then here we have total number of 55 flower, then it can be separated as,

Here we have to take 25 flowers on first vase and then we have to put the remaining 30 flowers on the second vase because here we have taken one 2 vase.

Then the partition can be written as

=> 25 + 30

If we take 3 vase, then we get the following combination on it.

In the similar way here we have take the 3 vases, and then we have to divide the flowers in the following manner,

=> 25 + 15 + 15

Similarly, if we take 5 vases, then we can put 11 flowers on each of them then we have the given combinations.

Then if we take the 5 vases then we have to put the flowers in the following manners,

=> 11 + 11 + 11 + 11 + 11

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The distance between the graph of the equations x =- 4 and x =- 1 is 3 units.

The equations x =- 4 and x =- 1 can be solved to be -4 and -1 respectively. The difference between these two numbers is 3, so the distance between the graphs of the equations is 3 units.

The distance between the graph of two equations can be found by subtracting the solutions of the two equations. For example, when subtracting the solution of x =- 4 and x =- 1, the difference between -4 and -1 is 3. Therefore, the distance between the graphs of the equations x =- 4 and x =- 1 is 3 units.

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Real numbers and imaginary numbers are distinguished because real numbers have real square roots whereas imaginary numbers do not.

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An absolute value inequality for 35 degrees C with the temperature able to vary as much as 1% is 34.65 ≤ x ≤ 35.35

The term inequality is defined as a relationship between two expressions or values that are not equal to each other

Here we have given that in your chemistry experiment, you are trying to keep the water temperature at 35°C.

And in the experiment to work properly, here the actual temperature can vary as much as 1%.

Here let us consider that x refers the actual temperature

Then it can be written as,

=> 1% of 35

When we simplify this one then we get,

=> 0.01(35) = 0.35

Here let us consider that the value is less that the simplified version, then it can be written as,

=> l x - 35 l ≤ 0.35    

Therefore, it can be rewritten as,

=> -0.35 ≤ x - 35 ≤ 0.35

When we simplify this by add the value 35, then we get the resulting inequality as,

=> 34.65 ≤ x ≤ 35.35

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The steps for using a compass and straightedge to construct a square are as follows :-

1. Use a straightedge to draw line a and label a point on the line as point P.

2. Construct a line perpendicular to line a through point P.

3. Label a point on this line as point R.

4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.

5. Label the points of intersection as points S and T.

6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.

7. Label the point of intersection as point Q.

8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .

9. Use the straightedge to draw QS ,QT,SR and RT.

In geometry, a square is a plane figure with four equal sides and four right angles (90°). A square is a special kind of parallelogram as well as an equilateral rectangle.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.

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The table shows a proportional relationship between the cups of milk used and number of tablespoons of chocolate syrup used. The scale factor shown is 3/2. The constant of proportionality for this relationship is 3/2. The units for the constant of proportionality are teaspoons of chocolate syrup used per cups of milk used.

When it comes to ratios and fractions, the concept of proportion is very connected. When two amounts with the same unit are compared, they form a ratio. When comparing two quantities, a ratio enables us to determine whether one is larger or smaller.

Two ratios or two fractions are equivalent when they are compared according to the proportional rule. To put it another way, two ratios are said to be proportional when they are equal. Performing arithmetic operations on both sides of the ratio taught us that a ratio can be expressed in a variety of ways.

Both the 3: 5 and 6: 10 are equivalent ratios. This indicates that these ratios are proportional. This proportionality can be expressed mathematically as follows:

                                                 [tex]$ \frac{3}{5} = \frac{6}{10}[/tex]

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The cost of fencing the triangular park  at the rate of  ₹18.50 per meter is ₹4903.65

To find the cost of fencing a triangular park with sides measuring 115m, 81.63m, and 69.27m, we first need to calculate the perimeter of the triangle. The perimeter of any two-dimensional figure is defined as the distance around the figure. We can calculate the perimeter of any closed shape just adding up the length of each of the sides.

Perimeter of triangle= Sum of the three sides

To do this, we add up the lengths of all three sides: 115m + 81.63m + 69.27m = 265.9m.

We can then multiply the perimeter by the cost per meter of fencing to find the total cost: 265.9m * ₹18.50/m = ₹4903.65.

So the cost of fencing the triangular park at the rate of ₹18.50 per meter is ₹4903.65

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The division expression that shows 3/4 is b. 3 div 4

It is vital to note that in Mathematics, an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

Un this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, division, etc.

In this case, 3/4 simply means 3 divided by 4. Therefore, the correct option to illustrate this is B.

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Answer:

Please see attached.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

There are 3 pairs of corresponding sides with proportional lengths.

The measurement of V can be calculated by adding the two equations: 10x-27 + 2x+29 = V. This simplifies to 12x+2 = V, so V = 12x+2.

Y=(10x-27)

W=(2x+29)

V=Y+W

V= 10x-27 + 2x+29

V= 12x+2.

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