Wilson's Woodworking Shop produces wood chairs and sells them for $250. The company's weekly profit, (y), depends on the number of $1.50 price increases (x) for each chair. Use the graph below to answer the question.

Graph of function with the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 300), increases to (40, 1100), and then decreases through (86.904, 0).

What is the approximate value of the maximized profit?

200
800
1000
1100

Answer: The slope of Line B is 1/-4 = -1/4.

Step-by-step explanation:

When two lines are perpendicular to each other, the product of their slopes is -1. If the slope of Line A is -4, the slope of Line B must be 1/-4 = -1/4 in order for the two lines to be perpendicular.

The list of most commonly used graph types are as follows:

Now, According to the question:

Types of Graphs and Charts

The list of most commonly used graph types are as follows:

All these graphs are used in various places to represent a specific set of data concisely. The details of each of these graphs (or charts) are explained below in detail which will not only help to know about these graphs better but will also help to choose the right kind of graph for a particular data set.

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Answer:

I believe the answer is 1195 dollars

Step-by-step explanation:

Properties of Special right angled triangle,

a) If the leg of a 45°-45°-90° right triangle is x units, then the length of hypotenuse is x√2 units.

b) If a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg, then longer leg is √3 times the shorter leg.

We have to discuss properties of special Right Triangles :

a) Properties of 45°-45°-90° Triangles : The sides of a 45°-45°-90° right triangle have a special relationship.

Example 1: If the leg of a 45°-45°-90° right triangle is x units, show that the hypotenuse is x√2 units.

Using the Pythagorean Theorem with

a = b = x, then c² = a² + b²

=> c² = x² + x²

=> c² = 2x²

=> c = √2x²

=> c = x√2

Thus, hypotenuse is x√2 units.

b) The sides of a 30°-60°-90° right triangle also have a special relationship.

Example 1: In a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg. Show that the longer leg is √3 times the shorter leg.

∆MNQ is a 30°-60°-90° right triangle, and the length of the hypotenuse MN is two times the length of the shorter side NQ. Use the Pythagorean Theorem, c² = a²+ b²

let length of shorter side of ∆MNQ, NQ= x units, so, length of hypotenuse,MN = 2x

=> MN² = NQ² + MQ²

=> MQ² = MN² - NQ²

=> MQ² = (2x)² - x²

=> MQ² = 4x² - x² = 3x²

=> MQ = √3x²

=> MQ = √3 x = √3 NQ

So, longer side of right angled triangle is √3 times the short side.

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Complete question:

8-3 study guide and intervention special right triangles

a) Properties of 45°-45°-90° Triangles

b) Properties of 30°-60°-90° Triangles

Answer:

Step-by-step explanation:

To answer this problem, we may use the information provided about the quadrilateral's side ratio and the difference between the smallest and longest sides.

To begin, we may utilize the difference in length between the shortest and longest sides (7.5 cm) to establish a baseline for one of the sides. We may infer that the shortest side is 7.5 cm and the longest side is (7.5 cm + 7.5 cm) = 15 cm since the difference between the shortest and longest sides is 7.5 cm.

We can calculate the length of the other three sides using the side ratio:

We sum together all the sides to find the quadrilateral's perimeter:

Perimeter = 67.5 cm = 7.5 cm + 11.25 cm + 18.75 cm + 30 cm

As a result, the quadrilateral's perimeter is 67.5 cm.

Answer:

x = -0.85

Step-by-step explanation:

First, you divide 3 by 3, so that means you also divide 5 by 3, which is 1.66666666666... Now it is -2x =1.66666666666... Technically, it is 1.7, or 1.66666666666..., 1.7 divided by -2 is -0.85. Or if you want to keep 1.66666666666... it will equal -0.8499999999999...

Answer:

8 Tickets

Step-by-step explanation:

40 / 5 = 8

Cesar's reasoning is incorrect because the degree of a polynomial is determined by the highest exponent of the variable in the polynomial, not the number of terms.

In the example given (2×2 = 3+1 = 4), the degree of the polynomial is not given. Therefore, it is not possible to determine the correct degree without more information about the polynomial in question.

The degree of a polynomial is a measure of the highest power of the variable in the polynomial. For example, the degree of the polynomial 3x2 + 2x - 4 is 2 (the highest power of x is 2), whereas the degree of the polynomial 4x3 + 3x2 - 2x + 1 is 3 (the highest power of x is 3).

Cesar's statement that the degree of the polynomial is 4 because 2×2 = 3+1 = 4 is not a valid way to determine the degree of a polynomial, as it is not related to the powers of the variables in the polynomial. To determine the correct degree of the polynomial, we need more information about the polynomial.

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The derivative of x² log x is 2x log x + x/ ln(10).

The derivative of a function f(x) is usually represented by d/dx (f(x)) (or) df/dx (or) Df(x) (or) f'(x). Let us see what a derivative technically means. Consider a curve of function f(x) and let two points on it be (x, f(x)) and ((x + h), f(x + h)). Then the slope of the secant line through these points is given by [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h. See the figure below and observe that when the distance between two points is closely equal to 0 (i.e., as h approaches 0), the second point overlaps the original point and the secant line becomes the tangent line. In calculus, the slope of the tangent line is referred to as the derivative of the function.

The derivative of a function at a point is the slope of the tangent drawn to that curve at that point.

It also represents the instantaneous rate of change at a point on the function.

The velocity of a particle is found by finding the derivative of the displacement function.

The derivatives are used to optimize (maximize/minimize) a function.

They are also used to find the intervals where the function is increasing/decreasing as well as the intervals where the function is concave up/down.

Given equation: y = x² log x

Differentiating this equation with respect to x, we get

dy/dx = 2x log x + x/ ln(10)

Thus, the derivative of x² log x is 2x log x + x/ ln(10).

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The zero slope means for every unit change in the horizontal distance there is no change of vertical distance.

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

The slope of the line describes the steepness of a line.

Also,  if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ

m = tan θ

If the slope is zero, i.e., m = 0 then,

tan θ = 0

θ = arctan(0)

θ = (nπ)                where n = 0, 1, 2, . . .

This means, the line with zero slope must be coincident or parallel to the x-axis.

Sometimes zero slope term is used to describe a line that has a constant rise.

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The adjacent angles share, option 2: a common side and option 3: a common vertex.

What are adjacent angels?

Angles that do not overlap but share a common vertex and arm (side) are said to be adjacent angles. Adjacent angles are ones that are consistently positioned next to one another and are generated when two rays intersect at a shared terminal.

Adjacent angles are placed side by side to each other.

They do not overlap each other.

Adjacent angles are drawn from a common point known as a vertex.

The adjacent angles are on the same side and are not opposite to each other.

The image for a pair of adjacent angles is given.

Adjacent angles do not share a common angle and are not equal.

Therefore, adjacent angles have a common side and a common vertex.

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The inverse of an exponential function is a logarithmic function.

A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.

Basically,

if y=ax

So, logₐ(y) = x

The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e

'e' is a mathematical constant having a value of around 2.718.

If the base is "e," we use a specific expression: ln(x)

Fundamentally,

ln(x)=loge(x)  

Here, e is the base.

Base-10 will be used if no base is provided, as in the formula

log(x)=log10(x)

Here 10 is the base

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Answer:

B) 0.5 (Arc XPQ-Arc XQ)

The value of expression in the form of fraction is, 13/15.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The expression is,

⇒ 7/10 + 1/6

Now, We can solve as;

⇒ 7/10 + 1/6

⇒ (7 × 6 + 1 × 10) /60

⇒ (42 + 10) / 60

⇒ 52/60

⇒ 26/30

⇒ 13/15

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Answer:

Direct Proportion

Step-by-step explanation:

It is linear, meaning that the ratio between the mass and gravity is proportional.

Answer:

the sun because u can't get energy from a bicycle yea kettle or a faucet.

A graph that does not show a straight line shows a non-proportional relationship between x and y.

A graph that does not show a straight line, but instead shows a curve, would represent a non-proportional relationship between x and y. A non-linear or curved graph indicates that the relationship between the two variables is not a constant ratio or proportionate relationship. The slope of a line that represents a non-proportional relationship will change depending on the x-value.

A non-proportional relationship exists between two variables when the ratio of their values does not stay constant. In other words, the relationship is not directly proportional. In mathematical terms, this means that the slope of a graph of the relationship is not constant, and the graph will not be a straight line. Instead, it will be a curved line. A non-proportional relationship is also known as a non-linear relationship.

For example, the relationship between the time it takes to run a certain distance and the distance run is non-proportional. If it takes you 10 minutes to run 1 mile, it will not necessarily take you 20 minutes to run 2 miles. The time it takes to run a certain distance increases at a faster rate than the distance run.

In a non-proportional relationship, there is no constant of proportionality. For example, y = 2x doesn't have a constant of proportionality because the ratio of y to x changes as x increases, and the slope of the line is not constant.

Therefore, A graph that does not show a straight line shows a non-proportional relationship between x and y.

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The answer of 10 more than 80 is 90.

The answer of 10 more than 80 is 90 which can be derived using simple mathematical calculations.

To find 10 more than 80, you can add 10 to the original number 80.

10 + 80 = 90

It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 80 is 90.

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Answer:

Step-by-step explanation:

To calculate the interest rate on Selena's debt, we may utilize the formula for continuous compounding of interest. A = P * e is the formula (rt)

Where:

A = the total amount (including interest)

P denotes the original principal (loan amount)

r denotes the interest rate (as a decimal)

t = time (in years)

We know Selena's total (A) is 8,000 + 2,292.77 = 10,292.77.

8,000 is the initial primary (P).

6 years have passed.

The interest (I) is calculated as A-P = 2,292.77.

We may use the formula for continuous compounding of interest to compute the interest rate on Selena's debt. The formula (rt) is A = P * e.

A denotes the whole sum (including interest)

P stands for the original principle (loan amount)

r represents the interest rate (as a decimal)

t = time (in years)

Selena's total (A) is 8,000 plus 2,292.77 = 10,292.77.

The initial primary is 8,000. (P).

6 years have gone by.

A-P = 2,292.77 is the interest (I) calculation.

Answer:

195

Step-by-step explanation:

Since: d / 13 = 15, we need to do the inverse which is multiplication:

15 x 13 = 195

Answer:

ayden earns $6 an hour for raking leaves in the yard, so the equation representing the amount of money he can earn is:

Earnings = 6 * (Number of hours worked)Brooklynn earns $9 for making everyone's beds and an additional $1.50 an hour for helping with the laundry, so the equation representing the amount of money she can earn is:

Earnings = 9 + (1.5 * (Number of hours worked))To find how many hours each need to work in order to earn the same amount of money, we can set the two equations equal to each other and solve for the number of hours worked.

6(Number of hours worked) = 9 + (1.5 * (Number of hours worked))Solving this equation gives us: Number of hours worked = 9/4 = 2.25 hoursSo after 2.25 hours, they each need to work in order to have earned the same amount of money.

Step-by-step explanation:

Jayden's equation: 6x

Brooklynn's equation: 9x + 1.5y

Equation to find how many hours each need to work: 6x = 9x + 1.5y

After 12 hours, they each need to work in order to have earned the same amount of money.

The solution of the given equations are; x = -10.5 and y = 8.25

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given that the system of equation are;

20y−25x=140

y+5/4x=-5

Therefore, solving the equations;

y = -5/4x -5

Substitute;

20y−25x=140

20(-5/4x -5)−25x = 140

-25 - 100 - 25x = 140

-125 - 25x = 140

-25x = 140 + 125

x = -10.5

Then y = -5/4x -5

y = 8.25

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Answer:

Area of square = side x side = 20 x 20 = 400 cm²

Cheers.

The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                [tex]Distance = speed * time[/tex]

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Answer: The 4th option

Step-by-step explanation:

The proportion 16 over 12 equals 12 over 9 shows the corresponding sides are proportional, so the triangles are similar by the SAS similarity postulate.

What is SAS similarity theorem?

According to the Side-Angle-Side Postulate (SAS) postulate, triangles are congruent if two sides of one triangle and the angle that connects them are congruent with two sides and the included angle of a second triangle. According to the SAS criteria for triangle similarity, two sides of one triangle are comparable to two sides of another triangle if their included angles are congruent.

The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;

Segment XZ is perpendicular to segment WY

∠WZX and ∠XZY are right angles by definition of XZ  perpendicular to WY

∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)

Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and

that the included angles between the two sides, ∠WZX and ∠XZY are

congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-

Side, SAS, similarity postulate.

The option that best completes the proof is therefore;

which is; 16 over 12 equals 12 over 9

The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.

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Completed question :

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?

Since segment XZ is perpendicular to segment WY, angles WZX and XZY are both right angles and congruent. The proportion ________ shows the corresponding sides are proportional, so the triangles are similar by the SAS Similarity Postulate.

16 over 12 equals 9 over 12

16 over 12 equals 12 over 9

12 over 12 equals 16 over 9

12 over 16 equals 16 over 9

In order to have an average speed of 6 miles per hour over the entirety of the trip, the man would need to travel 15 miles in the next 2 1/2 hours. This means that he would need to travel at a speed of 6 miles per hour for the remainder of the trip.

Answer: As x approaches positive infinity, y approaches positive infinity

As x approaches negative infinity, y approaches positive infinity.

Step-by-step explanation:

The key thing to keep in mind is the type of function. This is an absolute value graph that in general has a V shape. This one in specific is a V shape shifted to the right 7 unites from the origin, with positive and negative slopes for each piece-wise line.

Following that, the Pythagorean theorem states that the separation between the two points is equal to the square root of the sum of the squares on the horizontal and vertical sides: distance=√(Δx)2+(Δy)2=√(x2−x1)2+(y2−y1) 2.

As per the a sphere, a straight line connects any two points at their closest distance. The earth resembles a spherical in form. The distance between any two places on Earth is calculated using the perpendicular distance or a straight line between the two spots because the radius of the sphere is so large that humans see it as a plane. In the case of in the earth, the arc length and the perpendicular distance are about identical.

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