verify that the diagonals of the rectangle with vertices p(-1,4) Q (-2,1) R (4,-1) and S (5,2) bisect each other

The minimum number of hours Hiroto can tutor to make at least $180 is 2 hours.

From the information, Hiroto tutors Japanese for $15 an hour and works at a dairy for $10 an hour. He wants to work 15 hours this week and we want to calculate the minimum number of hours Hiroto can tutor to make at least $180.

Hiroto wants to earn at least $180 this week. If he works 15 hours at the dairy, he will earn 15 * $10 = $150.

To earn at least $180, he needs to earn an additional $180 - $150 = $30.

At $15/hour for tutoring, Hiroto needs to work 30 / 15 = 2 hours tutoring.

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When the graphs of a system of linear equations are parallel, there is no solution. There are infinite solutions. When the graphs are the same line, a system of linear equations has infinite solutions.

An inconsistent pair of linear equations is a system of linear equations that has no solution.

Furthermore, a linear equation with two variables has an unlimited number of solutions. Every linear equation in two variables has a straight line as its graph, and each point on the graph (straight line) indicates a solution to the linear equation.

The majority of linear systems have precisely one solution. It is feasible, however, that there are no answers or that there are infinitely many. (It is impossible for there to be exactly two answers.) In this case, the word unique denotes that there is a solution, and it is the only one.

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Answer:

Millions

Step-by-step explanation:

A 7 digit number is called "Millions"

1,000,000=Millions

and then the rest all the way till 9 is a seven digit million.

The answer are, 1) $ 162.18  , 2) $ 17500 ,  3) $28.4.

A percentage is a number or ratio that can be expressed as a fraction of 100.

here, we have,

from the given, we get,

1.) the total price you pay =$153+ $153*6%

                                         =$162.18

2.) you earned = $350000 *5%

                        =$17500

3.) you made = $ 710*4%

                      =$28.4.

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The two variables in this equation are x and y, and the nonzero value k is also referred to as the constant of variation. A line across the origin represents the graph of the equation y = kx, and its slope is k.

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.

How do you define "variable"?

A variable is a value that could alter when used in a mathematical problem or experiment. A variable is often represented by a single letter. Generic symbols used frequently for variables include the letters x, y, and z.

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If two lines intersect at a 90-degree angle, we can say those lines are perpendicular.

Perpendicular lines are lines that intersect at right angles.

This produces a measurement of 90 degrees for each of the four angles created by the intersection of the line.

As the measurement of a straight line is 180 degrees, creating an angle of 90 degrees by one line intersection the other necessitates that the adjacent angle must also be 90 degrees because

180−90=90

When lines intersect, they form four different angles. The measurement of those angles will depend on how the lines intersect. Opposite angles will always be congruent, while adjacent angles will always have a sum of 180 degrees.

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3 units is the distance from y-axis to the given point (3, 4).

Distance between two things or points is measured, and it can sometimes be quantitatively and sometimes qualitatively.

The word "distance" in physics can refer to a real-world length or, more frequently, to an estimate based on a number of other factors.

The length of the line segment that connects two points on a plane represents their distance.

To calculate the distance between two places, one usually uses the formula d=((x2 - x1)2 + (y2 - y1)2).

So, we have the point:

(3,4)

Any given point's x coordinate indicates how far it is from the y-axis, and then we can conclude that the distance of the point (3,4) from the y-axis is 3.

Therefore, 3 units is the distance from y-axis to the given point (3, 4).

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According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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The value of x and y in the angles of a triangle in the given diagram is x = 70°, y = 60°.

In ΔABC, we have

∠A = x

∠B = 50°

∠ACB = y

∠ACD = 120°

We know that,

If the exterior angle of a triangle is θ and the two opposite interior angles are θ₁ and θ₂, then the sum of θ₁ and θ₂ will be equal to the θ.

⇒θ = θ₁ + θ₂

⇒∠ACD = ∠A + ∠B

⇒120° = x + 50°

⇒x = 120° - 50°

⇒x = 70°

We know that,

If the angles of a triangle are θ₁, θ₂ and θ₃, respectively. Then the sum of θ₁, θ₂ and θ₃ is equal to 180°.

⇒θ₁ + θ₂ + θ₃ = 180°

⇒∠A + ∠B +  ∠ACD = 180°

⇒x + 50° + y = 180°

⇒70° + 50° + y = 180°

⇒120° + y = 180°

⇒y = 180° - 120°

⇒y = 60°

Hence, x = 70°, y = 60°

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Answer:

There are 86 acres of old-growth trees.

Step-by-step explanation:

In order to answer the question, we need to calculate the 0.2% of 43,000.

We can calculate this stating that exists a linear relationship between the percentage and the amount of acres. We also need to state that 43,000 acres are the 100% of the acres.

Therefore, we can write the following equation to calculate the percentage :

If we solve the equation in terms of ''x'' :

The function required in the right triangle is as follows;

tan A = 5 / 12

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The angles of a right angle triangle can be found using trigonometric ratios as follows:

Hence,

tan A = opposite / adjacent

opposite side = 20 units

adjacent side = 48 units

Therefore,

tan A = 20/ 48

tan A = 20/ 48 ÷ 4 / 4

Hence,

tan A = 5 / 12

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The ratio of correct answers to total questions will not remain the same.

From the information, in the trivia game, Levi answered 8 questions correctly out of 10 turns in the game. In this case, the ratio will be:

= 8 / 10

= 4/5

= 4: 5

He then answered the next three questions correctly. The new ratio will be:

= (8 + 3) / (10 + 3)

= 11 / 13

The ratio of correct answers to total questions will not remained the same. In this case, 4/5 is different from 11/13.

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The given number is a solution of 2(3x + 1) 2 7x + 4 is 0.

Analyze a number to see if it is an equation's solution.

For the variable in the equation, substitute the integer.

On both sides of the equation, simplify the expressions.

Check the equation to see if it's correct. The number provides a solution if it is accurate. The figure isn't a solution if it's false.

Equations with just one solution. If you solve an equation and the result is a variable equal to a number, the problem only has one solution.

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She used 1/12 kg of salt when preparing the dinner.

An equation shows the relationship between numbers and variables in an expression.

There are 5/6 kg of salt in the kitchen. Mrs. Jackson used 1/10 of the salt when she was preparing dinner. Hence:

Amount of salt used = (1/10) * (5/6)kg = 1/12 kg

She used 1/12 kg of salt

The amount of salt remaining is the difference between the initial salt available and the quantity of used salt. Hence:

Salt remaining = 5/6 kg - 1/12 kg = 3/4 = 0.75 kg

Mrs. Jackson had 0.75 kg of salt remaining.

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The height of the triangle as calculated from the data given above is found out to be as √60 meters.

The given question can be solved by the implication of Pythagorean theorem as the figure is in the form of a triangle.

Let the, base of the triangle be , 2 meters

the hypotenuse be , 8 meter.

Therefore the height of the pole will be ,

AB² = AC²  - BC²

      = 64 - 4

      = 60

Then , we can say that AB = √60

Therefore, the height of the pole is found to be as √60 meters.

Pythagoras theorem states that the sum of two side of a triangle is equal to the hypotenuse of that triangle , AB² = AC²  - BC² .

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If runners in the half marathon entered in 3 waves and 7 out of eight runners finished the race, runners that did  not finish is 119 runners.

First step is to find the total runners in the 3 waves

Total runners = 341 runners + 295 runners + 316 runners

Total runners = 952 runners

Second step is to find runners that finished the race

Runners (Finished) = 7/8 ×  952 runners

Runners (Finished) = 833 runners

Now let find runners that did not finished

Runners (Unfinished) = 952 runners - 833 runners

Runners (Unfinished) =119 runners

Therefore 119 runners did not finish.

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The probability that he draws a pair of tens is  1/2652 or approximately 0.000378 which is approx 0.04%

The probability of drawing a pair of tens from a standard deck of cards is (number of ways to get a pair of tens) / (total number of possible outcomes).

In this case there are 4 tens (2 of hearts, 2 of diamonds, 2 of spades, 2 of clubs) and he is drawing 2 cards from the deck, so there is only 1 way to get a pair of tens. There are 52 cards in a standard deck, so the total number of possible outcomes is 52 * 51 = 2652.

So the probability of drawing a pair of tens is 1/2652 or approximately 0.000378 which is approx 0.04%

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The solution of the given equation is 3+i or 3-i.

What is Quadratic Equation ?

Quadratic Equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where a, b , c are constants.

Given,

equation x^2-6x+10 = 0

So for solving the roots , here she used quadratic formula

so,

x = (-b + [tex]\sqrt{b^2 - 4ac}[/tex] )/ 2a  or (-b - [tex]\sqrt{b^2 - 4ac}[/tex] )/ 2a

here a = 1 b = -6 and  c = 10

x =( 6 + [tex]\sqrt{6*6 - 4 * 1*10}[/tex] )/ 2 or ( 6 - [tex]\sqrt{6*6 - 4 * 1*10}[/tex] )/ 2

x = (6 + [tex]\sqrt{36-40}[/tex] ) / 2 or (6 - [tex]\sqrt{36-40}[/tex] ) / 2

[tex]\sqrt{36-40}[/tex] = 2i

so,

x = 6+2i / 2  or 6-2i / 2

x = 3+i or 3-i

Hence, The solution of the given equation is 3+i or 3-i.

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Answer:

A

Step-by-step explanation:

9 x 2 = 18

9 x 5m = 45m

The volume of the prism ( above fig.) is equals to the 900 cubic units. So, first one option is right answer of this problem.

Prisms and pyramids are very important solid shapes. They have many uses in real life. Each type of pyramid or prism has different formulas for volume and area. The general formula of volume, V = Base area × Height

Here, we take the triangular part of the prism as the base. We have, a prism with triangular base.

Triangular base area = 1/2 × B × H

Base length of triangle, H = 15

Height of triangle, B = 8

Triangular base area = 1/2×15×8 = 60 square units

Volume of prism , V = 60 sq. units × 15 units

= 900 cubic units

Hence, the volume of prism is 900 cubic units.

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when the value of x=1 the value of y will be 0.

What is a function?

A function is a special form of relation where every input has exactly one output. In other words, for every input value, the function returns exactly one value. Given that one is mapped to two separate values, the graph above depicts a relation rather than a function. But if one were instead mapped to a single value, the relation above would change into a function. In addition, output values could match input values exactly.

The function machine receives the x-value input. The function machine then executes its operations and produces the y-values. Any function may be the function within.

If y varies directly as x, and y=2 when x=3

f(x)=y=x+c

So 2 = 3+c

c=-1

So function is y = x-1

y = 1-1

y=0

Hence, when the value of x=1 the value of y will be 0.

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Answer: (-4,2)

Step-by-step explanation:

To solve the system using the elimination method, you first need to adjust the equations a bit so that you can add or subtract to eliminate either x or y.

Eliminating x seems more convenient in this situation, so let's try.

We can multiply 3 to the second equation so that we end up with this:

3x+5y=-2

-3x+6y=24

Now, all we need to do is add up the two equations to get:

11y=22

y=2

Since we now know the value of y, let's plug it in to get x.

3x+10=-2

3x=-12

x=-4

Therefore, the answer is x=-4, y=2 or(-4,2)

Answer:

(-4, 2)

Step-by-step explanation:

The point (2,0), which is (-3,2), is √29 units away from the origin.

A pair of numbers called coordinates are used to locate a point or a shape in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. Coords are the collective noun for the abscissa and ordinate. The study of algebraic equations on graphs is known as coordinate geometry. The plotting of points, lines, and curves on an x and y axis is an illustration of coordinate geometry.

Here,

distance=√(y2-y1)²+(x2-x1)²

=√(2-0)²+(-3-2)²

=√2²+-5²

=√4+25

=√29

The distance of the point (-3,2) from the origin that is (2,0) is √29 units.

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Answer: Explain to them the game. Explain to them that you'll be giving them multiple numbers of elephants, and they need to try to figure out how many elephants there ...

Missing.

A vertical line's equation is provided by the expressions x = an or x = -a, where x denotes any point on the line's x coordinate and a denotes the point at which the line intersects the x-intercept.

The vertical line is either another line that is regarded as the base or a line that is perpendicular to the surface. The vertical lines in coordinate geometry are typically perpendicular to the horizontal lines and parallel to the y-axis. Whether it is going from top to bottom or bottom to top, a vertical line is always a straight line. The standing lines refer to the vertical lines.

A vertical line is a line on the coordinate plane with the same x-coordinate at each point. We discover that when the coordinates are joined when plotting the points for the function x = a on a coordinate plane, a vertical line results.

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A region on one side of a line might be used to visually depict an inequity IS X+4.

Rearrange the equation so that "y" is on the left and the rest is on the right.

Plot the "y=" line (make it a solid line for y or y and a dashed line for y or y>).

Shade above the line for "more than" (y> or y) or below the line for "less than" (y or y).

A region on one side of a line might be used to visually depict an inequity. Inequalities with or > symbols are displayed with a dashed line to indicate that the line is not part of the region. Inequalities with the symbols or are plotted with a solid line to demonstrate that the line is

Inequalities with the symbols or are plotted with a solid line to demonstrate that the line is X+4.

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The formula for a 30-60-90 triangle is as follows: the hypotenuse is always twice the length of the shorter leg, and the longer leg is the square root of 3 times the length of the shorter leg.

To calculate the sides of a 30-60-90 triangle, first determine the length of one of the shorter legs. Let's call this length "x". Then, the length of the hypotenuse is twice x (2x). The length of the other short leg is the square root of 3 times x (√3x). Finally, the length of the long leg is the square root of 2 times x (√2x). In summary, the formula for a 30-60-90 triangle is x, 2x, √3x, and √2x, where x is the length of one of the shorter legs. To calculate the angles in a 30-60-90 triangle, the angles are 30°, 60° and 90°, respectively. These angles are always the same in a 30-60-90 triangle regardless of the side lengths.

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Answer:b 81/256

Step-by-step explanation:

The solution of the system of equation x - y = 4, x + y = 2 is (-1, 3).

System of equation can be formed using different method such as graphical method, elimination method and substitution method.

Therefore, let's solve the system of equation by using elimination method.

x - y = 4

x + y = 2

subtract the equations

2y = -2

divide both sides of 2

y = -2 / 2

y = -1

Hence, let's substitute y in equation(ii)

x + y = 2

x - 1 = 2

x = 2 + 1

x = 3

Therefore, the solution is (-1, 3)

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