The points A ( 5, -2), B (2, 7), and C (-10, 4) are in the xy- plane. Find:
a. the equation of the line passing through A and parallel to BC,
b. the equation of the line passing through B, perpendicular to AC,
c. the point of intersection of the lines in (i) and (ii) above.​​

Average number of planes that will stack up waiting to land:  This can vary greatly depending on the size of the airport, the number of flights per day, and the number of runways available.

What is average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures.

To determine the average number of planes that will stack up waiting to land, we need to know the rate at which planes arrive at the airport and the rate at which they are able to land.

Generally, an airport can expect to experience a queue of up to 10 planes waiting to land at peak times.

Average time a plane must wait in line before it can land: This also varies significantly depending on the airport and the conditions. Generally, a plane must wait an average of 5-7 minutes before it is able to land.

Average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land: This time will depend on the size of the airport, the number of planes in the queue, and the amount of time it takes for the plane to taxi off the runway. Generally, a plane can expect to clear the runway in about 2-3 minutes.

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The profit per month for the contractor is obtained as $9425.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The profit of the contractor per job is given as $3250.

As per the given table the expected value can be obtained as,

E(x) = [tex]\sum_{x = 1}^{4} xP(x)[/tex]

⇒ E(x) = 1 × 0.1 + 2 × 0.2 + 3 × 0.4 + 4 × 0.3

⇒ 2.9

Then, the expected profit of is given as 3250 × 2.9 = $9425

Hence, the profit per month is obtained as $9425.

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The formula of x³ = 1 is 1.

A number's third power, or the outcome of multiplying three occurrences of the number n together, is known as the cube in mathematics and algebra. A superscript 3 represents the cube of a number or any other mathematical expression. A cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent real-world example and is useful for boosting cognitive function. Similar to this, there are several examples in everyday life, such as six-sided dice, etc.

Given

x³ = 1

Cubing both sides,

x = ∛1

x = 1

The formula of x³ = 1 is 1.

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The complete table is solved and shown below.

Given is to complete the output table as given.

Now, we can write -

for [x] = - 4,   y = - 3

for [x] = - 3, y = - 1 =  {- 3 + 2}

for [x] = 1, y = 1 + 2 = 3

for [x] = 2, y = 2 + 2 = 4

for [x] = 5, y = 5 + 2 = 7

Therefore, the complete table is shown and solved above.

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Answer:

Step-by-step explanation:

Part 1)

add their velocities

422+384= 806

now divide 6045 by 806 = 7.5  or  7 hours 30 minutes

7:30 = t   hours:minutes

Part 2)

For this part we will need to employ Pythagoras theorem. we need the hypotenuse to be 1,997

so, when will  plane traveling N ,  and plane traveling W be that far (1997)?

or

when does  [tex]1997^{2}[/tex] = [tex]N^{2}[/tex] + [tex]W^{2}[/tex]

then we're also given that  N = 422*t

and  that  W = 384 * t

so now our formula looks like

[tex]1997^{2}[/tex]  = [tex](422*t)^{2}[/tex] + [tex](384*t)^{2}[/tex]

rewrite this so it's making clear math sense

[tex]1997^{2}[/tex]  = [tex]422^{2}[/tex] * [tex]t^{2}[/tex] + [tex]384^{2}[/tex] * [tex]t^{2}[/tex]

now pull out the [tex]t^{2}[/tex]

[tex]1997^{2}[/tex]  = ( [tex]422^{2}[/tex]  +   [tex]384^{2}[/tex] ) * [tex]t^{2}[/tex]

now simplify some

3988009 = (178084 + 147456 ) * [tex]t^{2}[/tex]

now divide the left side by the numbers on the right

3988009 /  (178084 + 147456 )  = [tex]t^{2}[/tex]

12.12044234 = [tex]t^{2}[/tex]

[tex]\sqrt{12.25044234}[/tex] = t

3.500063191 = t

so at 3 and a half hours,  the planes will be 1997 miles apart

3:30 = t

The fraction simplifies to 1. Option A.

The difference of two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the difference of the square roots and the other shows the sum of the square roots, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.  This identity is often used in algebra where it is useful in applications to integer factorization, the quadratic sieve, the algebraic factorization, etc.

One thing to note about this theorem is that it does not apply to the SUM of squares.

(32008)²-(32006)²/ (32007)²-(32005)²

(32008 - 32006)² / (32007 - 32005)²

(2)² / (2)²

1

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The trick for table 13 are as follows.

A multiplication chart is a table that displays the products of two numbers.  One set of numbers is typically written in the left column, while another set is written in the top row. The numbers in the products are listed in a rectangular array. Addition is repeated when you multiply.

To learn table fast follow points,

1. To learn the 13 times table, we must first learn the 3 times table. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the multiples of 3.

2. Add natural numbers to the tenth digit of the multiples of 3 to get the multiples of 13. As a result, the 13 times table can be derived as follows: 1+0)3, (2+0)6, (3+0)9, (4+1)2, (5+1)5, (6+1)8, (7+2)1, (8+2)4, (9+2)7, (10+3)0 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130.

3. The 13 multiplication table does not have any rules that make it easy to remember, but there is a pattern for every ten multiples of three: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130. Students can remember these digits to help them with the 13 times table because the last digit of these multiples always repeats.

Hence, follow the steps to learn table of 13.

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Answer:9/5

Step-by-step explanation:

Answer:

A. 9/5

C. 1 4/5

Step-by-step explanation:

3 x 3/5 = (3 x 3)/5 = 9/5

9/5 = 5/5 + 4/5 = 1 4/5

Yes, a hole is considered an asymptote.

There are "holes" in the graph called vertical asymptotes where the function cannot have a value. They represent areas where the x-value is not permitted.

In particular, a rational function's denominator can never equal zero. A vertical asymptote is any value of x that would result in the denominator being equal to zero.

We may determine which direction the graph will incline as its x-values rise by looking for a horizontal or slant asymptote. In contrast to the vertical asymptote, a horizontal or slant asymptote can be touched or crossed by the graph.

Yes, a hole is considered an asymptote.

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In example, the denominator of a rational function can never be 0. Any value of x that would cause the denominator to equal 0 is known as a vertical asymptote.

By searching for a horizontal or slant asymptote, we may determine which direction the graph will incline as its x-values increase. The graph can touch or cross a horizontal or slant asymptote as opposed to the vertical asymptote.

An example of discontinuous change is an adolescent experiencing puberty.

The term "discontinuity" is used in the literature on behaviour in a number of distinct contexts. It should specifically relate to a rapid change in a system's properties.

A discontinuity is stated to have happened when a two-month-old human infant's attention, vocalisation, and sniffing scores do not predict their scores on the same test at four months. "Discontinuity" is also used to describe the rearrangement of rank on a specific measure.

The first twenty years of a person's life are when discontinuous change is most noticeable, such as during birth and puberty. These gaps in continuity are not puzzling. Many biological and physical systems have the capacity to change abruptly and discontinuously.

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When a human infant's attention, vocalization, and sniffing scores at two months do not predict their results on the same test at four months, a discontinuity is said to have occurred. Rearranging rank on a certain measure is referred to as "discontinuity."

Discontinuous change is most apparent throughout a person's first twenty years of life, such as during puberty and childbirth. These discontinuities are not mysterious. Many biological and physical systems are capable of rapid, discontinuous change.

The best graph to present the data is Multiple bar diagram

The term graph in math refers easiest ways to represent data is using graphs. And it is also used to compare different values, understand how different parts impact the whole, or analyze trends.

By using the graph you can easily understand the data.

Basically, the types of graph that are suitable for specific data depends on the nature and the given conditions of the data.

Here we have some mostly used types of diagrams used to represent data are line diagrams, bar diagrams, semi-logarithmic charts, multiple bar diagrams, subdivided bar diagrams, pie diagrams, stem and leaf plots, box plots, and ogives.

Here the best graph to display the data is a Multiple bar diagram (MBD).

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The x-intercept and y-intercept on the graph will cross the x and y axes accordingly.

In order to find the x-intercept and y-intercept represent in terms of the units on the axes, we must know the definition of each of them.

In math the x-intercept is defined as the value of the x coordinate of a point where the value of y coordinate is equal to zero.

Similarly, the y intercept in math is referred as the point where the graph intersects the y-axis.

While looking into the given definition, we have identified that intercept refer the intersecting point of the graph.

Based on these we have concluded that x and y intercept are the intersecting point of the graph.

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Answer:

340pounds

Step-by-step explanation:

volume of container = 20 x 8.5 x 8= 1360 cubic feet

weight = 0.25 pounds per cubic foot

0.25 x 1360 = 340 pounds

The triple integration of ∭E xy dV and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3), is 8 / 5.

What is integration?

When infinitesimal data are combined, concepts like displacement, area, and volume can be described by assigning numerical values to the functions that make up an integral. Integration is the procedure for locating integrals.

Given:

∭E xy dV  and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3),

Calculate the equation of plane passing through the vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3) as shown below,

x / 8 + y / 1 + z / 3 = 1

z = 24 - 3x -24y / 8

Put z = 0

y = 1 - 1 / 8x

Put y = o

x = 8

Calculate the integral as shown below,

[tex]\int \int\int_E xydV = \int _0^8 \int _0^{1-x/8} \int _0^{{24-3x-24y}/8} xy\ dz\ dy\ dx[/tex]

∫∫∫E = [tex]1/8 \int _0^8 [24xy^2 / 2 - 3x^2y^2 / 2 - 24xy^3 / 3]^{1-x /8}dx[/tex]

∫∫∫E = 1 / 8 × 64 / 5

∫∫∫E = 8 / 5

Thus, the triple integral is 8 / 5.

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Answer:

To get from Trisha's house to Brandon's house, Trisha should first walk 2 blocks west and 4 blocks north to get to school. From there, she should walk 4 blocks east and 2 blocks south to get to Brandon's house. This means that Trisha should follow the following directions to get from her house to Brandon's house:

Walk 2 blocks west

Walk 4 blocks north

Walk 4 blocks east

Walk 2 blocks south

These directions will take Trisha from her house to Brandon's house.

Step-by-step explanation:

Answer:

2 and 6 (A)

Step-by-step explanation:

The formula for determining a z-score is z = (x-μ)/σ, where x is the raw score, z is the population mean, and z is the population standard deviation.

X=(z)(SD) + mean

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Right triangles ABC and DEF are drawn to measure the slope of the line is:

a) run = 2 rise = 3 slope = 3/2

b) run = 6 rise = 9 slope = 9/6 = 3/2

c) Yes, they are similar because the 2 triangles are similar.

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal.

What is Right triangles?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

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Applying the triangle midsegment theorem, the length of segment TU = 100 units.

If a line connects the midpoints of two sides of a triangle, it is parallel to the third side, and according to the triangle midsegment theorem, it has a length that is half the measure of the third side of that triangle.

Given the triangle, TUV, where:

Segment TU is a third side to the midsegment HD = 50 units.

Thus, apply the triangle midsegment theorem to find the length of segment TU.

HD = 1/2(TU)

Substitute:

50 = 1/2(TU)

2(50) = TU

100 = TU

TU = 100 units

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The total number of hours driven can be represented by the expression "x + y." This represents the sum of the hours driven in one car (x) and the hours driven in another car (y).

The other expressions do not represent the total number of hours driven. "x y" is not a valid mathematical expression. "y 70" and "300 x" represent the number of miles driven by one car and the number of miles driven by another car, respectively, but do not represent the total number of hours driven. "70x" and "55y" represent the number of miles driven by one car and the number of miles driven by another car, respectively, but do not represent the total number of hours driven.

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No, we can not use SSA to prove triangles are congruent.

The side-side-angle congruence rule also referred to as the SSA congruence rule, deals with the congruence of two triangles.

According to the SSA congruence rule, two sides and an angle that is not contained between them must be equal to two sides and an angle of the other triangle in order for the two triangles to be equal. Due to the possibility that the sides of the two triangles may not be on the same corresponding sides, this congruence rule does not consider two triangles to be congruent. It's possible that the two triangles will wind up being of different sizes and shapes. The SSA congruence rule is therefore invalid.

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Answer:

3

Step-by-step explanation:

"Real zeros" are x-intercepts. So this graph crosses the x-axis three times. There are three real zeros.

Generally, you can (sloppy interpretation) interchange the words: zeros, solutions, roots and x-intercepts.

For any questions that ask for these, change y or f(x) to zero and solve it.

Answer:

1:3:2

Step-by-step explanation:

Sum of triangle is 180°

A : B : C

30 : 90 : (180 -90 - 30)

30 : 90 : 60

1 : 3 : 2

I hope my answer helps you.

The slope of 4y =- 4 is zero.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

Given equation:

4y =- 4

To find the slope:

First, we simplify the equation.

Divide by 4.

(4/4)y = -4/4

y = -1

Now, we know the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

Comparing, both the equation,

we get,

m = 0.

So, the slope is 0.

Therefore, the slope is 0. This produces a horizontal line.

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Answer:

B

Step-by-step explanation:

A = 0.5kg (Not close)

B = 0.05

C = 0.02 ( Not close)

D = 0.04

(Explanation why answer is B and not D)

B is closet because even we round off to two decimal places 0.05kg answer comes not 0.04kg

Plus 0.05 is 0.01kg away from 0.049, While 0.04kg is 0.09kg away from 0.049kg.

I hope my answer helps you.

1/20 kg is closest to 0.049 kg among the given choices. So, correct option is B.

To determine which option is closest to 0.049 kg, we can compare the given options to the target value and find the option with the smallest absolute difference.

A. ½ kg = 0.5 kg (Difference = |0.5 kg - 0.049 kg| ≈ 0.451 kg)

B. 1/20 kg = 0.05 kg (Difference = |0.05 kg - 0.049 kg| = 0.001 kg)

C. 1/50 kg = 0.02 kg (Difference = |0.02 kg - 0.049 kg| ≈ 0.029 kg)

D. 2/50 kg = 0.04 kg (Difference = |0.04 kg - 0.049 kg| = 0.009 kg)

Comparing the absolute differences, we can see that option B (1/20 kg = 0.05 kg) has the smallest difference from 0.049 kg, which is only 0.001 kg.

Therefore, option B (1/20 kg) is closest to 0.049 kg among the given choices.

When dealing with questions like this, it is helpful to compare the values using the absolute difference from the target value. The option with the smallest absolute difference is the closest approximation to the target value. In this case, 1/20 kg provides the closest value to 0.049 kg, making it the correct choice.

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The value of x for the given figure will be equal to √212.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Apply the Pythagorean theorem for the first triangle,

H² = x² - 6²

Apply the Pythagorean theorem for the second triangle,

B² = 27² - x²

Apply the Pythagorean theorem to the third triangle,

H² = 27² - x² - 21²

H² = -x² + 288

x² - 6² = -x² + 288

2x² = 424

x² = 212

x=√212

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The square root of 4 is 2 (2 x 2 = 4). This implies 4 is perfect square of 2.

Hence square root of 4 is not an irrational number.

What is an irrational number?

An irrational number is one that cannot be represented by whole numbers and/or fractions (also called ratios)  is an irrational number because those decimals just go on and on and there is no pattern to be represented by a fraction. Many square roots are also irrational numbers.

According to the given question:

The square root of 4 is 2 (2 x 2 = 4). This implies 4 is perfect square of 2. Squaring of 2 gives 4 and square root of 4 gives 2. 2 is a rational number i.e. it can be represented in p/q form.

Hence square root of 4 is not an irrational number.

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The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The graph of an inequality is shown below:

What is an inequality equation?

The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

Example -

Let us take an equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

Now, the graph becomes according to the slope-intercept form is:

Here we noticed that,

This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.

Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.

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The number of siblings is 41.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

we have given,

The graph represents the number of siblings each student in a class.

the graph which represents the frequency of the number of students on the y-axis and the number of siblings on the x-axis.

Number of siblings = (0 * 6) + (1 * 7) + (2 * 4) + (3 * 2) + (4 * 5)

= 41

Hence, the number of siblings is 41.

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Treat the,, >, or sign as a = sign when putting an inequality on a graph. The equation should be plotted as a dotted line if the inequality is either or. The equation should be graphed as a solid line if the inequality is either or.

What does a math inequality mean?

A relationship between two expressions or values that is not equal to each other is referred to as inequality in mathematics.

                              The term "inequality" refers to a mathematical equation in which the sides are not equal to one another. A comparison of any two values, known as an inequality, demonstrates that one value is less than, larger than, or equal to the value on the opposite side of the equation.

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Answer:

In astronomy, the celestial equator is the great circle in which the plane of the terrestrial Equator intersects the celestial sphere; it consequently is equidistant from the celestial poles. When the Sun lies in its plane, day and night are everywhere of equal length, a twice-per-year occurrence known as equinox.

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Step-by-step explanation: