A triangle has vertices A(-2,1), B(2,4), C(4,1).
Find the area of the triangle.

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 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 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:

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.

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 total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

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 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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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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Simplifying 3 to the 3rd power gives 27.

Raising a base number to an exponent is referred to as "power" in mathematics. It indicates that "base number" and "exponent" are the two fundamental components of powers. The exponent shows how many times the base number has been multiplied, whereas the base number is defined as a number that is multiplied by itself. In a nutshell, power is a number that has exponents used to express it. It means that the same element has been multiplied repeatedly. In the context of powers, the following specific terminology may be used:

Whenever a number:

Squared – power is 2

cubed – Power is 3

“to the power of” – used for powers more than 3

3 to power 3= [tex]3*3*3=27[/tex]

Simplifying 3 to the 3rd power gives 27.

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Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]x+3=8\\x=8-3\\x=5[/tex]

The system of equations has "no solution" because they are parallel lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.

The system of equations y = 0 and y = -5 describes two lines in the coordinate plane.

The first equation, y=0, is the x-axis.

The second equation, y=-5, is a horizontal line 5 units below the x-axis.

As we know, y = 0 and y = -5 are two parallel lines.

Therefore, no solution exists.

Hence, the system of equations has no solution.

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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.

By applying concepts of Quadratic Inequality and applying on graphs option C is correct.

A quadratic inequality of the form

y>ax^2+bx+c

(or substitute <,≥ or ≤ for > ) denotes a section of the plane enclosed by a parabola.

Graphing the parabola is the first step in graphing a quadratic inequality. Then, depending on the inequality, fill in the area either above or below it.

If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.

Otherwise, a dotted line should be drawn around the parabola to show that the region excludes the border if the inequality symbol is either <or >.

If it is > then the region above the dotted line is taken and if it is < the region below it is taken.

In the given question

y>(x-3)^2-1;

So the region above the dotted line should be taken which is option C.

By applying concepts of Quadratic Inequality and applying on graphs option C is correct.

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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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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

Since, The given line is the line which is parallel to the y-axis that is a vertical line, It makes 90 degree with the positive x-axis, The slope is undefined that is tan(90).

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

x=-4

This is a vertical line parallel to y-axis.

It makes 90 degree with positive x-axis in anti-clockwise direction.

slope = tan(90) = undefined.

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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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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.

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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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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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 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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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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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:

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:

Volume of the rectangle is estimated as;

Volume =  length x width x height

A three-dimensional object's volume is a measurement of the amount of space it occupies. We'll look at the procedure for calculate a box's volume on this page.

The size of a box:

View the box illustration below:

As you can see, there are three dimensions to take into account when dealing with a box or other three-dimensional object: length, width, and height.

Thus, the volume is calculated using the formula length x width x height:

V = l x w x h

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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 true equations among the given expression are

True equation has same value at the left hand side and the right hand side of the equations after simplifying

The true equation is shown below

48 ÷ 8 + 2³ = 5 + 3²

applying PEMDAS

Exponents

48 ÷ 8 + 8 = 5 + 9

Division

6 + 8 = 5 + 9

Addition

14 = 14

(8 * 7) / 2 − 12 = 22 − 2 * 3

Parenthesis

56/2 - 12 = 22 - 2 * 3

Division

28 - 12 = 22 - 2 * 3

Multiplication

28 - 12 = 22 - 6

Subtraction

16 = 16

since the values in LHS = RHS the both equation are true

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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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