85 POINTS!!! Just please help.

Binomial theorem is used to calculate the roots of the equations with highest degree in advance mathematical calculation in any subject.

Binomial theorem is represented by :

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Therefore, the binomial theorem help us to calculate the roots of the equations with highest degree in advance mathematical calculations in many subjects.

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The equation of the perpendicular line is y = -0.5x + 6.5

From the question, we have the following parameters that can be used in our computation:

y = 2x - 6

Also, from the question;

We have the following points

Point = (5, 4) i.e.  (x, y) = (5, 4)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2

This means that the slope is 2

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/2

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -1/2

(x₁, y₁) = (5, 4)

So, we have

y = -1/2(x - 5) + 4

Evaluate

y = -0.5x + 6.5

Hence, the line has an equation of y = -0.5x + 6.5

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In mathematics, a discontinuity is a point or set of points at which a function or curve is not defined, or is not "well-behaved," meaning it exhibits some kind of sudden or unexpected change in behavior.

Discontinuities can occur in functions or curves of all types, including functions of one variable, functions of several variables, and geometric curves.

There are several types of discontinuities that can occur in a function. For example, a function may have a jump discontinuity, which occurs when the function has a finite limit from one side but a different finite limit from the other side at a given point.

In all, the presence of discontinuities in a function can make it more difficult to analyze or work with, as the behavior of the function may not be predictable at these points.

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The roots of the quadratic equation 2x2 4x 7 will be two complex conjugate roots.

To determine the nature of roots of a quadratic equation, we can use the formula of the discriminant. The discriminant of a quadratic equation ax2 + bx + c = 0 is given by D = b2 - 4ac.

For the equation 2x2 4x 7, the discriminant is D = (-4)2 - 4(2)(7) = 16 - 56 = -40.

Since the discriminant is negative, the roots will be two complex conjugate roots.

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Answer: FOIL method

1. (a + b)(a + b) =

= a² + ab + b² + ab

= a² + 2ab + b²

2. (3a-2b) (3a - 2b) =

= 9a² - 6ab - 6ab + 4b²

= 9a² -12ab + 4b²

3. (x - 4y)(-3x - 2y) =

= -3x² -2xy +12xy +8y²

= -3x² + 10xy + 8y²

4.(-y-2z)(y-2z) =

= -y² + 2yz -2yz + 4z²

= -y² + 4z²

Step-by-step explanation:

According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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There are totally 4 terms in the given polynomial

We have a polynomial given by -x³+4x² +7x − 2

Algebraic expressions with coefficients and variables make up polynomials. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Since there are 4 terms with either an addition or a subtraction performed between them, the total number of terms is given by 4.

Those 4 terms are -x³ ,4x²,7x,−2

Therefore, there are totally 4 terms in the given polynomial.

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Yes, rigid motion is congruent?

A stiff motion occurs when an object is transported from one place to another while maintaining its original size and shape.

If and only if there is a stiff motion that establishes a correspondence of one figure as the likeness of the other, then two figures are said to be congruent. Interior angles are unchanged, as well as side lengths.

An object is rigidly moved from its initial place to the exact same location in a motion known as an identity motion. It appears as though the thing hasn't changed at all.

According to the Common Core, the "principle of superposition" states that two figures are congruent if there is a rigid motion projecting one onto the other.

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If 800g:1kg is equal to 1:n then the value of n is 1/8.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

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1, 2, 4, 8, and 16 are the components that make up 16. Similarly, the negative components of 16 are -1, -2, -4, -8, and -16. factors of 16: 1, 2, 4, 8, and 16.

The natural number 16 (or sixteen) comes after the number 15 and before the number 17. Since 42 = 4 4 is a square number, the number 16 is both a composite and a square. It has precisely five correct divisors, making it the lowest number. These are 1, 2, 4, and 8. The numbers 16 and 60 sound remarkably similar in English speech, which might lead to confusion.

There are three factor pairs of 16:

1 × 16 = 16.

2 × 8 = 16.

4 × 4 = 16.

1, 2, 4, 8, and 16 are the 16 factors. Likewise, the unfavorable factors of 16 are -1, -2, -4, -8, and -16. 1, 2, 4, 8, and 16 make up the number 16.

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ans is 4 I don't really know how to explain it

Answer:

y-intercept = (0,6)

slope = -2

Step-by-step explanation:

⭐What is the slope of a line?

⭐How can we find the slope of a line?

To find the slope, pick two coordinates you see on the line, substitute them into the slope formula, and solve for the slope!

I am choosing the coordinates (0,6) and (3,0), but you can choose any 2 coordinates that you see on the line.

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{0-6}{3-0}\\m = \frac{-6}{3}\\m = -2[/tex]

∴ The slope of the line is -2.

⭐ What is the y-intercept of a line?

⭐How do we find the y-intercept of a line?

When x=0, y=6

∴ The y-intercept of the line is (0,6)

The common multiple of 5y²- 45 and y + 3 is (y + 3).

For any two or more expressions, if any one of their factors is common in all of them, then that factor is said to be the common multiple of those expressions.

The given expressions are 5y²- 45 and y + 3

On factorizing them, we get

5y²- 45 = 5(y² - 9)

⇒ 5(y² - 3²)

From he binomial formula a² - b² = (a + b)(a - b), we can write

5y²- 45 = 5(y + 3)(y - 3)

Now, the second expression has no further simplification. The expression is itself a factor for it.

So, we can write their factors as

5y²- 45 = 5 × (y + 3) × (y - 3)

y - 3 = 1 × (y - 3)

From this, (y - 3) is the only factor that is a common factor for both the expression.

So, (y - 3) is the common multiple for the given expressions.

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750 cubic feet is the volume of the prism and Therefore, the volume of Jake's box is 8 times larger than Havana's box.

A right right triangle hypotenuse is its longest side, its "across" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe both sides of right triangles, we utilize specific terminology. The side opposing its right angle is always the tangent of a right triangle.

Dimensions of the Right Triangular Base

Base = 20 feet

Height= 120 inches = 10 feet

Base Area of the Prism

1/2 * 20 * 10

= 150 sq.feet

Height of the Prism = 5 feet

Volume of the Prism = Base Area X Height

= 150 X 5

=750 cubic feet

Jake's Box

Length: 12 inches

Width: 4 inches

Height: 8 inches

Volume = 12 X 4 X 8 =384 cubic inches

Havana's box

Jake's shipment crate is comparable to the one in Havana, except it is only half as long overall.

Therefore:

Length: 12/2=6 inches

Width: 4/2=2 inches

Height: 8/2=4 inches

Volume = 6 X 2 X 4 =48 cubic inches

Now:

384/48=8

Therefore, Jake's box has an 8-times higher volume than Havana's box.

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In order to prove that KFDE and KGHI are congruent by ASA, you need to know that KFDE and KGHI have two congruent angles (angle F and angle H) and a congruent side (side DE and side HI).

In order to prove that KFDE and KGHI are congruent by AAS, you need to know that KFDE and KGHI have three congruent angles (angle F, angle G, and angle H). This means that the angles in the triangle are equal, which implies that the sides in the triangle are also equal. Thus, for AAS, KFDE and KGHI must have two congruent sides (side DE and side HI).

Therefore, in order to prove that KFDE and KGHI are congruent by ASA or AAS, you must know that both triangles have two congruent angles and a congruent side (for ASA) or three congruent angles and two congruent sides (for AAS).

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The total surface area of the cone is calculated to be

Information given in the problem

the total surface area of the cone in the figure. (Use π = 3.14.)

A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.

The formula of the total surface are of a cone is given by

T = πr(r + l) square units.

calculating for l

l = √(12² + 5²) = 13

= 3.14 * 5 (5 + 13)

= 3.14 * 5 *(18)

= 282.6 cm^2

282.6 cm^2 is the  total surface area of the cone

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Answer:

580-80=500×6.5=3250 its ans iit

The formula to determine the consecutive odd numbers of a specific value "x" is:

x + 2n

Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.

If we want to know the consecutive numbers immediately we add +1, +2 and so on.

But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:

If we generalize an equation we have

x + 2n

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Answer:

28 apples

Step-by-step explanation:

29 - 1 = 28 apples

Answer:

28apples

Step-by-step explanation:

simple:29-1

hope this helps

The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g

what is mass of molecule ?

Watch your pronunciation. pronounced "muh-LEH-kyoo-ler mas" the total atomic mass of every atom in a molecule, calculated using a scale with hydrogen, carbon, nitrogen, and oxygen having atomic masses of 1, 12, 14, and 16, respectively.

solution:

The mass of one methane molecule should be "2.7 × 10⁻²³ gram" instead of "27 × 10⁻³ grams".

Mass of 60,000 molecules of methane

= (2.7 × 10⁻²³ g) × 60,000

= 1.62 × 10⁻¹⁸ g

Therefore,The mass of 60,000 molecules of methane is 1.62 × 10⁻¹⁸ g

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A collection of numbers, variables, and mathematical operations is referred to as an expression. The  expression is -2/5- 4/3P and 2/5+4/3P

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation .A collection of numbers, variables, and mathematical operations is referred to as an expression.

Given,

-4/3p - 2/5

= -20p - 6/15

= 2(10 p +3)/15

A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.

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A postulate is an unsupported assertion that is taken to be true. A provable true assertion is referred to as a theorem.

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A graph of the distance and time data for distance traveled by this train is shown in the image attached below.

In Mathematics, a scatter plot is sometimes referred to as scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting data points showing any association or correlation between the data set.

In this scenario, the time (in hours) would be plotted on the vertical axis (x-axis) of the scatter plot while the distance (in kilometers) would be plotted on the horizontal axis (y-axis) of the scatter plot by using an Excel worksheet.

From the scatter plot (see attachment) which models the relationship between the distance (in kilometers) and time (in hours), a linear equation for the line of best fit or trend line is y = 99.43x + 11.43.

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The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].

What is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

What is perpendicular ?

The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.

Let y = 3x + 1 is perpendicular ,

differentiate respect of x

[tex]\frac{dy}{dx} = 3[/tex] , m = 3

Thus , [tex]-\frac{1}{m}[/tex]

then [tex]-\frac{1}{3}[/tex]

The slope if it is perpendicular is [tex]-\frac{1}{m}[/tex].

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The weight of the package is 15 pound.

What is an linear equation?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.

Given that the fees for sending a package by media mail

For first pound : $2.41

For the next six pounds: $0.41 per pound

For additional pound: $0.39 per pound

The cost of first 7 pounds is = $(2.41 + (0.41 × 6)) =$4.87

$4.87 < $7.99. Thus the weight of the package is more than 7 pounds

Assume that, the weight of the package is (7 + x) pound.

The fee for (7 + x) pounds package is $(4.87 + 0.39x)

According to the question:

4.87 + 0.39x = 7.99

Subtract 4.87 from both sides:

0.39x = 3.12

Divide both sides by 0.39

x = 8

The weight of the package is (8 + 7) = 15 pounds.

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Answer:

7.62

Step-by-step explanation:

Simplify the following:

7 + 6/10 + 2/100

Express 6/10 in its lowest form by cancelling out gcd(6, 10) = 2 from the numerator and denominator. 6/10 = (2×3)/(2×5) = 3/5:

7 + 3/5 + 2/100

Express 2/100 in its lowest form by cancelling out gcd(2, 100) = 2 from the numerator and denominator. 2/100 = (2×1)/(2×50) = 1/50:

7 + 3/5 + 1/50

Put 7 + 3/5 + 1/50 over the common denominator 50. 7 + 3/5 + 1/50 = (50×7)/50 + (10×3)/50 + 1/50:

(50×7)/50 + (10×3)/50 + 1/50

50×7 = 350:

350/50 + (10×3)/50 + 1/50

10×3 = 30:

350/50 + 30/50 + 1/50

350/50 + 30/50 + 1/50 = (350 + 30 + 1)/50:

(350 + 30 + 1)/50

| 3 | 5 | 0

| | 3 | 0

+ | | | 1

| 3 | 8 | 1:

Answer: |

| 381/50

Latitude lines always have an equal distance between them, however longitude lines are separated from one another at the equator and come together at the poles. Longitude and latitude lines near the equator are equal in distance, with one degree covering 111 kilometers (69 miles).

Latitude lines are always equally spaced apart because they are always parallel to one another. Never do latitude lines converge or intersect. Distances north or south of the equator are measured by lines of latitude.

How do longitudes work?

Distance east or west of the prime meridian is measured by longitude. Meridians, which are also known as lines of longitude, are fictitious lines that divide the globe. They measure the distance either east or west, running from pole to pole from north to south. The units of longitude are degrees, minutes, and seconds.

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Factor (x+1) is the binomial factor for x³ - 6x²+ 3x + 10 using the rational roots test.

If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.

p = ±1,  ±10, ±2, ±5

q = ±1

Find every combination of ± p/q . These are the possible roots of the polynomial function.

±1, ±10, ±2, ±5

Substitute −1 and simplify the expression. In this case, the expression is equal to 0 so −1 is a root of the polynomial.

Substitute: −1 into the polynomial.

(−1)3−6(−1)2+3⋅(−1)+10

Raise −1 to the power of 3.−1−6(−1)2+3⋅−1+10

Raise −1 to the power of 2.−1 −6⋅1 + 3⋅−1+ 10

Multiply −6 by 1.−1−6+3⋅−1+10

Subtract 6 from −1.−7+3⋅−1+10

Multiply 3 by −1.−7−310

Subtract 3 from −7.−10+10

Add −10 and 10.0Since −1 is a known root, divide the polynomial by x+1 to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

x³− 6x²+ 3x+ 10x+ 1

Divide

x³−6x²+ 3x+ 10 by x + 1.

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We can identify quadrilateral because a regular polygon must have four equal sides in order to be called a quadrilateral.

Describe the quadrilateral.

Having four sides, four vertices, and four angles, a closed quadrilateral is a type of polygon. It consists of four connected non-collinear points. Quadrilaterals' internal angles always add up to 360 degrees.

According to the given question:

In a quadrilateral -

In order to be considered a quadrilateral, it must have four sides, four angles.

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Sandra sets the speed to 69 miles per hour. The equation that express how many hours it will take her to drive m miles is: h = m/69.

Speed or velocity 69 miles per hour means: in 1 hour she will travel 69 miles

69 miles need 1 hour

1 miles need 1/69 hours

m miles need m x 1/69 hours.

If h is the amount of time need to take her to drive m miles, then:

h = m x 1/69 = m/69 hours

We can also solve the problem, using formula:

s = vt

Where:

s = distance

v = speed = 69 mph

t = time

In the given problem, the distance is m, hence s = m, and t = h

Hence,

t = s/v

h = m/69

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