65 points
1. Find the pattern and then write a rule and an
equation that represents the pattern. Then
complete the table,
X= 0 2 10 16 20
Y= 0 1 5 8 10

A direct variation equation is: [tex]y = \frac{1}{8} x[/tex].

According to the question,

x and y vary directly proportional then the equation is

y =kx  ( where k is the constant of variation)

To find k use the given condition y = 1/7 when x = 8/7

we know that,

[tex]k = \frac{y}{x} = \frac{1/7}{8/7} = \frac{1}{8}[/tex]

Hence, the equation is: [tex]y = \frac{1}{8} x[/tex] .

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Matrix b is in reduced echelon form.

Therefore the answer is b. reduced echelon form.

In a reduced echelon matrix, the leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0. Matrix b satisfies these conditions, so it is in reduced echelon form.

Reduced echelon form is a special type of echelon form for matrices, which is used in linear algebra to solve systems of linear equations. In a reduced echelon form matrix, the following conditions are satisfied:

All non-zero rows are above any rows of zeros

The leading entry (the first non-zero entry from the left in a row) in each non-zero row is 1, and all entries above and below the leading entry are 0.

Each leading entry is the only non-zero entry in its column.

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Follow the example of long division to understand the method and concept of the same.

Let us understand the long division with an example. For this, let us take 13032 as the dividend and 24 is the divisor. Now, performing long division.

On division the quotient will be 5. Now, subtracting 120 from 130, the remainder will be 10. Now, we will take the dividend 103.

Dividing 103 by 24, the overall quotient will be 54. On subtraction we get 7. Taking 2, thus, the combined dividend is 72.

Dividing 72 by 24, the quotient will be 3. Thus, overall quotient will be 543. The remainder will be zero. Thus, the long division of 13032 by 24 yields 543 as quotient without remainder.

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The statement "if v in R3 and v · v = 0, then v is the zero vector" is true

In mathematics, a vector is an ordered tuple of numbers or scalars that can be used to represent a quantity that has both magnitude and direction. Vectors are used to model physical quantities such as displacement, velocity, and force, among others.

Here we have given that if v in r 3 and v · v = 0, then v is the zero vector.

It is true because if the dot product of a vector with itself is zero, it means that the magnitude of the vector is zero and thus it is the zero vector. Understanding the concept of a zero vector and its relationship with other vectors is important in mathematics and physics.

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The average value of the function f(x) = x² - 8x + 6 on [0, 4] is 38.

The two primary divisions of calculus, differential calculus and integral calculus, are concerned with rates of change and slopes of curves.

By dividing the definite integral of the function over the interval by the length of the interval, one can determine the average value of a function over the interval [a, b].

The function in this instance is f(x) = x3 - 8x + 6, and the range is [0, 4]. Using the definite integral of x3 and the definite integral of -8x, one can determine the definite integral of the function across the interval:

[tex]\int\limits^0_4 {x^{3} - 8x + 6 } \, dx[/tex]

= [tex]\frac{x^4}{4} - \frac{8x^2}{2} + 6x[/tex]

evaluated at x = 4 - x = 0 = [tex]0 - \frac{4^{4} }{4} - \frac{8.4^2 }{2} + 6.4\\[/tex]

= - 24

The length of the interval is b - a = 4 - 0 = 4. Hence, the average value of the function over the interval is given by:

Therefore, the average value of the function f(x) = x^3 - 8x + 6 on [0, 4] is 38.

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The minimum value of the function C = x - 2y at the vertex point (1,0) is 1.

So, when we substitute x = 1 and y = 0 into the function, we get:

C = 1 - 2 * 0 = 1.

Therefore, the minimum value of the function is 1.

The fraction that is equal to 0.84 repeating is 8/9 in simplest form.

If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase "lowest words" when referring to the simplest form.

0.84 repeating can be represented as a fraction in simplest form by using the following method:

Let x = 0.84 repeating,

Then 10x = 8.4 repeating.

Subtracting the two equations,

we have 9x = 8.

Dividing both sides by 9,

we have x = 8/9.

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I recommend the average fan buy season tickets when purchasing seats.

Based on the research, the average local baseball fan plans to attend 67 games during the season. For a fan who is planning to attend this many games, it would be more cost-effective to purchase season tickets rather than individual game tickets.

For fans considering season tickets, here are some recommendations based on the seating section:

Purchasing season tickets rather than individual game tickets is the most cost-effective choice for the average fan who plans to attend 67 games during the season. The best choice of section will depend on the fan's budget and personal preferences.

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Answer:

factors

Step-by-step explanation:

To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.

The derivative of a function of f at x is given by f′(x) = lim(h→0) f(x+h)−f(x)h provided the limit exists.

A function's immediate rate of change at one particular location is referred to as the derivative of that function. At a certain point along the curve, the derivative provides the precise slope. The symbol for the derivative of a function is dy/d x, which stands for the derivative of the function with respect to the variable.

Given that,

f(x + h) - f(x) = 16xh + 8h² + 2h

f(x)=8x²+2x+7.

then derivative is given by:

f'(x) = lim(h→0) [f(x + h) - f(x)] / h

f'(x) = lim(h→0) [8(x + h)²+2 (x+h) + 7] - [8x²+2x+7] / h

f'(x) = lim(h→0) 8x² + 16xh + 8h² + 2x + 2h + 7 - 8x² - 2x - 7 / h

f'(x) = lim(h→0) 16xh + 8h² + 2h / h

f'(x) = lim(h→0) 16x + 8h + 2

f'(x) = 16x + 8

f(x + h) - f(x) = [8(x + h)²+2 (x+h) + 7] - [8x²+2x+7]

f(x + h) - f(x) = 8x² + 16xh + 8h² + 2x + 2h + 7 - 8x² - 2x - 7

f(x + h) - f(x) = 16xh + 8h² + 2h

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The value of the sum of the series is 42

In an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:

Sn = n/2 * (a1 + an)

Where "a1" is the first term and "an" is the nth term.

In this series, a1=3 , an=3 , n=14

Plugging these values into the formula, we get:

Sn = 14/2 * (3 + 3)

= 14/2 * 6

= 7 * 6

= 42

So, the sum of the first 14 terms of the arithmetic series is 42

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The length longer diagonal is 174 cm.

In a rhombus, the diagonals bisect each other as well as the the vertex angles and adjacent angles are supplementary

So assuming that the 70 degree angle is opposite the 122 cm diagonal, we have

(1/2 length of the shorter diagonal) / sin (35)  = (1/2 length of the longer diagonal) / sin(55)

Multiply both sides by 2

( length of the shorter diagonal) / sin (35)  = ( length of the longer diagonal) / sin(55)

Multiply both sides by sin(55).

Length of the longer diagonal = sin (55) (122 cm) / sin (35) = 174 cm

Therefore, the length of the longer diagonal is 174 cm.

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Surface area of the cube can be S = 6x², if the side length of the cube is 7.7 cm, the surface area would be is S = 6(7.7)² = 391.16.

The surface area of an object refers to the total area of its exposed outer surface. It is a measure of the amount of space that an object's surface covers. Surface area is a two-dimensional concept, and is different from the object's volume, which is a three-dimensional concept.

The surface area of an object depends on its shape, and can be calculated using mathematical formulas specific to different shapes. For example, the surface area of a cube is the sum of the areas of its six faces, while the surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere.

Surface area is an important concept in a variety of fields, including physics, chemistry, and engineering. In physics, it is used to calculate the heat transfer between objects, while in chemistry it is used to calculate the amount of reactant needed to cover a given surface area in a reaction. In engineering, surface area is important in the design of heat exchangers, reactors, and other equipment where heat or chemical reactions take place on surfaces.

V = x³

So, if the side length of the cube is 7.7 cm, the volume would be:

V = (7.7)³ = 455.169

The surface area of the cube can be calculated as:

S = 6x²

So, if the side length of the cube is 7.7 cm, the surface area would be:

S = 6(7.7)² = 391.16

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The complete question is:

15mL is also equivalent to one tablespoon.

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The values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given is the system of simultaneous equations as -

{y} = -{2/3}x + 3

{y} = 2x - 5

Refer to the graph of the equations attached. The value of {x} and {y} for which both the equations are true is given by the point of intersection of both lines.

Therefore, the values of {x} and {y} for which both the equations are true are {x} = 3 and {y} = 1.

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The surface area of the cone with the given parametric equation is (4π + 4π√2) square units.

The parametric equations describe a cone that is generated by rotating a line segment in the xy-plane about the x-axis. The result is a 3-dimensional surface that has a circular base with radius 2 and a height of 2.

The surface area of the cone can be calculated using the formula:

A = πr^2 + πrs

where r is the radius of the circular base and s is the slant height.

The slant height is equal to the distance from the center of the circular base to the tip of the cone, which can be calculated using the Pythagorean theorem: s = √(h^2 + r^2), where h is the height of the cone.

Therefore, for this cone with radius 2 and height 2, the surface area can be calculated as:

A = πr^2 + πrs

= π * 2^2 + π * 2 * √(2^2 + 2^2)

= 4π + 4π√2

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Answer:

diameter=radius divided by 2

the original price is really "x", which oddly enough is the 100%.

now it decreased to $9235, and we know that's 38% less than "x", so 100% - 38% = 62%, so $9235 is really the 62% of "x", hmmm what the dickens is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 9235& 62 \end{array} \implies \cfrac{x}{9235}~~=~~\cfrac{100}{62} \\\\\\ \cfrac{ x }{ 9235 } ~~=~~ \cfrac{ 50 }{ 31 }\implies 31x=461750\implies x=\cfrac{461750}{31}\implies x\approx 14895[/tex]

An equation of the line that passes through the point (1, -3) and has a slope of -3 is y = -3x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At point (1, -3), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-3) = -3(x - 1)

y + 3 = -3x + 3

y = -3x + 3 - 3

y = -3x

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The mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.

The mean of the 400 richest Americans is calculated by summing up all of the net worth of each person on the list, and then dividing it by the total number of people on the list. The formula used to calculate the mean is:

Mean = (Sum of Net Worth) / (Total Number of People on the List)

For example, on September 19, 2012, the total net worth of the 400 richest Americans was $1.7 trillion. If we divide this by the total number of people on the list (400), then the mean net worth of the 400 richest Americans is $4.25 billion.

Therefore, the mean of the 400 richest Americans as of September 19, 2012 is $4.25 billion.

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Answer:4.1

Step-by-step explanation:

Answer: 4.1

Step-by-step explanation:

The number of ways 9 yellow marbles can be divided among 4 distinguishable cups is 126.

Dividing 9 marbles among 4 cups is a combination problem. The number of combinations is given by the formula C(n + r - 1, r - 1), where n is the number of items (marbles) and r is the number of groups (cups). In this case, n = 9 and r = 4. Plugging these values into the formula, we get:

C(9 + 4 - 1, 4 - 1) = C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220

This means that there are 220 ways to divide 9 yellow marbles into 4 distinguishable cups. However, since the cups are distinguishable, each combination is counted multiple times, once for each permutation of the cups. The number of permutations of n items taken r at a time is given by the formula n! / (n - r)!. In this case, the number of permutations is 4! = 4 * 3 * 2 * 1 = 24.

So, the total number of ways to divide 9 yellow marbles into 4 distinguishable cups is 220 / 24 = 9. This means that there are 126 distinct ways to divide 9 yellow marbles among 4 distinguishable cups.

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The total surface area of the hexagonal pyramid is 237.5 in²

An expression that depicts the relationship between two or more numbers and variables is called an equation. Depending on the degree, an equation may be linear, quadratic, cubic, or another type.

A solid figure's surface area is calculated by summing up all of its distinct surfaces.

Given the hexagonal pyramid with a base of 6 inches and each isosceles triangle having a height of 8 inches. Hence:

Area of pyramid base = 93.5 in²

The lateral face has 6 triangle faces, hence:

Area of each lateral face = 1/2 * base * height = 0.5 * 8 * 6 = 24 in²

Total area of lateral face = 6 * 24 in² = 144 in²

Total surface area = 144 in² + 93.5 in² = 237.5 in²

The surface area is 237.5 in²

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Answer:-5, 3

Step-by-step explanation:

its the answer. Period

Answer:

Of course you can :)

Answer provided in image !^^

Step-by-step explanation:

3. In the image shade 9 because 3/4x12=9

The domain is all x-values or inputs of a function & the range is all y-values or outputs of a function.

The numbers you supply to the function are referred to as the domain. The numbers it returns to you are referred to as the "range."

Take y=3x as an illustration. The domain of this function is "all real numbers," so you can substitute any number you like for x. (or everything from negative infinity to positive infinity, if you like). Furthermore, as you can probably guess, any actual number could result from it. (You desire the release of a specific real-world number. To get there, enter x as one-third of that number. As a result, "all real numbers" are included in this function's range.

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The second one because it passes through (0,0)

Based on the given expression representing each angle, the value of x is 47 and each angles are 135° and 45° respectively.

Based on the given diagram; the angles represented by the expression are referred to as supplementary angles.

So, we can find the unknown variable x by adding the expressions and equating it to 80°

(3x - 6) + (x - 2) = 180

3x - 6 + x - 2 = 180

combine like terms

3x + x - 6 - 2 = 180

4x - 8 = 180

Add 8 to both sides

4x = 180 + 8

4x = 188

divide both sides by 4

x = 188/4

x = 47

Therefore, the respective angles are;

3x - 6

= 3(47) - 6

= 141 - 6

= 135°

x - 2

= 47 - 2

= 45°

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