50 POINTS

Divide: 4x^3-3x^2+2x+1/x-1

The solution to the system of equations is [tex]x = 67/17 y = -42/17 z = -1[/tex].

Answer:

232 cubic centimeters

Step-by-step explanation:

V = Bh

= (7(2) + (1/2)(3)(3 + 7))(8)

= (14 + 15)(8) = 29(8)

= 232 cubic centimeters

The inner angles of 4 and 7 alternate and are congruent as the angles 3 and 8 are similar and coincide.

A geometric shape known as an angle is created by two rays of line segments that meet at a location known as the vertex of angle. The rays or splines that make up the angle are referred to as its sides or legs. Angles can be divided into different categories according to their size and shape and are commonly measured either degrees or radians. Right ratios, obtuse angles, reflex angles, acute angles, and straight angles are a few examples of common angles.

given

The following four claims could be used to demonstrate that lines r and s are parallel:

The angles 1 and 6 have comparable and congruent angles.

The inner angles of 2 and 5 alternate and are congruent.

The angles 3 and 8 are similar and coincide.

The inner angles of 4 and 7 alternate and are congruent as the angles 3 and 8 are similar and coincide.

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Answer:

[tex]v = 8.125 \: {units}^{3} [/tex]

Step-by-step explanation:

Given:

h (height) = 0,5 units

A (base area) = 16,25 units

Find: V (volume) - ?

[tex]v = a(base) \times h [/tex]

[tex]v = 16.25 \times 0.5 = 8.125[/tex]

Using expression (L/3) / (36t) = L / (108t),  the fraction of the total singing time that all three are singing at the same time is L / (108t).

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a quantity. Expressions can be composed of one or more terms, which are separated by addition or subtraction symbols.

For example, the expression 2x + 3y - 5 represents a value that depends on the values of the variables x and y. The term 2x represents a quantity that is twice the value of x, the term 3y represents a quantity that is three times the value of y, and the term -5 represents a constant value of negative five.

Now,

Let's call the length of the song "L" and the time it takes to sing one line "t". Then, we know that:

Rachel starts singing at t = 0, and she sings for a total of 4L.

Jenny starts singing at t = t, and she sings for a total of 4L.

Angela starts singing at t = 2t, and she sings for a total of 4L.

Since each line of the song is the same length, we can divide the total singing time for each person into three equal parts, one for each line. So, each person sings for a total of 12t.

Now, let's think about when all three people are singing at the same time. This happens during the second line of the first repetition of the song. Rachel is singing the first line, Jenny is singing the second line, and Angela is starting to sing the third line. The total length of time that all three people are singing together is just the length of one line, which is L/3.

Since each person sings for a total of 12t, the total singing time for all three people is 36t. Therefore, the fraction of the total singing time that all three are singing at the same time is:

(L/3) / (36t) = L / (108t)

So, the fraction of the total singing time that all three are singing at the same time is L / (108t).

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The word phrase for h + 6 is Six more h or the sum of six and h.

Converting algebraic expression to word phrase:

An algebraic expression is a mathematical phrase that uses variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Converting an algebraic expression to a word phrase means expressing the mathematical expression in words.

This can be useful in situations where mathematical symbols may not be understood or when communicating mathematical concepts to someone who may not be familiar with them.

Here we have the expression h + 6

Where 6 is added to h

Hence,

The word phrase for h + 6 is Six more h or the sum of six and h.

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Answer:

y=-4x+10

Step-by-step explanation:

y = -4x + c

2 = -4*2 + c

2= -8+c

c= 10

y=-4x+10

The linear equation y = (2/3)x - 3 represents the graph that passes through the points (0, -3) and (3, -1).

What is a linear equation, exactly?

A straight line on a graph is represented by a linear equation, which is a mathematical equation. It is an algebraic equation of the form y = mx + b, where x and y are variables, m represents the line's slope (or gradient), and b represents the y-intercept. The slope m denotes the pace at which y varies in relation to x. In other words, it reflects the slope of the line.

Now,

To determine the equation that represents the graph of a line passing through the points (0, -3) and (3, -1), we can use the slope-intercept form of a linear equation

First, we need to find the slope of the line:

slope = Δy / Δx

slope = (-1 - (-3)) / (3 - 0)

slope = 2/3

Next, we can use one of the given equations and substitute the slope and one of the points to find the y-intercept:

y = mx + b

-3 = (2/3)(0) + b

b = -3

Therefore, the equation is

y = (2/3)x - 3

The equation that represents the graph of a line passing through the points (0, -3) and (3, -1) is y = (2/3)x - 3.

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the volume of the rectangular prism is 1,080 cubic inches.

Why is it?

The volume V of a rectangular prism is given by the formula:

V = length x width x height

Substituting the given values, we get:

V = 10 inches x 18 inches x 6 inches

Simplifying, we get:

V = 1,080 cubic inches

Therefore, the volume of the rectangular prism is 1,080 cubic inches.

A rectangular prism is a three-dimensional solid shape that has six rectangular faces, where each pair of opposite faces are congruent and parallel to each other. It is also known as a rectangular parallelepiped.

A rectangular prism is characterized by its length, width, and height or depth. The length is the measurement of the longest side of the prism, the width is the measurement of the shorter side, and the height or depth is the measurement of the perpendicular distance between the two faces that are parallel to each other.

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A one-sample t-test was conducted to determine if the temperature increased in the first week of October 2019 compared to the average temperature from the previous 10 years. The result showed a p-value of 0.032, indicating a significant increase in temperature.

To determine if there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years, we can conduct a one-sample t-test with a null hypothesis that the population mean temperature this year is equal to the average temperature data from the previous 10 years (75) and an alternative hypothesis that the population mean temperature this year is greater than 75.

Using a statistical software, the calculated t-value is 2.17 with a corresponding p-value of 0.032. Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to show that the temperature has increased this year compared to the average temperature data from the previous 10 years. The p-value of 0.032 indicates that the probability of observing a sample mean temperature as extreme as 79.29 (the calculated sample mean temperature this year) or greater, assuming that the population mean temperature is equal to 75, is 0.032.

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If a and c are both less than 0, the following statements must be true:

A. The graph of h will be reflected over the x-axis.

C. The vertex of h will be at (0, c).

Statement A is true because a negative value for "a" causes the parabola to open downwards, which reflects the graph over the x-axis.

Statement C is true because the x-coordinate of the vertex is always -b/2a, which in this case is -0/2a = 0, and the y-coordinate is "c", so the vertex is at (0,c).

Statement B is not necessarily true, as the sign of "c" does not affect the horizontal shift of the graph. If "c" were positive, the graph would shift downwards instead of upwards, but it would still be centered at x=0.

Statement D is not necessarily true, as the sign of "a" determines whether the graph is wider or narrower than the parent quadratic function. A negative value of "a" makes the graph narrower than the parent function, while a positive value of "a" makes it wider.

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The properties for  parabolas 1 is:

Parabola 1:

Vertex: (-2, 1)

Max/min value: The vertex represents a minimum point, so the minimum value is 1.

Axis of symmetry: x = -2

Zero(s): There are two zeros, at x = -4 and x = 0.

Direction of opening: The parabola opens upwards.

Y-intercept: The y-intercept is (0, 5).

Parabola 2:

Vertex: (1, -2)

Max/min value: The vertex represents a maximum point, so the maximum value is -2.

Axis of symmetry: x = 1

Zero(s): There are two zeros, at x = -1 and x = 3.

Direction of opening: The parabola opens downwards.

Y-intercept: The y-intercept is (0, -1).

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Answer:

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Answer:

(x+2)(2x-9)

Step-by-step explanation:

2x^2 + 4x - 9x - 18

2x(x+2) -9(x+2)

(x+2)(2x-9)

Let's suppose that Tom drives x miles. Then, the total cost of the first plan will be:

C1 = 53.96 + 0.13x

And the total cost of the second plan will be:

C2 = 43.96 + 0.18x

To find how many miles Tom needs to drive for the two plans to cost the same, we need to solve the following equation:

53.96 + 0.13x = 43.96 + 0.18x

Simplifying:

10 = 0.05x

x = 200

Therefore, Tom needs to drive 200 miles for the two plans to cost the same.

Answer:

61st term = 547

Step-by-step explanation:

The formula for the nth term of an arithmetic sequence is

[tex]a_{n}=a_{1}+(n-1)d[/tex], where a1 is the first term, n is the term position (e.g., 1st or 61st) and d is the common difference.

We already know that a1 = 7 and the n = 61.  We can find the common difference by finding the difference of any two consecutive terms with the smaller term being subtracting from the larger:

Thus, if we use 7 and 16, our common difference (d) is:

d = 16 - 7 = 9

Now, we can simply plug in everything to the formula to find the 61st term:

[tex]a_{61}=7+(61-1)*9\\ a_{61}=7+60*9\\ a_{61}=7+540\\ a_{61}=547[/tex]

6 is value of x would prove these lines parallel ​.

Describe a parallel line?

Lines that are always the same distance apart in a plane are said to be parallel. Nothing can cross a parallel line. No matter how far in either direction they may be extended, parallel lines are ones that are equally spaced apart from one another and never cross. For instance, parallel lines are represented by a rectangle's opposing sides.

8x + 6 = 2x + 42

8x - 2x = 42 - 6

 6x = 36

    x = 36/6

     x = 6

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The solutions to the equation -x² + 2x = 0 are x = -1 and x = 2, which are the x-intercepts of the graph y = -x² + x + 2

To solve -x² + 2x = 0 using the graph y = -x² + x + 2, we need to first find the x-intercepts. These are the points where the graph intersects the x-axis, which are the solutions to the equation -x² + x + 2 = 0.

We can see from the graph that the vertex of the parabola is at (0.5, 2.25). Since the coefficient of x² is negative, the parabola opens downwards. This means that it intersects the x-axis twice, once on either side of the vertex.

To find the x-intercepts, we can draw a horizontal line at y = 0, which represents the x-axis. This line intersects the parabola at two points: (-1, 0) and (2, 0). These are the solutions to the equation -x² + 2x = 0.

We can also verify our answer by drawing the line y = 2x and seeing where it intersects the parabola. This line passes through the vertex and intersects the parabola at (-1, 3) and (2, 4). These points are symmetrical to the x-axis and have the same y-value, which confirms that they are the x-intercepts.
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Answer:

  2002.8 mm³

Step-by-step explanation:

You want the volume of a cylinder with radius 5 mm and height 25.5 mm.

The formula for the volume of a cylinder is ...

  V = πr²h

Using the given dimensions, it is found to be ...

  V = π·(5 mm)²(25.5 mm) = 637.5π mm³

  V ≈ 2002.8 mm³

The volume of the cylinder is about 2002.8 cubic millimeters.

The farmer can make at most 3 complete picture frames with some usable board left over after subtracting the scratched portion and dividing the usable length by the length needed for each picture frame.

To find the amount of usable board, we need to subtract the scratched portion from the total length of the board:

101/12 - 23/8

Converting to a common denominator, we get:

122/12 - 19/8 = 976/96 - 228/96 = 748/96

Simplifying, we get:

72/96 feet

Now, we can divide this usable length by the length needed for each picture frame:

722/96 ÷ 1 2/3

Converting the mixed number to an improper fraction, we get:

722/96 ÷ 5/3 = 748/96 ÷ 5/3 = 748/96 x 3/5 = 3.9

Therefore, the farmer can make at most 3 complete picture frames with some usable board left over.

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Answer:

The rate of change is 400

The altitude increases by 400 feet every minute.

Step-by-step explanation:

We Know

x = the number of minutes the balloon rises.

y = altitude of the balloon.

To find the Rate of change (slope), we can use rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, 150) (1, 550)

We see the y increase by 400 and the x increase by 1, so

The rate of change is 400

The altitude increases by 400 feet every minute.

The dοmain οf the functiοn f(x) =  {- 3, - 1, 0 2, 4}. Yes, because for each input there is exactly one output.

Suppοse we have an οrdered pair (x, y) then the dοmain οf the functiοn is the set οf values οf x and the range is the set οf values οf y fοr which x  is defined.

Given, The graph represents a relatiοn where x represents the independent variable and y represents the dependent variable.

The οrdered pairs are given by, (- 3, 4), (- 1, 1), (0, - 2), (2, 0), and (4, - 1).

We knοw the dοmain οf the functiοn are all the x cοοrdinates.

Therefοre, The dοmain οf the functiοn f(x) = {- 3, - 1, 0 2, 4}.

Yes, because for each input there is exactly one output.

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If f (x) = √2x + 4 and g(x) = 1/2(x-4)² then the function is f(g(x)) = √2 * (x-4) * √[1 + 2/[(x-4)²]]

What is function?

An expressiοn, rule, οr law in mathematics that specifies the relatiοnship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functiοns are fundamental fοr cοnstructing physical relatiοnships.

This relatiοnship is typically represented as y = f(x), οr "f οf x," and y and x are related such that fοr each value οf x, there is a specific value οf y. This means that f(x) can οnly have οne value fοr a given x. In set theοry jargοn, a functiοn cοnnects an element x tο an element f(x) in anοther set. The set οf x values is referred tο as the dοmain οf the functiοn, and the set οf f(x) values prοduced by the values in the dοmain are referred tο as the range οf the functiοn.

[tex]f(g(x)) = \sqrt{[2g(x) + 4]}[/tex]

Now we can substitute the expression for g(x):

[tex]f(g(x)) = \sqrt{[2(1/2(x-4)²) + 4]}[/tex]

We can simplify this expression by first expanding the square in the brackets:

[tex]f(g(x)) = \sqrt{[2(x-4)^2 + 4]}[/tex]

Then we can factor out the 2 from the square:

[tex]f(g(x)) = \sqrt{[2(x-4)²] * √[1 + 2/[(x-4)²]]}[/tex]

Simplifying further:

[tex]f(g(x)) = \sqrt{2 * (x-4) * \sqrt{[1 + 2/[(x-4)²]}]}[/tex]

Therefore, [tex]f(g(x)) = \sqrt{2 * (x-4) * \sqrt{[1 + 2/[(x-4)²]}]}[/tex]

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The multiplier (z*) for a confidence level will remain the same, if sample proportion and confidence level is unchanged.

The multiplier of confidence interval is defined as the number of standard errors at the distance from mean. It is dependent on confidence level and sample data distribution.

Confidence levels refers to the certainty of correctness and preciseness of interval. It is expressed as percentage.

The increase in sample size decreases the standard error. Moreover, as the question states, the unchanged values of confidence interval and sample size are there, which makes the multiplier constant.

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Complementary angles, Supplementary angles, Vertical angles, Adjacent angles and Linear pairs these are the  5 Pre algebra angle.

To summarize 5 angle relationships in pre-algebra, we can discuss the following:

1. Complementary angles: These are two angles that add up to 90 degrees. To find a complementary angle, subtract the given angle from 90 degrees. For example, if the given angle is 30 degrees, its complementary angle is 60 degrees (90 - 30 = 60).

2. Supplementary angles: These are two angles that add up to 180 degrees. To find a supplementary angle, subtract the given angle from 180 degrees. For example, if the given angle is 120 degrees, its supplementary angle is 60 degrees (180 - 120 = 60).

3. Vertical angles: These are angles that are opposite each other when two lines intersect. Vertical angles are always equal. For example, if one angle measures 40 degrees, its vertical angle will also be 40 degrees.

4. Adjacent angles: These are angles that share a common side and vertex but do not overlap. Adjacent angles can be complementary, supplementary, or neither, depending on their degree measures.

5. Linear pairs: These are adjacent angles that add up to 180 degrees,

forming a straight line. Both angles in a linear pair are supplementary.

When working with angle relationships in pre-algebra, remember these

five concepts to help you find missing angle measurements and solve problems.

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Answer:

x = 11

Step-by-step explanation:

35 + 5x = 90

5x = 55

x = 11

We use the normal distribution formula and standard normal distribution table to find the proportion of boys in a school with heights shorter than 67 inches.

To solve this problem, we need to use the normal distribution formula and the standard normal distribution table.

First, we need to convert the height of 67 inches into a standard score or a z-score. The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the height we want to convert, μ is the mean height of the population, and σ is the standard deviation.

So, for x = 67, μ = 70, and σ = 3.5, we have:

z = (67 - 70) / 3.5 = -0.8571

Next, we need to find the area under the standard normal distribution curve to the left of the z-score -0.8571 using the standard normal distribution table. This area represents the proportion of boys in the school who are shorter than 67 inches.

The table gives us that the area to the left of -0.8571 is 0.1950.

Finally, we need to multiply this proportion by the total number of boys in the school to find the expected number of boys who are shorter than 67 inches tall:

Expected number = proportion * total number of boys

Expected number = 0.1950 * 1019

Expected number ≈ 199

Therefore, to the nearest whole number, we can expect about 199 boys in the school to be shorter than 67 inches tall.

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Answer: Let's call the ages of the squirrels C, Celia, and Cecily, and let's represent the number of nuts they took with the variables c, ce, and ce2, respectively.

We know that the total number of nuts is 770, so we can write:

c + ce + ce2 = 770

We also know the ratios of the nuts each squirrel took relative to the others:

Cedric takes 3 nuts for every 4 nuts Celia takes, so we can write c : ce = 3 : 4, or c = (3/4)ce.

Cecily takes 7 nuts for every 6 nuts Celia takes, so we can write ce2 : ce = 7 : 6, or ce2 = (7/6)ce.

Now we can substitute these expressions into the first equation and solve for ce, the number of nuts Celia took:

(3/4)ce + ce + (7/6)ce = 770

Multiplying both sides by 12 to eliminate the fractions, we get:

9ce + 12ce + 14ce = 9240

Simplifying, we get:

35ce = 9240

Dividing both sides by 35, we get:

ce = 264

Now that we know Celia took 264 nuts, we can use the ratios to find how many nuts the other squirrels took:

Cedric took 3/4 as many nuts as Celia, so he took (3/4) * 264 = 198 nuts.

Cecily took 7/6 as many nuts as Celia, so she took (7/6) * 264 = 308 nuts.

Finally, to find how many nuts the youngest squirrel took, we can subtract the nuts taken by the other two squirrels from the total:

c + ce2 = 770 - ce

c + ce2 = 770 - 264 - 198 - 308

c + ce2 = 0

This means that the youngest squirrel did not take any nuts.

Step-by-step explanation:

The price of the house at the end of 2008 will be 39,60,000

We must determine the price following each rise in order to determine the cost of the house at the end of 2008.

First of all, in 2004 the price jumped by 10%.

10% of 30,00,000 = 0.1 x 30,00,000 = 3,00,000

As a result, the house's new price in 2004 was:

30,00,000 + 3,00,000 = 33,00,000

The price then rose by 20% in 2008.

20% of 33,00,000 = 0.2 x 33,00,000 = 6,60,000

The home's total price at the end of 2008 was therefore: 33,00,000 + 6,60,000 = 39,60,000.

As a result, the house cost 39,60,000 at the end of 2008.

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