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A student divided the rational expressions as follows:

Describe the errors made
I need help

Answer:25.5

Step-by-step explanation:

64.5+90=154

180-154=25.5

The range, given the stem and leaf plot above, can be found to be 33

The range of a data set refers to the difference that is seen between the highest number in that data set and the lowest number in that same set.

The highest number as given in the stem and leaf plot above is 50 and the lowest number is 17.

This means that the range is:

= 50 - 17

= 33

We can therefore conclude that the range for the data set is 33.

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The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The initial height of the rocket is given by the value of h when t = 0:

h(t)=-4t² + 16t + 24

h(0)=-4(0)² + 16(0) + 24

h(0)=24

So the initial height of the rocket is 24 metres.

The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:

0 = -4t²+ 16t + 24

-4t² + 16t + 24 = 0

t=-0.88 seconds

So the rocket will hit the ground after approximately 0.88 seconds.

The height of the rocket after 4 seconds is given by:

h(4)== -4(4)²+ 16(4) + 24

=-64+64+24

=24

So the height of the rocket after 4 seconds is 24 metres.

Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.

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The amount of the down payment, considering the median house price, is given as follows:

$41,980.

The down payment is obtained applying the proportions in the context of this problem.

A proportion is applied because the down payment is obtained with the multiplication of the median house price by the fraction.

The parameters are given as follows:

Hence the down payment is obtained as follows:

1/5 x 209900 = $41,980.

The problem asks for the amount of the down payment, considering the median house price.

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The time it will take Juan and Laura to meet each other is 25.88seconds

Velocity is the rate of change of velocity with time. It is a vector quantity and it is measured in meter per second. It can also be measured in Mikes per hour and so on.

Velocity = displacement /time

displacement = velocity × time

The total distance traveled = 220feet

220 = v1t + v2t

220 = (v1+v2) t

220 = ( 3.5 + 5) t

220 = 8.5 t

divide both sides by 8.5

220/8.5 = t

t = 25.88 seconds

therefore it will take Juan and Laura 25.88 seconds to meet each other

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Inequality shown is -3 ≤ x < 2.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

Graph of inequality

Line drawn on the number line between circle on -3 and circle on 2.

Here, -3 < 2

If x is the variable, it is between -3 and 2

then, -3 < x < 2

The circle on -3 is filled which means value of x can be equal to -3

then inequality becomes,

-3 ≤ x < 2

Hence, -3 ≤ x < 2 is the inequality shown on the number line.

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Nikhil has been with the company for 24 years, while Mae has been there for 4 years.

Option C is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 2 = 8 is an equation.

We have,

Number of years Nikhil worked =  x

Number of years Mae worked =  y

x = 6y ______(1)

x = 8 + 4y ______(2)

Substituting (1) in (2)

6y = 8 + 4y

Subtract 4y on both sides.

6y - 4y = 8

2y = 8

Divide 2 into both sides.

y = 4

Now,

x = 6y

x = 6 x 4

x = 24

Thus,

The number of years Nikhil worked is 24 years.

The number of years Mae worked 4 years.

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The volume is found using cylindrical shells and rotating the region bounded by xy = 3, x = 0, y = 3, and y = 5 about the x-axis.

To find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis, we will use the method of cylindrical shells. First, we need to draw the graphs of the functions given. The graph of xy = 3 is a parabola, x = 0 is a vertical line, y = 3 is a horizontal line, and y = 5 is also a horizontal line. The region bounded by these curves is the area between x = 0, y = 3, and y = 5 and xy = 3. Next, we need to find the area of the cylindrical shell. The area of the shell is given by 2πrh, where r is the radius of the circle and h is the height of the shell. The radius of the circle is the distance from the x-axis to the curve, which in this case is x. The height of the shell is the difference between the upper and lower limits of the integral, which in this case is y2 - y1. We can then integrate the area of the shell over the range of x and y values to get the volume. The integral is ∫[0, 3]∫[3, 5]2π(x)(y2 - y1)dxdy. Finally, we can evaluate the integral to get the volume of the solid.

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Answer: 92.0

Step-by-step explanation:

Calculating the perimeter of the rectangle. Perimeter of this rectangle = 2 * (length + width ) = 2 * (30.0 + 16.0) = 92.0 units

Answer: 92

Step-by-step explanation: To find the perimeter you add all four sides of the rectangle your equation should look like 30+30+16+16. Add 30+30 which is 60. Then 16+16 which is 32. Then add 60 plus 32 which equals 92.

The length of the other two sides are 4m and 5m

Using the Pythagorean theorem, we have that the square of the hypotenuse sides is equal to the sum of the squares of the other two sides of the triangle

This is represented as;

x² = y² + z²

From the information given, we have that;

z = 3m

x = x + 1

y = x

Substitute the values, we get

(x + 1)² = x² + 3²

Find the squares

(x + 1) ² = 9 + x²

expand the bracket

(x + 1) ( x + 1) - x² = 9

x² + x + x + 1 - x² = 9

collect like terms

2x = 8

x = 4

Then,

x + 1 = 5

x = 4

Hence, the values are 4m and 5m

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Therefore , the solution of the given problem of graph comes out to be x value is  √2.

Scholars use graphs to visually represent or chart facts or values in a logical way. Usually, a graph point will show the relationship of two or more objects. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts.

Here,

Given :

=> y =x² -2

To find the value of x :

at y = 0

So,

=> 0 = x² -2

=>x² =2

=>x = √2

Thus, x value is  √2.

Therefore , the solution of the given problem of graph comes out to be x value is  √2.

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The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

The x-intercept is at (-5, 0). Then the value of the abscissa is given as,

x = -5

The graph begins in the third quadrant near the line x = - 6. Then the equation x = - 6 represents the asymptote.

The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.

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To determine the magnitude and direction of the resultant force applied at b, we can use vector addition of the tensions in cables AB and BC. Let's assume that the positive x-direction is to the right, and the positive y-direction is upwards.

We can represent the tension in cable AB as a vector T1 = 4500 lb in the direction of AB, and the tension in cable BC as a vector T2 = 2000 lb in the direction of BC.

The magnitude of the resultant force applied at b is given by:

R = √(T1^2 + T2^2) = √(4500^2 + 2000^2) = 5000 lb

The direction of the resultant force can be found using the arctangent function:

θ = tan^-1 (T2/T1) = tan^-1 (2000/4500) = approximately 39.2 degrees

Therefore, the magnitude and direction of the resultant force applied at b are 5000 lb and 39.2 degrees, respectively.

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The slope of QR is 1/8.

The length of QR is 8.06 unit.

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

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The points Q (7, 6), R(-1,5), S(-5, -2), and T(3, -1) form a quadrilateral.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

The slope of QR,

= (5 - 6)/(-1-7)

= 1/8.

The length of QR = √{(5 - 6)² + (-1-7)²} = 8.06 unit.

Therefore, 1/8 is the slope and 8.06 unit is the length.

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The cost at Pickwick Books is $5.75 and the cost at Dickens Books is $5.50, so the books are cheapre in Dickens Books.

We know that the equation:

C = 5.75*b

Repersents the cost for b books at Pickwick Books.

Then the cost of each book there is $5.75

We also know that at Dickens Books, a customer can buy 3 used books for $16.50, then the cost of each book there is given by:

C = $16.50/3 = $5.50

So the books are cheaper, by $0.25, in Dickens Books.

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Using the greatest common factor (GCF), to simplify the expression we have: 5(-4a + 2b - 3)

A common factor is either a number or term that is a common denominator to two or more given expressions. Thus can be used to simplify a given expression by factorization.

To factor the simplified expression, we have:

10a + 5b + 3 - 25a + 2b - 18 + 3b - 5a

collect like terms

10a - 25a - 5a + 2b  + 5b + 3b + 3  - 18 = -20a + 10b - 15

So that the positive greatest common factor (GCF) of the simplified expression is 5.

-20a + 10b - 15 = 5(-4a + 2b - 3)

The required answer is 5(-4a + 2b - 3).

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Neither the addition property of equality nor the subtraction property of equality can be demonstrated by themselves. They are properties that must be satisfied by the operations of addition and subtraction respectively, in order for equality to hold.

The addition property of equality states that if two quantities are equal.

(a = b), then their sum with any other quantity (c) will also be equal (a + c = b + c). The subtraction property of equality states that if two quantities are equal (a = b), then their difference with any other quantity (c) will also be equal (a - c = b).

In other words, both properties say that when two quantities are equal, then the result of adding or subtracting the same quantity from both will also result in equal quantities.

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The time that it will take until Noah and Andre meet is; 2.5 hours

Let t represent the time it would take for Noah and Andre to meet.

Formula to find distance is;

Distance = speed × time

Noah rides at a constant speed of 4 miles per hour. This tells us that the distance that Noah would cover in t hours is expressed as 4t.

Andre rides at a constant speed of 2 miles per hour. This tells us that the distance that Andre would cover in t hours is 2t

Since the total distance is 15 miles, then we can form the equation as;

4t + 2t = 15

6t = 15

t = 15/6

t = 2.5 hours

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The required set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

Here,
Integers are whole numbers, both positive and negative, including zero. For example -4, -3, -2, -1, 0, 1, 2, 3, 4, etc. They are used to represent whole quantities and are a basic type of number in mathematics.

Thus, from the options set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.

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The standard deviation of the given variable is 0.95.

The standard deviation is a measure of the amount of variation or dispersion of a set of values. It is calculated as the square root of the variance. The variance is calculated by subtracting the mean from each data point and squaring the result. The variance is then divided by the number of data points. The standard deviation for the given table can be calculated as follows:

Mean = [tex](0 * 0.21) + (1 * 0.28) + (2 * 0.3) + (3 * 0.09) + (4 * 0.08) + (5 * 0.04) = 1.92[/tex]

Variance = [tex](0 - 1.92)2 * 0.21 + (1 - 1.92)2 * 0.28 + (2 - 1.92)2 * 0.3 + (3 - 1.92)2 * 0.09 + (4 - 1.92)2 * 0.08 + (5 - 1.92)2 * 0.04 = 0.907[/tex]

Standard Deviation = √0.907 = 0.95

Therefore, the standard deviation of the given variable is 0.95.

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The correct answer is option C. The system has a nontrivial solution.

One way to determine if a system has a nontrivial solution is to use Gaussian elimination to reduce the augmented matrix to row echelon form. If the row echelon form has a row of zeros except for the last entry in the augmented part, then the system has only a trivial solution.

If there is a row of zeros in the row echelon form that corresponds to a free variable, then the system has a nontrivial solution. In this case, it is possible to use Gaussian elimination to see that the row echelon form of the augmented matrix has a row of zeros except for the last entry in the augmented part, which is not zero, indicating that the system has a nontrivial solution.

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Let $abcd$ and $bedf$ be two $2 \times 3$ rectangles that overlap, the area of the overlap is 6 square unit.

The quantity of space occupied by a flat surface with a specific form is referred to as the area. It is calculated as a "number of" square units.

Given that we have to assume to rectangles

ABCD and BEDF

both have dimensions 2×3.

So the area of rectangles-

A=2(3)=6 square unit

Also given that both the rectangles overlap each other.

Since both the rectangle are of the same dimension so the overlapping area will be equal to their original area.

So the area of overlap- A=6 square unit.

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The solution is,  J. The mean and the median both decreased.

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table.

here, we have,

The amount of money Cole earned for each of six weeks is shown.

$45, $85, $43, $45, $37, $70

i.e. mean = 54.16

now,

Cole then earned $30 for working a seventh week.

so, now, mean = 50.71

i.e. The mean decreased.

Hence, The solution is,  J. The mean and the median both decreased.

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A an acute triangle

because all angles are less than 90

Answer: Acute Triangle

Step-by-step explanation:

By solving a system of equations we will see that:

x = 39

y = 123

First, we know that the sum of the 3 angles on the bottom part should be equal to 180°, then we can write:

(x - 10) + y + (x - 11) = 180

And the angle on the top is a vertical angle to the one that measures y degrees, then:

3x + 6 = y

So we have a little system of equations:

(x - 10) + y + (x - 11) = 180

3x + 6 = y

Replacing the second equation into the first one, we get:

(x - 10) + (3x + 6) + (x - 11) = 180

5x - 15 = 180

5x = 180 + 15

x = 195/5

x = 39

And the value of y is:

3*39 + 6 = y

123 = y

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Make that the target variable is in the numerator, not the denominator, of the rearrangement.

Variable

A variable is a placeholder sign for a varying quantity or other mathematical entity.

Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.

Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.

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The Correct answers are:

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

We have to find 70% of 42.

So, first Determine 1% of 42, and multiply the result by 70.

= 42 x 0.01 x 70

= 29.4

second, Determine 10% of 42, and multiply the result by 7.

= 42 x 0.1 x 7

= 29.4

Third, Determine 1% of 42, and multiply the result by 7.

= 42 x 0.01 x 7

= 2.94

Fourth, Determine 10% of 42, and multiply the result by 70.

= 42 x 0.10 x 70

= 294

and, the 70% of 42 = 0.7 x 42 = 29.4

Thus, the correct statement are:

Determine 1% of 42, and multiply the result by 70.

Determine 10% of 42, and multiply the result by 7.

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The value of distance cover is, 1/4 miles.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Driving speed = (s - 4) / (s²-9s+20)

And, Time = (s - 5) / 4

Now, We know that;

⇒ Speed = Distance / Time

⇒ Distance = Speed × Time

Substitute the given values, we get;

⇒ Distance = (s - 4) / (s² - 9s + 20) × (s - 5) / 4

⇒ Distance = (s - 4) / (s² - 5s - 4s + 20) × (s - 5) / 4

⇒ Distance = (s - 4) / (s (s - 5) - 4 (s - 5)) × (s - 5) / 4

⇒ Distance = (s - 4) / (s - 4) (s - 5) × (s - 5) / 4

⇒ Distance = 1/4 miles

Thus, The value of distance cover is, 1/4 miles.

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The points are evenly distributed above and below the line, which provides the best explanation for why the graph displays a line of best fit.

A statistical tool that shows the relationship between two variables is a regression line. It is employed specifically when a change in one (the dependent variable) is dependent on a change in the value of the other (the independent variable).

Given the graph,

for the line of best fit, A graph's nodes are connected by a mathematical concept known as the line of greatest fit. It is a kind of linear regression that uses scatter data to determine how to best define the relationship between the dots.

A change in the value of X causes a change in the value of the equation, which is written as Y on X.

X on Y is the equation, and the deviation of the Y variable determines how the X variable changes.

The graph shows a line of greatest fit because the spots are equally spaced above and below the line.

Hence the points are drawn uniformly above and below the line, thus the best explanation is that the graph displays a line of best fit.

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