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for the following questions, determine what values of x makes the rational expression equal to zero.
1. x+6 / x-4
2. (x+4)(x-2) / (x+6)
3. 2x+10 / 3x-12

thanks.

The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

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The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.

The linear equation

2x - 3y = -15

can be written in the form

y = mx + b,

where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us

y = (2/3)x - 5.

This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us

y = -5.

Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.

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On solving the provided question, we can say that - the linear equation y = 7x - 17 at x= 0; y = -17 and m = -17

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y = 7x - 17

at x= 0

y = -17

and m = -17

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The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.

Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.

Given that:

A = $10,000

r = 4% = 0.04

t = 5 years

n = 12 (since the compounding is monthly)

P = ?

The compound interest is given as follows:

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

Substituting the values in the formula we have:

[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]

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Bar charts display categorical variables, whereas histograms display numerical or quantitative data.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.

Therefore, the correct answer is option C. 6 or fewer.

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The percent of fans that are between 18 and 27 years old is 16.80%.

From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.

It should be noted that this will be Illustrated through the normal curve.

The probability will be:

P(18 ≤ X ≤ 27)

= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8

= P(-2.0 ≤ Z ≤ -0.875)

= 0.1908 - 0.02275 (From the standard normal calculator)

= 16.80%

The percentage is 16.80%.

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Answer:

A - $360

Step-by-step explanation:

Length times width equals area.

12 × 10 = 120

His office has 120 sq ft of space. If each sq ft costs $3

120 × 3 = $360

A

Answer:

A ($360)

Step-by-step explanation:

imagine a rectangle with one side 12ft and one side 10ft

multiply the length and the width to find the square footage:

12*10=120ft^2

each square foot is $3 so multiply 3 by 120

$3*120ft^2= $360

oops didn't realize someone already answered sorry

Answer:

28

Step-by-step explanation:

1 + 2 + 3 + 4 + 5 + 6 + 7

A scatter plot is the best graph for comparing two variables.

A scatter plot is a graph that uses dots to represent individual observations of two variables. It is a powerful tool for comparing two variables because it allows us to see the relationship between the two variables and how they are distributed. It also helps to identify any patterns or trends in the data, such as a positive correlation, a negative correlation, or no correlation at all.

Additionally, scatter plots allow us to see outliers, which are data points that are far away from the majority of the data points. This makes it easy to identify any extreme values that may be skewing the data and affecting the overall pattern of the graph. Overall, scatter plots are useful for identifying patterns, trends, and outliers in data sets, making it the best choice for comparing two variables.

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The perimeter of a square is given as 24x + 20 and can be written as 4 ×(5x+6) and  2 × (10x+12).

The perimeter of a square is the sum of all of the 4 sides of the square. Here, the perimeter of the square is given as the function of x, for finding the length of each side of the square.

Here, in the given problem,  we can factorize the expression 20x+24 as, 4 ×(5x+6) so this is the 1st different way of writing the given expression. For another expression, we can take 2 commons from 20 x+24 that will be 2 × (10x+12).

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The probability of not getting result is found as 24.7%.

The number of times an event happened during the experiment as a percentage of all the times the experiment was run is known as the experimental probability of that event occurring.

So,

P(Result) = 0.753.

P(no result) = 1 - 0.753

P(no result) = 0.247

Thus, the probability of not getting that result is found as 24.7%.

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The correct question is-

If the probability of getting a result in an experiment is 75. 3%, what i the probability of not getting that result?

Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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The positive value of the distance between the two objects

is  [tex]r = + \sqrt\frac{GM_1M_2}{F_g}[/tex]

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Considering the equation for determining the gravitational pull between two items [tex]F_g = \frac{GM_1M_2}{r^2}[/tex], where r is the distance between the objects M is the individual masses and G is the gravitational constant.

The answer to the r in the problem has two values. Since distance cannot be negative, there can only be one positive value, hence we want the positive value.

[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]

[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].

[tex]r = \pm\sqrt\frac{GM_1M_2}{F_g}[/tex]

[tex]r = +\sqrt\frac{GM_1M_2}{F_g}[/tex].

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Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

Answer: y=3/ 4x

Step-by-step explanation: in the linear equations y= Kx shows the proportionality relations . Where k is the proportionality constant which can be any number . x an y are the variables, so according to this answer will be y=3/

Answer:

y=3/4x

Step-by-step explanation:

Let's first define some words;

Proportional: If a line or a ray through the origin it proportional

Non proportional: If a line or ray that does not pass through the origin

Origin: Initial point or the starting point

Now we have define the words now let's graph these points by using Desmos.

Graphs are shown below.    

Base on the graphs below we can see that;

y=3/4x pass through the origin which means the that this linear equation is proportional.

RevyBreeze

The required simplified expression as a monomial is given as -12[z⁶].

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.

here,

Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]

Thus, the required simplified expression as a monomial is given as -12[z⁶].

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The missing code that can replace to assign the total of all values in purchase List to sum, is: REPEAT UNTIL (n > purchaseList.length)

The syntax for a REPEAT UNTIL loop in most programming languages is as follows:

REPEAT {

// code to be executed

} UNTIL (condition)

or

DO {

// code to be executed

} UNTIL (condition)

Looping is a programming construct that allows a certain block of code to be executed repeatedly. The two main types of loops are for loops and while loops.

A for loop is used to execute a block of code a specified number of times. It typically starts with a variable initialization, then a condition is checked, and if the condition is true, the code block inside the loop is executed, and then the variable is updated.

The missing code that can replace the empty parentheses in the REPEAT UNTIL statement to assign the total of all values in purchase List to sum, is:

REPEAT UNTIL (n > purchaseList.length)

This means that the loop will continue to execute until the value of n is greater than the length of the purchaseList. In each iteration, the value of purchaseList[n] is added to the sum, and then n is incremented by 1. So, this loop will iterate through all the elements in the purchaseList, adding each one to the sum, until it reaches the end of the list. This will give the total sum of all purchases made in the last month.

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The degree of polynomial 7x³ + 4x² is 3 as the highest power is 3.

One of the fundamental ideas in mathematics is the degree of polynomials, which determines the maximum number of solutions a function can have and how frequently a function will cross the x-axis on a graph.

Polynomials are also useful in understanding how functions can be represented mathematically. It has the highest exponential power in the polynomial equation.

The greatest power of a variable in a polynomial equation is its degree. When calculating the degree of a polynomial function, only terms with variables are considered. The degree of the polynomial can be determined by looking at the variable term with the highest exponential power.

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The ordered pairs are a linear equation if the graph plotted is the straight line.

A linear equation can be represented by a graph in the Cartesian coordinate system as a straight line. If the equation is in the form of "y = mx + b" where m and b are constants, it is a linear equation. The ordered pairs of a linear equation will always satisfy this equation, and when plotted on a graph, will fall on a straight line. To check if a set of ordered pairs is a linear equation, you can plot them on a graph and see if they form a straight line or can substitute the x- and y-values of the ordered pairs into the equation "y = mx + b" and see if they make the equation true.

So, if the graph plotted is the straight line, then the ordered pairs are of a linear equation.

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Answer:e5

Step-by-step explanation:

Here you go

The expected number of ball pens of a student is 2.4.

What is the expected number?

In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.

The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.

The weight for each group is the percentage of students that are in that group.

So, we can calculate the expected number of ball pens of a student by:

(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)

0.7 + 0.9 + 0.8 + 0.2

The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.

Here, the outcome is the number of ball pens.

Hence, the expected number of ball pens of a student is 2.4.

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Answer:

==================================

a1 = 85 = first term

d = -4 = common difference

an = a1 + d(n-1)

an = 85 - 4(n-1)

an = 85 - 4n + 4

an = -4n+89

a10 = -4*10+89

a10 = 49 is the tenth term

After 0.6412 years the average for mobile device and television usage will coincide.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here the equations as  y=-9.11x+280x and  y=12.34x + 169.9 the period for which the averages are equal will be given by

9.11x+280x=12.34x + 169.9

       x   = 0.6412 years

Again, after 7 years in 2021 the respective averages will be                  9.11 ×7+280×7 = 2023.77 and similarly for mobile device the time spent would be 256.28 minutes

Hence, the answers are After 0.6412 years the average for mobile device and television usage will coincide.

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The product for the given polynomial is [tex]8y^5 + 6y^4 + 20y^3.[/tex]

When multiplying two polynomials, it is important to keep track of the exponents of each term. The exponents will determine the degree of the resulting polynomial. To find the product, you multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.

In this case, the first polynomial is 4y^3 and the second polynomial is 2y^2 3y 5. To find the product, you would multiply 4y^3 by 2y^2, 4y^3 by 3y, and 4y^3 by 5. This would give you 8y^5, 12y^4, and 20y^3. Since these are the only terms in the product, you simply add them together to get the final answer of [tex]8y^5 + 6y^4 + 20y^3.[/tex]

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Answer: The middle number is 15

Step-by-step explanation:

45/3= 15 so the three numbers will be around there.

14+15+16= 45

The equation to find the root of the statement given in the question is , 12x = 2x - 24.

Let the number of tamp which Ritu have be x

Then the number of tamp which Raj have be 2x = 24

Now as Ritu has 6 times more than Raj , 6( 2x) = 24 x 6

Therefore, the required equation becomes,

12x = 2x - 24

=> 10x = 24

=> x = 2.4 answer.

An equation is a mathematical statement which is made up of constants , variables and operators. There are two parts of an equation which are equated using the equal sign . The right hand and the left hand side of the equation.

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The number of installations in September were forty that lead to John and Wesley earning same amount of money.

Let the number of installations be x. The equation of be formed for each paycheck will be -

Total paycheck = base pay + number of installations × comission on each installation

The total paycheck and number of installations is same. So equating the equations by keeping x.

2000 + 65.25x = 380 + 105.75x

Rewriting the equation -

105.75x - 65.25x = 2000 - 380

Performing subtraction on each side of the equation

40.5x = 1620

x = 1620/40.5

Performing division on Right Hand Side of the equation

x = 40

There were 40 installations.

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Answer: its D

Step-by-step explanation: 3 yard is bigger then 6 feet because 3 yards equals 9 feet hope this helps

The x-coordinate of the solution of the system of equations is x = 20/3

Here we have a system of equations below:

3x - y = 6

3x + y = 34

And we want to find the x-cordinate of the solution, so we need to solve this for x.

We can use the elimination method, you can see that if we add both equations we will get:

(3x - y) + (3x + y) = 6 + 34

6x = 40

x = 40/6

We can simplify that fraction to get:

x = 20/3

That is the x-coordinate of the solution.

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