How would increasing the value of a variable change the value of the expressions when evaluating an algebraic expression?Give two examples in your explanation.

Jim's and Susan's lawn care businesses charge different rates for a 10-hour shift; the difference is $40.

The groupings of numbers include ones, tens, scores, tens, millions, and so forth. Ones, tens, or hundreds are the three subgroups that make up each group. When printing or reading a huge number, start with both the largest group on the left and work your way right.

work done = force × distance. W = F s. When the amount of work (W) is expressed in joules.

It will be Susan's Charge for ten hours.

= 168 + 72 $

= 240 $

while Jim Charges was for 10 hours

= 120 + 80 $

= 200$

The rates Susan and Jim charge during 10 hours of labor in their respective lawn care businesses are as follows:

= 240 - 200 $

= 40$

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Solo acts are 7 minutes long and ensemble acts are 14 minutes long.

Two or more expressions with an Equal sign is called as Equation.

From the given data let us form the system of equations

10x+2y=98

5x+2y=63

To write system of equation you just need to sum all solo and ensemble acts and make it equal to how much they will last for.

Subtract both the equations

10x+2y-5x-2y=98-63

5x=35

Divide both sides by 5

x=7

Now plug in x value in any of the equation

70+2y=98

2y=98-70

2y=28

Divide both sides by 2

y=14

Hence, Solo acts are 7 minutes long and ensemble acts are 14 minutes long.

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m+n = 8. The probability that Kathy will be happy is 3/8. This can be seen by counting the total number of possible arrangements of red and green cards that would make her happy (6). There are a total of 8 arrangements, so the probability is 3/8.

There are 6 possible arrangements of red and green cards that would make Kathy happy:

RRRRR, GGGGG, RRGGG, GGRRR, GRRRG, and RGGGR.

There are a total of 10 cards and 5 of them are laid out in a row, so the total number of arrangements is

10C5 = 10!/5!(10-5)!

= 10*9*8*7*6/5*4*3*2*1

= 10*9*8/5*4*3

= 8*9

= 72.

The probability that Kathy will be happy is the number of arrangements that make her happy (6) divided by the total number of arrangements (72). Therefore, the probability is

6/72

= 3/8.

Therefore, m+n = 8.

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Answer:

y = 2x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{2}[/tex] x - 5 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (2, 7 ) into the partial equation

7 = 4 + c ⇒ c = 7 - 4 = 3

y = 2x + 3 ← equation of perpendicular line

Step-by-step explanation:

p and q are parallel.

let's first only look at a and it's intersections with p and q.

based on the rules of intersecting lines (the angles of intersecting lines are the same in both sides of any of the lines, they are only left-right mirrored) and then parallel lines at that (the intersecting angles of a line with parallel lines are the same with every parallel line, otherwise they are not parallel).

angle 2 = angle 5 = angle 10 = angle 13

therefore,

8x + 14 = 10x - 10

14 = 2x - 10

24 = 2x

x = 24/2 = 12

angle 2 = 8×11 + 14 = 88 + 14 = 102°

because of the same rules of intersecting lines and parallel lines. it is also clear that

angle 4 = angle 7 = angle 12 = angle 15

therefore,

13y + 19 = 15y + 5

19 = 2y + 5

14 = 2y

y = 14/2 = 7

angle 4 = 13y + 19 = 13×7 + 19 = 91 + 19 = 110°

if a and b would be parallel too, then the principle of the same angles would be true not only top-down (as for the pervious 2 problems) but also left-right.

and then angle 2 would be equal to angle 4.

but they are not.

although the difference is small, it means a and b will intersect somewhere.

and they are therefore not parallel.

The pairs of events that are disjoint and cannot occur at the same time are:

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time.

For example, the results of a single coin flip, which can result in either heads or tails but not both is a disjoint event since both head and tail cannot appear.

Considering the events given:

Event A: Spin an odd number

Event B: Spin a number greater than 5

Event C: Spin a 4

Event D: Spin a multiple of 2

Event A and Event C are disjoint because one cannot spin an odd number and a 4 since it is an even number.

Event A and Event D are disjoint because one cannot spin an odd number and a multople of 2 since it will an even number.

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When 60 gallons are used for 500 miles and 13 1/2 gallons are left, 100 miles can be traveled.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

From the question, we know that 60 gallons can be used for 500 miles.

= 500/60

= 8  gallons per mile.

The number of miles that a 13 1/2 gallons will use will be:

= 8 × 13 1/2

= 100 miles

When 60 gallons are used for 500 miles and 13 1/2 gallons are left, 100 miles can be traveled.

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Refer to the image uploaded, all the steps included

Step-by-step explanation:

-13 x 4 = -52

-52 x 0.5 = -25

-2 x 0.5 = -1

-1 + -25 = -26

The values of x and y in polygon D is 95 and 85, and the value of x and y in polygon E is 85 and 95

In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).

Given:

The polygon D having measure of an angle is 70°, 100°, 105°,

The polygon E has angles 100°, 95°, 70°

Calculate the value of x in the polygon D as shown below,

70 + 100 + 105 + y = 360

y = 360 - 275

y = 85

Hence, x = 180 - y (linear pair)

x = 180 - 85

x = 95

Calculate the value of x in the polygon E as shown below,

100 + 95 + 70 + y = 360

y = 360 - 265

y = 95

x = 180 - 95

x = 85

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Using the addition method to solve the given system of equations, It can't be solved because these are the set of parallel lines.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

There are three ways to solve systems of linear equations :

take first equation multiply it by 2 and subtract second equation from it,

We can't solve for any values,

This is because our equations are parallel in nature.

They never intersect each other.

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f-¹(x) is a line with slope -5/2. The correct option is 1.

The inverse of the function is calculated by replacing or interchanging the variables x and y with each other. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Given that the function is f(x) = -2/5x +4. The inverse function of the given function will be calculated as,

y = -2/5x + 4

x = -2/5y  + 4

2/5y = -x + 4

y = -5 /2x + 4

f-¹(x) = -5/2x + 4

Hence, the slope of the inverse function is -5/2.

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The total money remaining to be collected is given by -

R(x) = 8x² - 7x + 12.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given is that the three friends collected some amount of money to buy the earphones. It is asked to find the amount of money still remaining to be collected.

The total cost of earphones are -

T(x) = 9x² - 3x + 4

The total money collected by the friends is -

C(x) = x² + x - 12 + 3x + 4

C(x) = x² + 4x - 8

Money still need to be collected -

R(x) = T(x) - C(x)

R(x) = 9x² - 3x + 4 - (x² + 4x - 8)

R(x) = 9x² - x² - 3x - 4x + 4 + 8

R(x) = 8x² - 7x + 12

Therefore, the total money remaining to be collected is given by -

R(x) = 8x² - 7x + 12.

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Answer:

x = -5

Step-by-step explanation:

6(x+2) = (5x+7)

6x + 12 = 5x + 7

x = -5

The volume of the top section of the figure is 16 cm³.

Given is the solid cuboidal figure as shown in the image.

The volume of the top cuboidal figure will be -

V = L x B x H

V = 2 x 2 x 4

V = 4 x 4

V = 16 cm³

Therefore, the volume of the top section of the figure is 16 cm³.

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The monthly payment for the $300,000 mortgage, of 15 years, with a 4.4% interest rate and 20% down payment is given as follows:

$1,823.79.

The monthly payment formula is given by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are given as follows:

The down payment is of 20%, hence the amount subject to interest is given as follows:

P = 0.8 x 300,000 = 240,000.

The remaining parameters have the values given as follows:

r = 0.044, n = 15 x 12 = 180.

Hence:

r/12 = 0.044/12 = 0.003667.

Then the monthly payment is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 240000\frac{0.003667(1.003667)^{180}}{(1.003667)^{180} - 1}[/tex]

A = $1,823.79.

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The probability to know of it is a fair game depends on how the spinner is designed.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.

It depends on how the spinner is designed and the probability of landing on each number. If the spinner is fair and each number is equally likely to be spun, then the probability of winning is 1/2, or 50%.

This means that over the long run, you would be expected to win half of the games you play. If you and your friend agree that these are the rules of the game and you both understand the probability of winning, then the game could be considered fair.

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Step-by-step explanation:

To model this situation, we can set up two equations: one for the bird and one for the leaf.

For the bird, we can let t be the time in seconds and h be the height of the bird in feet. We know that the bird flies up at a rate of 4 feet per second, so we can write the equation:

h = 4t

This equation represents the height of the bird at any given time t.

For the leaf, we can also let t be the time in seconds and h be the height of the leaf in feet. We know that the leaf drops from a height of 21 feet and floats to the ground at a rate of 3 feet per second, so we can write the equation:

h = 21 - 3t

This equation represents the height of the leaf at any given time t.

Together, these two equations form a system of equations that can be used to model the situation.

A) If the original cost of the car was $90000 and it now costs 34% more, the price has increased by 0.34*90000 = $30600. Therefore, the price today is 90000+30600 = $120600.

B) During the sale, the price of the bicycle dropped from $160 to $125, a difference of 160-125 = $35. This represents a decrease in price of 35/160 = 21.875%. Therefore, the percentage decrease in price is approximately 22%.

Senior Math Online Content Active ical Models with Applications - MA4072 A Click to read the online material. when an element is removed from the RHS or LHS.

Think about a single-variable equation 2 x+5=4 x+3

If a variable is not dropped from either the LHS or the RHS, we obtain a different solution.

Put the variable on one side and the constant on the other.

[tex]$$\begin{aligned}& \rightarrow 4 x-2 x=5-3 \\& 2 x=2\end{aligned}$$[/tex]

on both sides, divide by two.

x=1

We will now only have constants, which may or may not be equal, if we remove the variables from both sides.

Now, suppose LHS if we drop inequality from one side.

4 x+3=5

4 x=5-3

[tex]$$\begin{aligned}& 4 \mathrm{x}=2 \\& x=\frac{2}{4} \\& =\frac{1}{2}\end{aligned}$$[/tex]

We eliminate inequity from the opposite side, or RHS.

[tex]$$\begin{aligned}& 5+2 x=3 \\& 2 x=3-5 \\& 2 x=-2\end{aligned}$$[/tex]

By dividing by 2, x equals -1 on both sides. As a result, we have three different solutions when no variable is dropped from any side; and when a variable is dropped from either the LHS or the RHS.

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Answer: One-third of a gallon divided by 3 gallons equals one-ninth.

Step-by-step explanation:  1/3 / 3/1  = 1/3 x 1/3 = 1/9

The data that is shown in a frequency table can be displayed in:

There are several types of graphs that can be used to display data from frequency tables, including bar graphs, line graphs, and histograms. Bar graphs are a type of graph that use bars to represent different categories or groups of data, with the height of the bars representing the frequency of each category.

Line graphs are a type of graph that use a series of connected points to show trends or changes in data over time, with the height of the points representing the frequency of the data.

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The fee is 50$

Step-by-step explanation: The way I got this is by checking the differences between each month and finding out that each one is 30 and then I subtracted it from 80 and got 50$

The solutions of the linear equation is

x      y

-8    9

-6    8

-4    7

-2    6

0     5

2      4

4      3

6      2

8      1

10     0

the graph is a straight-line graph

The solutions of the linear equation is the found by substituting an x value and solve for y

the given equation 1/2x + y = 5, rearranging the equation gives

y = 5 - 1/2 x

For x = -8,  y = 5 - 1/2 * -8 = 9

For x = -6,  y = 5 - 1/2 * -6 = 8

For x = -4,  y = 5 - 1/2 * -4 = 7

For x = -2,  y = 5 - 1/2 * -2 = 6

For x = 0,  y = 5 - 1/2 * 0 = 5

For x = 2,  y = 5 - 1/2 * 2 = 4

For x = 4,  y = 5 - 1/2 * 4 = 3

For x = 6,  y = 5 - 1/2 * 6 = 2

For x = 8,  y = 5 - 1/2 * 8 = 1

For x = 10,  y = 5 - 1/2 * 10 = 0

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The percentage of the marks scored by Ravi is 72%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Ravi scored 18 marks out of 25 in a maths unit test. The percentage of the marks will be calculated as,

Percentage = ( Marks obtained / total marks ) x 100

Percentage = ( 18 / 25 ) x 100

Percentage = 0.72 x 100

Percentage = 72%

Hence, the percentage will be 72%.

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The cost of the meal if a family has a 25% off coupon for a family of four between $60 and $100 is between $45 and $75.

A 25% off coupon is a discount price.

The cost of the meal if a family has a 25% off coupon for a family of four between $60 and $100 is calculated as follows:

For a $60 meal:

Cost of meal = $60 - 25% * $60

Cost of meal = $60 - $15

Cost of meal = $45

For a $100 meal:

Cost of meal = $100 - 25% * $100

Cost of meal = $100 - $25

Cost of meal = $75

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Complete question:

Predict the cost of a meal for a family of four between $60 and $100. Be sure to include dollars and cents.

Part A: If the family has a 25% off coupon, calculate the new price of the meal. Show all work or explain your steps. (6 points)

We can see that the words that are not defined precisely in geometry are:

Geometry is a branch of mathematics that deals with the properties and relationships of points, lines, angles, surfaces, and solids. It is concerned with the properties of space, shape, size, and position of figures, and can be divided into two main branches: Euclidean geometry and non-Euclidean geometry.

Euclidean geometry is named after the ancient Greek mathematician Euclid, who wrote "Elements", a comprehensive textbook on the subject that was widely used for centuries. Euclidean geometry is based on a set of axioms, or self-evident truths, that describe the properties of points, lines, and angles. It is the type of geometry that is typically taught in school and is used in everyday life to measure and describe the physical world.

Thus, line, point and plane are not precisely defined in geometry.

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The quotient of the two decimal numbers 42.4 and 7.28 as required to be evaluated in the task content is; 5.82.

It follows from the task content that the quotient of the two decimal numbers given; 42.4 and 7.28 is required to be determined.

On this note, since the given division operation is;

42.4 ÷ 7.28

which may alternatively be written as; 42.4 / 7.28

By the use of a calculator; the quotient is therefore equal to;

= 5.824175824

However, when rounded to the nearest hundredth; we have;

= 5.82.

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Answer:

9:37

Step-by-step explanation:

right!

Answer:

8:19

Step-by-step explanation: