The solution process is shown for an equation. Justify each step in the process with the appropriate property. Select the correct answer from each drop-down menu. 2 ⁢ ( 3 ⁢ y + 4 ) − 3 ⁢ ( y − 2 ) = 2 ⁢ y original equation 6 ⁢ y + 8 − 3 ⁢ y + 6 = 2 ⁢ y 3 ⁢ y + 14 = 2 ⁢ y combining like terms 14 = - y - 14 = y y = - 14

Time taken to travel from North Carolina to Florida driving an average speed of 70 mph is 7 hours.

Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.

Given,

Time taken to travel = 9hours

average speed =55 mph

distance between North Carolina to Florida = speed x distance

distance= 55 x 9

distance= 495 miles

if driving at speed of 70 mph

time taken = distance/speed

time taken=495/70

time taken=7 hours

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Answer:

C = $30 + $0.05M

Step-by-step explanation:

We know that renting the car will cost $30, regardless of whether you drive it any where or not

So far

C = $30

On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)

The second value is $0.05 multiplied by how many miles are travelled

Also expressed as $0.05M

Finally, just fix the two parts together

Answer:

Step-by-step explanation:

We know that renting the car will cost $30, regardless of whether you drive it any where or not

So far

C = $30

On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)

The second value is $0.05 multiplied by how many miles are travelled

Also expressed as $0.05M

Finally, just fix the two parts together

C = $30 + $0.05M

Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.

Age of Myrka = 3x + Age of Geoff

3x + 3 = 48

3x = 48 - 3

3x = 45 x = 15

Geoff is therefore 15 years old.

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Answer:

1.   f(x)=1-1/2

4.   y=10x

5.   yes

Step-by-step explanation:

1)
f(x) = 4(2 + 3x) + 3 is a linear function.

2)

The slope of the function is 6.

3)

The linear function is (1/2)x - 4.

4)

y = x² + 2 is not a linear function.

5)

No, it is not a linear function.

6)

Graph D does not represent a linear function.

7)

Graph B does not represent a linear function.

8)

Table D is a linear function.

9)

Table B is not a linear function.

10)

3x + 2y = 6 is a linear function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

1)

f(x) = 4(2 + 3x) + 3

f(x) = (1/2)x² - 5

f(x)= 5 - x²

f(x) = 1 - 1/x

The graph of each function is given below.

The red line in the graph represents f(x) = 4(2 + 3x) + 3.

This is a straight line which means it is a linear function.

2)

f(x) = 2(3x - 7)

f(x) = 6x - 14

It is in the form of y = mx + c where m is the slope.

So,

m = 6

3)

f(x) = (1/2)x - 4

f(x) = x³ - 2

The graph is given below.

The red line represents f(x) = (1/2)x - 4.

This is a linear function.

4)

y = 3x + 12

y = x² + 2

y = 10x

y = 9

The graph is shown below.

The green curve is y = x² + 2.

This is not a linear function.

5)

y = 2x² - 6

This is not a linear function because we have x².

The graph is given below.

6)

Graph D represents a non-linear function.

7)

Graph B represents a non-linear function.

8)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table D has the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

= (4 - 7) / (-1 + 2)

= -3/1

= -3

Table D is a linear function.

9)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table B does not have the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

Table B is not a linear function.

10)

The green line on the graph represents a straight line.

The green line is a linear function.

The green line is 3x + 2y = 6.

Thus,

The answers are given above.

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The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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The given sequence is arithmetic because the difference between consecutive terms is constant. The common difference is 1, since the difference between each pair of consecutive terms is 1 (e.g., 5 - 4 = 6 - 5 = 1). The common difference can be expressed in simplest form as 1/1 = 1.

Answer:

it is arithmetic, 6-5=1, 5-4=1

Answer:

1004 is the smallest four-digit palindrome that is divisible by 4.

The output of function g(r) = -5x + 13 when r is 3 is -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

g(r) = -5r + 13

Input r = 3

g(3)

= -5 x 3 + 13

= -15 + 13

= - 2

Thus,

The output is -2.

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Linear equations are mathematical equations that involve one or more variables. These equations can be solved by following a few simple steps:

Linear equations can be used to solve a wide range of mathematical problems and are an essential part of any mathematics curriculum.

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A. Commutative property of addition

B. Distributive property

C. Commutative property of addition

D. Associative property of multiplication

Answer:

12%

Step-by-step explanation:

A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal line.

Now, According to the question:

What is a Horizontal Line?

Horizontal lines are also known as sleeping lines. In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on the railway tracks, etc.

The x-axis is an example of a horizontal line.

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Answer: To determine the games in which a person who buys a ticket for each game every day for the next 400 days could expect to lose less than a total of $200, we need to find the games in which the probability of winning is greater than the probability of losing.

Since the tickets for all of the games cost $2 per ticket, the probability of winning any given game is equal to the prize money divided by the ticket cost. For example, if the prize money for a game is $10, the probability of winning is $10/$2 = 1/2.

If the probability of winning a game is greater than the probability of losing, the expected value of the game is positive, which means that the person can expect to win more than they lose over time. On the other hand, if the probability of winning is less than the probability of losing, the expected value of the game is negative, which means that the person can expect to lose more than they win over time.

Therefore, to determine which games the person could expect to lose less than $200 in total, we need to find the games in which the prize money is greater than $2 per ticket.

Step-by-step explanation:

By fraction , 3  3/7   will it take 7 men to do the job if they work at the same rate.

What is fraction in maths?

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the proportionate pieces of the whole.

                The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

per person per hour

           1/4*6  = 1/24

7 men per hour

       1/24 * 7 =   7/24

  total times

          1 ÷ 7/24  =  1   *  24/7  

                   =  3  3/7

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The room that would stop Barry from hosting the event is the semicircular room.

Would the first rectangular room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a rectangle = length x width

25 x 30 = 750 feet²

Number of people per square foot - 750 / 150 = 1 person for every 5 feet

Would the trapezoidal room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a trapezoid = 1/2 x (sum of parallel sides) x height

1/2 x (24 + 36) x 28 = 840 feet²

Number of people per square foot = 840 / 150 = 1 person for every 5.6 feet

Would the square room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a square = length x width

28 x 28 = 784 feet²

Number of people per square foot - 784 / 150 = 1 person for every 5.2 feet

Would the semi circular room allow Barry have the meeting?

The first step is to determine the area of the room

Area of a semicircle = 1/2πr²

Where:

r = 3.14

r = radius = diameter / 2 = 28 / 2 = 14 feet

1/2 x 3.14 x 14² = 307.72 feet²

Number of people per square foot - 307.72/ 150 = 1 person for every 2.05 feet

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Answer:

The semicircle

Step-by-step explanation:

ewomazinoade's answer is correct, not sure why at time of writing the rating is so low for their answer (3.7).

See pic!

The formula yields the radius $r$ of a circle that is inscribed within three circles with radii $a$, $b$, and $c$ that are mutually external tangents.

[tex][\frac{1}{r} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}][/tex]

The radius of the inscribed circle is related to the radii of the three mutually externally tangent circles using a method known as the radical centre formula. According to this equation, the reciprocals of the radii of the three externally tangent circles add up to the radius of the circle that is inscribed.

The power of point theorem states that the product of the distance between the point and the three points of tangency is equal to the product of the distance between the point and the centres of the circles. This formula is based on the fact that the circles are mutually externally tangent and their centres are collinear. It is crucial to note that the formula can only be used if the circles are mutually externally tangent; otherwise, it is invalid.

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62.5 of the yellow balloons lack strings. The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the probability.

The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood. The formula is: Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).

The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood.

A sample is created in this way, and using the data collected, the calculation can be done. The formula for calculating probabilities is probability = Favorable instances / Possible cases x 100, given as a percent.

25/40 * 100 = 0.625*100 = 62.5.

62.5 of the yellow balloons lack strings.

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Answer:

5 hours

Step-by-step explanation:

Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.

So she needs to work for 685 / 137 = <<685/137=5>>5 hours

The probability that at least one 6 will occur on two dice is 30.5%.

To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur. There are differences between probability and odds. Odds are calculated by dividing a situation's likelihood of occurring by its likelihood of not occurring.

1, 2, and 3 are the six factors. Four of the results of a single die's six possible outcomes are multiples of 6. It follows that 4/6 is the probability.

11.5%, or slightly less than 33.3% (2/6), out of 36 occasions. The probability that at least one 6 will occur on two dice is 30.5%. Without using the picture, one can also calculate this number mathematically.

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Using the concept of likelihood and probability ,The probability that at least one 6 will occur on two dice is 30.5%.

Probability is a measure of the likelihood that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event will not occur and 1 indicating that an event will certainly occur. For example, the probability of flipping a fair coin and it landing on heads is 0.5, or 50%. Probability is used in many fields, including mathematics, statistics, finance, and science. In statistics, probability is used to make inferences about a population based on a sample, while in finance, probability is used to evaluate the potential outcomes of investments.

Conditional probability is the probability of an event occurring given that another event has already occurred. It is written as P(A|B), which is read as "the probability of A given B." For example, the probability of rolling a 6 on a fair die given that the roll is an even number would be P(6|even) = 1/3, because there is only one way to roll a 6 out of the 3 possible even numbers (2, 4, 6).

1, 2, and 3 are the six factors. Four of the results of a single die's six possible outcomes are multiples of 6. It follows that 4/6 is the probability.

11.5%, or slightly less than 33.3% (2/6), out of 36 occasions. The probability that at least one 6 will occur on two dice is 30.5%. Without using the picture, one can also calculate this number mathematically.

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Answer:

7:50 am in the morning

Step-by-step explanation:

17:50pm = 5:50pm

first simply this by only adding 12 hours

12 hours later- 5:50 am

Then add 2 hours to get the answer

14 hours- 7:50 am in the morning.

( I think)

...

Answer: C

Step-by-step explanation:

Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.

A: incorrect

Looking at choice A, it says the interval is from -3<x<-2. This means we have to find x=-3 and x=-2. On the graph, that interval is above the x-axis, so it is positive, not negative.

B: incorrect

Looking at choice B, it says the interval is from 2<x<3. This means we have to find x=2 and x=3. On the graph, that interval is above the x-axis, so it is positive, not negative.

C: correct

Looking at choice C, it says the interval is from 4<x<5. This means we have to find x=4 and x=5. On the graph, that interval is under the x-axis, so it is negative.

Therefore, C is the correct answer.

Answer:

2.7n + 6.6 or 6.6 + 2.7n

Step-by-step explanation:

Algebraic Expressions are just like Numerical Expressions but instead of numbers, alphabets are used, these alphabets can also be used as variables. (BODMAS rule applies to Algebraic Expressions as well.)

Eg. 45x + 31x(2) = 45x + 62x = 107x

Given from the question:

[tex]0.3(9n + 22) \\ = 2.7n + 6.6 \: or \: 6.6 + 2.7n[/tex]

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

Explanation:

L = 6 inches = length

W = 3 inches = width

H = 5 inches = height

----------------------

V = volume

V = L*W*H

V = 6*3*5

V = 90 cubic inches is the volume

----------------------

SA = Surface Area

SA = 2*(LW + LH + WH)

SA = 2*(6*3 + 6*5 + 3*5)

SA = 126 square inches is the surface area

-----------------------

Unfortunately there isn't enough information to know the material cost. Please post the full problem, and any other relevant information connected to this question.

After combine they hold 115.84 ounces.

A process of combining or adding two or more numbers is called addition.

We have to given that;

One bottle holds 67.34 ounces and another bottle holds 48.5 ounces.

So, After combine, we get;

Both bottle hold = 67.34 ounces + 48.5 ounces

                         = 115.84 ounces

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Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.

sin is a trigonometric ratio.

If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.

sin Q = perpendicular / hypotenuse.

sin Q is the base of the trigonometry ratios and it is one of the ratio.

sine is an acute angle.

some formula of sine angle are ,

1- sine Q = 1/ cosec Q .

2- sin ^2 Q = 1- cos^2 Q .

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The class has a 45-minute, or 0.75-hour, climb to the summit planned to observe a nearby monument. The bus driver intended to travel at a steady 40 mph. Accordingly, the average speed is 0.888.

The time required to travel 20 miles at 40 mph is 30 minutes, and the time required to go 40 miles is 60 minutes. The journey of 60 miles will therefore take 90 minutes. In most cases, an hour's worth of time, this will tell you the average speed.

As a result, Ben's average speed was 50 miles per hour when he covered 150 miles in 3 hours. 40m in an hour. 12 hour to cover 20 miles. In fifteen minutes, ten miles. It is determined by dividing something's total travel distance by its total journey time. Take the earlier automobile, for instance. The average speed of the vehicle would be 70 / 2 = 35 miles per hour if it covered 70 miles in two hours.

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Complete question is: Hassan's history class is taking a field trip to the state capitol building. The capitol building is 50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to view a local monument. The bus driver plans to drive at an average speed of 40 miles per hour. Which equation can you use to find how many hours, x, the second part of the trip will take?

The three variable system is written as (x, y, z).

Here we have to find the definition of three variable system.

basically a solution of a system in three variables is an ordered triple (x, y, z) that makes all three equations true.

On the other hand it is what they all three have in common.

Where as the solution to a system of three equations in three variables (x, y, z) is called an ordered triple.

In order to solve these one we have to do the following:

First we have to pick any two pairs of equations from the system.

And then we have to eliminate the same variable from each pair using the Addition/Subtraction method.

Final step is to solve the system of the two new equations using the Addition/Subtraction method.

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The first figure is dilated to form the second figure, the statement according to will be the scale factor is 0.25.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is.

A ratio divides two quantities in order to compare them.

As per the given information in the question,

We have two side lengths,

First figure: This represents the object length, which is a diamond with a length equal to 5.8.

Second figure:The picture length is then represented by a small diamond with sides that measure 1.45.

So, the scale factor is,

k = Image length/Object length

k = 1.45/5.8

k = 0.25.

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