(03.03 MC) The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −6 0 −3 1 0 g(x) g(x) = 4x − 5 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) Part B: Which function has a greater y-intercept? Justify your answer. (4 points) (10 points)

Answer: LCM=672; HCF=12

Step-by-step explanation:

LCM=Least Common Multiple

HCF=Highest Common Factor

Factor of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factor of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

From the list we can see, the highest common factor between 84 and 96 is 12.

The easiest way to find least common multiple is to time the numbers together and then divide it by their highest common factor.

84×96÷12=672

Answer:

scalene

Step-by-step explanation:

none of the angles are the same size.

Answer:

JKL

Step-by-step explanation:

where is the problem

Answer:

Step-by-step explanation:

THE FIRST ONE HAVE TWO FACTORS( 5+2X)AND T-4

The expression |-4| has a value of 4 when evaluated

From the question, we have the following parameters that can be used in our computation:

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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The equations that can be used to determine the length of the room are:

y(y + 5) = 750

y²– 5y = 750

(y - 30) (y + 25) = 0

A rectangle is a two-dimensional object that has four sides and four right angles. The sides of a rectangle are known as the width and the length.  A rectangle has two diagonals of equal length which bisect each other at right angles.

Area of a rectangle = length x width

750 = y x (y - 5)

750 = y² - 5y

y² - 5y - 750 = 0

The factors of -750y² that add up to -5y are 25y and -30

(y² + 25y)(-30y - 750) = 0

y(y + 25) = 0

-30(y + 25) = 0

(y - 30) (y + 25) = 0

Here is the complete question:

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

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Answer:

Step-by-step explanation:

The formula for finding the perimeter is 2w+2L (2*width + 2*length)

So, since we know the width is "w" and the length is "3w-2", we can just substitute those into the equation.

2(w)+2(3w-2)

From there, if needed, you can simplify to:

2w + 6w-4

Add like terms:

8w - 4

Hope that helps.

Answer:

A

Step-by-step explanation:

If digits can be repeated, that means there are 10 options for each place in the pin code. 10*10*10*10 = 10,000

If digits can not be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit. 10*9*8*7 = 5040

Answer:

True

Step-by-step explanation:

Slope:

The slope of an equation represents how the y value changes as the x values changes, defined as: \(\frac{\text{change in y}}{\text{change in x}}\), so the slope of 60 can be represented as: \(\frac{60}{1}\), which tells us the amount of water (y-axis) increases by 60 units each hour (x-axis), or in other words, the rate at which the amount of water changes each hour.

Answer:

it is C.

Step-by-step explanation:

we know,

14+17= 31

so if we subtarct 17 from 31 we get 14

and if we subtract 14 from 31 we get 17

The graph of the arithmetic sequence is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Sequence: 4, 12, 20, 28....

The above sequence is an arithmetic sequence with the following parameters

First term, a = 4

Common difference, d = 8

So, the x-th term is

f(x) = a + (x - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(x) = 4 + (x - 1) * 8

This gives

f(x) = 8x - 4

So, the equation to plot is f(x) = 8x - 4

See attachment for the graph

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The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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Answer: 3x-27

Step-by-step explanation:

Answer:

3x-21

Step-by-step explanation:

3(x-9)+6

3x-27+6

3x-21

Answer:

Monthly payment-$67.78

Step-by-step explanation:

I didn't really know what you wanted so I just put that because that's the only thing to suit it but next time add in more information in your question please.

Answer:

I'm not so sure of 7 and 8. but for number 9 we have to do 10*10= 100 The solution is D

Step-by-step explanation:

First,You should know that a full circle has a 360° turn.

So,that infers that we should add 12 and 25 and 90(from the right angle) degrees together witch gives use 127.Then we subtract 360 by 127 witch gives us the answer 233°.

Thank you.

Texas' location and climate led to the development of the aviation industry.

What is the significance of Texas in the development of the aviation industry?

The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.

Reason what led to the development of the aviation industry :

Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.

Therefore, option (d) is correct.

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The Line chart should be used by the data analyst.

Option (A) is correct.

What is a line chart?

A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

Line chart

This type of chart is called a line chart. A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

It uses a horizontal x-axis and a vertical y-axis, with the data points connected by a line. It is great for visualizing trends and changes in data over a period of time, and it can be used to compare multiple variables at once.

Hence, the Line chart should be used by the data analyst.

Option (A) is correct.

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Answer

coochie man

Step-by-step explanation:

To solve this problem, first we need to define that the number is "x".

Then, we define what twice that number is, which would be

We decrease that 2x by 2:

And this would be equal to 14:

That would be the equation that represents the problem.

To solve that equation...

We add +2 to both sides of the equation:

and we divide both sides by 2:

Answer:

the equation is: 2x - 2 = 14

and the value of x is: x =8

Answer:

C

Step-by-step explanation:

None of the others are vertical angles

a is supplementary angles

b is supplementary angles

d is alternate interior angles

Answer:

(x,y) → (x+ 6,y - 3)

Step-by-step explanation:

I think you posted this question earlier as well? Basically, x moves left and right, while y moves down and up. Therefore, if you wanted to move 3 units down, you would use y-3.

Answer:

\(y=2x-3\)

Step-by-step explanation:

Find the equation of the line that passes through the points A and B.

\(A=(4,5)\\\\B=(2,1)\\\\\\\hrule\)

To find the equation of a line given two points, you can use the point-slope form of a linear equation, which is given by:

\(y-y_1=m(x-x_1)\)

Where...

To find the equation, follow these steps:

(1) - Determine the coordinates of the two points on the line. Let's call them (x₁, y₁) and (x₂, y₂).

(2) - Calculate the slope, "m," using the formula:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

This calculates the change in y divided by the change in x between the two points.

(3) - Substitute the slope, "m," and the coordinates of one of the points (x₁, y₁) into the point-slope form equation.

(4) - Rearrange the equation to get it into slope-intercept form. Which is written as:

\(y=mx+b\)

Where...

\(\hrulefill\)

Step (1) -

\((x_1,y_1) \rightarrow (4,5)\\\\(x_2,y_2) \rightarrow (2,1)\)

Step (2) -

\(m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\\\\Longrightarrow m=\dfrac{1-5}{2-4} \\\\\\\\\Longrightarrow m=\dfrac{-4}{-2} \\\\\\\\\therefore \boxed{m=2}\)

Step (3) -

\(y-y_1=m(x-x_1); \ (x_1,y_1) \rightarrow (4,5) \ and \ m=2\\\\\\\\\Longrightarrow \boxed{y-5=2(x-4)}\)

Step (4) -

\(y-5=2(x-4)\\\\\\\\\Longrightarrow y-5=2x-8 \ \text{(Applied the distributive property)}\\\\\\\\\Longrightarrow y-5+5=2x-8+5\\\\\\\\\therefore \boxed{\boxed{y=2x-3}}\)

Thus, the problem is solved.

Hello !

Answer:

\(\Large\boxed{\sf y=2x-3}\)

Step-by-step explanation:

The slope-intercept form of a line is of the form \(\sf y=mx+b\) where m is the slope and b is the y-intercept.

The line passes through two points :

- A(4,5)

- B(2,1)

Let's replace x and y with their values in the equation :

\(\begin{cases}\sf 5=4m+b \\\sf 1=2m+b\end{cases}\)

We get a system of two linear equations to solve.

Let's subtract the second line from the first one and solve for m :

\(\sf 5-1=4m+b-2m-b\\\iff 4=2m\\\iff m=\frac{4}{2}\\\iff \boxed{\sf m=2}\)

Now let's substitute 2 for m in the second equation :

\(\sf 1=2\times2+b\\b=1-4\\\boxed{\sf b=-3}\)

The slope-intercept form of the line is :

\boxed{\sf y=2x-3}

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Answer:

y=2047.05791602

y≈2047

A system of linear inequalities represented by the graph include the following:

y ≥ -x + 4

\(y\ge \frac{3}{2} x-9\)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the dashed line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(4 - 0)

Slope (m) = -4/4

Slope (m) = -1

At data point (0, 4) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -1(x - 0)  

y = -x + 4

y ≥ -x + 4 (since the dashed line is shaded above).

For the solid line, we have:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3 - 0)/(8 - 6)

Slope (m) = 3/2

At data point (6, 0) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 3/2(x - 6)  

y = 3/2(x) - 9

\(y\ge \frac{3}{2} x-9\) (since the solid line is shaded above).

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Complete Question:

Write a system of linear inequalities represented by the graph.

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

The slope would be -2  1/3 or -2.3 repeating

Step-by-step explanation:

The first point would be (-4, 9). The next point is (2, -5). We can tell that the slope will be negative, because the x values increased by 6, but the y values decreased by 4.

The slope would be -2  1/3 or -2.3 repeating

I Hope That This Helps! :)