Use the slope formula to find the missing coordinates (-6,0),(1,y);m=8/7

A two-variable equation having a graph in the form of a line is referred to as linear.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A two-variable equation with a line-shaped graph is said to be linear. The set of points in the coordinate plane that make up the graph of the linear equation are all the solutions to the problem.

Given, 2x - 3y = 7

(k + 1)x + (1 - 2k)y = 5k - 4

Here [tex]$a_1=2, b_1=-3, c_1=7$[/tex]

[tex]$$\mathrm{a}_2=\mathrm{k}+1, \mathrm{~b}_2=1-2 \mathrm{k}, \mathrm{c}_3=5 \mathrm{k}-4$$[/tex]

Since equations (1) and (2) have infinite solutions

[tex]$& \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_3} \\[/tex]

substitute the values in the above equation, we get

[tex]$& \Rightarrow \frac{2}{\mathrm{k}+1}=\frac{-3}{1-2 \mathrm{k}}=\frac{7}{5 \mathrm{k}-4} \\[/tex]

simplifying the equation, we get

[tex]$& \therefore \frac{2}{\mathrm{k}+1}=\frac{3}{1-2 \mathrm{k}} \\[/tex]

[tex]& \Rightarrow 2(1-2 \mathrm{k})=-3(\mathrm{k}+1) \\[/tex]

[tex]& \Rightarrow 2-4 \mathrm{k}=-3 \mathrm{k}-3 \\[/tex]

[tex]& \Rightarrow 2+3=-3 \mathrm{k}+4 \mathrm{k} \\[/tex]

Therefore, the value of K = 5.

The complete question is:

What value of K will be following pair of linear equations have infinite solutions

[tex]$$\begin{aligned}& 2 \mathrm{x}-3 \mathrm{y}=7 \\& (\mathrm{~K}+1) \mathrm{x}+(1-2 \mathrm{~K}) \mathrm{y}=(5 \mathrm{~K}-4)\end{aligned}$$[/tex]

To learn more about linear equations refer to:

https://brainly.com/question/2030026

#SPJ4

The expanded form of the expression is  1/2 x - 1/2 y which is determined by the distributive property.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

-1/2 (y - x)

We have to determine the expanded form of the expression.

As per the question, we have

⇒ -1/2 (y - x)

Apply the distributive property of the multiplication,

⇒ -1/2 × y - (-1/2) × x)

⇒ -1/2 y + 1/2 x

⇒ 1/2 x - 1/2 y

Hence, the expanded form of the expression is 1/2 x - 1/2 y.

Learn more about Expressions here :

brainly.com/question/21751419

#SPJ1

In this exponential growth function, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.

What is exponential function?

An exponential function is defined by the formula f(x) = aˣ, where the  x is any real number , acts as an exponent. The exponential curve depends on the exponential function  which  depends on the value of the x.

Where a>0 and a is not equal to 1.

If many functions, “x” is a variable and “a” is a constant, which is the base of the function.

Given that, every hour, the mass of bacteria in a sample multiplies by 3.

Then the exponential function can be taken as f(x)= 3ⁿ x where f(x)= mass of bacteria, n=time(hours), x= original mass.

Here x= 8 mg

a) if n=5 hours then the exponential function will be

f(x)= 3⁵ × x

putting x=8 we get,

f(8)= 3⁵ × 8

 = 1944

b) if n=6 hours then the exponential function will be

f(x)= 3⁶ × x

putting x=8 we get,

f(8)= 3⁶ × 8

 = 5832

Hence, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.

To know more about exponential function

https://brainly.com/question/30241796  from the link.

#SPJ1

An algebraic expression that contains one or more monomials.

A polynomial factor P(x) is any polynomial that divides evenly into P. (x). x + 2 is, for example, a factor of the polynomial x2 – 4. A polynomial’s factorization is its representation as a product of its components. For example, (x – 2)(x + 2) is the factorization of x2 – 4.

Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It is worth noting that if we multiply our answer by itself, we get the original polynomial. Polynomial. An algebraic expression containing one or more monomials. Monomial. A number, a variable, or a number-variable product

To learn more about  polynomial to refer:

https://brainly.com/question/20121808

#SPJ1

The value of x for the similar triangles is equal to 11.

The triangles are similar, this implies that the length 5 cm of the smaller triangle is similar to the length (3x + 7 + 5) cm of the larger triangle

and the length cm of the smaller triangle is similar to the length (48 + 6) cm of the larger triangle

so;

5/(3x + 12) = 6/54

6(3x + 12) = 5(54) {cross multiplication}

18x + 72 = 270

18x = 279 - 72 {subtract 72 from both sides}

18x = 198

x = 198/18 {divide through by 18}

x = 11

Therefore, the value of x is equal to 11 for the similar triangles.

Know more about similar triangles here:https://brainly.com/question/14285697

#SPJ1

The inequality that can be used to find the price that Jerome should charge for each cookie if he wants to have a profit of more than $25 is x > 0.9.

An inequality is a mathematical statement that compares the value of two expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to). Inequalities are used to express relationships between numbers and can be used to describe constraints or limitations in real-world problems.

Let x be the price Jerome charges for each cookie.

We can write the inequality as:

x(50) > 20 + 25

To solve for x, we divide both sides by 50:

x > (20 + 25)/50

x > 0.9

So Jerome should charge more than $0.9 for each cookie if he wants to have a profit of more than $25.

Learn more about inequality here: brainly.com/question/25275758

#SPJ4

Answer:-2, 4

Step-by-step explanation:

The probability that a 68-year-old will live to be 78 years old is approximately 60%. However, this number can vary depending on the individual's health, lifestyle, and family history.

The probability that a 68-year-old will live to be 78 years old is determined by their life expectancy. Life expectancy is the average number of years that a person is expected to live based on their age, gender, and other factors. According to the United States Census Bureau, the average life expectancy for a 68-year-old is 18.6 more years. This means that the probability of a 68-year-old living to be 78 is approximately 60%.

The probability that a 68-year-old will live to be 78 years old is approximately 60%. However, this number can vary depending on the individual's health, lifestyle, and family history.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Karen solved the equation by expanding it to 5x + x - 7 = 36. She then subtracted x from both sides to get 5x - 7 = 36. Next, she added 7 to both sides to get 5x = 43. Finally, she divided both sides by 5 to get x = 6.

Karen solved the equation

x - 7 + 5x = 36

by expanding it to

5x + x - 7 = 36.

This expands the equation to two terms, 5x and -7, which can then be manipulated to solve for the variable x. To do this, she subtracted x from both sides of the equation, leaving

5x - 7 = 36.

She then added 7 to both sides of the equation, leaving

5x = 43.

Finally, she divided both sides of the equation by 5 to get x = 6, which is the solution to the equation. This method works because, by subtracting x from both sides and adding 7 to both sides, she was able to isolate the variable and solve for it.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

To know more about algebra visit:-

brainly.com/question/24875240

#SPJ1

Answer:

definatly fan, i do not know about the water heater if it blows air then i think its true  last 2 i would select

Step-by-step explanation:

Answer:

it's a fan cause a turbine is currently a fan

The graph that matches the inequality equation represented as 3x − 2y ≥  4 is

A. The graph shows a solid line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading above the line.

There are some points that help in interpreting inequality graphs.

The first part is to arrange the equation in the form so that y is the subject of the formula and to the left.

3x − 2y ≥  4

-2y ≥ 4 - 3x

y ≤ 3/2 x - 2

Then watch out for dashed lines or solid lines

dashed lines means there is no equality sign in the inequality > OR <

solid line means there is equality in the inequality  ≤ OR ≥

Another part is the shaded portion

shading above the line defines greater than

shading below the line defines less than

comparing with y = mx + b shows that the intercept which is b is -2

Learn more about linear functions at:

https://brainly.com/question/29721668

#SPJ1

To graph the system of inequalities:

y ≤ −5x + 2

y < 3x − 1.5

We can start by graphing the boundary lines for each inequality:

For y ≤ −5x + 2, the boundary line is y = -5x + 2, which has a slope of -5 and a y-intercept of 2. Since the inequality includes "less than or equal to," we will use a solid line to represent the boundary.

For y < 3x − 1.5, the boundary line is y = 3x - 1.5, which has a slope of 3 and a y-intercept of -1.5. Since the inequality is "less than" and not "less than or equal to," we will use a dashed line to represent the boundary.

Next, we need to determine the shading for each inequality:

For y ≤ −5x + 2, we shade below the solid line because y is less than or equal to the other side of the inequality.

For y < 3x − 1.5, we shade below the dashed line because y is less than the other side of the inequality.

Based on the given options, the correct answer is:

The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

A system of equations that has no solution can be represented by two lines in a coordinate plane that are parallel.

A system of equations is said to have no solution if there is no set of values that can simultaneously satisfy both equations. This can occur when the equations are inconsistent, meaning that they cannot be true at the same time, or when the equations are dependent, meaning that one equation is a multiple of the other.

Parallel lines have the same slope but different y-intercept, this means that there's no point that belongs to both lines, that's why the system has no solution.

Learn more about system of equations here: brainly.com/question/13729904

#SPJ4

For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods. The solution is 1260 (9C3) (6C4)(2C2).

For the three red lights, we have a "9 sockets choose 3" option. In those 9C3 methods.

There are now just 6 open sockets after the 3 red bulbs have been installed.

Put three red bulbs in the first three sockets.

None = 9C3

There are 4 yellow bulbs in 4 sockets.

Way count is 6C4

Two sockets hold two blue bulbs.

Number of ways = 2C2

For the four yellow lights, we have a choice of "6 sockets, choose 4" 6C4 in that manner.

There are just 2 open sockets left once the 4 red lights are screwed in.

The blue lights are available in "2 sockets pick 2." Consequently, (2C2) = 1 way.

Once those two bulbs were screwed in, a bulb was present in each socket.

Total number of methods is 84 * 15 * 1 or 9C3 * 6C4 * 2C2.

1260 different ways in total.

So, there are 1260 total ways.

The solution is 1260 (9C3) (6C4)(2C2).

To Learn more About three red lights refer To:

https://brainly.com/question/28701913

#SPJ1

Step-by-step explanation:

a. The profit function, P(x), can be found by subtracting the cost function from the revenue function.

P(x) = R(x) - C(x)

P(x) = (-0.04x² + 320x) - (85x + 120,000)

P(x) = -0.04x² + 235x - 120,000

b. To find the profit if 1000 bicycles are produced and sold, substitute x=1000 into the profit function:

P(1000) = -0.04(1000)² + 235(1000) - 120,000

P(1000) = -40,000 + 235,000 - 120,000

P(1000) = 75,000

So, the profit would be $75,000 if 1000 bicycles are produced and sold.

c. To find the break-even point, we set the profit function equal to zero and solve for x:

P(x) = 0

-0.04x² + 235x - 120,000 = 0

Using the quadratic formula or factoring, we can find that the break-even point occurs when:

x = (235 +/- sqrt(235^2 - 4(-0.04)(-120,000)))/(2(-0.04))

x = (235 +/- sqrt(55,089,000))/(-0.08)

x = (235 +/- 7,500)/(-0.08)

x = (235 - 7,500)/(-0.08) or (235 + 7,500)/(-0.08)

x = -31,250/ -0.08 or 5,375/-0.08

x = 3906.25 or -64,375

Since negative values of x do not make sense in this context, the break-even point occurs when 3906.25 bicycles are produced and sold.

The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

Learn more about polygon https://brainly.com/question/30465198

#SPJ4

The height of the line in a frequency polygon and the height of the bars in a histogram both represent the frequency or count of the data in a particular category or range of values.

What is Polygon?

In two dimensions, a polygon is a closed object made up of segments of straight lines that join at least three points. A polygon in mathematics can be convex or concave and have any number of sides.

The height of the line in a frequency polygon is proportional to the frequency of the data. The frequency value is marked at the highest point of the line, which is drawn between the midpoints of each category or range of values.

The height of the bar in a histogram, which is proportional to the number of data points in that category or range of values, denotes the frequency of the data. To depict the frequency distribution of the data, bars are drawn next to one another with no space in between.

Learn more about polygon

brainly.com/question/30465198

#SPJ4

Answer:

y = 163°

Step-by-step explanation:

Vertically opposite angles are equal. So, y = 163°

Also, the points u give for the question is halved for the person who writes the answer. So, I will get 10 points, not 20. Anyways, Cheers!

Answer: The linear function is represented by f(x) = (4x/3) + 12

Step-by-step explanation: Taking a linear function's equation pattern to be the graph of y = ax + b, plot the sollutions for such:

(8) = (-3)a + b, and similarly: (-4) = 6a + b, solving for that will lead to a = (4/3) and b = (12), thus: f(x) = (4x/3) + 12.

The cost of each sixty minute tape is $1.083 and the cost of each ninety minute tape is $7.331.

Algebraic equation

This question can be solved using the algebraic equation:

Let x be the cost of each sixty minute tape and y be the cost of each ninety minute tape.

We can set up the following equations:

5x + 9y = 71.40

8x + 7y = 74.65

We can subtract the first equation from the second equation to solve for x:

8x + 7y = 74.65

-5x - 9y = -71.40

3x - 2y = 3.25

Divide both sides by 3 to solve for x:

3x - 2y = 3.25

3 3

x -  2 2

y =  1.083

Now substitute x = 1.083 into the first equation:

5(1.083) + 9y = 71.40

5.415 + 9y = 71.40

Subtract 5.415 from both sides to solve for y:

5.415 + 9y = 71.40

-5.415 -5.415

9y = 65.985

Divide both sides by 9 to solve for y:

9y = 65.985

9 9

y =  7.331

Therefore, the cost of each sixty minute tape is $1.083 and the cost of each ninety minute tape is $7.331.

To learn more about Algebraic equation refer to:

brainly.com/question/30294152

#SPJ1

So, the probability that a customer buys either pet supplies or baby supplies is 0.77.

The probability that a customer buys either pet supplies or baby supplies is represented by P(A U B).

Using the formula for the probability of the union of two events: P(A U B) = P(A) + P(B) - P(A ∩ B),

We can substitute in the given probabilities: P(A U B) = 0.64 + 0.25 - 0.12

Therefore, the equation that represents the probability that a customer buys either pet supplies or baby supplies is:

P(A U B) = 0.64 + 0.25 - 0.12 = 0.77

This means that the probability that a customer buys either pet supplies or baby supplies is 0.77.

To learn more about Probability

visit; brainly.com/question/30034780

#SPJ4

The proof of the area of the circle equation is shown below

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

Area of radius 1 = π

The area of a circle is proportional to the square of its radius.

When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.

So, the area of a circle of radius "r" is given by π * r^2 square units.

Read more about circle at

brainly.com/question/12823137

#SPJ1

There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent.

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:

sin Î= Opposite Side/Hypotenuse

cos Î= Adjacent Side/Hypotenuse

tan Î= Opposite Side/Adjacent Side

sec Î= Hypotenuse/Adjacent Side

cosec Î= Hypotenuse/Opposite Side

cot Î= Adjacent Side/Opposite Side

All these are taken from a right-angled triangle.

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas.

The reciprocal trigonometric identities are also derived by using the trigonometric functions.

To know more about trigonometric functions visit brainly.com/question/6904750

#SPJ4

The function value is 5/2 when x is 0 and value of function is 4 when x =-3.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=|1-x|/2 + 2

We need to find the value of function when x is 0 and when x is -3.

Plug in value x =0

f(0)=|1-0|/2+2

=1/2+2

f(0)=5/2

Now we have to find the function when x is -3

f(-3)=|1+3|/2+2

=4

Hence, the function value is 5/2 when x is 0 and value of function is 4 when x =-3.

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ1

The maturity value after 100 days as calculated from the data given in the question is found to be as $1032.87.

The formula to calculate the interest rate is ,

Interest = ( Principal x  rate x time )/100

Interest = 1000 x 12 x 100/365 x 100

Interest = 12000/365

Interest = 32.87

Therefore, the maturity value will be ,

= Principal + Interest

= 1000 + 32.87

= $1032.87.

Therefore , the maturity value thus becomes  $1032.87.

The rate of interest is referred to as the amount which the borrower will give to the lender once their contract period for a loan is over.

A lot of business is based upon rate of interest only, they lend money and earn their profit by this interest only after the given time period. Principal is the amount primary amount.

To learn more about interest

brainly.com/question/14930452

#SPJ4

All the mathematical expression are,

1) 15 + x = 3

2) 16y = 48

3) 3x - 12 = 33

4) 5 (x - 18) = 50

5) 10 + x/4 = 14

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We can translate the expressions as;

1. The sum of fifteen and a number is three.

Let a number = x

Hence, We get;

⇒ 15 + x = 3

2. The product of sixteen and a certain number is forty-eight.

Let a number = x

So, We get;

⇒ 16y = 48

3. Twelve less than thrice a certain number is thirty-three.

Let a number = x

Hence, We get;

⇒ 3x - 12 = 33

4. Five times the difference between a number and eighteen is fifty.

Let a number = x

Hence, We get;

⇒ 5 (x - 18) = 50

5. Ten more than the quotient of a number and four is fourteen.

Let a number = x

Hence, We get;

⇒ 10 + x/4 = 14

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The required center of the given circle is (-1, -4) and the radius is 1.

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

To put the equation x² + y² + 2x + 8y = 8 into this form, we need to complete the square for both x and y.

First, we'll complete the square for x:

x² + 2x = x² + 2x + 1 - 1

Next, we'll complete the square for y:

y² + 8y = y² + 8y + 16 - 16

Now we can add the two completed squares together and add the constant from the original equation:

(x² + 2x + 1) + (y² + 8y + 16) = 8 + 1 + 16

x² + 2x + 1 + y² + 8y + 16 = 25

Finally, we can divide both sides by 25 to get the equation in the standard form of a circle:

(x² + 2x + 1)/25 + (y² + 8y + 16)/25 = 1

(x + 1)² + (y + 4)² = 1

Thus, the center of the circle is (-1, -4) and the radius is 1.

Learn more about the equation of a circle here:

brainly.com/question/1554214

#SPJ1

The mean absolute deviation of Restaurant B's service ratings is equal to 1.0567111111111.

Mathematically, the mean for this set of service ratings can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of service ratings, we have;

F(x) = 4 + 4 + 2 + 1 + 4 + 4 + 2 + 3 + 5 + 1 + 5 + 3 + 2 + 2 + 2 + 3 + 1 + 2 + 2 + 4 + 2 + 2 + 3 + 2 + 2 + 3 + 2 + 4 + 5 + 3 + 3 + 2 + 5 + 3 + 5 + 1 + 3 + 1 + 3 + 1 + 2 + 4 + 3 + 3 + 2 + 4 + 4 + 1 + 3 + 5 + 1 + 3 + 3 + 4 + 5 + 4 + 2 + 3 + 5 + 2 + 4 + 3 + 2 + 4 + 4 + 4 + 1 + 2 + 5 + 5 + 5 + 3 + 5 + 4 + 1

F(x) = 226.

Note: The total number of data (n) is equal to 75.

Next, we would determine the mean ratings as follows;

Mean = [F(x)]/n

Mean ratings = 226/75

Mean ratings = 3.0133333333333.

In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;

MAD = 1/n ∑|x - μ|

Where:

Substituting the given parameters into the MAD formula, we have the following;

MAD = 1/75 [(4 - 3.0133333333333) + (4 - 3.0133333333333) + (2 - 3.0133333333333) + (1 - 3.0133333333333) + ........ + (1 - 3.0133333333333)]

MAD = 1/75 × 79.25333333325.

MAD = 1.0567111111111.

In conclusion, the mean absolute deviation (MAD) for Restaurant B's service ratings is 1.0567111111111.

Read more on mean absolute deviation here: https://brainly.com/question/17381861

#SPJ1

Answer:

6 1/2

Step-by-step explanation:

1 1/6+ 2 1/6+ 3 1/6=6 3/6

Then you would simplify and get 6 1/2

Answer:

32=3x-7

Step-by-step explanation: