Graph the line with slope 2/3
passing through the point (3,-1).

Step-by-step explanation:

this is very much doing the exact same things as the previous question, just with a little bit different numbers.

remember, gradient = slope.

the slope is always the factor of x in the slope-intercept form

y = ax + b

our in the point-slope form

y - y1 = a(x - x1)

"a" is the slope, b is the y-intercept (the y- value when x = 0).

(x1, y1) is a point on the line.

the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

a)

y = 2x + 7

b)

y - 4 = -2(x - 2) = -2x + 4

y = -2x + 8

c)

going from (2, 3) to (-1, 2)

x changes by -3 (from 2 to -1)

y charges by -1 (from 3 to 2)

the slope is -1/-3 = 1/3

we use one of the points, e.g. (2, 3)

y - 3 = (1/3)×(x - 2) = x/3 - 2/3

y = x/3 - 2/3 + 3 = x/3 - 2/3 + 9/3 = x/3 + 7/3

d)

y = 5

this is a horizontal line (parallel to the x-axis) and represents every point on the grid, for which y = 5.

the slope is 0/x = 0, as y never changes at all.

the y- intercept is 5, of course.

Answer:

[tex]\textsf{a) \quad $y=2x+7$}[/tex]

[tex]\textsf{b) \quad $y=-2x+8$}[/tex]

[tex]\textsf{c) \quad $y=\dfrac{1}{3}x+\dfrac{7}{3}$}[/tex]

[tex]\textsf{d) \quad $y=5$}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

Given values:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y=2x+7[/tex]

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

Point-slope form of a linear equation:  

[tex]y-y_1=m(x-x_1)[/tex]

where:

Given:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y-4=-2(x-2)[/tex]

[tex]\implies y-4=-2x+4[/tex]

[tex]\implies y=-2x+8[/tex]

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

Slope formula:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

where (x₁, y₁) and (x₂, y₂) are points on the line.

Given points:

Substitute the points into the slope formula to calculate the slope of the line:

[tex]\implies m=\dfrac{2-3}{-1-2}=\dfrac{-1}{-3}=\dfrac{1}{3}[/tex]

Substitute the found slope and one of the points into the point-slope formula to create the equation of the line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=\dfrac{1}{3}(x-2)[/tex]

[tex]\implies y-3=\dfrac{1}{3}x-\dfrac{2}{3}[/tex]

[tex]\implies y=\dfrac{1}{3}x+\dfrac{7}{3}[/tex]

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

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

If the line is parallel to the x-axis, its slope is zero.

If the line intersects the y-axis at y = 5, then its y-intercept is 5.

Therefore:

Substitute the given values into the formula to create the equation of the line:

[tex]\implies y=0x + 5[/tex]

[tex]\implies y=5[/tex]

Mark's height last year was 46 inches.

Mark definitely grows over the past year. Let the height he grew be x.

Then, Mark's new height will be

Let us represent Mark's height with M and Peter's height with P.

This means that

and, from the question, Peter's height is

The question says that Mark's height is 3 inches less than Peter's height. This we can write as

Therefore, if we put Mark's and Peter's ages into equation c, we can find a value for x as follows:

Since 46 + x = M, then Mark's height is 48 inches

Okay, here we have this:

Considering the provided expression, we are going to identify to which is equivalent, so we obtain the following:

We obtain that the correct answer is the option C, because:

Answer:

D

Step-by-step explanation:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since line has slope of 2, equation is y = 2x + c.

Substitute (-8, 1) into the equation to find c

1 = 2(-8) + c

c = 17

Hence, equation of line is y = 2x + 17.

The correct answer is [D]

Hence, the equation of line is y = 2x + 17.

Finding the ratio of "vertical change" to "horizontal change" between any two unique locations on a line yields the slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. Negative "rise" refers to a diminishing line. The line could be functional, established by a road surveyor, or depicted in a graphic that represents a road or a roof as a description or a design.

The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope. A line's direction might be either horizontal, ascending, decreasing, or vertical.

Y = mx + c, where m is the slope and c is the y-intercept, is the equation for a line.

Since the line has slope of 2, equation is y = 2x + c.

Substitute (-8, 1) into equation to find c

1 = 2(-8) + c

c = 17

Hence, the equation of line is y = 2x + 17.

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$12180 the insurance company must set aside now at 6% interest compounded semiannually to pay this obligation to Apollo.

This is a problem from the compound interest system. We can solve this problem by following a few steps.

Apollo Enterprises has been awarded an insurance settlement of $6,000 at the end of each 6-month period for the next 12 years with a 6% interest rate. We have to calculate the total amount after 12 years.

To solve this problem we should know the formula for the compound interest method.

Formula:-

A = P {(1 + r/n)^(n.t)}

Here,

Now, we can calculate the value of A.

A = 6000 {( 1 + 6/200 )^2.12} = 6000 ( 1 + 6/200 )^24 = 6000 × 2.03 = 12180

Therefore, the total amount after 12 years is $12180

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The number of weeks that she orders them both in the same week again is 24 weeks.

From the information, the office manager orders computer paper every 6 weeks and printer ink cartridges every 8 weeks.

The weeks when they will order same will be the least common multiple for 6 and 8. This will be:

6 = 6, 12, 18, 24

8 = 8, 16, 24

The multiple is 24 weeks. This illustrates the information.

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The graph's range is 0 to M plus or minus 5.5.

The set of graph output values that make up a function's range.

This means that the set of y values in the graph is the range of a function.

The domain

We can observe the following on the function's graph:

The x values range from zero to seven and a half.

This indicates that the domain is 0=x=7.5.

The range

We can observe the following on the function's graph:

Beginning at 0, the x values go all the way up to 5.5.

In other words, the range is 0 = M = 5.5.

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We are asked to determine the probability of rolling a 6 and then rolling a number less than 2. To do that we will use the product rule probabilities since we want to find the probability of two independent events happening:

Where:

To determine the probability of rolling a 6 we need to have into account that there are 6 possible outcomes out of which only one is a 6. Therefore, the probability is:

To determine the probability of B we need to have into account that in a 6-sided die the numbers that are less than 2 are (1), this means that there is only one number less than 2 out of 6 possible numbers. Therefore, the probability is:

Now, we substitute in the product rule:

Solving the product:

Therefore, the probability is 1/36.

Using the elimination method,  the value of A and B must 3 and 4 respectively to eliminate x in the equation. The value of A and B must be 3 and 7 respectively to eliminate y.

System of equation can be solved using elimination method, substitution method of graphical method.

But we are asked to use elimination method.

Therefore, the system of equation are as follows:

Equation 1: A [-4x + 7y = 4]

Equation 2: B [3x - 3y = 6]

Therefore,

If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 4.

If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 7.

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The diameter of the Earth is 11.3 times less than the diameter of the Jupiter

Fractions are written as a ratio of two integers. Given the following parameters;

Diameter of Jupiter = 1.43•10^5km

Diameter of Earth = 1.27 * 10^4km

Find the ratio

Ratio = Jupiter/Earth

Ratio = 1.43•10^5/1.27*10^4

Ratio = 1.13 * 10^1

Ratio = 11.3

Jupiter = 11.3 of Earth

This shows that the diameter of Jupiter if 11.3 times greater than Earth.

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Answer: {(1,3),(1,4),(2,3),(2,4)}

Step-by-step explanation:

Step -1: Define the Cartesian product.

              Cartesian product: If A and B are two non empty sets, then  

              Cartesian product A×B is set of all ordered pairs (a,b) such that a∈A and b∈B.

Step -2: Find the Cartesian product of given sets.

              We have given,

              A={1,2} and B={3,4}

              So, A×B={(1,3),(1,4),(2,3),(2,4)}

Hence, option A. {(1,3),(1,4),(2,3),(2,4)} is correct answer.

The given equation is

We will solve it in this way

For the 1st equation

Subtract 7 from each side

Subtract 4x from both sides

For the 2nd equation

Subtract 3x from both sides

Divide both sides by -7

The solutions are

7, -1

The answer should be B

Answer:2.5

Step-by-step explanation:

        l

        I

------------------ x intersept

        I

        I

y intersept

The width of the border will be 8 inches.

In the given question, it is stated that a rectangular board has dimensions of 18*14 around which a person has to put a border of shells. If there are enough shells for the border of an area of 320 square inches, we need to find out the Width of the border.

Firstly, we know the Area of Rectangle is l*b => Length*Breadth

So, now we calculate the area of the board with dimensions l = 18 and b = 14

=> A₁ = l*b

=> A₁ = 18*14

=> A₁ = 252 square inches

We get the Area of the Board as 252 Square inches.

Now, there are shells enough to cover a border area of 320 square inches.

So, the Board and Border area will be A₁ + A, where A₁ and A are the areas of the Board and border respectively.

So, Total Area = 252 + 320

Total = 572 Square inches.

Now, let 'w' be the width of the border. Then the dimensions for the board will be

l = (18 + w)

b = (14 + w)

Using the formula for the Area of the rectangle, we get

=> Total = l * b

=> Total = (18 + w)*(14 + w)

=> 572 = w² + 32m + 252

=> w² + 32m - 320 = 0

=> w² + 40w -8w -320

=> w(w + 40) -8(w + 40)

=> (w+40) (w-8)

We get factors as w = -40 and 8

Since Width can not be negative quantity, width w will be 8 inches.

Hence, the width will be 8 inches for the border.

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The monthly rate of change in demand is -$40.7.

The slope of a graphed function is determined using the average rate of change formula. The method for finding the slope is differentiation.

A price-demand relation equation is given.

2x²-5xp + 55p²=23,200.

Differentiate the given equation with time

[tex]\begin{aligned}&4 x \frac{d x}{d t}-5\left(x \frac{d p}{d t}+p \frac{d x}{d t}\right)+110 p \frac{d p}{d t}=0 \\&4 x \frac{d x}{d t}-5 p \frac{d x}{d t}=5 x \frac{d p}{d t}-110 p \frac{d p}{d t} \\&(4 x-5 p) \frac{d x}{d t}=(5 x-110 p) \frac{d p}{d t} \\&\frac{d x}{d t}=\frac{(5x-110 p)}{(4 x-5p)} \frac{d p}{d t}\end{aligned}[/tex]

Put the value of p in the original equation.

For p=20

[tex]2x^{2} -5x\times 20+ 55\times20^{2}=23200\\2x^{2}-100x+22000=23200\\2x^{2}-100x-1200=0\\x^{2}-50x-600=0\\x=60 \text{ or }-10[/tex]

Since the price can not be negative, x=60.

Putting these values in the differential equation.

[tex]\frac{d x}{d t}=\frac{(5 x-110 p)}{(4 x-5 p)} \frac{d p}{d t}\\=\frac{(5\times60-110\times 20)}{(4\times60-5 \times20)} \times3\\=\frac{300-2200}{140}\times3\\ =-40.7[/tex]

So, the monthly rate of change in demand is -$40.7.

The minus sign indicates that demand is decreasing.

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Answer:

f¯¹(x) =9x+18, for the pictorial(image) question

what is the send question is it asking derivative or inverse

If it is inverse f¯¹(x)=-x-2 as it is

Or if it is derivative f'(x)=-1

Step-by-step explanation:

For the image question f(x)=1/9x-2,f¯¹(x)=?

f(x)=1/9x-2............given

y=1/9x-2................swapping f(x) by y to Easily write

x=1/9y-2................interchanging x and y

1/9y-2=x................changeling side of equation

9(1/9y-2)=(x)9.......multiplying both sides by 9 to override the fraction on the right side

y-18=9x

y=9x-18.................Return to where it were

f¯¹(x)=9x+18..........swap back f¯¹(x) in the y

For the question f(x)=-x-2,f¯¹(x)=?

following the ☝️ arrangement

y=-x-2

x=-y-2

-y-2=x

-y=x+2

y=-x-2

f¯¹(x)=-x-2

The Scalar and Cross Product of Vectors

Given two vectors:

The scalar product is defined as:

The cross product is the result of computing the following determinant:

Where i, j, and k are the unit vectors in each of the directions x, y, and z, respectively.

This concept will be applied to the following physics problem.

Given a force F= (2, 3, 0) and the distance vector d = (4, 0, 0), the torque is defined by:

Calculating:

Calculating the determinant:

Expressing in vector form τ = (0, 0, 12) <= should use angle brackets

The magnitude of the torque is:

The power P is equal to the scalar product of the torque by the angular velocity w. We are given the angular velocity w = (3, 3, 2), thus:

P = 24

A) To solve the formula for h:

1. Divide both sides of the equation into π*r²:

B) You have the next data:

V=300πfeet³

r=5feet

Substitute those values in the formula you get in A) and calculate the h:

d) n + (n +1) = 67

1) Let's call the first number as n, and its consecutive as n +1

Then we can write:

n + (n +1) = 67

n +n +1 = 67

2n +1 = 67

2n = 66

n= 33

and n+1 = 34

2) Hence, the answer is n + (n +1) = 67

A graph's domain, which is defined as the entire set of input values visible on the x-axis, refers to the set of possible input values. The possible output values are displayed on the y-axis and make up the range.

Asymptotes are a distinctive feature of the graphs of rational functions. When a curve is nearing the edges of a coordinate plane, it is said to be asymptote. A rational function's vertical asymptotes happen as its denominator gets closer to zero.

In order to cross a vertical asymptote, a rational function must divide by one, which is impossible. When the x-values increase significantly in size, either positively or negatively, horizontal asymptotes develop. You can pass through horizontal asymptotes.

A vertical asymptote of a graph is a vertical line with the equation x = a, where the graph tends toward positive or negative infinity as the inputs get closer to a.

A graph's horizontal asymptote is a horizontal line, y = b, where the graph moves toward the line as the inputs move toward ∞+ or ∞-.

Three problem about finding DOMAIN, X-intercept, Y-intercept, Vertical Asymptote, Horizontal asymptote

1) Determine the vertical asymptote(s), horizontal or slant asymptote, x-intercept(s), y-intercept, and domain. Then, sketch a graph of the function on the given set of axes. Label all asymptotes and intercepts.

[tex]m(x) = \frac{3x^2 -12}{x^2 -7x + 6}[/tex]

2) Determine the Domain, Y-intercept, x-intercept(s), Vertical Asymptote(s), and Horizontal Asymptote, if the exist: Include the multiplicity of the x-intercepts if the multiplicity is greater than 1. Then graph the ratio function.

[tex]v(x) = \frac{3x - 1}{x^2+5x +6}[/tex]

3) What are the Domain, x-intercept, y-intercept, vertical asymptote and horizontal asymptote of the rational function [tex](x^3-x+12/x^2-3x-4)[/tex]?

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Two rays that contain the given line segment BC is  [tex]\overrightarrow {EC}[/tex]  and line segment GH is [tex]\overrightarrow {EH}[/tex] .

The length of a line segment is its measurement. Unlike a line that extends continuously, a line segment has a set length and is easy to measure.

The next link in the chain is Ray. It is made up of a line and even a mix of line segments with one terminating end and an eternally extending end.

Due to one of its ends not terminating, its length cannot be determined. Line segments are parts of a line that have two endpoints.

The construction of various shapes, such as triangles, polygons, hexagons, and squares, involves the use of a number of line segments.

From the diagram we can see that the rays EC and EH contains the given line segments. From the Rays the other line segments are BD, CD , GH.

AH is another ray.

Two rays that contain the given line segment BC is  [tex]\overrightarrow {EC}[/tex]  and line segment GH is [tex]\overrightarrow {EH}[/tex] .

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Answer: in the picture

Answer:

Quadrilateral ABCD

Step-by-step explanation:

Answer:

Student P made a mistake at step 1

Student Q made a mistake at step 3

Explanation:

First, let's analyze what are the correct steps to find the value of the expression.

So, the first step is to apply the distributive property:

Then, we need to solve the multiplication of the last term:

Now, we can factorize the sign minus, but we will need to change the signs of all terms:

Finally, we can add the term to get:

Therefore, the errors made by student P were at step 1, when this student applies the distributive property, he or she made a mistake with the sign of 7.75. This number should be negative. The next steps are correct by taking into account that the error was in the first step, the result will be wrong.

For student Q, we have that everything was correct until step 3, where he or she factorize the minus sign but he or she doesn't change the signs of all signs. After that, the procedure is correct but the answer will be wrong due to the mistake made at step 3.

The probability a single event A occurs is:

The probability P two consecutive events A and B occurs is:

So, let's consider the probability of the first event: getting tails.

Favorable outcomes: Tail

Number of favorable outcomes: 1

Total outcomes: Tail, Head

Number of total outcomes: 2

So, the probability of getting a tail is:

So, let's consider the probability of the second event: getting tails in the second time.

Favorable outcomes: Tail

Number of favorable outcomes: 1

Total outcomes: Tail, Head

Number of total outcomes: 2

So, the probability of getting a tail is:

Finally, let's calculate the probability of getting a tail twice.

Answer: The probability is 1/4.

Given the functions

The graph of the given functions

From the graph of the functions above, it can be seen that each of the functions have the same domain

The answer is the first option.

B) b*1.13

1) Since the College textbook's price has been raised up 13%, then we can write:

b(1 +0.13)

b(1.13)

Plugging b = $197 we have:

197(1 +0.13)

197 (1.13)

$222.61

2) So the factor that expresses that difference (13% up) is 1.13

For 1 is equivalent to 100% and 0.13 to 13%

3) Hence, the answer is b* 1.13 calling b that $197.

To find out the unit rate

Divide cups of sugar by the teaspoon of vanilla

so

The answer is 1/3

Option A

The cost of the new heating and air conditioner equipment is:

A = $4122

They make a down payment of 20%

A. The down payment is:

B The amount of the loan is the remaining amount after paying the down payment:

L = $4122 - $824.40

L = $3297.60

Given:

GCF of 24 and 12.

Explanation:

We are told that the rate at which the pump dumps the pollutant per day to be

To solve the question, let us assume that t is the number of days

So, to find the amount dumped after 3 days, we will put t =3 into the equation

Therefore, the answer is 0.115