How do you graph a linear equation 3x 2y 6?

She read that it's not advisable to operate any heavy machinery if you have more than 50 mg of Vicodin left in your system, but she still wants to drive her friend's automobile.

In order to treat moderate to fairly severe pain, hydrocodone is used as an antitussive (cough suppressant) and narcotic analgesic. According to studies, hydrocodone is about equally effective to morphine for pain management and just as effective as codeine for suppressing coughs. Do not pack another person's medication in your bag, even if you are traveling together.

The name on the prescription for every drug you take should be your own; each person should stand on their own two feet in this situation. Since Percocet is a stronger opioid than Vicodin, it carries a higher risk of abuse than Vicodin. This is typical of stronger opioids. Only use Percocet and Vicodin as directed by your doctor; they are only meant for the temporary relief of pain.

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The 100th term in the given Arithmetic sequence is - 505

The series where the common difference between any two next terms stays constant is known as an arithmetic sequence.

It is a collection of numbers or integers that follow a pattern called a sequence. It is also defined as "every term in a sequence is obtained by adding or subtracting a fixed integer"

The formula for the common difference is given by

Common difference, d = Term2 - Term1  

The nth term in AP, T[tex]_{n}[/tex] = a + (n-1)d

Here we have

Arithmetic sequence -10, -15, -20, -25, . . .    

Here common difference, d = Term2 - Term1

=> -15 - (-10) = -15 + 10 = -5  

As we know,

nth term in AP = a + (n-1)d

100th term in AP = -10 + (100 - 1)(-5)

= - 10 + (99)(-5)

= -10 - 495

= - 505

Therefore,

The 100th term in the given Arithmetic sequence is - 505

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The 100th term of the sequence is -505

The first term of the sequence is -10, and the common difference is -5. We can use the formula: to determine the 100th term.

nth term = a + (n-1)d

Where:

a = first term = -10

n = desired term = 100

d = common difference = -5

Plugging in these values, we get:

nth term = -10 + (-5)(100 - 1)

nth term = -10 + (-5)(99)

nth term = -10 -495

nth term = -505

Therefore, the 100th term of the sequence is -505

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The roots of the polynomial f(x) = x³ - x² - x - 15 are  3, -1 + 2i and -1 - 2i

A root of a polynomial is a value of x that makes the polynomial equal to zero. A polynomial is a mathematical expression that is made up of terms, each of which includes a variable (x) raised to a power, such as x^2, x^3, x^4, etc. The powers of x are called the degrees of the polynomial.

For example, the polynomial equation x^2 + 2x - 3 = 0 has two roots, x = -1 and x = 3.

The number of roots of a polynomial equation is determined by its degree. A polynomial equation of degree n has at most n roots. A polynomial equation of degree n can have n distinct roots, n-1 distinct roots, or even no roots at all.

f(x) = x³ - x² - x - 15

0 = x³ - x² - x - 15

The roots are 3, -1 + 2i and -1 - 2i

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Answer:Π/3 radians

Step-by-step explanation:We can express the 60 degree angle in radians using the formula: Angle in radians = Angle in Degrees × π/180. So, we have 60 degrees in radians = 60 × π/180 = π/3 radians.

The difference between exponential function and logarithmic function is their graph shows mirror image of each other.

A function of the form is a logarithmic function. It can be read as "y equals the log, base b, of x" or "y equals the log of x, base b." X > 0 and b > 0 and b 1 in both forms. y is not constrained in any way.

When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. An essential mathematical function of the form is the exponential function. f(x) = a^x.

Examples of exponential functions include 2x, 10x, and ex; they have the form axe, where an is a constant. The cube root function, for example, "undoes" the cube function: 323=2. The logarithmic functions are the inverses of the exponential functions, that is, functions that "undo" the exponential functions.

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Answer: b=90,d=100,c=80

Step-by-step explanation:

A parallelogram's interior angles have an interesting property.

Two adjoining angles add up to 180 degrees.

Therefore, we can find that d+b-10=180

d+b=190

next, let's use the same property again to find b

b-10+b+10=2b=180

Therefore, b = 90

Now let's set up the equation for c.

b+10+c=180

b+c=170

90+c=170

c=80

d+b=190

d+90=190

d=100

Therefore, b=90,d=100,c=80

The function x³ + 8x² + 19x + 12 in factored form knowing that one of the roots is -1 is (x+3)(x + 1)(x + 4).

Given function:

x³ + 8x² + 19x + 12

One of the roots is -1 so it must satisfy the factored form of the equation in the options.

f(x) = (x+3)(x + 1)(x + 4)

This factored form satisfies when x = -1. Hence the correct factored form.

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The fraction with the greatest value is 5/6;

Fractions are numbers that are represented by the quotients of two integers. Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

[tex]\dfrac{a}{b}[/tex]

Then, we can interpret it as:

[tex]\dfrac{a}{b}[/tex] = a parts out of b parts of a thing.

Given fractions are as follows;

1/6, 5/6, -1/6 and -5/6

Negative numbers are less than positive numbers.

So, the remaining fractions are;

1/6 and 5/6

Both fractions have the same denominator.

So, we consider the numerator

5 is greater than 1;

Therefore, the fraction with the greatest value will be 5/6

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{80 + 56 \rightarrow \boxed{\textsf{8{(10 + 7)}}}\rightarrow 136}\\\\\large\text{Now let us break down the distributive property to if it is really}\\\large\text{equivalent to the original equation. }\\\\\mathsf{8(10 + 7)}\\\mathsf{= 8(10) + 8(7)}\\\mathsf{= 80 + 56}\\\mathsf{= 136}[/tex]

[tex]\huge\text{Therefore your answer should be: }\\\\\huge\boxed{\mathsf{8(10 + 7)}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Given: in ΔABC ∠ B = 30° , AB= 10 cm

in ΔADC ∠ D = 25° , AC = Perpendicular = 5 cm

to find: length of CD, AC

final answer: CD = 10.7 cm, AC = 5 cm

trigonometry is a subfield of mathematics that deals with the connections between angles and length-to-width ratios. the most commonly used trigonometry ratios are sin, cos and tan. we can use these with respect to triangles and apply trigonometry identities to find your answer.

using trigonometry identity in ΔABC ∠ B = 30° , AB= 10 cm,

sin = perpendicular/ hypotenuse

sin 30 = AC/ 10 (sin 30 = 1/2)

AC = 1/2 *10 = 5 cm

using trigonometry identity in ΔADC ∠ D = 25° , AC = Perpendicular = 5 cm,

tan = perpendicular/ base

tan 25 = 5/CD (tan 25 ° =  0.466 (approx))

CD = 5/0.466

CD = 10 .7cm ( approx )

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The complete question is:

Find the length of AC. Use that length to find the length of CD. What is the length of CD? Round to the nearest tenth.

A) 2.3 cm

B) 4.0 cm

C) 10.7 cm

D) 18.6 cm

The area of shaded region when the rectangle sits inside a circle is 422.39 cm².

The area of a shape simply had to do with the total space that is taken by a particular shape. It shows the extent of the region on a curved surface and plane.

Since the rectangle sits inside the circle. Thus, the area of the shaded region will be the area of the circle minus the area of the rectangle.  That is:

area of shaded region = area of circle - area of rectangle

area of shaded region = πr² - LW

area of shaded region = (π × 12²) - (3 × 10)

area of shaded region = 144π - 30

area of shaded region = 422.39 cm²

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The solutions for the given equations would be

x =14

x = -96

x = 53

What is a linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where x is the variable, a and b are coefficients, and a is not equal to zero. The variable x is the unknown value in the equation and the goal is to find the value(s) of x that makes the equation true.

9x = 126

x = 126/9

x = 14

x/8 = -12

x = -12 * 8

x = -96

x + 19 = 72

x = 72 - 19

x = 53

Hence, the solutions for the given equations would be

x =14

x = -96

x = 53

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The speed of a train can be calculated by dividing the distance traveled by the amount of time it took to travel that distance. For example, if a train travels 300 miles in 2 hours, the speed of the train is 150 miles per hour.

The speed of a train can be calculated by dividing the distance traveled by the amount of time it took to travel that distance. To calculate the speed of a train, simply take the total distance traveled and divide it by the total amount of time that it took to travel that distance. For example, if a train traveled 300 miles in 2 hours, then the speed of the train would be 150 miles per hour. This equation can be used to calculate the speed of any type of vehicle, including cars, trucks, and planes. By understanding this basic equation, it becomes much easier to accurately calculate the speed of any vehicle.

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The probability that a particular person win the raffle will be;

[tex]\dfrac{5}{^9C_4}[/tex]

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that special raffle ticket lists 5 different numbers. The numbers range from 1 to 9.

To choose a winner, 9 balls numbered 1 to 9 are placed in a container and mixed thoroughly. Then 5 balls are drawn at random.

Also, the person who has the same numbers as the numbers on the 5 balls, in any order, wins a prize.

The probability that a particular person win the raffle;

[tex]\dfrac{5}{^9C_4}[/tex]

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The slope of the function is 6.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given function is F(x) =6x-1

y=6x-1.

When we compare the given function with the slope intercept form we get m=6

Hence, the slope of the function is 6.

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Carl, who purchased four packages, has more red apples than green apples.

A fruit stand sells red and green apples each type of Apple comes in packages of 10 apples and packages of one apple Carl Buys four packages of red apples and three packages of green apples.

Carl purchased four packages of red apples and three packages of green apples. Each package of red apples contains 10 apples, so Carl has 40 red apples.

Each package of green apples also contains 10 apples, so Carl has 30 green apples. 40 red apples are greater than 30 green apples, so Carl has more red apples than green apples.

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The equation of the line passing through the origin is given by y = mx where m is the slope of the line.

As given in the question,

Let us consider equation of the line passing through two coordinates

( x₁ , y₁ ) and ( x₂ , y₂).

Standard form of the equation of the line is  equal to:

( y - y₁ ) / ( x - x₁ ) = ( y₂ - y₁ ) / ( x₂ - x₁ )

Where slope m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

⇒( y - y₁ ) / ( x - x₁ ) = m

Now line passing through origin that is ( x₁ , y₁ ) = ( 0, 0 ) gives

⇒ ( y - 0 ) / ( x - 0 ) = m

⇒ y / x = m

⇒ y = mx

Therefore, the equation of the line passing through origin is equal to y = mx where slope m =  ( y₂ - y₁ ) / ( x₂ - x₁ ).

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Distance is calculated using the formula distance=√(y2²-y1²)+(x2²-x1²).

A pair of numbers called coordinates are used to locate a point or a shape in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. Cord's are the collective noun for the abscissa and ordinate. The study of algebraic equations on graphs is known as coordinate geometry. The plotting of points, lines, and curves on an x and y axis is an illustration of coordinate geometry.

Here,

The formula of distance according to class 9th is distance=√(y2²-y1²)+(x2²-x1²).

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Answer: y = -4/3x + 31/3

Step-by-step explanation:

First, covert 4x + 3y = 24 into slope-intercept form.

4x + 3y = 24

3y = -4x + 24

y = -4/3x + 8

Then, we know that it is given that the two lines are parallel, which shows that the two equations will have the exact same slope.

y = -4/3x + b

It is also given that line s passes through (4, 5).

5 = -4/3(4) + b

5 = -16/3 + b

31/3 = b

y = -4/3x + 31/3

We can write {8 x 8 x 8 x 8 x 8} as -

Given is the expression as -

{8 x 8 x 8 x 8 x 8}

We can write {8 x 8 x 8 x 8 x 8} in the following ways -

{8 x 8 x 8 x 8 x 8} = 8⁵

{8 x 8 x 8 x 8 x 8} = {2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2} = 2¹⁰

{8 x 8 x 8 x 8 x 8} = {4 x 2 x 4 x 2 x 4 x 2 x 4 x 2} = {4⁴ x 2⁴}

Therefore, we can write {8 x 8 x 8 x 8 x 8} as -

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{Complete question is

Which of the following expressions is equivalent to 8⋅8⋅8⋅8⋅8?}

Answer::8/24 are RedPick and return 2So it will be 7/25Again pick and return 2Then it is 6/26Now multiply the results8/24 …

Step-by-step explanation:

There are 5 elements in 32 proper subsets.

What are subsets?

If every element of set A is also an element of set B, then set B is a superset of set A, and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Here, we have

Given:  32 proper subsets.

We have to find how many elements are in 32 proper subsets.

Subsets of a set having n elements = 2^n

2ⁿ = 32

n = 5

Hence, there are 5 elements in 32 proper subsets.

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The values of x and y in the parallelogram PQRS 3 and 10 respectively.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

Given a parallelogram PQRS

diagonals intersect at T

PT = y, TR = 3x + 1,

QT = 3y, TS = 7x + 9

since diagonals of a parallelogram bisect each other, so PT = TR and

QT = TS

PT = TR  => y = 3x + 1

QT = TS => 3y = 7x + 9

we can compute both the equations for common values of x and y,

substitute value of y in equation 3y = 7x + 9

3(3x + 1) = 7x + 9

9x + 3 = 7x + 9

9x - 7x = 9 - 3

2x = 6

x = 6/2

x = 3

and y = 3x + 1

y = 3(3) + 1

y = 10

Hence the value of x is 3 and y  is 10.

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Answer: $42.65

Step-by-step explanation: multiply

$8.63 by 5

Answer:

42.65$

Hope this helps!

Step-by-step explanation:

1 box = 8.53

5 boxes = 8.53 * 5

8.53 * 5 = 42.65

The probability that you get exactly one pair, and three other distinct numbers are 271901

Since the order of distribution doesn't matter we will apply concepts of combination.

combination = nCr =n!/(r!(n-r!)

where n is the total number of objects

r is the number of chosen objects from the total.

Let us consider the pair as 1 so we have to choose 4 out of 52 cards

i.e., 52C4=52!/4!48!

= 270725

now for the pair cards, we have to choose 2 cards from 49 cards

i.e, 49c2=49!/2!47!

1176

Total ways = 1176 +270725

271901

Therefore, The probability that you get exactly one pair, and three other distinct numbers is 271901

Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!

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To write a quadratic equation in vertex form, you can use the following steps: Rearrange the equation to standard form, Complete the square and Write the equation in vertex form.

Rearrange the equation to standard form, which is ax² + bx + c = 0, where a, b, and c are constants.

Complete the square to get the equation in the form (x - h)² = k, where h and k are constants.

Write the equation in vertex form, which is y = a(x - h)² + k, where a is the coefficient of x², h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

For example, let's consider the equation x² - 4x + 5 = 0.

Rearranging it in standard form: x² - 4x + 5 = 0

Completing the square: (x - 2)² = -1

Write it in vertex form: y = (x - 2)² - 1

The vertex of this equation is (2, -1)

Note that the vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola that graph the equation.

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The meaning of the point ( 7 ,15 ) in the given scatter-plot which represents the amount of battery life and the age of battery is given by :

Option C. Point ( 7,15 ) represents a 7 year old battery has 15 hours of battery life remaining.

As given in the question,

Scatter-plot is attached.

Given scatter-plot represents ,

x-axis represents age of battery in years and y - axis represents battery life in hours.

Meaning of the given point ( 7 , 15 ) is as follow :

Coordinate 7 belongs to x-axis

7 represents battery is 7 years old.

Coordinate 15 belongs to y - axis.

15 represents the 15 hours battery life remaining.

Therefore, point ( 7, 15 ) in the scatter-plot represented by :

Option C.  Point ( 7,15 ) represents a 7 year old battery has 15 hours of battery life remaining.

The above question is incomplete, the complete question is :

A recent study investigated the amount of battery life remaining in alkaline

batteries of different ages. The scatter-plot shows this relationship between the different alkaline batteries tested. Describe the meaning of the point (7, 15) in this situation?

Scatterplot is attached.

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Dm(x,y)=∑i=1D|xi−yi| is the L1 distance formula.

A taxicab geometry, also known as Manhattan geometry, is a type of geometry in which the standard Euclidean distance function or metric is swapped out with a new one in which the distance between any two points is equal to the product of their absolute differences in Cartesian coordinates.

The taxicab metric is also known as snake distance, city block distance, Manhattan distance, or Manhattan length. It is also known as L1 distance, L1 distance, or L1 norm (see Lp space).

The magnitudes of the vectors in space are added to form the L1 Norm.

The sum of the absolute differences between the components of the vectors is the most straightforward technique to calculate the distance between them.

All of the vector's elements are given the same weight in this norm.

The L1 distance formula: Dm(x,y)=∑i=1D|xi−yi|

Therefore, Dm(x,y)=∑i=1D|xi−yi| is the L1 distance formula.

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The factored form of the polynomial is:

x3 - x2 - 20x + 20 = (x + 1)(x - 1)(x + 20)

What is the polynomial?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with non-negative integer exponents and coefficients, that is either a constant or the sum of a finite number of non-zero terms. Each term consists either of a single variable raised to a non-negative integer power or of the product of a constant and a single variable raised to a non-negative integer power.

One method to factor a polynomial is to use synthetic division to determine the other roots and then factor the polynomial with those roots.

Since one of the roots is 1, we know that (x - 1) is a factor of the polynomial.

Synthetic division with x = 1 gives:

1 | 1 -1 -20 20

|____

-20 -19

The quotient is -19 and the remainder is 0, which means that (x - 1) is a factor of the polynomial.

So, the factored form of the polynomial is:

x3 - x2 - 20x + 20 = (x + 1)(x - 1)(x + 20)

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Answer:

I'd say the answer is B. (Sorry if I'm wrong, I'm not good with angles!)