On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). A point is at (negative 3, 1).
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

y – 1=Negative three-halves(x + 3)
y – 1=Negative two-thirds(x + 3)
y – 1= Two-thirds(x + 3)
y – 1= Three-halves(x + 3)

Answer:

A. y = -4x

B. y = 20

Step-by-step explanation:

A. y = xk

Where k is constant

Substitute y for -8 and x for 2

-8 = 2k

Divide both sides by 2

-8/2 = 2k/2

-4 = k

k = -4

y = x(-4)

y = -4x

B. y when x = 5

y = 5(-4)

y = 20

Answer:

y+3=2x+4

Step-by-step explanation:

The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

In the question ,

two points are given as  (-6 , 2) and (-4 , -1) .

we need to find the equation of the line passing through the given points .

to find the equation First we need to find the slope  ,

slope = (-1-2)/(-4-(-6))

slope = -3/(-4 + 6)

slope = -3/2

So , the equation of the line passing through the point (-6 , 2) with slope -3/2 is  

(y - 2) = (-3/2)(x - (-6))

y - 2 = (-3/2)(x + 6)

y - 2 = (-3/2)x - 9

y = (-3/2)x - 9 + 2

y = (-3/2)x - 7

2y = -3x - 14

3x + 2y = -14

Therefore , The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

The given question is incomplete , the complete question is

Write the equation for the line that passes through the point (-6, 2) and (-4,-1) , write the answer in fully reduced form .

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A cosine function has an amplitude of 1/3, period of π/3, horizontal shift of -2π, and vertical shift of -3, x=π, then the value y is -2.8889

The general cosine function is given by

f(x)= A cos (B x -C) +D

where A= 1/3 is the amplitude,

period =  2π /B

π/3 =2π/B

B= 2/3

C= -2π is the horizontal shift and  D= -3s a downward vertical shift.

If we substitute all these values into the formula we obtain;

f(x)= 1/3 cos (2/3 x +2π ) -3

if x= π then we have to calculate y

y= 1/3*0.3333 -3

y= -2.8889

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By using the trial method we get a total number of trials taken by Charlie to see both sides of both the coins is 4.

Probability is the name of the area of mathematics that deals with the examination of random events. The ratio of favorable occurrences to the total number of events is used to calculate an event's probability.

P(E) = F(E)/T (E)P(E)

It stands for the probability that an event will occur.

F(E) = Amount of favorable occurrences

Total number of trials (T(E))

Given that Charlie has 2 fair coins.

If he tosses the pair of coins simultaneously, then the number of samples can be HH, HT, TH, TT.

So to see both sides of both the coins he should toss the coin four times.

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The value of angle ∠5 will be equal to 120°.

Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.

Given that In the given figure, l ∥ m and n are transversal and the angles are ∠1=80° and ∠5=100°.

First, calculate angle 2,

∠1 = ∠2  = 80 ( By alternate interior angles)

Calculate the angle ∠4,

∠4 = 180 - 80 - 40

∠4 = 180 - 120

∠4 = 60°

Calculate the angle ∠5,

∠5 = 180 - 60

∠5 = 120

Therefore, the value of angle ∠5 will be equal to 120°.

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Answer:

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Step-by-step explanation:

sin(-5x)=0.1

-sin(5x)=0.1

sin(5x)=-0.1

sin(5x)=1/10

5x=arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)+2kπ

5x=π-arcsin(- 1/10)+2kπ

x=arcsin (1/10)/5 + 2kπ/5

x=arcsin (1/10)/5 + 2kπ/5

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Applying the definition of exterior angle, the measure of angle B is: c. 33°

When a side of a triangle is extended through an interior angle, the angle formed is called the exterior angle of a triangle.

The angle to the exterior angle of the triangle, when added to the exterior angle will have a sum of 180 degrees, which means their supplementary angles.

Therefore:

4x - 15 + 14x - 21 = 180

4x + 14x - 15 - 21 = 180

18x - 36 = 180

18x = 180 + 36

18x = 216

18x/18 = 216/18

x = 12

m∠B = 4x - 15 = 4(12) - 15 = 33°

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Answer:

its B. 33

Step-by-step explanation:

Numerous other sorts of numbers exist, including natural, whole, rational, real, and integers. Positive and negative numbers, but not decimals or fractions, make up the category of integers.

Q      What are integers in mathematics?
ANS An integer is a whole number without any fraction or decimal part.

The traits of each group of numbers are as follows:

8 is the  sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!

We are asked the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!.

As, the largest perfect square that divides 12! is

2^10 * 3^4 *5^2 = 2073600.

Now, the square root of the number 2073600 is,

1440

Now, we have to find the prime factorization of 1440

1440 = 2×2×2×2×2×3×3×5

Now, in the prime factorization of 1440

the exponent of 2 is 5, exponent of 3 is 2 and the exponent of 5 is 1.

So, the sum of the exponents of the prime factors be 5+2+1 = 8

Hence, 8 is the  sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!

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

Explanation:

The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.

R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}

R U S = {2, 3, 5, 17, 19, 37,      3, 5, 7, 11, 13, 37}

R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}

This list of values consist of items in set R, set S, or both.

There are 9 items in set R U S.

This is out of 12 items total in the universal set rectangle.

The probability of randomly selecting something from set R U S is 9/12 = 3/4

Considering a circle whose equation is x² + y² – 2x – 8 = 0. The statements that are true about it is as follows

Information given in the question

a circle whose equation is x² + y² – 2x – 8 = 0

Equation of a circle is given as

(x - h)² (y - k)² = r²

The equation of the circle is written in standard form by completing the square of each of the quadratic equation involved

x² + y² – 2x – 8 = 0

x² - 2x + 1 + y² + 0 = 8 + 1

(x – 1)² + (y - 0)² = 3²

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110 additional miles he will have to drive .

To calculate : additional miles qiang will have to drive

Let the additional no. of miles he has to drive be x .

⇒ Total Distance = 15 + x

    Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )

The equation becomes ,

[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50

On simplification we get ,

15 + x = 25 + ( 10x / 11 )

x = 110

Therefore , 110 additional miles he will have to drive .

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The advantages of bankruptcy include the following: e. All of these choices are correct.

In Financial accounting, bankruptcy can be defined as a legal process that is initiated when an individual or business organization (debtors) is relieved of the responsibility to pay their debts, honor its financial obligations to creditors, or protect them while they are trying to repay their debt.

Generally speaking, there are several advantages of bankruptcy and these include the following:

In conclusion, we can reasonably infer and logically deduce that bankruptcy is generally considered as both a friend and foe (enemy).

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With the help of sets we can conclude our answer.

acc to our qusetion-

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Each motorcycle travel a distance of 240 miles for the faster motorcycle and 120 miles for the slower motorcycle.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = time it took the faster motorcycle to travel

If the faster motorcycle travels 1 hr longer than the slower motorcycle, then the slower motorcycle travels x - 1 hours.

The product of the rate of speed and time is equal to the distance.

Hence, the distance traveled by the faster motorcycle is 80x, while the distance traveled by the slower motorcycle is 60(x - 1).

If the faster motorcycle travels twice the distance of the slower motorcycle, then the distance traveled by the slower motorcycle is 80x/2.

60(x - 1) = 80x/2

Simplify and solve for x.

60(x - 1) = 80x/2

60x - 60 = 40x

20x = 60

x = 3

distance traveled by the faster motorcycle = 80x = 80(3) = 240 miles

distance traveled by the slower motorcycle = 80x/2 = (80)(3)/2 = 120 miles

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0.05093 is the probability that exactly 13 students will take up application development in the coming year .

Describe probability using an example?

Average rate (number) of students who chose to study Application Development (λ)= 18

Poisson random variable(number of students taking up Application Development in the coming year)(x)=13

Poisson distribution = P(X = x) = e^−λ (λ)^x/ x!

Here, probability of 13 students choosing application development next year= P(X=13)

               =   ^(−18 ) 18^13/  13!

P(X=13) = 0.0509286= 0.05093

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Answer:

  16 square inches

Step-by-step explanation:

You want the largest rectangle that can be inscribed in a semicircle with radius 4 inches.

The equation of a circle centered at the origin with radius 4 is ...

  x² +y² = 16

The height (y) of a rectangle whose corner is on the circle will be ...

  y = √(16 -x²)

The width of such a rectangle is 2x, so the area of it is ...

  A = WH = (2x)√(16 -x²)

The maximum area will be had when the derivative of the area with respect to x is zero.

  A' = 2√(16 -x²) - 2x²/√(16 -x²) = 0

Multiplying by √(16 -x²)/2 gives ...

  16 -x² -x² = 0

  16 = 2x²

  x = √(16/2) = 2√2

The corresponding area of the rectangle is ...

  A = 2(2√2)√(16 -(2√2)²) = 16

The largest rectangle has an area of 16 square inches.

__

Additional comment

As is often the case with rectangle optimization problems, the largest rectangle that can be inscribed in the quarter circle in each quadrant is a square. It has a diagonal of 4 inches, so an area of 4²/2 = 8 square inches.

The attachment shows the cubic curve representing the area of that square as a function of its width. As above, the rectangle area is double this value.

Answer:

Point-slope: y-5=x-6

Slope intercept: y=x-1

Step-by-step explanation:

y-y1=m(x-x1) Point slope form

y-5=1(x-6)

y-5=x-6

y=x-1

Answer:

Step-by-step explanation:

The line perpendicular to y = 4 will be a vertical line through the point (−2, 1). The equation of the vertical line is x = −2.

The interquartile range of the reaction times is 0.528 or 52.80%

A normal model is represented as (μ, σ). Therefore for (1.5, 0.18), the mean (μ) = 1.5 and the standard deviation (σ) = 0.18

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The z score shows by how many standard deviations the raw score is above or below the mean. It is given as:

The interquartile range is x = 1.45 and x = 1.75

For x = 1.45

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z=(1.45-1.5)/0.18

 = -0.28

For x = 1.75

Z=(1.75-1.5)/0.18

 = -1.39

From the normal distribution table,

P(1.45 < x < 1.75) = P(-0.28 < z < 1.39)

                            = P(z < 1.39) - P(z< - 0.28)

                            = 0.9177 - 0.3897

                           = 0.528

                          = 52.8%

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The expression that represents the area of the triangle is given as follows:

A = (c - a)[8 - (c - a)]/4.

The area of a triangle is obtained as half the multiplication between the base b and the height h, that is:

A = 1/2 x b x h.

For the triangle in this problem, the base is composed by these following vertices:

Hence the length of the base is of:

b = c - a.

The height is given by the difference between the y-coordinate of the vertex (b,4) and the midpoint of the base ac, hence:

h = 4 - (c - a)/2 = [8 - (c - a)]/2

Hence the area is given as follows:

A = 1/2 x (c - a) x [8 - (c - a)]/2

A = (c - a)[8 - (c - a)]/4.

The problem asks for which expression gives the area of the triangle with these vertices.

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Solving the system of equations we can see that:

We can define the variables:

x = price of a Douglas Fir trees

y = price of a Noble Fir trees.

By using the given information we can write:

6x + 16y = 986

6x + 24y = 1368

That is our system of equations

If we take the second equation and we subtract the first one we get.

(6x + 24y) - (6x + 16y) = 1368 - 986

8y = 382

y = 382/8 = 47.75

now that we know the value of y, we can find the value of x using the first equation.

6x + 16y = 986

6x = 965 - 16y

x = (965 - 16y)/6

x = (965 - 16*47.75)/6 = 33.5

So:

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Balck car can overtake the red car in 2 hrs  

The Relationship between Speed, Distance & Time can be understood by the following formulas

Speed = Distance/Time  

Time = Distance / Speed

Distance = Speed X Time  

Constant speed is also called the uniform rate which involves something traveling at a fixed and steady pace or something moving at some average speed.

Here we have

Two cars are traveling in the same direction along the same route.  

The speed of the Red car = 40 miles per hr

The speed of the Black car = 50 miles per hr  

From above data

The difference between speeds of cars = 50 - 40 = 10 miles per hr

Which means the Black car is chasing the Red car at 10 miles per hr

Given that distance between two cars = 20 miles  

The time taken by the Black car to cover 20 miles

=> Distance/ speed = 20/10 = 2hrs

Balck car can overtake the red car in 2 hrs  

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Answer:

Yes

Step-by-step explanation:

(1)-4=3((-2)+1)

-3=3(-1)

-3=-3

The answer is yes because if you substitute x and y for -2 and 1 you can simplify the equation. Then you get the answer -3=-3 which means that the equation is equal.

Answer:

A

Step-by-step explanation:

Domain is the set of x values, so we can cross off C and D as answer choices as those would be possible answer choices for range. Looking at the graph, you can see the graph continues infinitely. The domain of the function is all real numbers, or A.

Answer:

11

Step-by-step explanation:

x = 2(-x) + 33

x = -2x + 33

x + 2x = 33

3x = 33

3/3 x = 33/3

x = 11