Find the slope of the line that passes through (4,8) and (2, 1)


Please help

The decimal equivalent of (27)/(32) is 0.84375, which corresponds to option (C). None of the other options listed match the correct decimal representation.

To convert a fraction to a decimal, divide the numerator by the denominator. In this case, 27 divided by 32 equals 0.84375. This decimal represents the fractional value as a decimal number.

Option (A) 0.76418 is not equivalent to (27)/(32).

Option (B) 0.764bar (18) implies that the decimal repeats indefinitely after the "bar" symbol. However, the decimal equivalent of (27)/(32) does not have a repeating pattern.

Option (D) 0.84bar (375) also suggests a repeating pattern, but there is no repeating pattern in the decimal equivalent of (27)/(32).

Therefore, the correct answer is option (C) 0.84375, as it matches the correct decimal representation of (27)/(32).

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Given that "a" is an approximate value for a quantity with a true value of "t" and a relative error of "r," we need to prove that "a" can be expressed as "t(1+r)" using the definitions of these terms.

The relative error "r" is defined as the absolute difference between the true value "t" and the approximate value "a," divided by the true value "t." Mathematically, this can be expressed as r = |t - a| / t.

To prove that a = t(1 + r), we start by rearranging the definition of relative error:

r = |t - a| / t

Multiply both sides by t:

rt = |t - a|

Since the absolute value of t - a is equal to a - t (as the true value "t" is assumed to be larger than the approximate value "a"), we can rewrite the equation as:

rt = a - t

Rearranging the equation, we have:

a = t + rt

Factoring out t, we get:

a = t(1 + r)

Thus, we have proven that "a" can be expressed as "t(1 + r)" based on the definitions of "a," "t," and "r." This equation shows the relationship between the approximate value "a," the true value "t," and the relative error "r."

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Answer:

The answer would be D.

Step-by-step explanation:

Answer:

x + 3

Step-by-step explanation:

Combine like terms.

You can subtract the 2x from the 3x and the 2 from the 5.

Answer:

in still water, a boat averages 8 miles per hour. It takes the same amount of time to travel 30 miles downstream, with the current, as 18 miles upstream, against the current. What is the rate of the water's current.

Step-by-step explanation:

Let c=speed of current in mph

c+8=speed of boat downstream in mph

c-8=speed of boat upstream in mph

Travel time= distance/speed

30/8+c=18/8-c

240-30c=144+18c

48c=96

c=2 mph

ans

rate of water's current = 2 mph

Answer:

If each box of cookies cost $4: -15.65

If both boxes of cookies together cost $4: -11.65

Answer:

2

Step-by-step explanation:

Y ∩ S means the intersection of sets Y and S.

The intersection of two sets is the set that contains the element present in both sets.

In this case, 2 students are both in the yearbook club and in the student council.

Answer: 2

Answer:

The slope is  \(s =\) $0.1774 / pounds

Step-by-step explanation:

From the question we are told that

   The weight of the rat is \(w_1 = 3.5 \ pound\)

     The cost of feeding the rat per week is \(c_1 =\)$4.50

     The weight of a Beagle is  \(w_2 = 30 \ pound\)

     The cost of feed a Beagle per week is  \(c_2 =\)$9.20

Now the slope can be evaluated mathematically as

           \(s = \frac{c_2 -c_1 }{w_2 -w_1 }\)

substituting values

            \(s = \frac{9.20 -4.50 }{30 -3.5 }\)

           \(s =\) $0.1774 / pounds

The additional information that would have to be true for the parallelogram to also be a rhombus is D. Opposite angles congruent

All rhombuses are parallelograms, but not all parallelograms are rhombuses. In a rhombus, all four sides are equal and the diagonals intersect at 90 degrees. In a parallelogram, the opposite sides are equal and the diagonals bisect each other.

Because its sides are parallel to one another, a rhombus can also be referred to as a particular kind of parallelogram. 360° is the total number of angles in a rhombus. Angles on either side of one another are equal, and adjacent angles are supplementary angles.

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Barbara draws a parallelogram. Jason thought it might be a rhombus. What additional information would have to be true for the parallelogram to also be a rhombus?a. Opposite sides congruent.b. Diagonals are perpendicular.c. Consecutive angles supplementary.d. Opposite angles congruent.

An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.

He found that before launching the new marketing plan, there were 4,800 visits.

Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.

Over the course of the next 5 weeks, initial visitor at x = 0, 4800

Increasing factor = 1.5

Equation of the model is given as:

f(x) = a(b)^x

From the question b = 1.5

Now the equation of model is:

f(x) = a(1.5)^x

At x = 0, f(x) = 4800

Now the equation of the model is:

4800 = a(1.5)^x

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The probability that the second card is a jack given that the first card was a 2 is 52/51.

To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.

When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.

The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:

P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)

Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.

The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.

P(Second card is a jack | First card is a 2) = (4/51) / (4/52)

Simplifying the expression:

P(Second card is a jack | First card is a 2) = (4/51) * (52/4)

P(Second card is a jack | First card is a 2) = 52/51

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The value of x is 7.

A proportion is an equation in which two ratios are set equal to each other.

Now, setting up the proportion we have

6/4 = x+6 / 4+8

3/2 = x+6 / 12

12*3 = 2(x+6)

36 = 2x + 12

2x = 36-12

2x= 14

x=7

Hence, the value of x is 7.

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Answer:

3

Step-by-step explanation:

x+10=13

x+10-10=13-10

Simplfiy

x=3

Hi! Your answer is x = 3.

Please see an explanation for a clear and better understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Step-by-step explanation:

Our goal is to find the value of x. That means what we have to do is to isolate x-term first.

\(\huge{x+10=13}\)

To isolate a variable means that to make a variable as a subject or also known as leaving a variable alone. To isolate the x-term for this problem, simply subtract both sides by 10 so we can get rid of 10 from the left side.

\(\huge{x+10-10=13-10}\\\huge{x+0=3}\\\huge{x=3}\)

If you are not sure that the answer is correct or not. We can substitute the value of x in the equation.

\(\huge{x+10=13}\)

Substitute x = 3 in the equation.

\(\huge{3+10=13}\\\huge{13=13}\)

The equation is true for x = 3. Hence, we can conclude that x = 3 is the solution to the equation.

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

Step-by-step explanation:

x = 3y

x + y = 180°

3y + y = 180° ⇒ y = 45° = a

x = 3( 45° ) ⇒ x = 135° = b

The sizes of angles represented by a and b​ are 45 and 135 degrees.

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.

We are given that

x = 3y

Since we know that the linear pair is

x + y = 180°

Therefore, 3y + y = 180°

y = 45° = a

x = 3( 45° )

x = 135° = b

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Answer:

a = P - b - c

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define equation

P = a + b + c

Step 2: Solve for a

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\(P = a + b + c\)

\(a + b + c = P\)

Subtract sides c

\(a + b + c - c = P - c\)

\(a + b = P - c\)

Subtract sides b

\(a + b - b = P - c - b\)

\(a = P - b - c\)

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Joanne, as the store manager at Glitter, is exercising her legitimate power that she obtains from her position of authority.

Legitimate power refers to the authority that comes with a specific role or position within an organization. In this case, Joanne's role as store manager grants her the power to make decisions and direct her sales staff. She uses this power to require her team to stay after normal work hours to complete tasks such as pricing and displaying new merchandise before each holiday season. This demonstrates that her power is derived from her position within the company rather than her personal attributes or expertise.

It is important to differentiate legitimate power from other forms of power, such as expert power, coercive power, and soft power. Expert power is based on one's knowledge and skills in a specific area, while coercive power involves using threats or force to get others to comply. Soft power, on the other hand, refers to influencing others through persuasion, diplomacy, and personal appeal.

In the context of this scenario, Joanne's power is primarily legitimate, as it stems from her position as store manager, rather than her expertise or personal influence.

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Answer:

Step-by-step explanation:

y=Mx+c

M=6 c=-2

Answer:

85

Step-by-step explanation:

You have to subtract 150-65 to find the other interior angle which would be 85, unless there is another option then I am fairly sure this is the answer.

Hope this helps :)

Answer:

95*

Step-by-step explanation:

180-150=30

30+65=95

180-95=85

180-85=95

The metric unit that you would probably use to measure the length of a computer keyboard is centimeters (cm). A keyboard is measured in length from one end to the other, and it is easier to measure it in centimeters.Centimeters (cm) is a metric unit of length, and it is a smaller unit of measurement compared to meters (m).

A standard computer keyboard ranges from about 43 to 53 cm in length, so centimeters are a more appropriate unit for measuring its length than meters or kilometers. You could also use millimeters (mm) to measure the length of the keyboard, but this would be a less practical unit as it would give a very large number.A meter stick or a tape measure can be used to measure the length of the keyboard in centimeters.

To ensure accurate measurement, you should measure from one end of the keyboard to the other while making sure to keep the measuring instrument straight. You should also measure the keyboard along its longest dimension, which is usually from left to right.

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Answer:

Please check explanations

Step-by-step explanation:

Mathematically;

csc 2 theta = 1 / sin 2 theta

Sin 2 theta = sin (theta + theta)

= 2sin theta cos theta

So therefore;

csc 2 theta = 1/2(sin theta cos theta)

= 1/2 * 1/sin theta * 1/ cos theta

1/sin theta = csc theta

1/cos theta = sec theta

Thus;

csc 2 theta = 1/2 * csc theta * sec theta

csc 2 theta = 1/2 sec theta csc theta

The inverse of a function when x = -1 is g^-1(-1) = -5/2

Linear functions are function that has a leading degree of 1. Given the expression below;

g(x) = 2x + 4

Determine the inverse

y = 2x + 4

Replace y with x

x = 2y + 4

Make y the subject of the formula

2y = x - 4

y = (x-4)/2

g^-1(x) = (x-4)/2

Substitute x = -1 into the equation

g^-1(x) = (-1-4)/2

g^-1(-1) = -5/2

Hence the inverse of a function when x = -1 is g^-1(-1) = -5/2

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To find the point on the surface 6x = y^2 + z^2 where its tangent plane is parallel to a given plane, we need to find a point on the surface and determine the normal vector of the surface at that point.

Then, we can compare the normal vector of the surface to the normal vector of the given plane to check if they are parallel.

Let's first find a point on the surface by substituting a value for either y or z and solving for x. Let's choose y = 0:

6x = 0^2 + z^2

6x = z^2

x = z^2/6

So, one point on the surface is (z^2/6, 0, z).

To find the normal vector of the surface at this point, we can calculate the partial derivatives with respect to x, y, and z:

∂/∂x (6x) = 6

∂/∂y (y^2 + z^2) = 0

∂/∂z (y^2 + z^2) = 2z

The normal vector is then N = (6, 0, 2z) = (6, 0, 2z) / ||(6, 0, 2z)||, where ||N|| represents the magnitude of N.

To determine if the tangent plane is parallel to a given plane, we compare the normal vector of the surface to the normal vector of the given plane. If they are parallel, their direction vectors should be proportional.

If the given plane is parallel to the xy-plane and has a normal vector N_1 = (0, 0, 1), we can compare it to the normal vector of the surface. In this case, we see that the z-component of N (2z) is not proportional to the z-component of N_1 (1). Therefore, the tangent plane of the surface at the chosen point is not parallel to the given plane.

To find a point on the surface where its tangent plane is parallel to the given plane, we would need to choose a different point on the surface such that the normal vector of the surface at that point is parallel to the given plane's normal vector.

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Answer:

  see attached

Step-by-step explanation:

The area of a square is the square of the side length.

For example, (√125)² = 125.

__

The side length of a square is the square root of the area.

For example, √98 = √(7²·2) = 7√2.

The 10%-90% rise time of the response is approximately 0.3 seconds, to the nearest third decimal place.

To determine the 10%-90% rise time of a response, we need to find the time it takes for the response to go from 10% of its steady-state value to 90% of its steady-state value.

Looking at the graph or response data provided, we can estimate that the steady-state value of the response is approximately 1.4.

10% of 1.4 is 0.14, and 90% of 1.4 is 1.26.

So we need to find the time it takes for the response to go from 0.14 to 1.26.

By examining the graph or data, we can see that this occurs between t = 0.9 seconds and t = 1.2 seconds.

The difference between these two times is:

1.2 - 0.9 = 0.3 seconds

Therefore, the 10%-90% rise time of the response is approximately 0.3 seconds, to the nearest third decimal place.

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If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.

The sum of the three numbers is:

x + (x+2) + (x+4) = 3x + 6

We know that the sum is 114, so we can set up the equation:

3x + 6 = 114

Subtracting 6 from both sides gives:

3x = 108

Dividing both sides by 3 gives:

x = 36

Therefore, the three consecutive even numbers are 36, 38, and 40.

Answer:

37, 38, 39

Step-by-step explanation:

let the 3 consecutive numbers be

n , n + 1 , n + 2

then summing and equating to 114

n + n + 1 + n + 2 = 114

3n + 3 = 114 ( subtract 3 from both sides )

3n = 111 ( divide both sides by 3 )

n = 37

n + 1 = 37 + 1 = 38

n + 2 = 37 + 2 = 39

the 3 consecutive numbers are 37 , 38 , 39

Answer:3x10^0 or 3x10 to the power of 0

Step-by-step explanation:

I did the same exact one with my teacher i hope this helps you