When a variable is eliminated from the equation during the equation solving process, what are the two possible solutions and what do they mean? Give an example of your own and explain what each answer would look like.

Answer:

Given the series : 83 , 79 , 75 ,  71 , 67, ?

Difference of two consecutive terms;

79 -83 = -4

75 -79 = -4

71-75 = -4

67-71= -4

Since, you can see that the number is decreases by 4 every time.

Let unknown term be x

then;

x - 67 = -4

x = 67-4

x = 63.

Therefore, the next term in the series is 63.

The next number in the series is 63.

In the given series, each number is decreasing by 4.

We can observe that the first number, 83, is decreased by 4 to get the next number, 79.

Similarly, each subsequent number is obtained by subtracting 4 from the previous number.

Following this pattern, the next number would be obtained by subtracting 4 from the last number in the series, which is 67.

67 - 4 = 63

Therefore, the next number in the series is 63.

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Final answer:

The term 1/2i most likely pertains to complex numbers, where 'i' is the imaginary unit. It's not typically covered in Calculus I or II but in pre-calculus or algebra courses. The principles of working with fractions apply similarly for complex numbers as they do with real numbers.

Explanation:

The term 1/2i likely refers to the fractional unit in the context of complex numbers, where 'i' is the imaginary unit. This concept is not commonly taught in Calculus I or II but is a part of complex number arithmetic, which is sometimes covered in pre-calculus or algebra. When calculating with complex numbers, it is crucial to remember that 'i' represents the square root of -1.

Let's consider the calculation of 'half' of something in more familiar terms. If you have half a pie, and you're looking to find half of that, you would intuitively know that you now have one-quarter of a pie. Likewise, if you are trying to understand how to combine fractions such as 1/2 and 1/3, you look for a common denominator. Multiplying denominators can often provide this common base for addition, just like multiplying 2 and 3 to get 6 as a common denominator.

However, when working with complex numbers and encountering a term like 1/2i, it can seem less intuitive. Nonetheless, the basic principles of fraction manipulation remain the same. The student might be looking at a problem involving complex fractions, which would require familiarity with the algebraic rules governing complex numbers.

Answer:

25%

Step-by-step explanation:

Just here to help cause im doing this too lol

85% = 0.85

1-0.85 = 0.15

80 x 0.15 = 12

the price now is $12

Answer:

A   12 chairs per 3 table

Step-by-step explanation:

4/1 is equivalent to 12 chairs for every 3 tables.

Fractions are used to represent smaller pieces (or parts) of a whole.

Given a statement, 12 chairs for every 3 tables.

The statement represents 12 chairs per 3 tables, which means 12/3 = 4/1

Therefore, there are 4 chairs for every table.

Hence, 4/1 is equivalent to 12 chairs for every 3 tables.

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The area under the graph by using the first two and then four rectangles is [tex]2.958[/tex] units square.

For reference use the below-given graph.

Given function is

[tex]f(x)=x^{2}[/tex]  when [tex]x=1[/tex] to [tex]x=2[/tex] .

The first rectangle of the first part graph goes from [tex]1.0[/tex] to [tex]1.6[/tex], so the width will be [tex]0.6[/tex] units. And the height measured from the middle point i.e. [tex]1.3[/tex] is

[tex]f(1.3)=(1.3)^{2}[/tex]

[tex]=1.69[/tex] units.

Then the area of the first rectangle is [tex]0.6\times1.69=1.014[/tex] units square.

Similarly, the second rectangle of the first part graph goes from [tex]1.6[/tex] to [tex]2.0[/tex], so the width will be [tex]0.4[/tex] units. And the height measured from the middle point i.e. [tex]1.8[/tex]  is

[tex]f(1.8)=(1.8)^{2}[/tex]

[tex]=3.24[/tex] units.

So, the area of the second rectangle is [tex]0.6\times3.24=1.944[/tex] units square.

Hence, the final area under the graph will be [tex]1.014+1.944=2.958[/tex] units square.

Further, we can do the same for another part of the graph to find the area under the graph by using four rectangles.

For example,  the first rectangle of the four has a width of [tex]0.6[/tex] units and a height of [tex]f(1.1)=(1.1)^{2}[/tex]

[tex]=1.21[/tex] units.

Therefore, the area under the graph by using the first two and then four rectangles is [tex]2.958[/tex] units square.

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The estimated areas under the curve of the function f(x)=x^2 between x = 1 and x = 2 are 2.3125 using two rectangles and 2.3281 using four rectangles

To estimate the area under the graph of the function f(x)=x^2 between x = 1 and x = 2 using rectangles, we use the method of midpoint Riemann sums. For this question, let's use 2 rectangles and then 4 rectangles.

First, for 2 rectangles, the interval from 1 to 2 is divided into 2 equal parts: [1, 1.5] and [1.5, 2]. The midpoints of these intervals are 1.25 and 1.75. The height of each rectangle is given by the function value at these midpoints: [tex]f(1.25) = (1.25)^2 =1.5625, and f(1.75) = (1.75)^2 = 3.0625.[/tex] The total area of the rectangles is thus (0.5 * 1.5625) + (0.5 * 3.0625) = 2.3125.

Next, for 4 rectangles, the interval from 1 to 2 is divided into 4 equal parts: [1, 1.25], [1.25, 1.5], [1.5, 1.75], [1.75, 2]. The midpoints of these intervals are 1.125, 1.375, 1.625, 1.875. The height of each rectangle is given by the function value at these midpoints: [tex]f(1.125) = (1.125)^2 = 1.26562, f(1.375) = (1.375)^2 = 1.8906, f(1.625) = (1.625)^2 = 2.6406[/tex], and f(1.875) = (1.875)^2 = 3.5156. The total area of the rectangles is thus [tex](0.25 * 1.26562) + (0.25 * 1.8906) + (0.25 * 2.6406) + (0.25 * 3.5156) = 2.3281.[/tex]

These are the estimated areas under the curve for 2 rectangles and 4 rectangles respectively. And as you can see, the more rectangles we use, the closer we get to the actual area under the curve.

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1.
The midpoint MPQ of PQ is given by  (a + c / 2, b + d / 2)

2.
Let the x coordinates of the vertices of P_1 be : 

x1, x2, x3,…x33

the x coordinates of P_2 be :

z1, x2, x3,…z33

and the x coordinates of P_3 be:


w1, w2, w3,…w33

3.
We are given with: 

X1 + x2 + x3… + x33 = 99

We also want to find the value of w1 + w2 + w3… + w33.

4.

Now, based from the midpoint formula:

Z1 = (x1 + x2) / 2

Z2 = (x2 + x3) / 2

Z3 = (x3 + x4) / 2

Z33 = (x33 + x1) / 2

and 

W1 = (z1 + z1) / 2


W2 = (z2 + z3) / 2

W3 = (z3 + z4) / 2

W13 = (z33 + z1) / 2

.
.

5.

W1 + w1 + w3… + w33 = (z1 + z1) / 2 +  (z2 + z3) / 2 + (z33 + z1) / 2 = 2 (z1 + z2 + z3… + z33) / 2

Z1 + z1 + z3… + z33 = (x1 + x2) / 2 + (x2 + x3) / 2 + (x33 + x1) / 2

2 (x1 + x2 + x3… + x33) / 2 = (x1 + x2 + x3… + x33 = 99


Answer: 99

The expected mean square value (E(x^2)) can be found using the formula E(x^2) = μ^2 + σ^2. With the given mean (μ) and standard deviation (σ) as 5, insertion into the formula gives E(x^2) = 5^2 + 5^2 = 50.

The mean square value, often denoted as E(x2), is calculated from the mean (μ) and standard deviation (σ) using this formula: E(x2) = μ2 + σ2. Based on the given distribution values, you're provided with a mean (μ) of 5 and a standard deviation (σ) of 5. By following the formula, you input these values, and it becomes E(x2) = 52 + 52. Thus, E(x2) = 25 + 25 which is equal to 50. So, the mean square value or the expected value of x2 for this distribution is 50.

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Final answer:

To find the max value of a line integral over a closed curve using Green's Theorem, consider the curl of the given vector field and apply the theorem to express the result. The maximum value of the line integral is -2y²dy, determined through vector calculus and Green's Theorem application.

Explanation:

Green's Theorem states that for a vector field f in the form given, the max value of the line integral over any positively oriented closed curve C can be found by considering the curl of f.

By applying Green's Theorem, we can find that the maximum value of the line integral is -2 y²dy.

This computation involves utilizing vector calculus and understanding how to apply Green's Theorem to find the extremum of the line integral.

Yes,

If a quadrilateral has four congruent facets and 4 right angles, then it's a square (reverse of the square definition).

If consecutive aspects of a rectangle are congruent, then it is a square neither the reverse of the definition nor the speak of a assets.

If we can display that the slopes of the alternative sides are identical, then the other facets are parallel. The slopes of the opposites have been the same, so ABCD is a parallelogram. Step three: subsequent, show that the parallelogram is a rectangle.

The slope is just the upward thrust over the run, which is defined as the change in y over the change in x meaning the distinction of the y coordinate factors divided with the aid of the distinction of the x-factors? So we have the two x-factors, so this is six minus two, divided by the, the x-factors 3 minus one.

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Answer:

An employee’s rate of pay is $36 per hour, with time and a half for all hours worked in excess of 40 during a week. The employee worked 48 hours during the week. The amount of the employee’s gross pay for the week is:

Step-by-step explanation:

Using the law of sines, the length of side a to the nearest tenth is 58.1 units.

Law of sines states that When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.

In ΔABC,

∠A=72°

∠B=16°

∠A + ∠B + ∠C = 180° (angle sum property)

72° + 16° + ∠C = 180°

∠C = 180° - (72° + 16°) = 92°

Using sine law, (refer to the figure attached)

[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} =\frac{sin\ C}{c} \\\\\frac{sin72}{a} = \frac{sin16}{b} = \frac{sin92}{61} \\\\\frac{sin72}{a} =\frac{sin92}{61} \\\\a = sin72 * \frac{61}{sin92} \\\\= 0.9511 * \frac{61}{0.9994} \\\\=58.05193116\\\\= 58.1[/tex]

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Value

Depreciation is defined as the reduction in value of an asset over time. In this case, value reduction is due to wear and tear of an equipment (bicycle).

a. The depreciation value would simply be the difference in initial and salvage value divided by time in years.

Depreciation = (Initial value – Salvage value) / Number of years

b. Substituting the given values into the equation where:

Initial value = $1200

Salvage value = $940

Number of years = 10 months = 10/12 years

Calculating:

Depreciation = ($1200 - $940) / (10/12 years)

Depreciation = $312 / year

or

Depreciation = $26 / month

Final answer:

Harris ate 12/k - 1 slices of pizza after a 12-slice pizza was divided evenly among k friends and he ate one less than he was given.

Explanation:

To find out how many slices of pizza Harris ate, we initially need to determine how many slices each person would get if the 12-slice pizza is divided evenly among k friends.

Each friend would get 12/k slices.

Since Harris ate 1 fewer slice than he was given, we subtract 1 from the number of slices he was supposed to get.

Therefore, the expression for the number of slices Harris ate is 12/k - 1.

total = 450

 parts = 150

450-150 = 300

 50 per hour

300/50 = 6

it took 6 hours