Because the values of circular functions repeat every 2x, they are used to describe things that repeat periodically.
For example, the maximum afternoon temperature in a given city might be modeled by the formula below. In
the formula, t represents the maximum afternoon temperature in month x, with x = 0 representing January, x = 1
representing February, and so on.
t=85-25 cos
ХЛ
6

To calculate SS E(Sum of Squared Error ) we use the formula of

SSE Total SS - Regression SS but this answer does not make sense

because the SSE cannot be negative.

In statistics, the discrepancy between the observed and anticipated

values is known as the sum of squared error (SSE). Since it is the sum

of the squares of the residual or the difference between predicted

values and actual values, it is also known as the sum of squares

residual (SSR).

To calculate the Sum of Squared Error (SSE), we can use the formula:

SSE = Total SS - Regression SS

We are given the value of Regression SS as 3538.71 and the value of

Total SS as 18. Therefore, we can calculate the value of SSE as:

SSE = Total SS - Regression SS

SSE = 18 - 3538.71

SSE = -3520.71

However, this answer does not make sense because the SSE cannot

be negative. This suggests that there may be an error in the given

information. Specifically, the value of Total SS should be greater than

or equal to the value of Regression SS. Without additional information,

we cannot provide a correct answer to this question.

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The answer to this question is a 4 point increase. This is because the change in value of the stock is measured based on the difference between the current value and the previous value.

It is determined by the supply and demand of buyers and sellers in the market. The price of a stock can fluctuate daily and is a reflection of the market's opinion of the company. It is important for investors to keep track of stock prices in order to make informed decisions about their investments.

In this case, the stock price increased from 1 point to 4 points, indicating a 4 point increase.

This can be expressed mathematically as follows:

Change in stock price = Current Value - Previous Value

Change in stock price = 4 - 1

Change in stock price = 3

Therefore, the stock's value increased by 4 points. This is because the change in value is calculated by subtracting the previous value from the current value.

In this case, the stock price increased by 3 points, resulting in a 4 point increase.

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Mariah fοrmulate the equatiοn as 150= 2B+3T

And Chris fοrmulate the equatiοn as T = 50-2/3B

A assertiοn that twο expressiοns are equal is knοwn as an equatiοn. Twο things are equal, accοrding tο an equatiοn.

Given,

A grοcer will spend $150 οn beans and tοmatοes cοmbined. Beans cοst $2 per pοund and tοmatοes cοst $3 per pοund.

Here B be a number οf pοunds οf beans and T the cοrrespοnding number οf pοunds οf tοmatοes the grοcer cοuld buy.

Sο we can write

2B + 3T= 150…….(1)

Mariah says she has a simple equatiοn but it's nοt in the fοrm B= (sοme expressiοn) οr T= (sοme expressiοn)

Sο the equatiοn we can write in the fοrm οf cοst

150= 2B+3T

Chris tries tο fοrmulate an equatiοn in the fοrm οf T

2B + 3T= 150

Or, 3T= 150-2B

Or, T = 50-2/3B

Equatiοn that is fοrmed by Mariah is 150= 2B+3T

Chris fοrmulate the equatiοn as T = 50-2/3B

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Answer:

[tex] \frac{91}{400} [/tex]

Step-by-step explanation:

Given:

A square (all sides are equal)

AC = 20 (diagonal)

PI = 7

First, we can find the side length of the whole square:

[tex]d(diagonal) = a \sqrt{2} [/tex]

[tex]a \sqrt{2} = 20[/tex]

Divide both sides of the equation by √2 to make a the subject:

[tex]a = \frac{20}{ \sqrt{2} } = \frac{20 \sqrt{2} }{2} = 10 \sqrt{2} [/tex]

Now, let's do the same thing, but with the smaller square on the top right:

[tex]pr \sqrt{2} = 7[/tex]

[tex]pr = ri = \frac{7}{ \sqrt{2} } = \frac{7 \sqrt{2} }{2} = 3.5 \sqrt{2} [/tex]

[tex]ic = 10 \sqrt{2} - 3.5 \sqrt{2} = 6.5 \sqrt{2} [/tex]

We also have to find the areas of the shaded rectangles and the whole square:

[tex]a(shaded) = 6. 5\sqrt{2} \times 3.5 \sqrt{2} = 45.5[/tex]

[tex]a(square) = ({10 \sqrt{2}) }^{2} = 200[/tex]

Let's call the event A:

A - "The dart hits the shaded region"

All outcomes:

n = 200 (since it can randomly hit the whole area)

Favorable outcomes:

m (A) = 45,5 (since it only need to hit the shaded region)

[tex]p(a) = \frac{m(a)}{n} = \frac{45.5}{200} = \frac{91}{400} [/tex]

Based on the information provided, the decimal number used to calculate the sales tax would be 0.055.

To convert the percentage to a decimal number, we divide by 100. So, to find the decimal number used to figure the sales tax on a purchase with a sales t axrate of 5 1/2%, we can divide 5.5 by 100:

5.5 ÷ 100 = 0.055

Therefore, the decimal number used to figure the sales tax on a purchase with a sales tax rate of 5 1/2% is 0.055. To calculate the sales tax on a purchase, we multiply the purchase amount by the decimal rate of the sales tax. For example, if the purchase amount is $100, the sales tax would be:

$100 × 0.055 = $5.50

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Answer:

D.

Step-by-step explanation:

temos transformar todos os termos e frações em .../4.

2/8 = 1/4

4 + 3/2 - 5/4 + 2/8 = 4×4/4 + 3/2 × 2/2 - 5/4 + 1/4 =

= 16/4 + 6/4 - 5/4 + 1/4 = 16/4 + 2/4 = 18/4 = 9/2

Answer: B. (1)

Step-by-step explanation: On the first day, Phil used 1 gallon of paint and Lindsey used 3 gallons of paint. Therefore, the total amount of paint they used on the first day is:

1 gallon + 3 gallons = 4 gallons

To find how many gallons of paint were left after the first day, we need to subtract the amount of paint used on the first day from the original amount of paint:

5 gallons - 4 gallons = 1 gallon

Answer:

To calculate how much will be in Tallulah's account after 6 weeks, we need to find out how much her balance will increase each week due to her steady deposits, and then add that to her current balance.

Since Tallulah is depositing $21.35 per week, her balance will increase by that amount each week. After 6 weeks, her balance will have increased by:

$21.35/week x 6 weeks = $128.10

To find out how much will be in her account after 6 weeks, we need to add the amount of her balance increase to her current balance:

-$39.35 + $128.10 = $88.75

So after 6 weeks of making steady deposits, Tallulah's account will have a positive balance of $88.75.

Answer: $88.75

b r a i n l i e s t ?

Answer:

The answer to your problem is, 1364.21 or C. 252π ft2

Step-by-step explanation:

Here is our formula and what we will be using:

A = π r ( r + [tex]\sqrt{h^2 + r^2}[/tex]

Radius = 12

Height = 21

Area = π r l + π [tex]r^2[/tex]

Length = [tex]\sqrt{r^2 + h^2}[/tex]

A = π r ( r + [tex]\sqrt{h^2 + r^2}[/tex] = π x 12 x ( 12 + [tex]\sqrt{21^2 + 12^2}[/tex]

= 1364.20921 or 1364.21

Thus the answer to your problem is, 1364.21 or C. 252π ft2

To compare the magnitudes of 0.009 and 0.09, we can divide 0.09 by 0.009:

0.09 / 0.009 = 10

This means that 0.09 is 10 times greater than 0.009.

To compare the magnitudes of 0.009 and 0.1, we can divide 0.1 by 0.009:

0.1 / 0.009 = 11.111...

This means that 0.1 is approximately 11.111 times greater than 0.009.

To compare the magnitudes of 0.009 and 1, we can divide 1 by 0.009:

1 / 0.009 = 111.111...

This means that 1 is approximately 111.111 times greater than 0.009.

Therefore, 0.009 is much smaller than both 0.1 and 1.

Since m_MN = m_AB, we can conclude that the segment joining the midpoints of two sides of a triangle is parallel to the third side.

Triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is usually considered the simplest type of polygon. Triangles are distinguished by their sides, angles, and whether or not they are equilateral, isosceles, or scalene. The sides of a triangle are always connected, and the angles of a triangle always add up to 180°.

Let A(x1, y1), B(x2, y2), and C(x3, y3) be the vertices of a triangle. Then the point M, which is the midpoint of the side AB, coordinates M(x1 + x2 / 2, y1 + y2 / 2). Similarly, the point N, which is the midpoint of the side AC, has coordinates N(x1 + x3 / 2, y1 + y3 / 2).

The slope of the segment MN is given by:
m_MN = (y1 + y3 / 2 - (y1 + y2 / 2)) / (x1 + x3 / 2 - (x1 + x2 / 2))

The slope of the segment AB is given by:
m_AB = (y2 - y1) / (x2 - x1)

Substituting the coordinates for M and N into the equation for m_MN, we get:
m_MN = (y1 + y3 / 2 - (y1 + y2 / 2)) / (x1 + x3 / 2 - (x1 + x2 / 2))
= (y3 - y2) / (x3 - x2)

Substituting the coordinates for A and B into the equation for m_AB, we get:
m_AB = (y2 - y1) / (x2 - x1)
= (y3 - y2) / (x3 - x2)

Since m_MN = m_AB, we can conclude that the segment joining the midpoints of two sides of a triangle is parallel to the third side.

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If the graph of f (x) is translated one unit down and 5 units left, that gives us a new function named g(x), the equation that represents g(x) is D. g(x) = 1/3(x-12)^3 + 5.

The given function is f(x) = 1/3 (x+7)³ -4.

To translate the graph one unit down, we need to subtract 1 from the function f(x). Similarly, to translate the graph 5 units left, we need to add 5 to x inside the function.

So the new function g(x) will be:

g(x) = 1/3 ((x+5+7)³) - 4 - 1

g(x) = 1/3 (x+12)³ - 5

Comparing this with the given options, we see that the correct equation is option D.

Therefore, the answer is g(x) = 1/3(x-12)^3 + 5.

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Answer:

Step-by-step explanation:

o show that the two triangles are similar, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.

The two triangles share a common angle at vertex E, which is congruent to angle DCE, since they are vertical angles. Additionally, angle CED is congruent to angle A because they are alternate interior angles formed by a transversal intersecting parallel lines.

To show that the corresponding sides are proportional, we can use the side-angle-side (SAS) similarity theorem. In particular, we can compare the ratio of the length of corresponding sides:

DE/EC = 8/4 = 2

ED/AC = 4/6 = 2/3

CD/AD = 3/5

Since the ratios are equal, we can write the similarity statement as:

Triangle ACD ~ Triangle CED

The theorem used is the side-angle-side (SAS) similarity theorem.

To show that the two triangles are similar, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.

The two triangles share a common angle at vertex P, which is congruent to angle QPR since they are vertical angles. Additionally, angle APR is congruent to angle URP because they are alternate interior angles formed by a transversal intersecting parallel lines.

To show that the corresponding sides are proportional, we can use the side-angle-side (SAS) similarity theorem. In particular, we can compare the ratio of the length of corresponding sides:

PR/AP = 12/4 = 3

UR/QA = 21/7 = 3

RU/PA = 12/4 = 3

Since the ratios are equal, we can write the similarity statement as:

Triangle APQ ~ Triangle PRU

The theorem used is the side-angle-side (SAS) similarity theorem.

The account will be worth $7536 about 5.76 years after the year 2000, which is approximately mid-2005.

Exponential growth is a type of growth pattern where a quantity increases at a constant percentage rate over time.

The formula used in this problem is [tex]A = Pe^{rt}[/tex], where A is the final amount, P is the initial amount, r is the rate of growth, and t is the time elapsed.

Here we have

The value of your investment t years after 2000 is given by the exponential growth model[tex]A = 5500e^{0.063t}[/tex]

Where t is the number of years

We can start by setting up an equation where A (the value of the investment) equals $7536:

=> [tex]7536 = 5500e^{ (0.063t)}[/tex]

To solve for t, we need to isolate t on one side of the equation. We can start by dividing both sides by 5500:

=> [tex]\frac{7536}{ 5500} =e^{ (0.063t)}[/tex]

Next, we can take the natural logarithm (ln) of both sides of the equation to eliminate the exponent:

[tex]ln(7536/5500) = ln(e^{(0.063t)})[/tex]

Using the rule that ln(e^x) = x, we can simplify the right-hand side:

ln(7536/5500) = 0.063t

Finally, we can solve for t by dividing both sides by 0.063:

t = ln(7536/5500) / 0.063

Using a calculator, we get:

t ≈ 5.76

Therefore,

The account will be worth $7536 about 5.76 years after the year 2000, which is approximately mid-2005.

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The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

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Part A:

Part B:

Part C:

Additionally, the question itself may have influenced the results, as some teenagers may have preferred to watch news on television simply because they do not regularly read newspapers.

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Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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To identify the equilibrium price on a graph, you would need to locate the point where the supply and demand curves intersect. At this point, the quantity demanded by consumers is equal to the quantity supplied by producers, resulting in a market equilibrium.

Without seeing the graph in question, it's difficult for me to give a specific answer. However, if you have a graph that shows the supply and demand curves for a particular product or service, you can look for the point where these curves intersect to find the equilibrium price.

[tex]\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]{\bigstar{\underline{\boxed{\sf{\textbf{\color{red}{Sumit\:Roy}}}}}}}\\[/tex]

As a result, the right triangle's area is 71.875 square yards.

A triangle is considered to be correct if one of its angles is 90 degrees. The hypotenuse and legs are terms used to describe the two sides that are not the correct angle.

A basic mathematical theorem that has to do with right triangles is the Pythagorean theorem. According to this rule, the square of a right triangle's hypotenuse is equal to the sum of its other two sides' squares. With those words:

a² + b² = c²

where the triangle's legs are measured by letters a, b, and c, and the hypotenuse is measured by letter c.

Geometry, trigonometry, and physics are just a few of the fields in mathematics and science where right triangles are crucial.

The following formula can be used to determine the area of a right triangle:

(Base * Height) / 2 = Area

In this instance, the height is 6 1/4 yards, and the base is 23 yards. The height must be converted to yards:

25/4 yards times 6 1/4 yards

Now, we can enter these values as substitutes in the formula:

Area is equal to (23 × 25/4)/2

Area is (575/4)/2

Area is (575/8), = 71.875 square yards.

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If you have the same plan as the company that is advertising for $59, but your bill is 15% more, it's possible that you are receiving additional services or features that are not included in the $59 plan.

It's common for companies to offer different pricing plans for their services, and these plans often come with different features and levels of service.

It's important to review the details of both plans to determine what the differences are.

Some questions you may want to consider are:

Once you have a clear understanding of the differences between the plans, you can decide whether the additional services you are receiving are worth the 15% increase in cost. If you feel that you are not receiving enough value for the additional cost, you may want to consider switching to the lower-priced plan or negotiating with your current provider for a better deal.

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Answer:

Step-by-step explanation:

To calculate the amount of money David will have in his account after 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money at the end of the period

P is the principal amount (the initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = $300 (the initial investment)

r = 0.023 (the annual interest rate of 2.3% as a decimal)

n = 2 (the interest is compounded semiannually, or twice per year)

t = 10 (the time period in years)

Plugging these values into the formula, we get:

A = 300(1 + 0.023/2)^(2*10)

A = 300(1.0115)^20

A = $388.68

Therefore, David will have $388.68 in his account after 10 years if he keeps his initial investment of $300 in an account with a 2.3% interest rate that is compounded semiannually.

The six trigonometric ratios of angle C are sin C = 3/5, cos C = 4/5, tan C = 3/4, csc C = 5/3, sec C = 5/4 and cot C = 4/3

What are Trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. They are commonly used in geometry, physics, and engineering to solve problems involving triangles and periodic phenomena.

To find the trigonometric ratios of angle C, we first need to label the sides of triangle ABC relative to angle C. We can use the convention of labeling the side opposite angle C as "a", the side adjacent to angle C as "b", and the hypotenuse of the triangle as "c".

Using this labeling, we have:

a = AB = 24

b = BC = 32

c = AC = 40

Now we can calculate the trigonometric ratios of angle C:

sin C = opposite/hypotenuse = a/c = 24/40 = 3/5

cos C = adjacent/hypotenuse = b/c = 32/40 = 4/5

tan C = opposite/adjacent = a/b = 24/32 = 3/4

csc C = 1/sin C = hypotenuse/opposite = c/a = 40/24 = 5/3

sec C = 1/cos C = hypotenuse/adjacent = c/b = 40/32 = 5/4

cot C = 1/tan C = adjacent/opposite = b/a = 32/24 = 4/3

Therefore, the six trigonometric ratios of angle C are:

sin C = 3/5

cos C = 4/5

tan C = 3/4

csc C = 5/3

sec C = 5/4

cot C = 4/3

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The factored form of the quadratic equation with a = -4, b = -10, and c = 6 is (-2x - 2)(2x - 3).

A quadratic equation is a second-degree polynomial equation in a single variable, where the variable is typically denoted by x.

To factor a quadratic equation in standard form (ax² + bx + c), we need to find two binomials whose product is equal to the quadratic expression. The binomials have the form:

(x + m)(x + n)

where m and n are constants that we need to find.

To factor the quadratic equation with a = -4, b = -10, and c = 6, we can first multiply the coefficient of the leading term (a) and the constant term (c) to get -4*6 = -24. We need to find two numbers whose product is -24 and whose sum is equal to the coefficient of the middle term (b), which is -10.

One way to find these numbers is by trial and error or by using the AC method. We can write -24 as the product of two factors in the following way:

-24 = (-2) * 12

Now, we look for two numbers whose sum is -10 and whose product is (-2)*12 = -24. We can choose -2 and -12 because they satisfy these conditions:

-2 + (-12) = -14 (the sum is equal to b)

(-2) * (-12) = 24 (the product is equal to ac)

Therefore, we can factor the quadratic equation as:

-4x² - 10x + 6 = (-2x - 2)(2x - 3)

We can check that this is correct by using the distributive property:

(-2x - 2)(2x - 3) = -4x² + 6x - 4x - 6 = -4x² - 10x + 6

So the factored form of the quadratic equation with a = -4, b = -10, and c = 6 is (-2x - 2)(2x - 3).

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Answer: Emily should add 43 gallons of water to her fish tank to fill it up to 7/8 of its capacity.

Step-by-step explanation:  If Emily's fish tank has a capacity of 64 gallons, she should fill it up to 7/8 of its capacity to allow the pump to work properly and avoid water overflowing.

So, the amount of water that Emily should have in her fish tank is:

64 x 7/8 = 56 gallons

Emily has already added 13 gallons of salt water. Therefore, the amount of additional water she should add to the tank is:

56 - 13 = 43 gallons

Emily should add 43 gallons of water to her fish tank to fill it up to 7/8 of its capacity.

The area of the regular polygon is approximately 50 in². Option B

Since the regular polygon has 4 sides and looks like a square, we can use the information about the distance from the midpoint to a vertex (which is given as 5 inches) to find the side length of the square.

The distance from the midpoint to a vertex in this case is equal to half the diagonal of the square. Let's call the side length of the square 's' and the diagonal 'd'. By using the Pythagorean theorem for a right triangle formed by the diagonal and two sides of the square, we can write:

(d/2)^2 + (d/2)^2 = s^2

Since the distance from the midpoint to a vertex is 5 inches, the diagonal of the square (d) is 10 inches. Now, we can substitute this value into the equation:

(10/2)^2 + (10/2)^2 = s^2

5^2 + 5^2 = s^2

25 + 25 = s^2

50 = s^2

Now, take the square root of both sides:

s = √50

s ≈ 7.07 inches

Now that we have the side length of the square, we can calculate its area:

Area = s^2

Area ≈ 7.07^2

Area ≈ 50 in²

The above answer is in response to the full question below;

What is the area of the regular polygon? From the midpoint of the regular polygon is 5in.

a. 25in²

b 50in²

c. 100 in²

d. 200in²

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It is not a one-size-fits-all solution and may have both positive and negative effects on the economy as a whole.

Income refers to money that a person or entity receives on a regular basis, typically as compensation for work, services, or investments. Income can come from various sources, including wages or salaries from employment, profits from running a business, rental income from property ownership, interest or dividends from investments, and government benefits or subsidies. It is usually measured on an annual basis and is subject to taxation by governments. Income is a crucial factor in determining an individual's or household's overall financial well-being and their ability to meet their basic needs, save for the future, and participate in the economy through spending and investing.

Prompt 1:

Individuals:

If someone with lots of side income loses their main job, they may have a cushion to fall back on in the short-term until they find another full-time job. However, if their side income is not enough to sustain them for an extended period of time, they may eventually need to dip into their savings or take on debt to make ends meet. On the other hand, if someone without a lot of side income loses their main job, they may struggle more immediately to pay bills and maintain their standard of living. They may have to take on part-time work or rely on government assistance until they can secure another full-time job.

Population:

If everyone built side income, it could have both positive and negative effects on the economy. On the positive side, it would diversify income streams for individuals, potentially leading to greater financial stability and resilience. It could also boost overall consumer spending and stimulate economic growth, as people with more disposable income are likely to spend more. However, if everyone built side income, it could also lead to increased competition and lower wages in certain industries, as more people are competing for the same jobs or selling the same goods or services. It could also exacerbate income inequality, as those who are already wealthy or have more resources to invest in side income opportunities may benefit disproportionately.

In terms of specific types of income, passive income streams such as rental properties, stocks, or investments can be particularly beneficial for individuals with side income. These sources of income require less time and effort to maintain than active income streams such as freelancing or running a business, which may be more difficult to maintain if someone is also working a full-time job. However, passive income streams may also require significant upfront investment or ongoing expenses, making them less accessible for some individuals.

Overall, while side income can provide a helpful financial cushion and diversify income streams for individuals, it is not a one-size-fits-all solution and may have both positive and negative effects on the economy as a whole.

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The end behavior of function M is a downward slope, while the end behavior of function N is an upward curve.

The end behavior of a function describes the behavior of the function as the input (x) becomes very large in either the positive or negative direction. It is determined by the degree and leading coefficient of the function.

Here we have

M(x) = -8x + 10

N(x) = 5x²- 9

For function M(x) = -8x + 10, as x becomes very large in either the positive or negative direction, the output (y) becomes increasingly negative.

This is because the leading coefficient is negative, and the degree of the function is 1 (linear). Therefore, the end behavior is described as follows:

As x → ∞, M(x) → -∞

As x → -∞, M(x) → +∞

For function N(x) = 5x²-9, as x becomes very large in either the positive or negative direction, the output (y) becomes increasingly positive.

This is because the leading coefficient is positive, and the degree of the function is 2 (quadratic). Therefore, the end behavior is described as follows:

As x → ∞, N(x) → +∞

As x → -∞, N(x) → +∞

Therefore,

The end behavior of function M is a downward slope, while the end behavior of function N is an upward curve.

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This matches the original polynomial, so we know our factoring is correct. Therefore, the answer is:

[tex]x^2 + 3x - 70=(x-7)(x+10)[/tex].

In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. In other words, a factor is a quantity that can be multiplied by another quantity to produce a given result.

For example, if we consider the number 12, its factors are 1, 2, 3, 4, 6, and 12 because they can be multiplied together to give 12.

In algebra, the term factor often refers to an algebraic expression that can be written as a product of simpler expressions. For example, the expression x^2 - 4 can be factored as (x - 2) (x + 2), which means that it can be written as the product of the two factors (x - 2) and (x + 2).

To factor the polynomial x² + 3x - 70, we need to find two factors that multiply to give -70 and add to give 3.

One way to approach this is to list all the factor pairs of -70 and look for a pair that adds up to 3:

[tex]-1 * 70 = -70[/tex]

[tex]-2 * 35 = -70[/tex]

[tex]-5 * 14 = -70[/tex]

[tex]1 *-70 = -69[/tex]

[tex]2 * -35 = -70[/tex]

[tex]5 * -14 = -70[/tex]

From this list, we see that -7 and 10 are the only factor pair that add up to 3. So, we can write:

[tex]x^2 + 3x - 70 = (x - 7)(x + 10)[/tex]

To check our answer, we can use FOIL to expand the product of (x - 7) (x + 10):

[tex](x - 7)(x + 10) = x(x) + x(10) - 7(x) - 7(10)[/tex]

[tex]= x^2+ 10x - 7x - 70[/tex]

[tex]= x^2 + 3x - 70[/tex]

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