Solve the following system of equations and show all work.
y = 2x2
y =-3x -1

The expression represents the product of two terms = (x - 6) × (x + 2)

An equation in mathematics that is linear has a variable whose maximum power is 1. Alternatively said, it is an algebraic equation of the following form:

ax+ b = 0

where an is a constant that cannot equal zero, b is a constant, and x is a variable. Another way to express a linear equation in its general form is as follows:

y = mx + b

where the y variable is the dependent variable, the independent variable is x, the slope is m, and the y-intercept is b.

The product of 6 less than a number and 2 more than the number can be translated into the mathematical expression:

(x - 6) × (x + 2)

Here, x represents the unknown number, and the expression represents the product of two terms: "6 less than a number" (x - 6) and "2 more than the number" (x + 2).

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y=200(0.5)2t  this functiοn represents decay, y=12(2.5)t6 this functiοn represents grοwth and y=(0.65)t4 this functiοn represents decay.

In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range.

In general, we can determine whether a functiοn represents grοwth οr decay by examining the base οf the expοnential term.

If the base is greater than 1, the functiοn represents grοwth.

If the base is between 0 and 1, the functiοn represents decay.

Here are the classificatiοns fοr each οf the given functiοns:

y=200(0.5)2t

The base οf the expοnential term is 0.5, which is between 0 and 1. Therefοre, this functiοn represents decay.

y=12(2.5)t6

The base οf the expοnential term is 2.5, which is greater than 1. Therefοre, this functiοn represents grοwth.

y=(0.65)t4

The base οf the expοnential term is 0.65, which is between 0 and 1. Therefοre, this functiοn represents decay.

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Complete Question:

Select "Growth" or "Decay" to classify each function.

Function Which ones are growth or decay

f(x)=(1.05)t4

y=100(0.4)t

f(x)=14(10)t12

Answer: 3/20 and 15%

Step-by-step explanation:

The correct area models are 4e and none of the given models for 4d and 4c.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.

The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).

When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.

The area model of 4d is incorrect because it does not properly represent a factorable polynomial.

It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.

Therefore, the correct area models are 4e and none of the given models for 4d and 4c.

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As f(3) is not equal to zero, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.

Given the polynomial in the question;

f(x) = -x⁴ -8x²-x-5

Given number: 3

To check if 3 is a zero of the polynomial f(x) = -x⁴ -8x²-x-5, we need to substitute x = 3 into the polynomial and see if the result will give zero.

f(x) = -x⁴ -8x²-x-5

plug i x = 3

f(3) = -3⁴ - 8(3)² - 3 - 5

= -81 - 72 - 3 - 5

= -161

Therefore, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.

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To find the mean of the number of stamps for these four friends, we need to add up the total number of stamps and divide by 4 (the number of friends). 
Samir has 60 stamps. Lisa has 2 1/2 times as many stamps as Samir, which can be calculated as follows: 2 1/2 * 60 = 150 

Kwame has 443 stamps. 
Jake has 159 fewer stamps than Kwame, which can be calculated as follows: 443 - 159 = 284 To find the total number of stamps, we add up the number of stamps each friend has: 60 + 150 + 443 + 284 = 937 

To find the mean, we divide by 4: 937 / 4 = 234.25 

Therefore, to the nearest whole number, the mean of the number of stamps for these four friends is 234. 
Therefore, the answer is K. 234.

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Answer:

-------------------------------

Angles at vertex V and Y are of same measure since they intercept same arc WX:

Angle measure of V and Y is:

Arc measure of WX is double the inscribed angle:

the expressions that could be used to find the volume of the sculpture are A and B and  the volume of the sculpture is 364 cubic feet.

Part A:

To find the volume of the sculpture, we need to add the volumes of the two rectangular prisms: the original one and the one that was cut from it. We can express the volume of the original prism as:

9 × 7 × 8

And the volume of the cut prism can be expressed as:

7 × 7 × 4

So, the expressions that could be used to find the volume of the sculpture are A and B:

A. (7 × 8 × 2) + (7 × 7 × 4)

B. (8 × 2 × 7) + (9 × 4 × 7)

Part B:

Using expression A, we get:

(7 × 8 × 2) + (7 × 7 × 4) = 112 + 196 = 308 cubic feet

Using expression B, we get:

(8 × 2 × 7) + (9 × 4 × 7) = 112 + 252 = 364 cubic feet

Therefore, the volume of the sculpture is 364 cubic feet.

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There is no solution to the given system of equations. Therefore, the system is inconsistent.

How to solve the equation using substitution method?

To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation. Let's solve the first equation for y:

2x - y = 7

-y = -2x + 7

y = 2x - 7

Now we substitute this expression for y into the second equation:

-6x + 3y = 21

-6x + 3(2x - 7) = 21

-6x + 6x - 21 = 21

-21 = 21

This is a contradiction, and there is no solution to the system of equations. Therefore, the system is inconsistent.

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Answer:

Step-by-step explanation:

[tex](x-5)-(x + 1)=x-5-x-1=-6[/tex]

[tex](x-5)+ (x + 1)=x-5+x+1=2x-4[/tex]

[tex](x-5)+ (x-1)=x-5+x-1=2x-6[/tex]

[tex](x-5)-(x-1)=x-5-x+1=-4[/tex]

The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.

An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).

Here,

To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.

For the first equation, we can simplify it as follows:

x + 14 = 2x

Subtracting x from both sides, we get:

14 = x

For the second equation, we can simplify it as follows:

3x + 9 = 2x + 23

Subtracting 2x and 9 from both sides, we get:

x = 14

Now that we know x = 14, we can find the measure of the angles in each triangle.

In triangle ARST, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle R = 2x

= 2(14)

= 28 degrees

angle S = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

angle T = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

In triangle ANSP, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle N = 3x + 9

= 3(14) + 9

= 51 degrees

angle S = 180 - (angle A + angle N)

= 180 - (28 + 51)

= 101 degrees

angle P = 180 - (angle N)

= 180 - 51 = 129 degrees

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Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.

To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:

Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84

= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84

= 16.1

Therefore, the estimated mean age of this extended family group is 16.1 years.

To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:

s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)

= (2254.05 + 537.08 + 220.89 + 253.68) / 83

= 50.47

Therefore, the estimated sample variance is 50.47 square years.

We simply take the square root of the sample variance to calculate the sample standard deviation:

s = [tex]\sqrt{s2}[/tex]

= s[tex]\sqrt{50.47}[/tex]

= 7.10

Therefore, the estimated sample standard deviation is 7.10 years.

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A)  The annual rate of change or APR between 1991 and 2000 is approximately -0.1091.

B) The correct answer to part A in percentage form is approximately -10.91%.

C) The value of the car in 2003 is $7,750.

What is annual rate?

The car depreciated from $45,000 to $12,000 in 9 years. Using the formula for annual rate of change or annual percentage rate (APR):

r = [tex](Vf/Vi)^{1/n}[/tex] - 1

where Vf is the final value, Vi is the initial value, n is the number of years, and r is the annual rate of change or APR.

Substituting the given values:

r = [tex]($12,000/$45,000)^{1/9}[/tex] - 1

r ≈ -0.1091

Therefore, the annual rate of change or APR between 1991 and 2000 is approximately -0.1091.

B) The correct answer to part A in percentage form is approximately -10.91%.

What is APR?

To express the answer as a percentage, multiply the annual rate of change by 100 and round to the nearest 0.01%:

r = -0.1091 × 100

r ≈ -10.91%

Therefore, the correct answer to part A in percentage form is approximately -10.91%.

C) The value of the car in 2003 is $7,750.

What is the value?

To find the value of the car in 2003, we need to use the same percentage rate of decrease from 2000 to 2003. Since 2003 is 3 years after 2000, the value will be:

value = $12,000 × (1 + r)³

value ≈ $7,729.18

Rounding to the nearest 50 dollars, the value of the car in 2003 is $7,750.

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Answer:

It must be greater than 4

Step-by-step explanation:

We know that 36 ÷ 9 = 4.

Therefore, if the denominator is less than 9 and the numerator is greater than 36, the quotient would only increase since the numerator increases while the denominator decreases.

Therefore, it must be greater than 4.

We know that the area of a parallelogram is given by the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given the area and the base, and we need to find the height.

We can rearrange the formula to solve for h: h = A/b

Plugging in the given values, we get:

h = 14.4 sq ft / 4.5 cm

Note that the units are different for area and base, so we need to convert them to the same units. Let's convert the base to feet, since the area is given in square feet:

h = 14.4 sq ft / (4.5 cm / 30.48 cm/ft) [converting cm to ft]

h = 14.4 sq ft / 0.148 ft

h ≈ 97.3 cm

Therefore, the height of the parallelogram is approximately 97.3 cm.

This means that after two years since the purchase, the boat was worth $24.57.

In general, worth refers to the value or monetary equivalent of something. It can be used to describe the financial value of assets such as property, stocks, or commodities, or to describe the value of something in terms of its usefulness, importance, or significance.

Michael tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to find the function that models the data.

16.75

19.5

4

3

22.9

27.25

2

1

32

0

Years Since Purchase

To better understand the exponential function that models the data, let's break it down:

y = 10.92 * 1.50ˣ

The constant "10.92" represents the initial value of the boat when it was purchased. This means that the boat was worth $10.92 when Michael first bought it.

The constant "1.50" represents the growth factor of the boat's value. This means that each year, the value of the boat increases by a factor of 1.50.

The variable "x" represents the number of years since the boat was purchased. The function takes this input and returns the value of the boat at that time.

For example, if we plug in x=1 into the function, we get:

y = 10.92 * 1.50¹

y = 16.38

This means that after one year since the purchase, the boat was worth $16.38. Similarly, if we plug in x=2 into the function, we get:

y = 10.92 * 1.50²

y = 24.57

This means that after two years since the purchase, the boat was worth $24.57.

It's important to note that the exponential function assumes that the growth rate remains constant over time. In reality, the value of the boat may be affected by other factors such as wear and tear, maintenance, and market fluctuations. Nevertheless, the exponential function provides a useful model for understanding the trend in the data and making predictions about the future value of the boat.

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The supplied question's response based on the savings account is A geometric sequence is the sequence f.

A geometric sequence is a set of numbers where each term is obtained by multiplying the one before it by a predetermined quantity known as the common ratio. The following is the generic formula for a geometric sequence:

[tex]a, ar, ar^2,ar^3,ar^4,...[/tex]

There are two types of geometric sequences: finite and endless. While an infinite geometric sequence has no end, a finite geometric sequence has a set number of terms.

Because each term is created by multiplying the term that came before by a constant ratio of 1.1, the sequence f is a geometric sequence. (which accounts for the interest that has accrued on the preceding balance using the formula 1 + 0.1).

The first term is for $70, and each succeeding term is equal to the first term times 1.1. As a result, the nth term of the series can be

written as: [tex]f(n)=\$ \times 1.1^{n-1}[/tex]

where n is how long it has been since the first year of saving.

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Answer:

$43.96

Step-by-step explanation:

We first need to find the area of the patio which is 12-foot by 14-foot

12 ft * 14 ft = 168 sq ft

next, we need to know how many quarts are needed to cover the entire area of the patio, and we know a quart cover 53 square feet, so we divide the total area of the patio by 53:

168 sq ft ÷ 53 sq ft/quart ≈ 3.17 quarts

We'll need to buy 4 quarts of paint to cover the entire patio.
The cost of 1 quart of paint is $10.99, so the total cost of 4 quarts will be:

4 quarts x $10.99/quart = $43.96

Therefore, the estimated cost of painting the concrete patio will be around $43.96.

Trigonometric ratios connect angles and sides of right triangle. The cofunction of sinθ = cosecθ.

Trigonometric ratios are mathematical proportions that connect the angles and sides of a right triangle. The hypotenuse, adjacent, and opposing sides are the three sides of a right triangle, which is a triangle having one angle of 90 degrees.

For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensinal. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

Hence, The function equivalent to sinθ = cosecθ.

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Answer:

[tex]100\pi \text{ in}^3[/tex]

Step-by-step explanation:

Volume of a Cone Equation:

[tex]v = \frac{1}{3}\times \pi \times r^2 \times h[/tex]

1) Find h

Use the Pythagorean Theorem to find h

[tex]a^2 \times b^2 = c^2[/tex]

Change diameter to radius. (10 in ---> 5in)

a = 5

[tex]1) 5^2 + b^2 = 13^2\\\\2) 25 + b^2 = 169\\\\3) b^2 =144\\\\4) 12[/tex]

Step 2) Subtract 25 on both sides so [tex]b^2[/tex] is alone

Step 3) Square root both sides

Step 4) h = 12

2) Plug in known variables:

h = 12 in

r = 5 in;

Equation now:

[tex]v = \frac{1}{3} \times \pi \times 5^2 \times 12[/tex]

3) Solve:

[tex]1) \frac{1}{3} \times \pi \times 5^2 \times 12\\\\2) \frac{\pi}{3} \times 5^2 \times 12\\\\3) \frac{\pi}{3} \times 25 \times 12 \\\\4) \frac{\pi}{3} \times 300\\\\5) \frac{300\pi}{3} \\\\\text{Simplify:}\\100\pi[/tex]

Answer:

the answer is 5........

Answer: I rechecked and confirmed the answer. The answer is 5.

Answer: 59598

Step-by-step explanation:

It would be 12C2 for the teachers

and 43C2 for the students

12C2=66

43C2=903

66*903=59598

You should invest $139.07 each month to end up with $17,000 in 8 years, assuming a guaranteed APR of 4.5%.

The annual interest rate (also known as the annual percentage rate or APR) is the amount of interest that is charged on a loan or investment over the course of one year.

To calculate the monthly deposit needed to reach the target amount of $17,000 in 8 years at a guaranteed APR of 4.5%, we can use the formula for future value of an annuity:

FV = P * ([tex](1 + r/n)^(n*t)[/tex] - 1) / (r/n)

where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we want to find the monthly payment (P), and we know that:

FV = $17,000

r = 4.5% = 0.045 (decimal)

n = 12 (since we are making monthly deposits)

t = 8

When these values are added to the formula, we obtain:

$17,000 = P * ([tex](1 + 0.045/12)^(12*8)[/tex] - 1) / (0.045/12)

Simplifying and solving for P, we get:

P = $139.07

Therefore, you should invest $139.07 each month to end up with $17,000 in 8 years, assuming a guaranteed APR of 4.5%.

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Answer:

Step-by-step explanation:

the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.

How to solve the probability?

To find the expectation of the game, we need to calculate the probability of winning and losing and multiply them by their corresponding payoffs.

First, let's calculate the probability of rolling a sum of 2 or 12. There is only one way to roll a sum of 2 or 12, which is by rolling a pair of ones or a pair of sixes, respectively. So, the probability of rolling a sum of 2 or 12 is:

P(2 or 12) = P(1,1) + P(6,6) = (1/6) * (1/6) + (1/6) * (1/6) = 1/18

Next, let's calculate the probability of rolling a 7. There are six ways to roll a sum of 7, which are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So, the probability of rolling a 7 is:

P(7) = P(1,6) + P(2,5) + P(3,4) + P(4,3) + P(5,2) + P(6,1) = 6 * (1/6) * (1/6) = 1/6

Finally, the probability of losing is:

P(loss) = 1 - P(2 or 12) - P(7) = 1 - 1/18 - 1/6 = 11/18

Now, we can calculate the expectation of the game as follows:

E(X) = (12 * P(2 or 12)) + (5 * P(7)) - (1 * P(loss))

= (12 * 1/18) + (5 * 1/6) - (1 * 11/18)

= 2/9 + 5/6 - 11/18

= 0.22

So, the expectation of the game is $0.22 per game. This means that on average, for every game played, the player can expect to win $0.22. However, this does not guarantee that the player will actually win $0.22 every time they play the game. It simply means that over many plays of the game, the player's winnings will average out to $0.22 per game.

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The probability that a passenger is traveling for business is 67.1%.

The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.

The probability that a passenger is traveling for business can be calculated by adding the number of passengers traveling for business and dividing by the total number of passengers:

P(traveling for business) = (274 + 397) / 1000 = 0.671

Therefore, the probability that a passenger is traveling for business is 0.671 or approximately 67.1%.

b. The probability of a passenger bringing a laptop on a flight if the passenger is traveling for business can be calculated as follows:

P(laptop | traveling for business) = number of passengers with a laptop and traveling for business / number of passengers traveling for business

P(laptop | traveling for business) = 236 / 671 = 0.352

Therefore, the probability of a passenger bringing a laptop on a flight if the passenger is traveling for business is 0.352 or approximately 35.2%.

c. It should be noted that to determine if there is an association between bringing a laptop on a flight and traveling for business, we can compare the proportion of passengers who bring a laptop when traveling for business versus when not traveling for business. If the proportions are different, it suggests an association.

P(laptop | traveling for business) = 0.352

P(laptop | not traveling for business) = 0.093

The proportions are different, which suggests an association between bringing a laptop on a flight and traveling for business.

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