HELPPP!!!!
What should be reason 2 in the following proof?

We deduced the following from the given phrase:

1) The supplied expression is a sum with the four terms a, b, l, and c.

2) 2c is the result of the factors 2 and c on its own.

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. For each function, there is a corresponding range, codomain, and domain.

What follows is:

A + (b+1) + 2c is the function that has been discovered and written in the question.

As we can see, three distinct terms—a, b+1, and 2c—have been demonstrated to be a part of this function.

As a result, we deduced the following from the above formula:

1) With the four terms a, b, 1 and 2c, the complete equation is a sum.

2) 2c is the result of the factors 2 and c on its own.

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The complete question is:

On its own 2c is a product with

The final answer is:

4C+2D = [28 28]
       [14 26]

To find 4C+2D, we first need to multiply the matrices C and D by their respective scalars, 4 and 2. Then, we add the resulting matrices together.

First, let's multiply matrix C by 4:

4C = 4[5 3] = [20 12]
   [1 2]   [ 4  8]

Next, let's multiply matrix D by 2:

2D = 2[4 8] = [ 8 16]
   [5 9]   [10 18]

Now, we can add the resulting matrices together:

4C+2D = [20 12] + [ 8 16] = [28 28]
       [ 4  8]   [10 18]   [14 26]

So, the final answer is:

4C+2D = [28 28]
       [14 26]

I hope this helps! Let me know if you have any further questions.

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The fraction (4[tex]s^{(6)[/tex])(([tex]t^{(6)[/tex])[tex])^{3}[/tex]  in its simplest form is C. 64[tex]s^{(18)[/tex][tex]t^{(18)[/tex].  

To simplify the given fraction, we need to use the power of a power rule, which states that (a^b)^c = a^(b*c).

In this case, we have (4[tex]s^{(6)[/tex][tex]t^{(6)[/tex])^3 , so we need to multiply the exponents of each term by 3.

For the first term, [tex]4^{(3)[/tex] = 64. For the second term, [tex]s^{(6*3)[/tex] = [tex]s^{(18)[/tex]. And for the third term, [tex]t^{(6*3)[/tex]= [tex]t^{(18)[/tex].

Putting these terms together, we get 64[tex]s^{(18)[/tex][tex]t^{(18)[/tex], which is the correct answer.

So, the simplified form of (4[tex]s^{(6)[/tex])(([tex]t^{(6)[/tex])[tex])^{3}[/tex] is 64[tex]s^{(18)[/tex][tex]t^{(18)[/tex], or answer choice C.

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The value of x and y are 40° and 40° respectively

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

These are the few theorems of circle geometry

1. The angle at the centre is twice the angle at the circumference.

2. The angle in a semicircle is a right angle.

Angles in the same segment are equal.

3. Opposite angles in a cyclic quadrilateral sum to 180°

4. The angle between the chord and the tangent is equal to the angle in the alternate segment.

from triangle AOB,

angle 0 = 60° (opposite angles)

x = 180-( 80+60)

x = 180-140

x = 40°

x= y ( angle in the same segment are equal)

y = 40°

therefore the value of x and y are 40°

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The intersection point on the graph has an approximate x-value of 1a.

Making the curve that represents a function on a coordinate plane is the process of graphing a function. If the curve (or graph) represents the function, then each point on the curve will satisfy the function equation.

The line, also called the "curve," has a point at each point that fulfils the function.

The three lines are contemporaneous if they all cross at the same point.

From the second equation,

x = 8y + 19

Putting value of x,

2(8y + 19) + 3y = 0                              9(8y + 19) + 5y = 17

16y + 38 + 3y = 0                                 72y + 171 + 5y = 17

19y = -38                                                77y = -154

 y = -2                                                      y = -2

You'll see that the y value for the answer is the same for the two equations. Simply evaluate the second equation now to find x. Hence, we are aware that the y-coordinate is negative two at some x number.

x = 8(-2) + 19

x = -16 + 19

x = 3

The single point that these three equations share is (3, -2).

4x - 3y = 13                     eq1

-6x + 2y = -7                   eq2

Use the elimination method. Multiply eq1 by eq2 and multiply eq2 by eq3.

8x - 6y = 26                eq1

-18 + 6y = -21              eq2

Adding the equations to eliminate the y terms.

-10x = 5

 x = -1/2

Substituting this value of x into any of the equations to solve for the value of y.

Substituting the first equation into the second equation. In terms of x, this will translate the second equation. From that freshly created equation, find x. Once you solved for x, substitute that value of x into the first equation to solve for y.

You have a vertical line that passes all points that have the x coordinate 7 and you have a horizontal line that passes all point that have the y coordinate -5.

If you were to graph these two lines, they will be intersecting at (7, -5).

Now, draw the following lines on a coordinate system:

i) A vertical line passing through the points (3, 0).

ii) A horizontal line passing through the point (0, 6).

iii) A line passing through the points (0,0) and (1, -3).

Once you have drawn these lines, look for 3 points of intersection.

Area = (base × height) / 2

Lines that have the same slope never intersect.  Put both equations in y=mx+b  form where the slope is the coefficient of x.

2x + 3y = > 3y = -2x + 23

y = (-2 / 3) x + 23/3

7x + py = 8

py = -7x + 8

y = (-7 / p) x + 8/p

Set the slopes equal to each other.

-2 / 3 = -7 / p

Cross-multiply.

-2p = -21

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There are a total of 28 different 3-digit numbers that can be formed from the numbers 1,3,5,7,9 if each number formed is greater than 300. This can be found by using the formula for distinguishable permutations.

There are a total of 5 different 3-digit numbers that can be formed from the numbers 1,3,5,7,9 if each number formed is greater than 300. These numbers are 315, 357, 375, 397, and 359. This can be found by using the formula for distinguishable permutations, which is n!/(n-r)!, where n is the total number of items and r is the number of items chosen. In this case, n is 5 (the numbers 1,3,5,7,9) and r is 3 (the number of digits in each number formed).

The formula for distinguishable permutations is:

n!/(n-r)!

= 5!/(5-3)!

= 120/2

= 60

Therefore, there are a total of 60 different 3-digit numbers that can be formed from the number 1,3,5,7,9. However, we need to subtract the numbers that are less than 300, which are the numbers formed from the digits 1 and 3 in the hundreds place. There are 2 numbers in the hundreds place (1 and 3) and 4 numbers in the tens and ones place (3,5,7,9), so there are a total of 2*4*4 = 32 numbers less than 300. Subtracting these from the total gives us:

60 - 32 = 28

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The equation of the line through the points (-3,7) and (2, 17) is y = 2x + 13.

To find the equation of the line through the points (-3,7) and (2, 17), we need to first find the slope of the line and then find the y-intercept.

Step 1: Find the slope of the line
The slope of a line is given by the formula:
m = (y2 - y1)/(x2 - x1)
Where (x1, y1) and (x2, y2) are the two points on the line.

Plugging in the given points, we get:
m = (17 - 7)/(2 - (-3))
m = 10/5
m = 2

Step 2: Find the y-intercept
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We can plug in one of the given points and the slope we found to solve for b.

Using the point (-3,7), we get:
7 = 2(-3) + b
7 = -6 + b
b = 13

Step 3: Write the equation in slope-intercept form
Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:
y = 2x + 13

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Answer:

y=2x+3

Step-by-step explanation:

Using the point-slope form of the equation of a line, we can write:

y - 9 = 2(x - 3)

Simplifying, we get:

y - 9 = 2x - 6

y = 2x + 3

Therefore, the equation of the line that is parallel to y=2x+1 and goes through the point (3,9) is y=2x+3.

parallel → the same slope

slope: y = 2x +1 → m = 2

y=2x+3 ⇔ 2(3)+3=6+3=9

y=2x+9 ⇔ 2(3)+9=6+9=15≠9

⇒ answer: y=2x+3

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is 0.478

This probability problem can be solved using the binomial distribution. In this case, the probability of success is 0.40 (since 40% of consumers believe that cash will be obsolete), and the number of trials is 7 (since we are selecting 7 consumers).

To find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete, we need to find the probability of getting 0, 1, or 2 successes. We can use the binomial probability formula to calculate each of these probabilities and then add them together:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Where X is the number of consumers who believe that cash will be obsolete, and P(X) is the probability of getting X successes.

The probability of getting exactly X successes in a binomial distribution with probability of success p and number of trials n is given by the formula:

P(X) = (n CX) * p^X * (1 - p)^(n - X)

Where (nCX) represents the number of ways to choose X successes from n trials, and is calculated using the binomial coefficient formula:

(nCX) = n! / (X! * (n - X)!)

Where n! represents the factorial of n, which is the product of all positive integers up to and including n.

Using this formula, we can calculate the probabilities of getting 0, 1, and 2 successes as follows:

P(X = 0) = (7C0) * 0.40^0 * 0.60^7 = 0.028

P(X = 1) = (7C1) * 0.40^1 * 0.60^6 = 0.15

P(X = 2) = (7C2) * 0.40^2 * 0.60^5 = 0.30

Thus, the probability of getting fewer than 3 successes is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.028 + 0.15 + 0.30 = 0.478

Hence, the probability is 0.478.

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We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

Which nation experienced the hottest summer?

We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.

Country A: (21.4°C) (18+20+22+23+24)/5

(24+26+28+29+27)/5 = 26.8°C for Country B.

The summer was therefore hotter in Country B, with an average temperature of 26.8°C.

b) Over the summer, which nation saw more erratic weather?

We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.

24°C - 18°C equals 6°C in Country A.

29°C - 24°C equals 5°C in country B.

As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

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The correct interval for the area of triangle PQR is 2 <= A < 4.

To find the correct interval for the area of triangle PQR, we first need to calculate the area using the given points. We can do this by using the formula for the area of a triangle in three dimensions:

A = (1/2) * sqrt((x2*y3 - x3*y2)^2 + (x3*y1 - x1*y3)^2 + (x1*y2 - x2*y1)^2)

Plugging in the given points for P, Q, and R, we get:

A = (1/2) * sqrt((1*3 - 3*0)^2 + (3*0 - 0*1)^2 + (0*0 - 1*3)^2)

Simplifying, we get:

A = (1/2) * sqrt(9 + 9)

A = (1/2) * sqrt(18)

A = (1/2) * 3 * sqrt(2)

A = (3/2) * sqrt(2)

A = 2.12

Therefore, the correct interval for the area of triangle PQR is 2 <= A < 4. The correct answer is option b. 2 <= A < 4.

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Answer: 90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

[tex]\cfrac{1}{3}(9x+12)=15\implies \cfrac{9x+12}{3}=15\implies 9x+12=45 \\\\\\ 9x=33\implies x=\cfrac{33}{9}\implies x=\cfrac{3}{3}\cdot \cfrac{11}{3}\implies x=\cfrac{11}{3}\implies x=3\frac{2}{3}[/tex]

The domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0

The domain and range of a function are the set of possible inputs and outputs, respectively.

1. For the function \( f(x)=3 x^{2}+2 \), the domain is all real numbers because there are no restrictions on the input. The range is also all real numbers because the output can be any value.

2. For the function \( f(x)=\frac{1}{1-x} \), the domain is all real numbers except x=1, because when x=1, the denominator becomes 0 and the function is undefined. The range is also all real numbers except y=0, because the output can never equal 0.

3. For the function \( f(x)=\sqrt{x+2} \), the domain is all real numbers greater than or equal to -2, because the square root of a negative number is not a real number. The range is all real numbers greater than or equal to 0, because the square root of a number is always positive or 0.

In conclusion, the domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0

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The wind generator will produce 2744W of power in a 35mph wind.

To find the power generated by the wind generator in a 35mph wind, we can use the formula P = kV³, where P is the power generated, k is a constant, and V is the wind's speed.

First, we need to find the value of k. We can do this by plugging in the given values of P and V into the formula and solving for k:

1000W = k(25mph)³ 1000W = k(15625mph³)

k = 1000W/15625mph³

k = 0.064W/mph³

Now that we have the value of k, we can plug it back into the formula along with the new wind speed of 35mph to find the power generated:

P = (0.064W/mph³)(35mph)³

P = (0.064W/mph³)(42875mph³)

P = 2744W

Therefore, the wind generator will produce 2744W of power in a 35mph wind.

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Answer:

9/10

Step-by-step explanation:

Find a common denominator

4/5 × 2 = 8/10

8/10 + 1/10 = 9/10

Hey there!

4/5 + 1/10

= 4 × 2 / 5 × 2 + 1/10

= 8/10 + 1/10

= 8 + 1 / 10 + 0

= 9/10

Therefore, your answer should be:

9/10

Good luck on your assignment \& enjoy your day!

~Amphitrite1040:)

Based on the data showing the ordered pairs of a linear function, we can find the slope of the line, which will be: 2.4. The closest correct option is letter c.

We need to use the following formula to find the intended result:

Slope = (change in y) / (change in x)

To calculate slope, we can pick any two points from the table. Choosing the points (0, -9) and (10, 15) we have:

Therefore, using two points from the table, we find that the slope of the line is 2.4. The option c) 2.1 is the closest to the result.

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If the constant of variation is 12 and y = 36 and they vary directly, then x equals 3.

Direct variation is when two quantities, x and y, are related in such a way that the ratio of their values is always the same. This means that y = kx, where k is the constant of variation.

In this case, we are given that k = 12 and y = 36. We can plug these values into the equation to find x:

36 = 12x

To solve for x, we can divide both sides of the equation by 12:

36/12 = 12x/12

This simplifies to:

3 = x

Therefore, x equals 3.

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Answer:

Area of a circle = πr²

Plug in values (radius is half of the diameter so radius = 8)

π8² = 64π ≈ 201.0619 feet (rounded to four decimal places)

Hope this helps!

On a given day where the price of the stock is 2900AED, the stock broker should sell the stock.

The stock broker should sell the stock if the price is in the top 4% range. To determine if the price of 2900AED is in the top 4% range, we need to calculate the z-score and compare it to the z-score for the top 4% range.

The z-score formula is:
z = (x - μ) / σ

Where:
x = the value we are interested in (2900AED)
μ = the mean (2540AED)
σ = the standard deviation (150AED)

Plugging in the values, we get:
z = (2900 - 2540) / 150
z = 360 / 150
z = 2.4

The z-score for the top 4% range is 1.75. Since the z-score of 2.4 is greater than 1.75, the price of 2900AED is in the top 4% range. Hence, he should sell the stocks.

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The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , let the first equation be p

p = 3x⁴ - 8x² - 11x + 1

Let the second equation be q

q = ( x - 2 )

And , the value of A = p/q

On simplifying , we get

A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )

From the long division of polynomials , we get

Step 1 :

A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]

The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²

Step 2 :

A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]

Step 3 :

A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]

Step 4 :

A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

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The linear velocity of the bicycle is approximately 6.68 miles per hour.

a) The angular velocity of the wheel can be found by using the formula:
ω = v / r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the wheel.
In this case, v = 115 m/sec and r = (8 cm / 2) = 4 cm = 0.04 m.
So, the angular velocity of the wheel is:
ω = (115 m/sec) / (0.04 m) = 2875 radian per second.

b) The linear velocity of the bicycle can be found by using the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
In this case, ω = 125 revolutions per minute = (125 * 2π) / 60 = 13.09 radian per second and r = (18 inches / 2) = 9 inches = 0.75 feet.
So, the linear velocity of the bicycle is:
v = (13.09 radian per second) * (0.75 feet) = 9.82 feet per second.
To convert this to miles per hour, we can use the conversion factor 5280 feet = 1 mile:
v = (9.82 feet per second) * (60 seconds / 1 minute) * (60 minutes / 1 hour) * (1 mile / 5280 feet) = 6.68 miles per hour.
So, the linear velocity of the bicycle is approximately 6.68 miles per hour.

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To solve this problem, we can use a system of equations. Let's represent the amount invested in stocks as x, the amount invested in bonds as y, and the amount invested in CDs as z.

The first equation we can create is the total amount invested:

x + y + z = 85000

The second equation is the difference between the amount invested in bonds and CDs:

y - z = 20000

The third equation is the total interest earned:

0.064x + 0.052y + 0.055z = 4780

We can use substitution to solve this system of equations. Let's rearrange the second equation to solve for y:

y = z + 20000

We can then substitute this value of y into the first equation:

x + (z + 20000) + z = 85000

Simplifying gives us:

x + 2z = 65000

Now, let's substitute the value of y into the third equation:

0.064x + 0.052(z + 20000) + 0.055z = 4780

Simplifying gives us:

0.064x + 0.107z = 3780

We can now use the first and third equations to solve for x and z. Let's rearrange the first equation to solve for x:

x = 65000 - 2z

We can then substitute this value of x into the third equation:

0.064(65000 - 2z) + 0.107z = 3780

Simplifying gives us:

4160 - 0.128z + 0.107z = 3780

Combining like terms gives us:

-0.021z = -380

Solving for z gives us:

z = 18095.24

We can now use this value of z to solve for y:

y = z + 20000 = 18095.24 + 20000 = 38095.24

And finally, we can use the value of z to solve for x:

x = 65000 - 2z = 65000 - 2(18095.24) = 28809.52

So, Maricopa Success invested $28809.52 in stocks, $38095.24 in bonds, and $18095.24 in CDs.

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The area of the sign is 35 square feet. The solution has been obtained by using the area of the trapezoid.

The entire area occupied by the sides of a trapezoid is its area. A trapezoid's area is determined by how many unit squares fit inside of it.

We know that area of the trapezoid is

Area (A) = (a + b ) * h/ 2

Now, here we are given the following:

a = 8

b = 6

h = 5

Now, on substituting these values in the formula, we get

⇒A = (8 + 6 ) * 5 / 2

⇒A = (14 * 5) / 2

⇒A = 70 / 2

⇒A = 35 square feet

Hence, the area of the sign is 35 square feet.

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The two statements that are correct include the following:

B. s is inversely proportional to t.

C. s is directly proportional to 1/t.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Additionally, an inverse variation can be modeled by this mathematical expression:

s ∝ 1/t

s = k/t

Where:

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The value of x is approximately 7.21 and the side lengths do not form a pythagorean triple.

The figure in the image is a right traingle.

We can use the Pythagorean theorem to solve for the missing leg of the right triangle:

a² + b² = c²

Where a and b are the legs of the triangle and c is the hypotenuse.

Plugging in the given values, we get:

12² + b² = 14²

144 + b² = 196

Subtracting 144 from both sides:

b² = 52

Taking the square root of both sides:

b = 7.21

Therefore, the second leg of the right triangle is approximately 7.21 units long.

This is not a Pythagorean triple because the three sides (12, 7.21, and 14) do not form a set of integers that satisfy the Pythagorean theorem.

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We can conclude that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, as shown in the diagram.

What are the attributes of a good conclusion?

The key argument raised throughout the argument's discussion must be summarized in the good conclusion.

a. In below diagram, each city is represented by a point, and the distances between the cities are shown as line segments with the distance in miles labeled above the segment. The distances are labeled in the order in which they appear in the diagram, so for example, the distance between Kadoka and Rapid City is labeled as 96 because that is the distance between the two cities as you move from Kadoka to Rapid City.

b. To support the conclusion that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, we can use the distances given in the problem to show that it is possible to travel from any one city to any other city using only Interstate 90.

First, we note that Kadoka is connected to Rapid City by Interstate 90, because the distance between them is given as 96 miles and no other route is mentioned. Similarly, Rapid City is connected to Alexandria by Interstate 90, because the distance between them is given as 292 miles and no other route is mentioned.

Finally, to show that Alexandria is connected to all the other cities by Interstate 90, we note that the distance between Alexandria and Rapid City is given as 292 miles, and the only way to travel between the two cities is on Interstate 90. Also, since Kadoka is connected to Rapid City by Interstate 90 and Rapid City is connected to Alexandria by Interstate 90, it follows that Kadoka is connected to Alexandria by Interstate 90.

Therefore, we can conclude that Kadoka, Rapid City, Sioux Falls, and Alexandria are all connected by Interstate 90, as shown in the diagram.

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The correct statement about the functions f(x) and g(x) include the following: B. f(x) has a steeper slope than g(x).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m of g(x) = (1 - (-3))/(0 - (-2))

Slope, m of g(x) = 4/2

Slope, m of g(x) = 2.

Slope of f(x) = 3. Therefore, 3 is greater than 2.

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