The graph of a polynomial function continues down on the left and continues up on the right. Which of the following must be true about this polynomial function?
a The function is even, with a positive leading coefficient. b The function is odd, with a positive leading coefficient. c The function is even, with a negative leading coefficient. d The function is odd, with a negative leading coefficient.

The required measure of q in the given triangle is 3.

Trigonometric ratios are mathematical functions used to relate the angles of a right-angled triangle to the lengths of its sides. There are three basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan), which can be defined as follows:

Sine (sin) = opposite/hypotenuse

Cosine (cos) = adjacent/hypotenuse

Tangent (tan) = opposite/adjacent

Here,
Applying the Sine rule,
sin45 = q/3√2
q = 3

Thus, the required measure of q in the given triangle.

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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 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 measure of angle ABC is 64°.

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

Given that, BM bisects ∠ABC and ∠MBC=32°.

Here, ∠ABC=∠MBC+∠MBA

Since, BM bisects ∠ABC, ∠MBC=∠MBA

∠ABC=∠MBC+∠MBC

∠ABC=2∠MBC

∠ABC=2×32°

∠ABC=64°

Therefore, the measure of angle ABC is 64°.

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By the concept of vertically opposite angles, m∠MDH = 44°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know, Pair of vertically opposite angles are equal.

Therefore, 2y + 130 = 3y + 127.

y = 3.

So, 2y + 130 = 136°

Again, ∠PDG = ∠MDH.

Now, 2∠PDG = 360° - 2(136°)

2∠PDG = 360° - 272°.

∠PDG = 44° = ∠MDH.

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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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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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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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It will take approximately 2.9 years (or 2 years and 11 months) for the $2500 investment to earn $400 interest at a rate of 8% compounded quarterly.

A = [tex]P(1 + r/n)^{nt}[/tex]

Where:

A = the total amount that includes principal and interest, P = the principal that is the initial amount invested, r = the annual interest rate, n = the number of times is the interest is compounded per year, and t = the time

$2900 = [tex]$2500(1 + 0.08/4)^{4t}[/tex]

Simplifying this equation, we get:

1.16 = (1 + 0.02

By calculating the natural logarithm of both sides, we arrive at:

ln(1.16) = 4t ln(1.02)

t ≈ 2.9 years

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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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The answer is yes, more than one triangle can be formed using the three angle measures of triangle QPC. This is because the sum of the three angle measures of a triangle is always equal to 180 degrees.

A triangle is a three-sided geometric figure, consisting of three straight lines connecting three vertices. It is one of the most fundamental shapes in geometry and is used as the basis for a variety of mathematical concepts.

If two angle measures are given, any third angle measure between 0 and 180 degrees can be chosen to form a triangle. Thus, if two angle measures of triangle QPC are given, any third angle measure between 0 and 180 degrees can be used to form a triangle.

For example, if two angle measures of triangle QPC are 45 degrees and 65 degrees, then any third angle measure between 0 and 180 degrees can be chosen to form a triangle. Thus, if the third angle measure chosen is 70 degrees, then a triangle with three angle measures of 45 degrees, 65 degrees and 70 degrees can be formed. Similarly, if the third angle measure chosen is 30 degrees, then a triangle with three angle measures of 45 degrees, 65 degrees and 30 degrees can be formed.

Thus, it can be concluded that more than one triangle can be formed using the three angle measures of triangle QPC.

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Answer:

La cofunción del seno de un ángulo es igual al coseno de su complemento. Similarmente, la cofunción del coseno de un ángulo es igual al seno de su complemento.

Entonces, para encontrar la cofunción de sec(y-π), primero encontramos el complemento de (y-π), que es (π/2 - (y-π)) = (π/2 - y + π) = (3π/2 - y).

Por lo tanto, la cofunción de sec(y-π) es igual al coseno de su complemento, que es el coseno de (3π/2 - y):

cos(3π/2 - y) = -sin(y)

Entonces, la cofunción de sec(y-π) es igual a -sin(y).

Answer:

The height of the building is approximately 55 meters.

Step-by-step explanation:

Let's call the height of the building "h" and the distance from point P to the foot of the building "d".

According to the problem, we have:

d = 50m

T = 23.6m

Using the Pythagorean theorem, we know that:

h^2 = T^2 + d^2

Substituting the values we have:

h^2 = (23.6m)^2 + (50m)^2

h^2 = 556.96m^2 + 2500m^2

h^2 = 3056.96m^2

Taking the square root of both sides, we get:

h = sqrt(3056.96m^2)

h = 55.28m

Rounding to the nearest meter, we get:

h ≈ 55m

Therefore, the height of the building is approximately 55 meters.

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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We can plot the two points (-2, 3) and (0, 4) and draw a straight line passing through both points. The resulting line has a slope of 1/2 and y-intercept of 4.

Graphs are used to help people understand and interpret information in a way that is easy to see and analyze. There are many different types of graphs, each with its own characteristics and applications.

Some common types of graphs include:

Line graph: A line graph displays data as a series of points connected by lines, typically used to show trends or changes over time.

Bar graph: A bar graph displays data as bars of different heights, typically used to compare values or quantities.

Pie chart: A pie chart displays data as a circle divided into slices, typically used to show proportions or percentages.

To find the y-coordinate for each x-coordinate, we can substitute each value of x into the equation y = (1/2)x + 4 and simplify:

When x = -2:

y = (1/2)(-2) + 4

y = -1 + 4

y = 3

So, the point (-2, 3) is on the line.

When x = 0:

y = (1/2)(0) + 4

y = 0 + 4

y = 4

So, the point (0, 4) is on the line.

We can complete the table as follows:

x y = (1/2)x + 4 y

-2 y = (1/2)(-2) + 4 3

0 y = (1/2)(0) + 4 4

To graph the line, we can plot the two points (-2, 3) and (0, 4) and draw a straight line passing through both points. The resulting line has a slope of 1/2 and y-intercept of 4.

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To find the minimum final score you need to get a 77%,

you can use the following formula:
(weight of weighted grade * weighted grade) + (weight of final * final grade) = desired overall grade
Plug in the given values:
(0.65 * 89) + (0.35 * final grade) = 77
Solve for the final grade:
57.85 + 0.35 * final grade = 77
0.35 * final grade = 19.15
final grade = 19.15 / 0.35
final grade = 54.71

Therefore, the minimum final score you need to get a 77% overall is 54.71%.

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Answer: Explanation below

Step-by-step explanation:

R4000 is the money to be split

5:3:2 is the ratio

We can add the ratios together.

5+3+2=10

The first winner = 5/10 x 4000

                           = R2000

The second winner = 3/10 x 4000

                                 = R1200

The third winner = 2/10 x 4000

                             = R800

Hope this helped :)

a) The null and alternative hypotheses are:
H0: µ1 = µ2
Ha: µ1 ≠ µ2

b) The test statistic is:
t = 0.117

c) The P-value is:
P-value = 0.9072

To test the null hypothesis at α= 0.05 using the pooled t-test, we need to follow these steps:

Step 1: Choose the null and alternative hypotheses. The null hypothesis is that the mean page views per visit for website 1 are equal to the mean page views per visit for website 2. The alternative hypothesis is that the mean page views per visit for website 1 are not equal to the mean page views per visit for website 2.

H0: µ1 = µ2
Ha: µ1 ≠ µ2

Step 2: Calculate the test statistic. The test statistic for the pooled t-test is given by:

t = (y1 - y2) / (sp * √(1/n1 + 1/n2))

where sp is the pooled standard deviation, given by:

sp = √(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

sp = √(((70 - 1) * 4.9^2 + (90 - 1) * 5.4^2) / (70 + 90 - 2)) = 5.178

t = (7.5 - 7.4) / (5.178 * √(1/70 + 1/90)) = 0.117

Step 3: Calculate the P-value. The P-value is the probability of observing a test statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true. We can use a t-distribution table or a calculator to find the P-value. The degrees of freedom for the pooled t-test are n1 + n2 - 2 = 70 + 90 - 2 = 158.

Using a t-distribution table or a calculator, we find that the P-value is 0.9072.

Step 4: Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. There is not enough evidence to suggest that the mean page views per visit for website 1 are different from the mean page views per visit for website 2.

Thus:

a) The null and alternative hypotheses are:
H0: µ1 = µ2
Ha: µ1 ≠ µ2

b) The test statistic t = 0.117

c) The P-value = 0.9072

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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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Subtraction of  the polynomials using the horizontal format (3x³ + x² + 2) from 7x³- x - 8 is 4x³ - x² - x - 10.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

To subtract the polynomials using the horizontal format, we will first write the two polynomials next to each other with the subtraction sign in between, then subtract the corresponding terms.

7x³- x - 8 - (3x³ + x² + 2)

Next, we will distribute the negative sign to each term inside the parentheses:

7x³ - x - 8 - 3x³- x²- 2

Now we will combine like terms:

4x³ - x² - x - 10

So, the final answer is 4x³ - x² - x - 10.

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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!

The domain of f cannot include any values of x that make the equation x^(2)-4x-12=0 true. This is because if x satisfies this equation, then the denominator of the function f(x) will be zero, which is not allowed in a function's domain.

To find the values of x that satisfy this equation, you factored it to get (x+2)(x-6)=0. Now you can use the Zero Product Property to find the values of x that make each factor equal to zero.

For the first factor, x+2=0, we can solve for x by subtracting 2 from both sides to get x=-2. For the second factor, x-6=0, we can solve for x by adding 6 to both sides to get x=6.

So the values of x that satisfy the equation and are not included in the domain of f are x=-2 and x=6.

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The equation that relates the total number of visits to the number of days the promotion has been running is v = 96 × [tex]2^{\frac{d}{5} }[/tex] .

When an equal sign connects two expressions then, it is called an equation.

According to the question, the total number of visits doubled after every 5 days.

So, after 5 days visits= 96×2

After 10 days visits= 96×2×2

After 15 days visists= 96×2×2×2

Therefore, it is a proportional sequence.

Hence, the equation that relates the total number of visits, v, to the number of days the promotion has been running, d comes out to be:

v = 96 × [tex]2^{\tfrac{d}{5} }[/tex]

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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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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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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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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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