+
ent will
A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
+
Dillon says to write the equation of the tangent line you need the opposite-reciprocal
slope of the slope of the radius and Chelsey says you need to use the same slope as
the radius. Who is correct and why? Write the equation of the tangent line.
Part B: Find the perimeter of BCDE.
Part C: Find the area of BCDE.
Part D: Prove BCDE is a square.

1. The second party has more pizza in terms of area

2. The width of the track is approximately 3.50 cm.

1. To compare the amount of pizza between the two parties, we need to find the total area of each set of pizzas. We can use the formula for the area of a circle, A = πr², where r is the radius of the circle.

For the large pizzas, the diameter is 16 inches, so the radius is 8 inches. The area of one pizza is:

A = π(8)²

A = 64π square inches

Since there are 5 pizzas, the total area of pizza for the first party is:

Total area = 5(64π) = 320π square inches

For the small pizzas, the diameter is 12 inches, so the radius is 6 inches. The area of one pizza is:

A = π(6)²

A = 36π square inches

Since there are 9 pizzas, the total area of pizza for the second party is:

Total area = 9(36π) = 324π square inches

Therefore, the second party has more pizza in terms of area.

2. We can start by finding the length of the arc of the sector. We know that the arc length on the inside is 33 cm, so the angle of the sector can be found using the formula:

angle = (arc length / radius)

angle = (33 / 6) radians

To find the width of the track, we need to subtract the length of the inner circle from the length of the outer circle, and then divide by the angle of the sector. Let's call the width of the track "x". Then we have:

55 cm - 33 cm = 2π(6 cm + x) - 2π(6 cm)

22 cm = 2πx

x = 11 / π cm

So the width of the track is approximately 3.50 cm.

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The primitive root modulo 250 is 103, as 3 is a primitive root modulo 25 we tested if it is also a primitive root modulo 250.

To find a primitive root modulo 250, we need to first factor 250 as 2 x 5³. Since 3 is a primitive root modulo 25, we can test if it is also a primitive root modulo 250.

Using Euler's totient function, we know that [tex]\phi(250)[/tex] = 100. Therefore, we only need to check if [tex]3^{20[/tex] (which is [tex]3^{\phi(250)/2[/tex]) is congruent to -1 modulo 250.

Calculating [tex]3^{20[/tex] modulo 250 gives us 1. Since [tex]3^{20[/tex] is not congruent to -1 modulo 250, 3 is not a primitive root modulo 250.

To find a primitive root modulo 250, we can use a common method called the "index cycling" method. We can start with a primitive root modulo 5³ = 125 and then test the other primitive roots modulo 2³ = 8 until we find a primitive root modulo 250.

Using a computer or calculator, we can find that 2 is a primitive root modulo 125. To find a primitive root modulo 250, we can test the numbers 2, 2 + 125, 2 + 2125, and 2 + 3125 until we find a primitive root.

Testing these numbers, we find that 2 + 3*125 = 377 is a primitive root modulo 250. Therefore, 377 is a primitive root modulo 250.

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Ion has a total of $4,378.05 in his savings account at the end of 3 years.

To solve this problem, we need to use the formula for compound interest:

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

Where:

A = the total amount of money in the account at the end of the time period

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

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

t = the time period (in years)

In this case, we have:

P = $120

r = 0.029 (2.9% expressed as a decimal)

n = 12 (compounded monthly)

t = 3 (years)

We also need to calculate the total number of deposits made during the 3-year period. Since a deposit of $120 is made at the end of every month, and there are 12 months in a year, the total number of deposits made is:

12 deposits/year × 3 years = 36 deposits

Now we can plug in the values into the formula:

A = [tex]120(1 + 0.029/12)^(12 × 3) + 120[(1 + 0.029/12)^(12 × 3) - 1]/(0.029/12)[/tex]

A = $4,378.05

Therefore, Ion has a total of $4,378.05 in his savings account at the end of 3 years.

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The number of triangles that can be formed using 14 points in a plane such that 4 points are collinear is 360.

If 4 points are collinear, then we can choose any 3 of those points to form a line segment, which cannot be extended to form a triangle.

we need to choose 3 points from the 14 points such that no 3 of them are collinear.

The number of triangles that can be formed from n non-collinear points in a plane is given by the formula:

                  C(n,3) = n(n-1)(n-2)/6

where C(n,3) is the binomial coefficient for choosing 3 items out of n.

So, to find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear,

we first need to find the number of ways to choose 3 points from 14 points, and then subtract the number of ways to choose 3 points from the 4 collinear points.

That is:

Total number of triangles = C(14,3) - C(4,3)

Total number of triangles = 364 - 4

Total number of triangles  = 360

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The length of the shorter diagonal is approximately 7.07 units.

A rhombus is a four-sided polygon in which all sides are equal in length. It is also called a diamond shape because it is often used for diamond-shaped figures. In this case, we are given that the perimeter of the rhombus is 88. Since all sides of the rhombus are equal, we can divide the perimeter by 4 to find the length of one side.

88 ÷ 4 = 22

Therefore, each side of the rhombus measures 22 units.

We are also given that two of the angles in the rhombus are acute angles measuring 40° each. Since all angles in a rhombus are equal, we can find the measure of the other two angles by subtracting the sum of the acute angles from 360.

360 - 2(40) = 280

Each of the other two angles measures 140°.

To find the length of the shorter diagonal, we can use the formula:

Shorter diagonal = (2 × Area) / Length of longer diagonal

The area of a rhombus can be found by multiplying the length of the longer diagonal by the length of the shorter diagonal and then dividing by 2.

Area = (diagonal1 × diagonal2) / 2

We know that the longer diagonal is twice the length of the shorter diagonal.

Longer diagonal = 2 × Shorter diagonal

Substituting these values into the formula, we get:

Shorter diagonal = (2 × (22 × Shorter diagonal × sin 40°)) / (2 × Longer diagonal)

Simplifying, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / Longer diagonal

Plugging in the values we know, we get:

Shorter diagonal = (22 × Shorter diagonal × sin 40°) / (2 × Shorter diagonal)

Shorter diagonal = 11 × sin 40°

Using a calculator, we can find that:

Shorter diagonal ≈ 7.07

Therefore, the length of the shorter diagonal is approximately 7.07 units.

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The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:

To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2

These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.

The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.

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Answer:

Yes, there is evidence at the 10% significance level, but not at the 5% level

Step-by-step explanation:

Look at the p-value in bottom left corner (in the Height row).

It is less than 0.1, but greater than 0.05. Thus, Yes, there is evidence at the 10% significance level, but not at the 5% level. Got it right.

If Sarah uses 3/4 yard of ribbon to make a hair bow, she will need 6 and 3/4 yards of ribbon to make 9 hair bows.

To find out how many yards of ribbon Sarah will use to make 9 hair bows, we need to multiply the amount of ribbon used for one hair bow (3/4 yard) by the number of hair bows she wants to make (9).

So, the equation we need to use is:

3/4 yard of ribbon per hair bow x 9 hair bows = ? yards of ribbon

To solve for the answer, we can simplify the equation:

3/4 x 9 = 27/4

So Sarah will need 27/4 yards of ribbon to make 9 hair bows.

To convert this fraction to a mixed number, we can divide the numerator (27) by the denominator (4) and write the remainder as a fraction:

27 ÷ 4 = 6 with a remainder of 3

In summary, Sarah will need 6 and 3/4 yards of ribbon to make 9 hair bows, if she uses 3/4 yard of ribbon to make one hair bow.

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It will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.

To find the amount of total time it will take Keshia to complete the entire worksheet at the same pace, we can use a proportion:

20 problems / 25 minutes = 50 problems / x minutes

To solve for x, we can cross-multiply and simplify:

20 problems * x minutes = 25 minutes * 50 problems

20x = 1250

x = 1250 / 20

x = 62.5

Therefore, it will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.

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The expected value of the sale is $13,000.

The expected value is a statistical measure that represents the average outcome of a probability distribution, weighted by the probabilities of each outcome. In this case, the investor is planning to sell a property and wants to know what the expected value of the sale will be. To determine this value, we must consider the potential outcomes and their probabilities.

According to the real estate consulting firm, there is a 50% chance of making a profit of $50,000, a 30% chance of breaking even, and a 20% chance of suffering a $60,000 loss. To calculate the expected value of the sale, we multiply the potential profit or loss by the probability of each outcome occurring and then sum those products.

To determine the expected value of the sale, we need to multiply the potential profit or loss by the probability of each outcome occurring and then sum those products.

Expected value = (0.5 * $50,000) + (0.3 * $0) + (0.2 * -$60,000)

Expected value = $25,000 - $12,000

Expected value = $13,000

Therefore, the expected value of the sale is $13,000.

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Answer:

  (C)  Neither

Step-by-step explanation:

You want to know if the function values in the table represent an even function, and odd function, or neither.

An Even function is symmetrical about the y-axis:

  f(-x) = f(x)

An Odd function is symmetrical about the origin:

  f(-x) = -f(x)

The attached graph of the given points shows the function has no symmetry at all.

The table represents neither an even nor odd function.

Answer:

Neither

Step-by-step explanation:

In an even function, f(x) = f(-x).

Look at x = 2 and x = -2.

f(2) = -4; f(-2) = 2

Since f(2) ≠ f(-2), the function is not even.

In an odd function, f(x) = -f(-x).

Look at f(2) and f(-2).

f(2) = -4; f(-2) = 2

Since f(2) ≠ -f(-2), the function is not odd.

Answer: C  Neither

The solution of the system of equation

x = 8 and y = 17

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation by substitution method.

Therefore,

y = 49 - 4x

y = 73 - 7x

Hence, using substitution,

73 - 7x = 49 - 4x

73 - 49 = -4x + 7x

24 = 3x

divide both sides of the equation by 3

x = 24 / 3

x = 8

Therefore,

y = 73 - 7(8)

y = 73 - 56

y = 17

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Answer:

C) 6

Step-by-step explanation:

n=6

6( 6 + 1) + 3 =45

36 + 6 + 3 = 45

36 + 9 = 45

A total number of 59.6001 tiles (approximately 60 tiles) are needed to complete the tiling for the kitchen and bathroom.

To calculate the total area that needs to be tiled, we'll start by converting the given dimensions from millimeters to meters:

Bathroom Inner Dimensions:

Length = 6030 mm = 6.03 m

Width = 5130 mm = 5.13 m

Bathroom Outer Dimensions (including bedroom areas):

Length = 12330 mm = 12.33 m

Width = 4680 mm = 4.68 m

Kitchen Dimensions:

Length = 6030 mm = 6.03 m

Width = 5130 mm = 5.13 m

Total area to be tiled in the bathroom (excluding the bath area):

Area = Length x Width = 6.03 m x (5.13 m - 0.86 m) = 6.03 m x 4.27 m = 25.7701 m²

Total area to be tiled in the kitchen:

Area = Length x Width = 6.03 m x 5.13 m = 30.9919 m²

Total area to be tiled (bathroom + kitchen):

Total Area = 25.7701 m² + 30.9919 m² = 56.762 m²

To account for breakages, we need to purchase 5% more tiles. So, the total number of tiles needed is:

Total Number of Tiles = Total Area x 1.05 (to account for 5% extra)

Total Number of Tiles = 56.762 m² x 1.05 = 59.6001 tiles

The building manager stated that 150 tiles are needed. Comparing this with our calculation:

150 tiles < 59.6001 tiles

Therefore, the statement made by the building manager is not valid. According to our calculations, a total of 59.6001 tiles (approximately 60 tiles) are needed to complete the tiling for the kitchen and bathroom.

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The linear function for the repair cost is given as follows:

C(h) = 30h + 40.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

Each hour the cost increases by $30, hence the slope m is given as follows:

m = 30.

Hence the function is:

C(h) = 30h + b

When h = 2, C = 100, hence the intercept b is given as follows:

60 + b = 100

b = 40.

Then:

C(h) = 30h + 40.

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The intercepts of the line are (6/5, 0) and (0, -3/4).

We have,

To find the x-intercept, we need to set y = 0 and solve for x:

5x - 9 = -3

5x = 6

x = 6/5

So the x-intercept is (6/5, 0).

To find the y-intercept, we need to set x = 0 and solve for y:

-9 = -8y - 3

8y = -6

y = -3/4

So the y-intercept is (0, -3/4).

Therefore,

The intercepts of the line are (6/5, 0) and (0, -3/4).

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Based on the information, the three numbers are 14, 34, and 70.

Based on the information, the second number = 3x - 8

The third number is five times the first number, which can be written as:

third number = 5x

The sum of the three numbers is 118, so we can write an equation:

x + (3x - 8) + 5x = 118

9x - 8 = 118

Adding 8 to both sides:

9x = 126

x = 236 / 914

Now we can use this value of x to find the other two numbers:

second number = 3x - 8 = 3(14) - 8 = 34

third number = 5x = 5(14) = 70

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The required values are HJ = 2√15 units, ∠G = 67.5 Degrees, ∠J = 61.04 degree.

A triangle with two sides that are perpendicular to one another is known as a right triangle, right-angled triangle, or orthogonal triangle. It was previously known as a rectangled triangle. Trigonometry is based on the relationship between the right triangle's sides and other angles.

Given data

GH = 14 units and GJ = 16 units

Using Pythagorean theorem;

[tex]16^2 = 14^2 + HJ^2[/tex]

[tex]HJ = \sqrt{16^2-14^2}[/tex]

HJ = √60

HJ = 2√15 units

And

Cos(G) = 14/16 = 7/8

∠G = cos⁻¹(7/8)

∠G = 67.5 Degrees

And

Sin(J) = 14/16 = 7/8

∠J = Sin⁻¹(7/8)

∠J = 61.04 degree

Thus, required values are HJ = 2√15 units, ∠G = 67.5 Degrees, ∠J = 61.04 degree.

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The measure of angle x is 77 degrees.

We have two angles given: 65 degrees and 38 degrees. Let's call the measure of angle x as "x".

From the information, we have the measure of the missing angle of the angles in a triangle are 38°, 65° and x. Then we can set up an equation:

x + 65 + 38 = 180 (the sum of the measures of the angles in a triangle is 180)

Simplifying this equation, we get:

x + 103 = 180

x = 77

Therefore, the measure of angle x is 77 degrees.

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Complete question

Find the measure of the missing angle of the angles in a triangle are 38°, 65° and x.

The landscaper will need 10.99 feet of fencing to place around the circumference of the pond. Option B is the correct answer.

We need to find how many feet of the fence is needed to decorate the fence around the circumference of the pond. we can determine it by finding the circumference of a pound or circle. The circumference of a circle is calculated using the formula,

C = 2πr

Where:

C = the circumference

r = radius

Given data:

π = 3.14

r =  1. 75 feet.

Substuting the value of the radius in the formula we get

C = 2πr

C = 2π(1.75)

= 10.99

Therefore, the landscaper will need 10.99 feet of fencing to place around the circumference of the pond.

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So the expression that represents the average distance of a planet from the sun using radicals is: d = k/2√13 * √x

An exponent, also known as a power, is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is usually written as a small number (the exponent) placed to the right and above a larger number (the base). Exponents are used in many mathematical concepts, including logarithms, roots, and scientific notation.

Here,

The expression ((1)/∛(52)x)²) can be simplified using exponent rules:

((1)/∛(52)x)²) =((1)/∛(52)x)²) * ∛x²)

= 1/(∛52² * ∛x²)

The average distance of a planet from the sun measured in astronomical units can be represented using the formula:

d = k * √T

where d is the distance from the sun, T is the time it takes for the planet to orbit the sun, and k is a constant of proportionality.

We can rewrite this formula in terms of Earth weeks by noting that there are 52 weeks in a year, so T = (1/52)x years. Substituting this into the formula, we get:

d = k * √((1/52)x)

Simplifying this expression using exponent rules, we get:

d = k * √(1/52)* √x

So an equivalent expression using radicals to represent the average distance of a planet from the sun is:

d = k * √(1/(52)) * √x

which simplifies to:

d = k/√(52) * √x

or

d = k/2√13 * √x

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The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is y = 400x + 60,000.

The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is determined as follows;

Using general linear equation;

y = mx + b

where:

The initial volume as at March = 60,000

the rate = 400 volumes / month

The equation is determined as;

y = 400x + 60,000

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The calculated value of the circumference of the circle is 31.4 units

From the question, we have the following parameters that can be used in our computation:

Radius, r = 5

Using the above as a guide, we have the following:

Circumference = 2 * π * r

Substitute the known values in the above equation, so, we have the following representation

Circumference = 2 * 5 * 3.14

Evaluate the products

Circumference = 31.4

HEnce, the value of the circumference is 31.4 units

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Jay has 7 $100 bills in his wallet.

Let's assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as x - 5.

Now, the total amount contributed by $50 notes is $50x.

And the total amount contributed by $100 bills is $100*(x-5).

Since the total amount of money in his wallet is $1300, we can write an equation:

$50x + $100*(x-5) = $1300

Simplifying this equation, we get:

$50x + $100x - $500 = $1300

$150x = $1800

x = 12

So, Jay has 12 $50 bills in his wallet.

Using the earlier equation, the number of $100 bills can be found:

x - 5 = 12 - 5 = 7

Therefore, Jay has 7 $100 bills in his wallet.

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According to the information, and example of a counterexample is: A line can cross the circle only at one point.

To find a counterexample to this statement we must read it carefully and identify the main idea of it. In this case you are stating that a line always crosses a circle at two points.

Later we must analyze this statement and evaluate if it is true or false. In this case it is false because we can make a line that crosses a circle only once. So, the counter example sentence would be.

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La altura del mástil es de aproximadamente 20.87 metros.

Para resolver el problema, se puede utilizar la ley de cosenos para encontrar la longitud del mástil:

c² = a² + b² - 2ab cos C

Donde:

c es la longitud del mástil (lo que se busca)

a es la longitud de la parte delantera del barco (25m)

b es la longitud de la parte trasera del barco (también 25m)

C es el ángulo entre a y b, que se puede calcular utilizando la tangente: tan C = 1.5 (pues tan 60° = √3, y tan 45° = 1)

Resolviendo para c:

c² = 25² + 25² - 2(25)(25)cos(arctan 1.5)

c = √(25² + 25² - 2(25)(25)(1/√(1+(1.5)²)))

c ≈ 31.08 m

Por lo tanto, la altura del mástil es de aproximadamente 31.08 metros.

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The volume, in cubic feet, of the right rectangular prism is 9 cubic feet

From the question, we have the following parameters that can be used in our computation:

A right rectangular prism has a length of 2 feet, a width of 3 feet, and a height of 1 2/4 feet

Using the above as a guide, we have the following:

Volume = Length * Width * height

Substitute the known values in the above equation, so, we have the following representation

Volume = 2 * 3 * (1 2/4)

Evaluate

Volume = 9

Hence, the volume is 9 cubic feet

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Since 1.1584 > 1, the truck cannot pass under the archway without going into the other lane.

A semi-elliptic archway with a height of 15 feet at the center and a width of 50 feet can be visualized as half of an ellipse.

The major axis of the ellipse corresponds to the width, while the minor axis corresponds to the height. In this case, the major axis (a) is 25 feet, and the minor axis (b) is 15 feet.

To determine if a truck that is 12 feet high and 14 feet wide can drive under the archway without going into the other lane, we can use the equation of an ellipse: (x²/a²) + (y²/b²) = 1.

The truck will occupy half of the road width, which is 25 feet, so its horizontal distance from the center (x) is 25 - 7 = 18 feet, and its height (y) is 12 feet.

Plugging these values into the equation, we get: (18²/25²) + (12²/15²) = (324/625) + (144/225) ≈ 0.5184 + 0.64 = 1.1584.

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The latus rectum of an ellipse is 288/13 when the ellipse equation is given as [tex]x^2/169 + y^2/144 = 1[/tex]. Option A is correct.

The standard form of an ellipse equation is given as  

[tex](x2/a2) + (y2/b2) = 1[/tex]

where :

a = lengths of the semi-major axes

b = length of semi-minor axes

The length of the chord through one of the foci that are perpendicular to the major axis is defined as the latus rectum of an ellipse.

From the given data the equation of the ellipse is given as :

x² / 169 + y² / 144 = 1

By comparing the standard equation and the given equation of the ellipse we get :

a² = 169

a = √169

[tex]a = 13[/tex]

b² = 144

b = √144

[tex]b = 12[/tex]

The distance between the center and one of the foci is given by

c = √(a² - b²)

= √(13² - 12²)

= 5

We can find the latus rectum by substuting a and b values in the latus rectum of an ellipse formula,

= 2×b²/a

= 2 × 12² / 13

= 288/13

Therefore, the latus rectum of an ellipse is 288/13.

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The slope of the line through points (6,3) and (12,7) is 2/3.

To find the slope of a line, we use the formula:

Slope = (y2 - y1) / (x2 - x1)

In this case, we have two points: (6, 3) and (12, 7). We can label them as follows:

x1 = 6
y1 = 3
x2 = 12
y2 = 7

Now we can plug these values into the formula:

Slope = (y2 - y1) / (x2 - x1)
Slope = (7 - 3) / (12 - 6)
Slope = 4 / 6
Slope = 2/3

Therefore, the slope of the line through the points (6, 3) and (12, 7) is 2/3.

The slope of a line tells us how steep it is. A positive slope means the line goes up as you move from left to right, while a negative slope means the line goes down. In this case, since the slope is positive (2/3), we know that the line goes up as we move from left to right.

The slope also tells us how much the y-value changes for every one unit of x-value. In this case, for every one unit we move to the right, the y-value goes up by 2/3.

To learn more about slope of the line refer here

https://brainly.com/question/14511992#

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