After decreasing the price of an article by 23% the price was ghc308. 0. What was the original price

Answer:

To calculate the mass of copper needed to make the cone, we can use the following formula:

Volume of Cone = (1/3) * π * r^2 * h

where r is the radius of the base of the cone and h is the height of the cone.

Given that Allen wants the cone’s base to have a diameter of 8 cm, we can calculate that the radius of the base is 4 cm. The height of the cone is given as 10 cm.

Substituting these values into the formula above, we get:

Volume of Cone = (1/3) * π * (4 cm)^2 * 10 cm = 167.55 cubic centimeters

The density of copper is given as 8.96 grams/cubic centimeter. Therefore, we can calculate the mass of copper needed to make the cone as follows:

Mass of Copper = Volume of Cone * Density of Copper

Mass of Copper = 167.55 cubic centimeters * 8.96 grams/cubic centimeter = 1500.98 grams

Therefore, Allen will need approximately 1500.98 grams of copper to make the cone.

The amount of money this car would be worth in 5 years include the following: B. $19,011.21.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided above, the yearly value of a used ford f-150 can be modeled by the following exponential function;

[tex]y = 28845(0.92)^x\\\\y(5)= 28845(0.92)^5[/tex]

y(5) = $19,011.21.

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The volume is (8π/3) cubic units.

To find the volume of the solid enclosed by the paraboloid z = 3 + x² + (y − 2)²and the planes z = 1, x = −2, x = 2, y = 0, and y = 2, we need to use a triple integral.

The limits of integration for x, y, and z are as follows:

-2 ≤ x ≤ 2

0 ≤ y ≤ 2

1 ≤ z ≤ 3 + x² + (y − 2)²

Therefore, the triple integral for the volume is:

V = ∫∫∫ (3 + x² + (y − 2)²- 1) dx dy dz, where the limits of integration are as given above.

Simplifying this integral, we get:

V = ∫∫∫ (x² + (y − 2)²) dx dy dz

Using cylindrical coordinates, we can express x and y in terms of r and theta:

x = r cos(theta)

y = r sin(theta)

The limits of integration for r and theta are:

0 ≤ r ≤ 2

0 ≤ theta ≤ 2π

Substituting these values into the triple integral, we get:

V = ∫∫∫ r² dr dtheta dz

Integrating with respect to r and theta first, we get:

V = ∫0² ∫0^2π (r²) dtheta dr ∫1^(3 + r²- 4r sin(theta)) dz

Simplifying the innermost integral, we get:

V = ∫0²∫0^2π (r²) dtheta dr (2 + r² - 4r)

Evaluating the integrals, we get:

V = ∫0^2 (2πr²  - 4π[tex]r^3[/tex] + (4/3)[tex]r^4[/tex]) dr

V = (8π/3)

Therefore, the volume of the solid enclosed by the paraboloid z = 3 + x² + (y − 2)² and the planes z = 1, x = −2, x = 2, y = 0, and y = 2 is (8π/3) cubic units.

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There are 10,000 possible combinations if there are no restrictions on the number of times talula can use each number.

since the lock has four number positions and each position can have any number from 0 to 9, we can use the multiplication    principle   to determine the total number of possible combinations:

10 options for the first position x 10 options for the second position x 10 options for the third position x 10 options for the fourth position

this gives us:

10 x 10 x 10 x 10 = 10,000

biking talula got a new bicycle lock that has a four-number combination. each number in the combination is from 0 to 9. a. how many combinations are possible

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The most appropriate test for this scenario would be a two-sample t-test, assuming equal variances.

The alternative hypothesis would be:

There is a significant difference in the average time it takes to receive an order between the counter and the drive-thru.

We have,

The two friends conducted an experiment to compare the average time it takes to get their food at a fast-food restaurant using the counter and drive-thru.

They recorded the times it took for 555 visits for each method.

Now, they want to test if there is a significant difference in the average time between ordering at the counter and the drive-thru.

They need to choose an appropriate statistical test and form an alternative hypothesis that reflects what they are trying to test.

Thus,

The most appropriate test for this scenario would be a two-sample t-test, assuming equal variances.

The alternative hypothesis would be:

There is a significant difference in the average time it takes to receive an order between the counter and the drive-thru.

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The angle with cosine equal to is either the first quadrant angle or the fourth quadrant angle.

Let x be the acute angle in standard position whose cosine is . Then, we have:

cos x =

Taking the inverse cosine (or arccosine) of both sides, we get:

x = arccos

Since cosine is positive in the first and fourth quadrants, we have two possible values for x: one in the first quadrant and one in the fourth quadrant.

In the first quadrant, x is the acute angle whose cosine is . We can find this angle using a calculator or by recognizing that it is a special angle in the unit circle.

Specifically, if we draw the unit circle and look at the point on the x-axis with a distance of from the origin, we can see that the angle between the positive x-axis and the line connecting the origin to that point is . Therefore, one possible value for x is .

In the fourth quadrant, the reference angle is , but since cosine is negative in the fourth quadrant, we need to add to find the actual angle. Therefore, the other possible value for x is .

Hence, the angle with cosine equal to is either the first quadrant angle or the fourth quadrant angle.

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If a t-distribution with 20 degrees of freedom is used to test a hypothesis with a Type I error value of 5%, then the critical t-value corresponding to the given significance level is 1.725.

The critical t-value is the value beyond which we reject the null hypothesis in a t-test. The value is determined by the significance level (Type I error) and the degrees of freedom.

In this case, with a significance level of 5% and 20 degrees of freedom, the critical t-value is 1.735. This means that if the calculated t-value for a sample falls beyond 1.735, we reject the null hypothesis at the 5% level of significance.

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The two positive numbers that satisfy the given requirements are 20 and 10.

Let's call the two positive numbers x and y. We want to find x and y such that the product is 200 and the sum of x and 2y is a minimum.

From the first requirement, we know that:

x*y = 200

We can solve for y in terms of x by dividing both sides by x:

y = 200/x

Now we can substitute this expression for y into the second requirement:

x + 2y = x + 2(200/x) = x + 400/x

To find the minimum value of this expression, we can take the derivative with respect to x and set it equal to zero:

d/dx (x + 400/x) = 1 - 400/x^2 = 0

400/x^2 = 1

x^2 = 400

x = 20

So the first number is 20. We can substitute this value for x in the expression we found for y:

y = 200/x = 200/20 = 10

So the second number is 10. Therefore, the two positive numbers that satisfy the given requirements are 20 and 10.

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The first five terms of the sequence are -2, -10, -24, -44, and -70.

It seems there is a typo in the formula for the nth term of the sequence. However, to interpret it as an = n - 3n(n). To find the first five terms, we will plug in the values n = 1, 2, 3, 4, and 5:

1. For n = 1, a1 = 1 - 3(1)(1) = 1 - 3 = -2
2. For n = 2, a2 = 2 - 3(2)(2) = 2 - 12 = -10
3. For n = 3, a3 = 3 - 3(3)(3) = 3 - 27 = -24
4. For n = 4, a4 = 4 - 3(4)(4) = 4 - 48 = -44
5. For n = 5, a5 = 5 - 3(5)(5) = 5 - 75 = -70

The first five terms are -2, -10, -24, -44, and -70.

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we have y = [-1, -1, -1] + [-10, 5, 5], where [-1, -1, -1] is in W and [-10, 5, 5] is orthogonal to W.

To write vector y as the sum of a vector in W and a vector orthogonal to W, we need to find the projection of y onto W and then subtract it from y to obtain the orthogonal component.

Let's first find the projection of y onto W. The projection of a vector onto a subspace is given by the formula:

proj_W(y) = (y⋅u / ||u||^2) * u

where ⋅ represents the dot product and ||u|| represents the norm (magnitude) of vector u.

Given the information, we have:

y = [-11, 4, 4]

u = [1, 1, 1]

First, calculate the dot product of y and u:

y⋅u = (-11)(1) + (4)(1) + (4)(1) = -11 + 4 + 4 = -3

Next, calculate the norm squared of u:

||u||^2 = (1^2) + (1^2) + (1^2) = 1 + 1 + 1 = 3

Now, substitute these values into the projection formula:

proj_W(y) = (-3 / 3) * [1, 1, 1]

= [-1, -1, -1]

The projection of y onto W is [-1, -1, -1].

To obtain the orthogonal component z, we subtract the projection from y:

z = y - proj_W(y)

= [-11, 4, 4] - [-1, -1, -1]

= [-11 + 1, 4 + 1, 4 + 1]

= [-10, 5, 5]

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(a) Most calculators can find logarithms with base 10 and base e. To find logarithms with different bases, we use the change of base formula:

log_b(x) = log(x) / log(b)

Using this formula, we can find:

log_3(6) = log(6) / log(3) ≈ 1.631

log_5(258) = log(258) / log(5) ≈ 3.424

(b) No, the result is not the same. If we perform the calculation in part (a) using In in place of log, we get the natural logarithm instead of the base-10 logarithm. To find the logarithm with a different base, we need to use the change of base formula as shown above.

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The quadrant bounded by the y-axis, the line y=x, the circle x^2+y^2=16, and the circle x^2+y^2=25 is the quadrant containing the points (-2√2,-2√2) and (0,4), and is located in the top left corner of the coordinate plane.

To find the quadrant bounded by the y-axis, the line y=x, the circle x^2+y^2=16, and the circle x^2+y^2=25, we can start by graphing the two circles and the line on a coordinate plane.

The first circle, x^2+y^2=16, is a circle with center at the origin (0,0) and radius 4. The second circle, x^2+y^2=25, is a circle with center at the origin and radius 5. The line y=x is a diagonal line that passes through the origin and has a slope of 1.

To find the quadrant bounded by these shapes, we need to find the points where they intersect. The first circle intersects the x and y axes at (4,0) and (0,4), respectively. The second circle intersects the x and y axes at (5,0) and (0,5), respectively. The line y=x intersects both circles at two points, which we can find by substituting y=x into the equations of the circles:

For the first circle, we get x^2+y^2=16 becomes x^2+x^2=16, which simplifies to 2x^2=16 and x=±2√2. Therefore, the points of intersection are (2√2,2√2) and (-2√2,-2√2).

For the second circle, we get x^2+y^2=25 becomes x^2+x^2=25, which simplifies to 2x^2=25 and x=±(5/√2). Therefore, the points of intersection are ((5/√2),(5/√2)) and (-(5/√2),-(5/√2)).

Now that we have the points of intersection, we can see that they divide the plane into four quadrants. The quadrant we are interested in is the one bounded by the y-axis, the line y=x, and the first circle. This quadrant contains the points (-2√2,-2√2) and (0,4).

In summary, we can state that the quadrant bounded by the y-axis, the line y=x, the circle x^2+y^2=16, and x^2+y^2=25 is the quadrant containing the points (-2√2,-2√2) and (0,4), and is located in the top left corner of the coordinate plane.

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First Image

By looking at the function machine below, the missing input and the missing output are d and (8k - 5) respectively.

We can view a function as something that can take an object and turn it into a different object.

Given,

Input x (8) - 5 = 8d -5

Comparing both the sides,

⇒Input = d

k x (8) - 5 = Output

⇒Output = (8k - 5)

Therefore, Input = d and Output = (8k - 5)

Second Image

Given,

840 → ? ? → 89

840/ 10 = 84 + 5 = 80

So, the functions will be (÷10) and (+5)

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The area of region inside lemniscate is 23.73 square units.

To find the area of the region inside the lemniscate and outside the circle, we first need to sketch the graphs of both equations.

The polar graph of the lemniscate is given by r^2 = 42 cos(2θ), which has a central point and two loops that intersect at the origin.

The polar graph of the circle is given by r = √21, which has a center at the origin and a radius of √21.

To find the area of the region inside the lemniscate and outside the circle, we need to subtract the area of the circle from the area of the lemniscate.

Using the polar area formula, we can find the area of the lemniscate and circle as follows:

Area of lemniscate = (1/2) ∫(π/4)0 [√(42cos(2θ))]^2 dθ + (1/2) ∫(5π/4) (3π/4) [√(42cos(2θ))]^2 dθ

= (1/2) ∫(π/4)0 42cos(2θ) dθ + (1/2) ∫(5π/4) (3π/4) 42cos(2θ) dθ

= 21 [sin(2θ)]|(π/4)0 + 21 [sin(2θ)]|(3π/4)(5π/4)

= 21 [sin(π/2) - sin(0) + sin(5π/2) - sin(3π/2)]

= 84 square units

Area of circle = π(√21)^2 = 21π square units

Therefore, the area of the region inside the lemniscate and outside the circle is:

Area = Area of lemniscate - Area of circle

     = 84 - 21π

     ≈ 23.73 square units

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The strategy that will accomplish the intended design is Randomly select 6 graduate students and 24 undergraduate students for the survey. So, option b. is correct.

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

Based on the given information, the college professor wants to survey a sample of 30 students from his course, considering the differences between graduate and undergraduate students. The best strategy to accomplish his intended design is: Randomly select 6 graduate students and 24 undergraduate students for the survey.

This approach ensures that the sample includes a proportional representation of both graduate and undergraduate students, taking into account the difference in their numbers (50 graduate students and 200 undergraduate students) within the 250 total students.

So, option b. is correct.

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The slope of the tangent line to the given polar curve at the specified point is √3.

What is polar equation?

Cartesian coordinates, which may be found by moving across an x-axis and up and down the y-axis in a rectangular pattern, are complemented by polar coordinates. Polar coordinates are written as (r,) as opposed to the (x, y) used for Cartesian coordinates.

A point's location in polar coordinates is determined by its r from the origin and the angle θ (measured in radians) between the line leading to the point and the x-axis.

As given,

For the polar equation r = 4 sin θ, we have

x = r cosθ

x = 4 sinθ cosθ

x = 2sin2θ

y = r sinθ

y = 4 sin²θ

Differentiate obtained values of x and y with respect to θ respectively,

dx/dθ = d(2sin2θ)/dθ

dx/dθ = 2cos2θ (2)

dx/dθ = 4cos2θ

Similarly,

dy/dθ = d(4sin²θ)/dθ

dy/dθ = 4sin2θ

Evaluate the slope (dy/dx) as follows:

dy/dx = (dy/dθ) / (dx/dθ )

dy/dx = (4 sin2θ) / (4 cos2θ)

dy/dx = (sin2θ) / (cos2θ)

dy/dx = (tan2θ)

At θ = π/6

slope = dy/dx

Substitute values,

slope = tan2( π/6)

slope = tan( π/3)

slope = √3.

Hence, the slope of the tangent line to the given polar curve at the specified point is √3.

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To find and simplify the integral of 1/x from ac to bc, where 0 < a < b and c > 0, we can split the integral into two parts and then simplify the result.

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Using the properties of definite integrals, we can rewrite the integral as:

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Next, we can pull out the constant factors from the integral:

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Now, let's simplify the limits of integration:

When x = ac, we substitute it into the expression 1/x:

1/(ac) = 1/ac

When x = bc, we substitute it into the expression 1/x:

1/(bc) = 1/bc

Therefore, the integral becomes:

∫[ac, bc] (1/x) dx = ∫[ac, bc] (1/x) dx

Simplifying further:

∫[ac, bc] (1/x) dx = ln|x| evaluated from ac to bc

∫[ac, bc] (1/x) dx = ln|bc| - ln|ac|

Using the properties of logarithms, we can combine the two logarithms:

∫[ac, bc] (1/x) dx = ln(bc/ac)

Therefore, the integral of 1/x from ac to bc simplifies to ln(bc/ac).

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The equation that demonstrates the use of a simple interest formula to compute the interest earned on $70 at 3% for 12 years is I = (70) times (0.03) times (12).

The formula for calculating simple interest is I = P r t, where I represents the interest earned, P is the principal amount (initial investment), r is the interest rate (expressed as a decimal), and t is the time period in years. In this case, the correct equation is I = (70) times (0.03) times (12), which calculates the interest earned on $70 at a 3% interest rate for 12 years. By substituting the given values into the formula, we can determine the interest amount.

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The major multivariate technique for examining variable interdependence is factor analysis.

Factor analysis is a multivariate statistical technique used to identify patterns in the relationships among a large number of variables. Specifically, it is used to examine variable interdependence, which refers to the degree to which variables are related to one another in a dataset.

In factor analysis, the goal is to identify underlying factors or dimensions that account for the observed patterns of correlation among the variables. By doing so, it is possible to reduce the number of variables to a smaller set of factors that capture the essential information contained in the original variables. This can be useful for a variety of purposes, such as data reduction, hypothesis testing, and exploratory data analysis.

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The length of |PR| as shown in the diagram is 9.3.

Length is the distance between two points.

To calculate the length of PR, we use the formula below

Note:

Formula:

From the question,

Given:

Substitute these values into equation 1 and solve for y

Hence,  |PR|  = 9.3

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Answer:

I believe that your overall grade would be a 65.5%

Step-by-step explanation:

I'm not entirely sure but this is what I think it is.

Rounded to four decimal places, the point estimate for p is approximately 0.3659.

To find the point estimate for the population proportion, we divide the number of students who own their cars by the total number of students surveyed.

In this case, out of 410 college students surveyed, 150 said they own their car. Therefore, the point estimate for p, the population proportion of students who own their cars, is:

Point Estimate = Number of students who own their cars / Total number of students surveyed

= 150 / 410

≈ 0.3659

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Answer: P(X=28) ≈ C(100, 28) * (1/4)^28 * (3/4)^72 ≈ 0.0368 (rounded to 4 decimal places)

Step-by-step explanation:

Using the binomial probability formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

n = 100 (number of trials)

k = 28 (number of successes)

p = 1/4 (probability of success for each trial, since there are 4 sides)

C(n, k) = n! / (k! * (n-k)!)

Plugging the values:

P(X=28) ≈ C(100, 28) * (1/4)^28 * (3/4)^72 ≈ 0.0368 (rounded to 4 decimal places)

There are 126 different combinations of four letters that can be made from the letters in "Tennessee", and there are 3,024 different permutations of four letters that can be made from the letters in "tennessee".

The word "tennessee" contains 9 letters, including 4 "e"s, 2 "n"s, and 1 each of "t", "s", and "s".

To find the number of permutations of four letters that can be made from the letters in "tennessee," we can use the formula for permutations of n objects taken r at a time:

P(n, r) = n! / (n - r)!

Using this formula, we get:

P(9, 4) = 9! / (9 - 4)! = 9! / 5! = 9 x 8 x 7 x 6 = 3,024

So there are 3,024 different permutations of four letters that can be made from the letters in "tennessee".

To find the number of combinations of four letters that can be made, we can use the formula for combinations of n objects taken r at a time:

C(n, r) = n! / (r! * (n - r)!)

Using this formula, we get:

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = 126

So there are 126 different combinations of four letters that can be made from the letters in "Tennessee"

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The function f(x, y) = 24xy, for 0 < x < 4 and 0 < y < 3, represents a rectangular region in the xy-plane. This region is bound by the lines x = 0, x = 4, y = 0, and y = 3.

The function f(x, y) defines a surface where the height at each point (x, y) is given by 24xy.

To find the volume under this surface within the given region, we can integrate f(x, y) over the rectangular region. The volume V can be calculated as follows:

V = ∫∫R f(x, y) dA

where R represents the rectangular region and dA is the differential area element.

Evaluating this double integral will yield the volume V, which represents the total accumulation of the function f(x, y) over the given region.

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It may involve using logical equivalences or truth tables to demonstrate that p(n) is true for all possible values of n.

Without knowing the specific propositional function p(n), it is not possible to determine for which positive integers n the statement p(n) must be true.

However, in general, to determine for which values of n the statement p(n) must be true, we would need to carefully analyze the definition of p(n) and any given conditions or constraints on n. This may involve using logical reasoning, algebraic manipulation, or even induction.

To justify our answer, we would need to provide a clear and rigorous argument that demonstrates why p(n) is true (or false) for all appropriate values of n. This could involve showing that p(n) is true for a specific base case (such as n = 1), and then using induction to prove that p(n) is true for all larger values of n. Alternatively, it may involve using logical equivalences or truth tables to demonstrate that p(n) is true for all possible values of n.

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The statement (p ∧ ~q) ∨ r means "either p and not q are true, or r is true." the truth value of the statement (p ∧ ~q) ∨ r is true under both conditions.

a) If p is true and q is true, then ~q is false. So, (p ∧ ~q) is false. Since r is also true, the entire statement becomes true: (false ∨ true) = true.

b) If p is false and q is true, then (p ∧ ~q) is false (both p and ~q need to be true for this part to be true). However, since r is true, the entire statement becomes true: (false ∨ true) = true.

So, the truth value of the statement (p ∧ ~q) ∨ r is true under both conditions.

Let's evaluate the truth value of the statement (p ∧ ~q) ∨ r under the given conditions:

a) p is true, q is true, and r is true.
(p ∧ ~q) ∨ r = (True ∧ ~True) ∨ True = (True ∧ False) ∨ True = False ∨ True = True
The statement is true under these conditions.

b) p is false, q is true, and r is true.
(p ∧ ~q) ∨ r = (False ∧ ~True) ∨ True = (False ∧ False) ∨ True = False ∨ True = True
The statement is true under these conditions as well.

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To model the consumer expenditure (revenue for the vendor) as a function of price, we can use a linear equation in the form of:

Expenditure = m * Price + b

Where:

Expenditure represents the consumer expenditure or revenue for the vendor.

Price is the price of the product in dollars.

m is the slope of the linear equation.

b is the y-intercept of the linear equation.

To determine the values of m and b, we need additional data points or information about the relationship between price and consumer expenditure. Without specific data points, it is not possible to determine the exact values of m and b.

However, if you have a specific data set or information on the relationship between price and consumer expenditure within the range of 20 to 32 dollars, I can assist you in calculating the values of m and b using linear regression or provide alternative modeling approaches based on the available information.

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If the songs can be played in any order, there are 3,628,800 different ways for the DJ to play the 10 songs.

If the first song must be a slow song and the last song must be a slow song, there are 203,212,800 different ways for the DJ to play the 10 songs.

If the first two songs must be fast songs, there are 241,920 different ways for the DJ to play the 10 songs.

A) If the songs can be played in any order, the DJ has 10 songs to play, out of which 7 are slow songs and 3 are fast songs. This is a permutation problem since the order matters. The total number of ways to play the songs can be calculated using the formula for permutations:

Total number of ways = 10P10 = 10!

Here, "!" represents the factorial function. Evaluating the expression, we get:

Total number of ways = 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800 ways

Therefore, if the songs can be played in any order, there are 3,628,800 different ways for the DJ to play the 10 songs.

B) If the first song must be a slow song and the last song must be a slow song, we fix the positions of the first and last songs. The remaining 8 songs can be arranged in the middle in any order. This is a permutation problem with repetition since there are repeated elements (slow songs). The calculation is as follows:

Total number of ways = 7P1 * 8P8 = 7! * 8!

Here, 7P1 represents permuting the slow songs for the first position, and 8P8 represents permuting the remaining songs in the middle positions.

Simplifying the expression, we get:

Total number of ways = 7! * 8! = 5,040 * 40,320 = 203,212,800 ways

Therefore, if the first song must be a slow song and the last song must be a slow song, there are 203,212,800 different ways for the DJ to play the 10 songs.

C) If the first two songs must be fast songs, we fix the positions of the first two songs as fast songs. The remaining 8 songs can be arranged in the remaining positions in any order. This is again a permutation problem with repetition:

Total number of ways = 3P2 * 8P8 = 3! * 8!

Simplifying the expression, we get:

Total number of ways = 3! * 8! = 6 * 40,320 = 241,920 ways

Therefore, if the first two songs must be fast songs, there are 241,920 different ways for the DJ to play the 10 songs.

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The equation in slope intercept form that can be used to model this relationship is  [tex]y= \boldmath{\underline{\frac{7}{3}}} x + \boldmath{\underline{\frac{-2}{\ \ 3}}}[/tex] . So the correct answer to first box will be [tex]\frac{7}{3}[/tex] and the second box will be [tex]\frac{-2}{\ \ 3}[/tex] .

Slope = [tex]\frac{\(\Delta y}{\Delta x}[/tex]

Using the coordinates (-4, -10) and (5,11)

⇒ Slope = [tex]\frac{11-10}{5 \ +\ 4} = \frac{21}{9} = \frac{7}{3}[/tex]

Taking (-4, -10) and a general point (x, y),

⇒ [tex]\frac{y - (-10)}{x-(-4)}= \frac{7}{3}[/tex]

⇒ [tex]\frac{y+10}{x+4}= \frac{7}{3}[/tex]

⇒ [tex](y+10) = \frac{7}{3}(x+4)[/tex]

⇒ [tex]y=\frac{7}{3}x + \frac{28}{3}-10[/tex]

⇒ [tex]y= \frac{7}{3}x-\frac{2}{3}[/tex]

Therefore, the equation in slope intercept form will be [tex]y= \frac{7}{3}x-\frac{2}{3}[/tex].

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