Need help fast response

Answer:

The given polynomial already has two terms that can be factored out:

9x^2y^6 - 25x^4y^8 = (3xy^3)^2 - (5x^2y^4)^2

Now we have a difference of squares:

= (3xy^3 - 5x^2y^4)(3xy^3 + 5x^2y^4)

Therefore, 9x^2y^6 - 25x^4y^8 can be rewritten as the product of (3xy^3 - 5x^2y^4) and (3xy^3 + 5x^2y^4).

Answer: The answer would be   (3xy^3-5x^2y^4)(3xy^3+5^2y^4)

(C)

Step-by-step explanation: Cant explain how to but for a quick answer it is C, and you can check the image for proof.

The number of students who would be there are 24 students .

The number of both students and chaperones on the trip are 28 in number. Again , this is both the chaperones and the students .

There are 4 chaperones according to the question . So to find the number of students on the field trip, the formula would be :

= Total number of both students and chaperones - Total number of chaperones

= 28 - 4

= 24 students

The number of students who would be on the field trip is 24 students .

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The correct numerical expression for "12 times the sum of 5 and 25 minus 2" by simplification is option (b) , i.e 12 x (5 + 25) − 2.

Simplification means simplifying an expression by reducing it to a simpler form. Approximating means simplifying the formula to the nearest value, which is not exactly correct. 

BODMAS stands for Bracket, Off, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction. 

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Answer:

12 x (5 + 25) − 2

Step-by-step explanation:

hope this helps!

Answer: To find the perimeter of triangle JKL, we need to find the length of each side and add them up. We can use the distance formula to find the length of each side:

Side JK = sqrt[(2 - (-5))^2 + (3 - (-7))^2] = sqrt[7^2 + 10^2] = sqrt[149]

Side KL = sqrt[(-1 - 2)^2 + (-7 - 3)^2] = sqrt[(-3)^2 + (-10)^2] = sqrt[109]

Side LJ = sqrt[(-1 - (-5))^2 + (-7 - (-7))^2] = sqrt[4^2] = 4

Therefore, the perimeter of triangle JKL is:

P = JK + KL + LJ = sqrt[149] + sqrt[109] + 4

To find the area of triangle JKL, we can use the formula:

A = 1/2 * base * height

We can choose any side as the base, and the corresponding height will be the perpendicular distance from the opposite vertex to the base. Let's choose side KL as the base. The height from vertex J to side KL is the perpendicular distance between J and the line containing KL. We can find this distance using the formula for the distance between a point and a line:

Area = 1/2 * KL * h

where h = |(2 - (-1))( -7 - 3) - (-5 - 2)(-1 - 3)| / sqrt[(-1 - 2)^2 + (-7 - 3)^2]

Simplifying the above expression, we get:

h = 24 / sqrt[109]

Therefore, the area of triangle JKL is:

A = 1/2 * KL * h = 1/2 * sqrt[109] * 24 / sqrt[109] = 12

So, the perimeter of triangle JKL is sqrt[149] + sqrt[109] + 4, and the area of triangle JKL is 12.

Step-by-step explanation:

Answer: The equation x = 7y + 2 is a linear equation in two variables, x and y. To find ordered pairs of x and y that satisfy this equation, we can choose values of y and then solve for x.

For example, if we choose y = 0, then:

x = 7y + 2

x = 7(0) + 2

x = 2

Therefore, the ordered pair (2, 0) satisfies the equation x = 7y + 2.

Similarly, if we choose y = 1, then:

x = 7y + 2

x = 7(1) + 2

x = 9

Therefore, the ordered pair (9, 1) satisfies the equation x = 7y + 2.

We can continue in this manner to find more ordered pairs. However, note that there are infinitely many ordered pairs that satisfy this equation, as the equation represents a line with a slope of 7 and a y-intercept of (0, 2). Therefore, we can choose any value of y and obtain a corresponding value of x that satisfies the equation.

Step-by-step explanation:

The cost of 6 sets of cards is $105.95

Each set has 100 cards, then in 6 sets there are 6*100 = 600 cards.

We know that the first 200 cards costs $49.95, and from then, the cost per set is $14.

So we have a piecewise function which can be written as:

y = $49.95   if x ≤ 200

y = $49.95 + $14*(x - 200) if x > 200.

Then we have 200 cards and 4 sets, then the total cost will be:

$49.95 + 4*$14 = $105.95

That is the cost of the 6 sets.

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According to the given values London's statement is incorrect.

Simple interest is a type of interest that is calculated based on the principal amount of a loan or investment and the length of time for which the money is borrowed or invested. It is called "simple" because the interest is calculated only on the initial principal amount and does not take into account any interest that may have accrued in previous periods.

Let's calculate the interest earned by each person after one year:

London:

The amount deposited by London is $100. The simple interest rate is 3.4%. Therefore, the interest earned by London after one year is:

[tex]$$\text{Interest}[/tex] = [tex]\text{Principal} \times \text{Rate} \times \text{Time}[/tex] = [tex]$100 \times 3.4%[/tex] [tex]\times 1[/tex]= [tex]$3.40$$[/tex]

Chen:

The amount deposited by Chen is $200. The simple interest rate is 2.2%. Therefore, the interest earned by Chen after one year is:

[tex]$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]= [tex]$200 \times 2.2%[/tex] [tex]\times 1[/tex] = [tex]$4.40$$[/tex]

As we can see, even though London's interest rate is higher than Chen's, Chen will earn more interest in one year because he deposited a larger amount of money.

Therefore, according to the given values London's statement is incorrect.

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Answer: -5

Step-by-step explanation:

from slope-intercept form, y=mx + b, where b is (-2), and the slope/m is (-5).

hope this helps, and please respond if I'm wrong

M = -5

That’s the answer

Therefore , the solution of the given problem of area comes out to be

option B 864 sq. centimetres is the correct response.

The amount of area it takes to cover the outside is a good indicator of its overall size. When calculating a trapezoidal shape surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capacity of a cuboid is the sum of the limits for each of its six rectangular edges. Utilize the following technique to determine the box's dimensions: The area is the same in 2lh, 2lw, but also 2hw (SA). The area is represented by the adaptable shape's face.

Here,

The following algorithm determines a cube's surface area:

=> SA = 6s²

where s represents the cube's edge lengths.

=> S =12 cm in this instance.

The result of substituting into the algorithm is:

=> SA = 6 (12)²

=> 6 (144 )²

=> 864 square centimetres.

The cube's surface size is 864 sq. cm as a result.

B) 864 sq. centimetres is the correct response.

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The answer is (iv) 150. This result can be obtained by applying the alternate segment theorem.

A circle is a shape with all points at an equal distance from the center. It has no sides or angles and is the only two-dimensional shape with this property. It is also the most basic of all shapes, and is found in nature in many forms, such as raindrops, the sun, and even the human pupil. Circles are often used in art, design, and architecture, and are sometimes even used to represent infinity.

This theorem states that if two chords of a circle intersect at right angles, then the angles in the alternate segments of the circle are equal. In this case, the alternate segments are APQ and CQP. Hence, ∠APQ + ∠CQP = 150°.

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The derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

Differentiation is a mathematical process used to find the rate at which a function changes with respect to one of its variables. It is the process of finding the derivative of a function, which is a measure of how much the function changes as its input changes. The derivative is used to analyze the behavior of functions, find maximum and minimum values, and solve optimization problems. It is an important concept in calculus and is used in many areas of mathematics, science, and engineering.

We can use the quotient rule to differentiate ƒ(x):

[tex]f(x) &= \frac{2+3\log(x)}{x^2+5} \ \\ \\ \\f'(x) &= \frac{(x^2+5)\frac{d}{dx}(2+3\log(x)) - (2+3\log(x))\frac{d}{dx}(x^2+5)}{(x^2+5)^2} \\ \\\ &\\= \frac{(x^2+5)\left(0+\frac{3}{x}\right) - (2+3\log(x))(2x)}{(x^2+5)^2} \\\ \\ \\ &= \frac{3x^2-6-6\log(x)}{x(x^2+5)^2}[/tex]

Therefore, the derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

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By answering the above question, we may state that Debra would thus function need to travel 150 miles for the price of the two plans to be the same.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

The starting charge and the cost per mile would be added together for the first plan's total cost:

Costs for plan 1 total 47.96 plus 0.19x.

The first charge and the cost per mile would be added together for the second plan's total cost:

Plan 2's overall cost is 53.96 plus 0.15x.

Set the two total cost expressions equal to one another and solve for x to get how many miles Debra would need to go for the two plans to be the same in price:

47.96 + 0.19x = 53.96 + 0.15x

0.04x = 6

x = 150

Debra would thus need to travel 150 miles for the price of the two plans to be the same.

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The only solution to the system of inequalities y < −x+5 and y ≥ 3x+1 is (1,3).

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

For the inequality y < -x + 5, any point below the line y = -x + 5 will satisfy the inequality. For the inequality y ≥ 3x + 1, any point on or above the line y = 3x + 1 will satisfy the inequality.

To find the solutions that satisfy both inequalities, we can shade the region that is below the line y = -x + 5 and also on or above the line y = 3x + 1. This region is the shaded triangle bounded by the lines y = -x + 5, y = 3x + 1, and the x-axis.

Therefore, the solutions to the system of inequalities are the points in this shaded triangle. To check which options are solutions, we can substitute the values of x and y given in each option into both inequalities and check if they satisfy both.

Hence, the only solution is (1,3).

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Complete question:

Which of the following are solutions to the system of inequalities y < −x+5 and y ≥ 3x+1?

Select all that apply.

a. (0,2)

b. (1,3)

c. (2,1)

d. (3,6)

The values of the limits of g(x) as x approaches 33 minus and 33 plus can be determined by examining the table of values and looking for the values of g(x) as x gets closer and closer to 33 from the left and the right sides.

As x approaches 33 from the left (i.e., values of x slightly less than 33), we can see from the table that the values of g(x) decrease from -7 to -16. Therefore, the limit of g(x) as x approaches 33 from the left is -16.

As x approaches 33 from the right (i.e., values of x slightly greater than 33), we can see from the table that the values of g(x) increase from -6.1 to -7. Therefore, the limit of g(x) as x approaches 33 from the right is -7.

Therefore, the correct answer is:

Limit of g(x) = negative 16 as x approaches 33 minus and limit of g(x) = negative 7 as x approaches 33 plus.

Answer:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we can consider the distance from home to Best Buy as the hypotenuse, and the distance traveled west and south as the other two sides.

Let's call the distance from home to Best Buy "x". Then, using the Pythagorean theorem:

x^2 = (distance south)^2 + (distance west)^2

We know that the distance west is 5 miles, and the distance home is 25 miles. We don't know the distance south, so let's call that "y".

Then we have:

x^2 = y^2 + 5^2

25^2 = y^2 + 5^2

Solving for y, we get:

y^2 = 25^2 - 5^2

y^2 = 600

y = sqrt(600)

y = 24.49 (rounded to two decimal places)

Now we can plug in y to find x:

x^2 = y^2 + 5^2

x^2 = 24.49^2 + 5^2

x^2 = 625.12

x = sqrt(625.12)

x = 25.00 (rounded to two decimal places)

Therefore, the distance from home to Best Buy is approximately 25 miles.

Step-by-step explanation:

Answer:

19 and - 8

Step-by-step explanation:

( u ￮ w )(3)

evaluate w(3) then substitute the value obtained into u(x)

w(3) = - 2(3)² = - 2(9) = - 2 × 9 = - 18 , then

u(- 18) = - (- 18) + 1 = 18 + 1 = 19

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

( w ￮ u )(3)

evaluate u(3) then substitute the value obtained into w(x)

u(3) = - 3 + 1 = - 2 , then

w(- 2) = - 2(- 2)² = - 2(4) = - 2 × 5 = - 8

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Using compound interest, each payment should be $948.86, rounded to two decimal places.

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

[tex]A = P (1 + r/4)^t[/tex]

To determine the size of each payment that needs to be made at the end of every 2 months, we can use the formula for the future value of an annuity:

[tex]FV = Pmt x [(1 + r)^{n - 1}] / r[/tex]

When we enter these values into the formula, we obtain:

In this instance, we know that the sinking fund's future value should be $61,000, the interest rate each 2-month period is 5.9%/6 = 0.983%, and there are a total of 54 periods (9 years x 12 months/year / 2 months/period = 54 periods) in the sinking fund's life.

[tex]$61,000 = Pmt x [(1 + 0.00983)^{54 - 1}] / 0.00983[/tex]

Solving for Pmt, we get:

[tex]Pmt = $61,000 x 0.00983 / [(1 + 0.00983)^{54 - 1}][/tex]

= $61,000 x 0.00983 / 0.6346

= $948.86

Therefore, each payment should be $948.86, rounded to two decimal places.

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Answer:

(a) The interest on a simple interest loan is calculated using the formula:

Interest = Principal x Rate x Time

where:

Principal is the amount of the loan

Rate is the interest rate per time period

Time is the duration of the loan in the same time period as the interest rate

In this case, the principal is $8000.00, the rate is 9.00% per year, and the time is 9 months. To calculate the interest, we need to convert the time to years by dividing by 12:

Time in years = 9 months / 12 months per year = 0.75 years

Plugging in the values, we get:

Interest = $8000.00 x 0.09 x 0.75

Interest = $540.00

Therefore, the student must pay $540.00 in interest.

(b) The future value of a simple interest loan is calculated using the formula:

Future Value = Principal + Interest

In this case, the principal is $8000.00 and the interest is $540.00, so the future value is:

Future Value = $8000.00 + $540.00

Future Value = $8540.00

Therefore, the future value of the loan is $8540.00.

Step-by-step explanation:

A statement is not true about the dot plot to the right include the following: A. the French Club has a greater mean than the Spanish Club.

In Mathematics, a dot plot is a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

Mean of French Club = 1/12(18 + (19 × 4) + (20 × 4) + (21 × 2) + 22)

Mean of French Club = 1/12(238)

Mean of French Club = 119/6 = 19.83.

Mean of Spanish Club = 1/12(18 + (19 × 2) + (20 × 3) + (21 × 3) + (22 × 3))

Mean of Spanish Club = 1/12(246)

Mean of Spanish Club = 123/6 = 20.5.

Therefore, 19.83 is less than 20.5.

Median of French Club = 20

Median of Spanish Club = (20 + 21)/2 = 20.5.

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The answer to this question is that the parasailer is 600 feet high. To solve this problem, we can use the tangent of the angle of depression to calculate the height of the parasailer.

Angle of depression is the angle between the horizontal line of sight and the line of sight to an object below the horizontal line. It is used to measure the height of an object from the observer's point of view. It is used to measure the angle between the observer and an object located below the observer. It is sometimes referred to as the inverse of the angle of elevation.

The formula for the tangent of an angle is opposite/adjacent. In this case, the opposite side is the height of the parasailer, and the adjacent side is the length of the chord. Therefore, the equation becomes height/400 = tangent (36°).

Solving for the height, we get height = 400 * tangent (36°). Plugging in the value of the tangent (1.732050808) gives us a height of 692.82 feet.

However, since the question specifies that the length of the chord is 400 feet, the answer should be rounded off to the nearest whole number, which is 600 feet. Therefore, the parasailer is 600 feet high.

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Answer:

Step-by-step explanation:

[tex]\tt y+4+3\left(y+2\right)[/tex]

Expand by distributing terms:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\boxed{\tt y+3y}+\boxed{\tt 4+6}[/tex]

[tex]\tt y+3y=\underline{\bf 4y}[/tex]

[tex]\tt 4+6=\underline{\bf 10}[/tex]

⇒ [tex]\underline{\bf 4y+10}[/tex]

Therefore, A. 4y + 10 is our answer!

_______________________

Hope this helps! :)

Answer:

4y+10

Step-by-step explanation:

у + 4 + 3(y + 2) =

y + 4 + 3y + 6

y + 10 + 3y

4y +10

Answer:

A, B, D

Step-by-step explanation:

for y = 3x + 2

for (#,#), the first number is x and the second number is y

A. if x = -2

y = 3(-2) + 2 = -6 + 2 = -4

which is corresponding to the number -4

so A is true

B. if x = -1

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

so B is true

C. If x = 3

y = 3(3) + 2 = 9 + 2 = 11

so C is false

D. if x = 2

y = 3(2) + 2 = 6 + 2 = 8

so D is true

Answer:

These are three possible solutions to the equation:

(0,2), (1,5), 2,8

The answer is D

Step-by-step explanation:

look at the pictures

Therefore , the solution of the given problem of volume comes out to be  chocolate bar therefore has a 2940 cubic centimetre (cm3) capacity.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are the numbers cm3 as well as in3. But mass can be used to measure an object's dimensions. Typically, an object's weight is transformed into mass units like kilos or kilogrammes.

Here,

The length, breadth, and height of the rectangular, prism-shaped chocolate bar can be multiplied to determine its volume.

Size = 15 centimetres

Width = undefined

Size equals 2 centimetres (thickness)

To solve for the width, we can rearrange this algorithm as follows:

=> Area/Length =  Width

We are aware that the necessary length is 15 centimetres and the necessary area is 1470 cm2, so:

=> width =  1470/15

=>  98 centimetres.

Now that we are aware of every aspect of the chocolate bar, we can calculate its volume:

=> Volume = Length * Width * Height

=>  15 cm x 98 cm x 2 cm = 2940 cm³

The chocolate bar therefore has a 2940 cubic centimetre (cm3) capacity.

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Kevin will have 6 ounces of fruit snack left over after filling the 4 pound containers.

There are several systems of measurement units, including the International System of Units (SI), the United States customary system, and the British imperial system. The SI is the most widely used system and is based on seven base units, including the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity).

To determine how many containers Kevin can fill, we need to first calculate the total weight of the fruit snack.

Total weight of the fruit snack = Weight of dried apples + Weight of dried cranberries

= 48 ounces + 22 ounces

= 70 ounces

Since there are 16 ounces in 1 pound, we can convert the total weight to pounds as follows:

Total weight in pounds = 70 ounces ÷ 16 ounces/pound

= 4.375 pounds

Therefore, Kevin can fill 4 pound containers with fruit snack, with 0.375 pounds of fruit snack left over.

To determine if any fruit snack will be left over, we need to convert the remaining weight of 0.375 pounds back to ounces:

0.375 pounds × 16 ounces/pound = 6 ounces

Therefore, Kevin will have 6 ounces of fruit snack left over after filling the 4 pound containers.

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803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.

Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given values, we get:

Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8

= 401.92 + 401.92

= 803.84 square inches

the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.

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Answer:

Lo siento, como modelo de lenguaje de IA, no tengo la capacidad de visualizar o dibujar gráficos. ¿Puedo ayudarte con algo más?

The surface area of the figure is 549.5 square ft

Given that

The composite figure comprises of a cone and a cylinder of the following dimensions

Cone: Radius = 5 ft and Height = 12 ft

Cylinder: Radius = 5 ft and Height = 6 ft

The surface area of the figure is calculated as

Surface area = Cone + Cylinder -  Circle

So, we have

Surface area = πr(r + √[h² + r²]) + 2πr(r + h) - πr²

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

Surface area = 3.14 * 5 * (5 + √[12² + 5²]) + 2 * 3.14 * 5 * (5 + 6) - 3.14 * 5²

Evaluate

Surface area = 549.5

Hence, the surface area is 549.5

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The slope of the lines are given as

a) m₁ = -2

b) m₂ = 4/3

c) m₃ = 5/2

d) The equation of line is y = ( 1/2 )x + 9/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 3 , 5 )

Let the second point be Q ( 7 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( -3 - 5 ) / ( 7 - 3 )

Slope m₁ = -8/4

Slope m₁ = -2

b)

Let the first point be P ( 4 , 2 )

Let the second point be Q ( 10 , 10 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₂ = ( 10 - 2 ) / ( 10 - 4 )

Slope m₂ = 8/6

Slope m₂ = 4/3

c)

Let the first point be P ( -1 , -2 )

Let the second point be Q ( -3 , -7 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₃ = ( -7 - ( -2 ) ) / ( -3 - ( -1 ) )

Slope m₃ = -5/-2

Slope m₃ = 5/2

d)

Let the first point be P ( 5 , 7 )

The slope of the line is y = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 7 = ( 1/2 ) ( x - 5 )

y - 7 = ( 1/2 )x - 5/2

Adding 7 on both sides , we get

y = ( 1/2 )x + 9/2

e)

The slope of the line is y = 5/2 and the points are linear

Hence , the equation of line is y = ( 1/2 )x + 9/2

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The complete question is :

Determine the slopes between the points in lowest terms

a) ( 3 , 5 ) and ( 7 , -3 )

b) ( 4 , 2 ) and ( 10 , 10 )

c) ( -1 , -2 ) and ( -3 , -7 )

d) Draw and accurate graph of the line with the slope of ( 1/2 ) that passes through the point ( 5 , 7 )