Triangle XYZ has vertices X: (0,2) Y: (3,8), and Z: (6,2). Show that the triangle is isosceles by determining the length of each side.

Please help!!!

Answers

Answer 1

Sides XY and YZ are both equal to √45 units, therefore, triangle XYZ is an isosceles triangle.

What is an Isosceles Triangle?

If a triangle has two side lengths that are equal to each other, the triangle is called an isosceles triangle. Therefore, two of the sides of an isosceles triangle must be equal.

Given the vertices of triangle XYZ as:

X(0, 2)

Y(3, 8)

Z(6, 2).

Find the length of each side using the distance formula, [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

XY = √[(3−0)² + (8−2)²]

XY = √45

XZ = √[(6−0)² + (2−2)²]

XZ = √36

XZ = 6

YZ = √[(6−3)² + (2−8)²]

YZ = √45

The triangle has two equal sides YZ and XY, therefore it is an isosceles triangle.

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Related Questions

Select the correct answer.
What is the domain of y= cos (x)

a.2pie
b. [-1,1]
c. (-infinity, infinity)
d. [0,infinity)

Answers

The answer should be C.

The range of definition of the cosine function is all real numbers. [tex]R[/tex]

It is also periodic in [tex]2\pi[/tex].

It is an even function. [tex]f(x)=f(-x)[/tex]

It can also be written in this form.

[tex]cos(x)=\frac{e^{-ix}+e^{ix}}{2}[/tex]

HELP PLEASE!! WILL THANK AND MARK BRAINLIEST!

Answers

The analysis of the tables based on the first difference values indicates

1 a. The function is a linear function

b The reason the function is linear is because the rate of change in the x and y-values are constant, such that the rate of change of the function is also constant

2. a. The function is not linear

b. This is so because the changes in the consecutive terms of the x-values is not constant while the change in the y-values is constant making the overall rate of change of the function (the slope of the function) to vary

3. a. The table is not a linear function

b. The reason why the table does not represent a linear function is because the change in the terms of the y-values is not constant

4. a. The table is a linear function

b. The reason why it is a linear function is because the changes in the x and y-values are constant

What is a linear function?

A linear function is a function that when plotted on a graph, forms a straight line.

1) The changes in x-values are;

Δx₁ = -2 - (-3) = 1

Δx₂ = -1 - (-2) = 1

Δx₃ = 0 - (-1) = 1

Δx₄ = 1 - 0 = 1

The changes in y-values are;

Δy₁ = 2 - 1 = 1

Δy₂ = 3 - 2 = 1

Δy₃ = 4 - 3 = 1

Δy₄ = 5 - 4 = 1

a. Is it a linear function? Yes

b. Why it is a linear function is because the first difference of the y-values and the change between consecutive x-values are both constant

2. The changes in x-values are;

Δx₁ = -2 - (-5) = 3

Δx₂ = -1 - (-2) = 1

Δx₃ = 2 - (-1) = 3

Δx₄ = 5 - 2 = 3

The changes in y-values are;

Δy₁ = 4 - 2 = 2

Δy₂ = 6 - 4 = 2

Δy₃ = 8 - 6 = 2

Δy₄ = 10 - 8 = 2

a. Is it a linear function? No

b. The reason why it is not a linear function is because the rate of change in the y-values is constant while the rate of change in the x-values varies, which indicates that the rate of the function also varies resulting in a non linear function.

3. The changes in x-values are;

Δx₁ = -5 - (-10) = 5

Δx₂ = 0 - (-5) = 5

Δx₃ = 5 - 0 = 5

Δx₄ = 10 - 5 = 5

The changes in y-values are;

Δy₁ = 4 - 9 = -5

Δy₂ = 2 - 4 = -2

Δy₃ = 0 - 2 = -2

Δy₄ = -3 - 0 = 2

a. Is it a linear function? No

b. The reason why the table of values does not represent the values of a linear function is that the first difference, which is the change in the consecutive y-values is not constant, such that the rate of changes of the ordered pairs of the function function is not constant and the graph therefore does not follow a straight line pattern

4) The changes in x-values are;

Δx₁ = 3 - (-1) = 4

Δx₂ = 7 - 3 = 4

Δx₃ = 11 - 7 = 4

Δx₄ = 15 - 11 = 4

The changes in y-values are;

Δy₁ = -4 - (-9) = 5

Δy₂ = 1 - (-4) = 5

Δy₃ = 6 - 1 = 5

Δy₄ = 11 - 6 = 5

a. Is it a function? yes

b. The reason why it is a function is because the first difference in the y-values is constant and the difference between consecutive x-value terms is also constant

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BRAINLIST! Please answer!!Parallelogram Properties
1. In Parallelogram JKLM if m

Answers

Answer:

60

Step-by-step explanation:

I believe two angles should add up to 180 in a parallelogram

(PLEASE HELP FAST) A 9-member team plans to run a 4-mile relay race. Distance markers are placed on the racecourse every 0.25 mile. Will any of the relay exchanges take place at any of the 0.25-mile markers? If so, which one(s)? List the locations of all of the exchanges in decimal form.

Answers

No there will be no relay exchange in any of the 0.25-mile markers

the exchanges are

0.44440.88891.33331.77782.22222.66673.11113.55564

Further explanation of the exchanges are treated

In a 4 mile race the exchanges are made equal by the number of the team members

therefore the exchanges will be at interval of 4/9 and repetitive addition give other points and the list are

4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4

In decimal form this will be listed in four decimal place

0.4444

0.8889

1.3333

1.7778

2.2222

2.6667

3.1111

3.5556

4

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A cup of coffee is poured at 190° Fahrenheit, and is allowed to cool in a 70° room. If the temperature of
the coffee is 170° after half an hour,
a. What will the temperature be after 70 minutes?
b. How long will it take the coffee to cool to 120°2

Answers

Answer:

a) 190 - 70(2/3) = 430/3 = 143 1/3 degrees

b) 190 - (2/3)x = 120

70 = 2x/3

210 = 2x

Step-by-step explanation:

x = 105 minutes

how do i do these?

i'm having trouble figuring out which is x and which is y.

Answers

Answer:

X is horizontal axis, Y is vertical axis

Step-by-step explanation:

(x,y) in the notation

Answer is x and y axis are labeled on the graph.
X is horizontal, goes left and right of (0).
Y is vertical, goes up and down from (0).
Ordered pairs are always in x,y order. So
(-2,3) is -2 on the x axis (going left 2), and moving up + 3.

I’m not sure what else you need on the questions for these 3 attachments.

Solve this system of equations using the LINEAR COMBINATION method, then answer the questions below.
2x - y = - 4 6x + 5y = 4
• What did you get for the (x, y) solution to this system? (2.5 points)
• Explain what you did to create a pair of opposites so that you could combine the equations. (2.5 points)

Answers

The solutions to the system of equation (x, y) are (-1, 2)

System of Equations

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

The equations given are;

2x - y = -4 ... eq(i)

6x + 5y = 4 ... eq(ii)

Solving the equations

x = -1 , y = 2

The solutions of the problem are x = -1 and y = 2

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18. Construction workers will test to see if two walls meet at a right angle by using a 3-4-5
Pythagorean triple or a multiple of this triple. Two walls meet as shown below and a worker
marks a point on each wall with an %.
(a) If these walls met at a right angle, how much
distance should be between the two marked
points?
12 ft
19.5 ft
16 ft

Answers

Construction workers will test to see if two walls meet at a right angle by using a Pythagorean triple or a maltiple of this triple. Two walls meet as shown below and a worker marks a point on each wall with an . (a) If these walls met at a right angle, how mach distance should be between the two marked. points? walls do not meet at a right angle because the length between the two points does not form a Pythagorean triple. What type of angle do they meet at? Explain.

What is the slope-intercept equation of the line that includes (0, 12) and (4, 36)? A. y = –12x + 6 B. y = 6x + 12 C. y = 6x – 12 D. y = 12x – 6

Answers

Answer:

B. [tex]y=6x+12[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{36-12}{4-0}=6[/tex].

The [tex]y[/tex] intercept is 12, so the equation is [tex]y=6x+12[/tex].

Find the sum if it exists of the infinite geometric series related to the infinite geometric sequence described by an=12(0.2)^n-1

Answers

The sum of the infinite geometric sequence exists and is equal to 15.

We are given an expression for terms in a geometric progression. The term at position "n" is given by the following formula.

T(n) = 12(0.2)^(n - 1)

The general representation for the terms in a geometric sequence is given by : T(n) = a*r^(n - 1).

Here, the variables "a" and "r" represent the first term and the common ratio for the geometric progression. On comparing the given formula with the standard representation, we conclude that the first term of the given geometric progression is 12 and the common ratio is 0.2.

a = 12

r = 0.2

The sum of an infinite geometric sequence exists if the common ratio lies between -1 and 1.

-1 < r < 1

-1 < 0.2 < 1

The above inequality holds true, so the sum exists. Let the sum of the infinite geometric sequence be denoted by "S". The formula and calculations are below.

S = a/(1 - r)

S = 12(1 - 0.2)

S = 12/0.8

S = 15

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BRAINLIEST FOR THE BEST ANSWER!

Question:
WRITING-Your friend is having trouble understanding the Midpoint Formula.

a. Explain how to find the midpoint when given the two endpoints in your own words.

b. Explain how to find the other endpoint when given one endpoint and the midpoint in your own words.

PLEASE DO NOTE THAT THIS IS WRITING NOT OPTIONS. Thank you in advance! :)​

Answers

The formula that is used to calculate the midpoint for the given two point is written as ( (x₁ + x₂)/2 , (y₁ + y₂)/2).

Mid point:

Midpoint refers the point on a line that is at an equal distance from either end.

Given,

Here we have to explain the concept of midpoint in a simple manner.

According to the definition, midpoint refers the central point between the two points.

So, in a simple manner we have said that the mid point is calculated by finding the average of the two given point.

For example, (x₁, y₁) and (x₂, y₂) are the points, then the midpoint (xₙ, yₙ) is calculated by using the formula,

(xₙ, yₙ) = ( (x₁ + x₂)/2 , (y₁ + y₂)/2)

Similarly, if one point and the midpoint is given, then the another point is calculated by apply the remaining point as (x, y) and solve it accordingly, then we can get the value of it.

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pls help
In a set of eight consecutive integers, the smallest integer is more than $\frac35$ of the largest integer. What is the smallest possible value of the sum of the eight integers?

Answers

The smallest possible value of the sum of the eight integers is given by:

116.

What are the integers?

The eight integers in the problem are given as follows:

n, ..., n + 7.

Hence:

The smallest integer is of n.The largest integer is of n + 7.

The smallest integer is more than 3/5 of the largest integer, hence the following inequality is built to relate them:

n > 3/5(n + 7)

Applying the distributive property on the right side, we have that:

n > 0.6n + 4.2.

0.4n > 4.2

n > 4.2/0.4

n > 10.5.

Hence the integers are:

11, 12, 13, 14, 15, 16, 17, 18.

(as 11 is the smallest integer possible).

Then the value of the sum is obtained as follows:

11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 116.

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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5. 50 service fee. The total cost in dollars for ordering 5 tickets is $108. 0. Which linear function represents c, the total cost, when x tickets are ordered? c(x) = 5. 50 + 20. 50x c(x) = 5. 50x + 20. 50 c(x) = 5. 50 + 21. 60x c(x) = 5. 50x + 21. 60.

Answers

The Linear function representing the total cost , where x is the number of tickets is  c(x) = 5. 50 + 20. 50x  , the correct option is (a) .

In the question ,

it is given that ,

the total cost for 5 tickets = $108

the service fees for the tickets to a basketball game = $5.50

we need to find the cost function for 5 tickets .

we substitute , the value of x = 5 in each option and check which option gives the cost as $108 .

Option (a)

c(x) = 5.50 + 20.50x

= 5.50 + 20.50(5)

= 108

Option(b)

c(x) = 5. 50x + 20. 50

= 5.50(5) + 20.50

= 48

Option(c)

c(x) = 5. 50 + 21. 60x

= 5.50 + 21.60(5)

= 113.5

Option(d)

c(x) = 5. 50x + 21. 60

= 5.50(5) + 21.60

= 49.1

So, from the answers above we can conclude that the cost function representing the cost for 5 tickets is c(x) = 5. 50 + 20. 50x   .

Therefore , The Linear function representing the total cost , where x is the number of tickets is  c(x) = 5.50 + 20.50x  .

The given question is incomplete , the complete question is

Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108 . Which linear function represents c, the total cost, when x tickets are ordered ?

(a) c(x) = 5.50 + 20.50x

(b) c(x) = 5.50x + 20.50

(c) c(x) = 5.50 + 21.60x

(d) c(x) = 5.50x + 21.60.

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suppose 1,872 of 2,600 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?

Answers

The interval estimate for the population proportion
(1778, 2470).here we can use normally .

Given 1,872 of 2,600 registered sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence.
Here given that the 95% is rhe for people will for the Republican candidate for president
So 95 percent of 26,00 is given by
95/100*2600
2470
If we say that 1872 people say that then can go for voting 2600 that means 72 percent of people will atleast
So 72 percent of 2470 is
1778
So the interval (1778, 2470).

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Babe Ruth, professionl bseball player known for hitting home runs, had a batting average of 0.342. Hank Aaron, another record home urn hitter, had a batting average of 0.305 . How much greater was Babe Ruth's batting avarage that Hank Aaron's ?

Answers

Babe Ruth's batting average is 0.037 more than that of Hank Aaron's

From the question, we have

difference = 0.342-0.305

=0.037

Babe Ruth's batting average is 0.037 more than that of Hank Aaron's

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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19. Factor to find the zeros: f(x) = x² + 6x.
(-6,0)
no solution
(0,0) and (-6,0)
(6,0)

Answers

Zeros of f(x) = [tex]x^{2} +6x[/tex] is (0,0) and (-6,0).

Given, f(x) = [tex]x^{2} +6x[/tex]

                = x(x+6)

For zeros, function f(x) = 0

x(x+6) = 0

x = 0    x+6 = 0

                x = -6

Putting values of x in equation,

For x = 0

f(x) = [tex]0^{2}+6(0)[/tex]

     = 0

Therefore, (0,0)

For x = -6

f(x) = [tex](-6)^{2}+6(-6)[/tex]

     = 36 - 36

     = 0

Therefore, (-6,0)

Hence, zeroes for f(x) is (0,0) and (-6,0).

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c) (f + a)(ƒ +9) (f - 4) = f³ +7f²-26f - 72
Without fully expanding the brackets. Find a

Answers

Answer:

a = 2

Step-by-step explanation:

the constant terms inside the factors will multiply to give the constant term of the expansion, that is

a × 9 × - 4 = - 72

- 36a = - 72 ( divide both sides by - 36 )

a = 2

Jason is training to run in a marathon. His goal for this week is to run a minimum of 35 miles. So far this week, he has already run 15 miles. Which inequality could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal?.

Answers

As per the concept of inequality, the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is 15 + 4m ≥ 35

Inequality

Inequality shows a non equal relationship between two numbers or two expressions.

Given,

Jason is training to run in a marathon. His goal for this week is to run a minimum of 35 miles. So far this week, he has already run 15 miles.

Here we need to determine the inequality could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.

Here we know that, his goal for this week is to run a minimum of 35 miles.

For this week, he has already run 15 miles.

In the given inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal.

=> 15 + 4m ≥ 35

Here we know that, 4m = number of m miles run in 4 days.

Therefore, inequality that could be used to determine the mean number of miles, m, he would need to run each day for 4 more days to achieve his goal is written as,

=> 15 + 4m ≥ 35

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Malik took a survey to find out how many students in his school have a pet. There are 628 students in the school. 50% of them have a pet. How many students in Malik's school have a pet?

Answers

Step-by-step explanation:

628x50/100 = 314

Answer: 314 students have a pet

Step-by-step explanation: 628 divided by 2 = 314

what is 7 times [(7+7)divided by 7

Answers

Answer: 14

Step-by-step explanation: do the parentheses first, 7+7 is 14, multiply by 7 to get 98 divide by 7 to get 14

Answer:

14

Step-by-step explanation:

bc 7x7 us 49 and u divided by 7 your answers is going to be 14

Write a number with one decimal place, that is bigger than 6 wholes and 4 fifths but smaller than 7

Answers

The value 6 4/5 is equivalent to 6 8/10 as a decimal, 6.8.Since the requirements in the problem are (1) 1 decimal place , (2) greater than 6.8, and (3) less than 7, the only answer fulfilling all requirements is 6.9.

8. Aleks is writing a report about recycling in the local town. In 2021: There were 2341 people living in the town Each person in the town recycled an average of 264.6kg of waste. Aleks knows that 1tonne = 1000kg. How many tonnes of waste were recycled in town in total in 2022?​

Answers

The tons of waste recycled in 2021 was 619.4286 tons.

According to the question,

We have the following information:

In 2021: There were 2341 people living in the town. Each person in the town recycled an average of 264.6kg of waste. Aleks knows that 1 ton = 1000kg.

Now, the total waste recycled in 2021 can be found using multiplication:

Number of people*waste recycled by each person

2341*264.6

619428.6 kg

Now, we will convert this from kilogram to tons.

1 ton = 1000 kg

1 kg = 1/1000 ton

So, we will divide the waste in kilogram by 1000:

Total waste recycled = 619428.6/1000

Total waste recycled = 619.4286 tons

Hence, the tons of waste recycled in 2021 was 619.4286 tons.

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8 < x (7 − x)
Please help, no one has answered this question

Answers

I Think thatthe answer is 2

7j+5−8k when j = 0.5 and k = 0.25

Answers

Answer:6.5

Step-by-step explanation:

Here j = 0.5 and k = 0.25

7j+5-8k

= 7(0.5)+5-8(0.25)

= 3.5+5-2

= 6.5

PLEASE HELP!!


Ian buys a two-gallon bottle of juice for $28.16. What is the unit rate of the cost of the juice per fluid ounce?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces

Before you try that problem, answer the question below.
How many fluid ounces of juice did Ian buy?

Answers

There is 128 ounces in one gallon. So for two it would be 256 oz. He bought 256 oz.

Then since it’s $28.16 just divide that by 256 oz which would give you $.11.

So $0.11 per fluid ounce.

Answer: 11 Cents per ounce of Juice

Step-by-step explanation:

The first step here is going to be to find how many ounces are in a gallon. This can be determined as shown using the given information you stated above:

1 gallon * 4 quarts * 2 pints * 2 cups * 8 ounces = 128 ounces in 1 gallon

Step 2 is multiplying 128 ounces by 2 because we have two gallons of juice in the bottle:

128 ounces per gallon* 2 gallons = 256 ounces

Step 3 is dividing the total cost of the juice, which is $28.16, by the number of total number ounces (256)

$28.16 / 256 ounces = .11 dollars per ounce (aka 11 cents per ounce)

!*EMERGENCY, WILL GIVE BRAINLIEST QUICK*!

This table represents the cups of coffee, c, a coffee shop has left after being open for h hours. When graphed, all of the points in the table lie on the same line. What is the slope and y-intercept of the line? Drag and drop the slope and y-intercept into the corresponding boxes.
Slope -48, 9 ,48 ?
y-intercept 432, C, 6, 9?

(LEFT SIDE IS HOURS, RIGHT SIDE CUPS)
TABLE-------
HOURS, H / CUPS, C
0 / 432
3 / 288
6 / 144
9 / 0​

Answers

Answer:

Slope is -48, y-intercept is 432

[tex]y = - 48x + 432[/tex]

Step-by-step explanation:

[tex]m = \frac{432 - 288}{0 - 3} = \frac{144}{ - 3} = - 48[/tex]

[tex]432 = - 48(0) + b[/tex]

[tex]432 = 0 + b[/tex]

[tex]b = 432[/tex]

[tex]y = - 48x + 432[/tex]

Please help!!!

How many complex roots does the equation 0= 3x^5-x^4-5x^2 +1 have?

Answers

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

Below is a polynomial equation that is given:

0 = 3x⁵ − x⁴ − 5x² + 1

Which can also be written as

3x⁵ − x⁴ − 5x² + 1 = 0

A polynomial of degree 5 is used in the accompanying polynomial equation.

Using a graphing application to solve it graphically is the simplest approach.

The polynomial equation obviously has a maximum of 5 roots because it is an equation of degree 5.

Now that we have the graph, we can use it to find the equation's roots.

There are 2 complex roots because there are only 3 real roots and 2 remaining are complex roots.

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

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Help pls

2 Answers and I can make brainliest whoever has the correct answer

Answers

Check the picture below.

so if we look at those dimensions in centimeters, let's get the area of the cross-section, keeping in mind the volume of the bar is simply the area of the cross-section times the length.

[tex]\stackrel{\textit{\Large area of the cross-section}}{(2)(15)cm^2~~ + ~~(2)(15)cm^2~~ + ~~(8)(2)cm^2\implies 76~cm^2} \\\\\\ \stackrel{\textit{\LARGE bar's volume}}{76cm^2\cdot 120cm\implies 9120~cm^3}[/tex]

now, we know the density of the metal for the bar is 8 g/cm³, so let's do a quick conversion for the whole bar

[tex]\begin{array}{ccll} grams&cm^3\\ \cline{1-2} 8 & 1\\ g& 9120 \end{array} \implies \cfrac{8}{g}~~=~~\cfrac{1}{9120}\implies 72960=g\implies 72.960Kg[/tex]

so if one bar has 72.960 Kg, how many bars are there in 250Kg?

[tex]\begin{array}{ccll} bars&Kg\\ \cline{1-2} 1 & 72.960\\ b& 250 \end{array} \implies \cfrac{1}{b}~~=~~\cfrac{72.960}{250} \\\\\\ 250=72.96b\implies \cfrac{250}{72.96}=b\implies 3.43\approx b\qquad \textit{so only \underline{three whole bars}}[/tex]

Please write a linear equation that passes through (5,2) and (6,4)!

Answers

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{5}}} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-2=2x-10\implies {\Large \begin{array}{llll} y=2x-8 \end{array}}[/tex]

use the communitive property to simplify the expression. 1/3 + 3/5 + 2/3

Answers

The simplified expression using the commutative property is in the first option :  1/3 + 2/3 + 3/5   = 1 + 3/5 = 1 3/5 .

now the given expression is 1/3 + 2/3 + 3/5 .

Therefore this expression can be simplified using the commutative property where we put the like terms together.

1/3 + 3/5  + 2/3

= 1/3 + 2/3 + 3/5 (here we use commutative property on the second and third terms of the expression)

= 1 + 3/5 (we know that 1/3 +2/3 = 1)

=1 3/5

Hence by using the commutative property we calculate the sum easily.

The commutative property applies to the arithmetic operations of addition and multiplication. This suggests that no matter how the numbers are arranged or placed, the result of adding or multiplying them remains the same.

As an illustration, 1 + 5 = 6 and 5 + 1 = 6. No matter how two numbers are added, the sum is unaffected. Multiplication uses the same principle. The commutative property does not hold for division and subtraction because the results are completely different when the numbers are rearranged.

To learn more about commutative property visit:

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