The x-axis represents the distance traveled (in miles).
Considering that the x-axis shows the distance travelled (in miles) and the y-axis represents the amount of gas left in the tank (in gallons), the x-intercept would represent the point at which Brianna's gas tank is empty, and she would need to refill her tank to continue traveling. In other words, the x-intercept is the distance Brianna can travel before running out of gas, assuming her car's fuel efficiency remains constant and she does not refill her tank.
Two key lines known as the x and y axes are the building blocks of a graph.
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what is the problem from y=x+1
Answer: Change x to a number, and that number + 1 will be y
Step-by-step explanation: the reason for this is simple, change the independent variable, which is always in the problem, and you can figure out the dependent variable.
Answer:
X +1
Step-by-step explanation:
the graph is x +1.....
5. Find tn for the geometric sequence where t3 = 24 and t9 = 1536. Why are there 2 answers? (4 marks)
Answer: A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is constant. Let's call the common ratio "r". We can use this property to find "r" and then calculate other terms in the sequence.
Given that t3 = 24 and t9 = 1536, we can use the formula for the nth term in a geometric sequence: tn = t1 * r^(n-1), where t1 is the first term in the sequence.
Since we know t3 and t9, we can find r by dividing t9 by t3:
r = t9/t3 = 1536/24 = 64
Now that we have found "r", we can use it to find t1 by dividing t3 by r^(3-1):
t1 = t3 / r^(3-1) = 24 / 64^(3-1) = 24 / 64 = 3/2
Now that we know t1 and r, we can find any term in the sequence by using the formula: tn = t1 * r^(n-1).
Therefore, there are two possible sequences with two different first terms:
Sequence 1: t1 = 3/2, r = 64
Sequence 2: t1 = -3/2, r = -64
These are the two possible geometric sequences that satisfy the conditions t3 = 24 and t9 = 1536.
Step-by-step explanation:
11) Dalton calls a local moving company to determine how much it will cost him to move. If he hires 2 movers and rents a truck for an hour it costs $65. It costs $80 to hire 3 movers and rent a truck for an hour. What is the hourly rate to hire a mover? What is the hourly rate to rent the truck?
Answer: $35.
Step-by-step explanation: Let A = 2 movers and one truck for hour = $65
B = 3 movers and one truck for hour = $80
So, 1 mover = B - A
= $80 - $65
= $15
Hence, 2 movers cost = 2 × $15
= $30
SO, rent of the truck hourly = A - cost of 2 movers
= $65 - $30
= $35
Therefore cost of renting the truck for an hour = $35
how many solutions do 2(x-4)=2x-8 have
The equation 2(x - 4) = 2x - 8 has infinitely many solutions.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is 2(x - 4) = 2x - 8.
Solving this,
Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).
Substituting in the original equation,
(2 × x) - (2 × 4) = 2x - 8
2x - 8 = 2x - 8
2x - 2x = -8 + 8
0 = 0
Right hand side and left hand side are equal if we put any value for x.
So it has infinitely many solutions for x.
Hence the given equation has infinitely many solutions.
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what's the geometric mean between 3√5 and 6√5
Answer:
3√10
Step-by-step explanation:
[tex]GM=\sqrt{(3\sqrt{5})(6\sqrt{5})}=\sqrt{18*5}=\sqrt{90}=3\sqrt{10}[/tex]
Answer: [tex]3\sqrt{10}[/tex]
Work Shown:
Part 1
[tex]g = \text{geometric mean of x and y}\\\\g = \sqrt{\text{x}\text{y}}\\\\g = \sqrt{3\sqrt{5}*6\sqrt{5}}\\\\g = \sqrt{(3*6)*(\sqrt{5}*\sqrt{5})}\\\\g = \sqrt{18\sqrt{5*5}}\\\\g = \sqrt{18\sqrt{5^2}}\\\\g = \sqrt{18*5}\\\\g = \sqrt{90}\\\\[/tex]
Part 2
[tex]g = \sqrt{90}\\\\g = \sqrt{9*10}\\\\g = \sqrt{9}*\sqrt{10}\\\\g = 3\sqrt{10}\\\\[/tex]
the days to maturity for a sample of five money market funds are shown here. the dollar amounts invested in the funds are provided. days to maturitydollar value ($ millions) 1515 1110 725 515 410 use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds. round your answer to decimal places. days
The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.
To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.
The calculation for the weighted mean is as follows:
Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)
where D represents the days to maturity and V represents the dollar value.
Using the given values, we can plug them into the formula and get:
Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)
Weighted Mean = 8.95 (rounded to two decimal places)
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The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of p hat ?
Mu Subscript p hat = p = 0.12
Mu Subscript p hat = n p = 100 (0.12) = 12
Mu Subscript p hat = 1 minus p = 1 minus 0.12 = 0.88
Mu Subscript p hat = n (1 minus p) = 100 (1 minus 0.12) = 88
The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.
The sampling distribution of p hat follows a normal distribution thus,
Mu Subscript p hat = p
Here, the value of p = 0.12
Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.
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Answer:
A. Mu Subscript p hat = p = 0.12
Step-by-step explanation:
the product 2√3 and 3√12 in simplified form is
The product of 2√3 and 3√12 in simplified form is 6√36. To simplify this expression, we can first multiply 2 and 3 to get 6. Then, we can simplify the square root of 3 and the square root of 12 by finding their prime factorizations:
√3 = √(3 * 1) = √3
√12 = √(12 * 1) = √(2^2 * 3) = 2√3
So, 2√3 = 2 * √3 = 2 * √3
And, 3√12 = 3 * 2√3 = 6√3
Finally, the product of 2√3 and 3√12 is 6 * 6√3 = 6√36.
if the true population proportion for a sample size of 200 is found to be 0.2, then the standard error will be
The correct option is SE is 0.04. In statistics, a sample proportion is a statistic that represents the proportion of individuals in a sample who have a particular characteristic or belong to a certain category.
The standard error of the sample proportion can be calculated as follows:
SE = sqrt(p * (1 - p) / n)
Where p is the sample proportion and n is the sample size. In this case, the sample proportion is 0.2, and the sample size is 200. So, plugging these values into the formula, we get:
SE = sqrt(0.2 * (1 - 0.2) / 200)
SE = sqrt(0.16 / 200)
SE = 0.04
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Louise is planning to renovate her house. She intends to spend no more than $30 000. She has
$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.
Answer: To solve this problem, we can use the formula for calculating the future value of an investment:
FV = PV * (1 + r/n)^(nt)
where:
FV is the future value of the investment
PV is the present value of the investment (the initial amount Louise has to invest)
r is the annual interest rate (4.28%)
n is the number of times the interest is compounded in a year
t is the number of years the investment is made
Since the interest is compounded monthly, we need to convert the annual interest rate to a monthly rate:
r/12 = 4.28% / 12 = 0.3566666666666667%
Now, we can use the formula to calculate the future value of Louise's investment:
FV = $20,000 * (1 + 0.3566666666666667%)^(12t)
We can use trial and error or iterative methods to find the value of t that satisfies the condition: FV = $30,000.
A quick approximation is to use the formula for simple interest:
FV = PV * (1 + r * t) = $20,000 * (1 + 0.0428 * t)
t = ($30,000 - $20,000) / ($20,000 * 0.0428) = 2.857142857142857 years, or approximately 2.9 years.
This is an approximation, but it should be close to the actual answer. To get a more accurate answer, we can use an iterative method, such as Newton-Raphson or bisection, to solve for t in the formula above.
Step-by-step explanation:
There are eight groups of students, each working on a science project in the gym. Each group has the same number of students. Mr. Davids asks for 44 students from each group come with him to get more supplies. Now there are a total of 5656 students in the gym.
a. Write an equation to represent this situation, where xx represents the number of students in each group.
Preview
b. How many students are in each group? Simplify your answer completely.
Answer:
58585
Step-by-step explanation:
i know
a projectile travels a distance of 800 meters with an initial velocity of 200 m/s. what two firing angles could be used to launch the projectile? how long does it take each projectile to hit the ground
a. The two firing angles of the projectile are 5.65° and 174.35°
b. The time it takes the projectile to hit the ground is 4.02 s
What is a projectile?A projectile is an object that follows a parabolic path when thrown into the air.
a. How to find the two firing angles?Given that a projectile travels a distance of 800 meters with an initial velocity of 200 m/s, to find the firing angles, we use the formula for the range of a projectile.
What is the range of a projectile?The range of a projectile is its horizontal distance. It is given by R = u²sin2Ф/g where
u = initial velocity of projectile, Ф = angle of projection and g = acceleration due to gravity = 9.8 m/s²Given that we require Ф, the angle of projection. Making it subject of the formula, we have that
Ф = [sin⁻¹(gR/u²)]/2
Given that
u = 200 m/s and R = 800 mSubstituting the values of the variables into the equation, we have
Ф = [sin⁻¹(gR/u²)]/2
Ф = [sin⁻¹(9.8 m/s² × 800 m/(200 m/s)²)]/2
Ф = [sin⁻¹(9.8 m/s² × 800 m/(40000 m²/s²)]/2
Ф = [sin⁻¹(9.8 m²/s² × 1/50 m²/s²)]/2
Ф = [sin⁻¹(0.196)]/2
Ф = 11.30°/2
Ф = 5.65°
Since sin is positive in the second qudrant also, the second angle is
Ф = 180° - 5.65°
= 174.35°
So, the angle are 5.65° and 174.35°
b. How long does it take the projectile to hit thye ground?To find how long it takes the projectile to hit the ground, we use the formula for time of flight of a projectile.
T = 2usinФ/g where
u = initial velocity of projectile, Ф = angle of projection and g = acceleration due to gravitySince
u = 200 m/'sФ = 5.65° andg = 9.8 m/s²Substituting the values of the variables into the equation, we have
T = 2usinФ/g
T = 2(200 m/s)sin5.65° ÷ 9.8 m/s²
T = 400 m/s × 0.09845 ÷ 9.8 m/s²
T = 39.381 m/s ÷ 9.8 m/s²
T = 4.02 s
So, the time it takes the projectile to hit the ground is 4.02 s
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1) Operaciones con números escritos en notación científica
a) Después de reunir información, Kara decidió sumar algunas distancias. Decidió sumas la
distancia de la Tierra a Saturno con la distancia de la Tierra a Júpiter.
Aquí está lo que escribió.
5.95 × 108 + 8.87 × 108
¿Sabes cuál es el resultado?
We can write the equivalent expression as -
{5.95 × 10⁸ + 8.87 × 10⁸} = {10⁸ x 14.82}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is combination of terms both constants and variables. For example -
23 + 54
2x + 5
3x + 5y + z
Given is that after gathering information, Kara decided to add up some distances. She decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. He wrote -
5.95 × 10⁸ + 8.87 × 10⁸
The given expression is -
5.95 × 10⁸ + 8.87 × 10⁸
10⁸ x (5.95 + 8.87)
10⁸ x 14.82
Therefore, we can write the equivalent expression as -
5.95 × 10⁸ + 8.87 × 10⁸ = 10⁸ x 14.82.
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{Question in english -
1) Operations with numbers written in scientific notation
a) After gathering information, Kara decided to add up some distances. decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. Here is what he wrote.
5.95×108 + 8.87×108
Do you know what the result is?}
Alexa is saving up to buy a new jacket. She already has $45 and can save an
additional $7 per week using money from her after school job. How much total
money would Alexa have after 8 weeks of saving? Also, write an expression that
represents the amount of money Alexa would have saved in w weeks.
Answer:
Step-by-step explanation:
Answer: 101because if you multipled 7 times 8 you will get 56 and if you add it with 45 you will get 101
i hope this help
After 8 weeks of saving, Alexa will have a total of $101. The expression to show the money Alexa saves in 'w' weeks is 45 + 7w.
Explanation:The subject of this question is
Mathematics
and it is geared towards
Middle School
grades. To solve this problem, we need to use
algebraic expressions
. Based on the problem given, Alexa has $45 initially and saves $7 per week additionally from her after school job. So if she saves for 8 weeks, Alexa would have accumulated an additional $7 times 8 = $56. Therefore, the total amount of money Alexa would have after 8 weeks is her initial amount of $45 plus the additional $56, which equals $101. To represent this in terms of an expression, where 'w' stands for weeks, you can write 45 + 7w. This expression lets us calculate the total savings for any number of weeks 'w'.
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How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once?
Answer:
37
Step-by-step explanation:
AAA 1 way
AAB, AAC, AAD 3 ways each 3*3=9 ways
ABB, ACC, ADD 3 ways each 3*3=9 ways
ABC, ABD, ACD 3*2=6 ways each 3*6=18ways
1+9+9+18 = 37 ways
you leave a 20% tip on your $70 dinner bill. how much was the tip
Answer: The tip is $14.00
Step-by-step explanation: 20% of 70 is 14.
1589
Calculator
120°
126
What is the value of x?
125
139
Enter your answer in the box
121°
Answer:aaaa
Step-by-step explanation:because
a= 340 rounded to the nearest 10
b= 49.8 rounded to 1 DP
Find the minimum of a × b
Answer: First, we'll round the values of A and b:
A = 340 rounded to the nearest 10 = 340
b = 49.8 rounded to 1 decimal place = 49.8
Next, we'll find the product of A and b:
A × b = 340 × 49.8 = 16872
Finally, we'll find the minimum of A × b:
Minimum of A × b = 16872
So, the minimum value of A × b is 16872.
Step-by-step explanation:
hi can i have help with this question please i can’t figure out what c is
Answer: Decagon
Step-by-step explanation:
That would be a decagon because it has 10 sides. It does not matter if the shape looks wonky.
Hope this helps :)
Multiply 2 by 2 until you get 4 numbers.
I got 1024 but its not right
Answer: 1024
Step-by-step explanation:
2 x 2 is 4
4 x 2 is 8
8 x 2 is 16
16 x 2 is 32
32 x 2 is 64
64 x 2 is 128
128 x 2 is 256
256 x 2 is 512
512 x 2 is 1024
Select the correct point
One linear equation is defined by points (1,6) and (3, 7), while the other is defined by points (3,6) and (5,8). Which point represents the solution of
this system of equations?
Answer:
Step-by-step explanation:
o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.
The first linear equation can be determined by finding its slope and y-intercept using the given points:
m = (7 - 6) / (3 - 1) = 1
b = 6 - m * 1 = 6 - 1 * 1 = 5
y = mx + b
y = x + 5
The second linear equation can be found similarly:
m = (8 - 6) / (5 - 3) = 1
b = 6 - m * 3 = 6 - 1 * 3 = 3
y = mx + b
y = x + 3
Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.
8x^{2}-8x8x
2
−8x from -6x^{2}-10x+4−6x
2
−10x+4.
The value of the equation 8x² - 8x + 2 -( 6x² - 10x + 4) is 2x² + 2x - 2.
How to illustrate the equationIt should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that
two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
The equation can be illustrated thus:
8x² - 8x + 2 -( 6x² - 10x + 4)
8x² - 8x + 2 - 6x² + 10x - 4
= 2x² + 2x - 2
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What is 42−6×4(12) to the third power?
Answer:
Step-by-step explanation:
First, we need to evaluate the expression inside the parenthesis: 4(12) = 4 * 12 = 48.
Next, we can simplify the expression: 42 - 6 * 48 = 42 - 288 = -246.
Finally, we raise the result to the third power: (-246)^3 = (-246) * (-246) * (-246) = -158,048.
So, the result is -158,048.
What is the solution to the system of equations?
x + 3y + 2z = 8
3x + y + 3z = -10
-2x - 2y -z = 10
Answer:
x = 8 - 3y - 2z
Step-by-step explanation:
Step-by-step explanation:
x + 3y + 2z = 8
3x + y + 3z = -10
-2x - 2y - z = 10
we solve this by eliminating variables or expressing sine variables by others, and then solve for the remaining one. with that value we then cancer back to solve for the other variables.
in our case the easiest way is the elimination via combinations of equations.
let's first multiply equating 1 by -3 and then add that to equation 2 :
-3x - 9y - 6z = -24
3x + y + 3z = -10
----------------------------
0 - 8y - 3z = -34
8y + 3z = 34
then multiply equation 1 by 2 and add it to equation 3 :
2x + 6y + 4z = 16
-2x - 2y - z = 10
--------------------------
0 4y + 3z = 26
now we subtract this result from the previous result :
8y + 3z = 34
- 4y + 3z = 26
----------------------------
4y 0 = 8
y = 8/4 = 2
4×2 + 3z = 26
3z = 18
z = 18/3 = 6
x + 3×2 + 2×6 = 8
x = -10
so,
x = -10
y = 2
z = 6
1. An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50' with the wall.
The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation
of the Sun is more than 65'. See the figure. Find the length of L of the awning. Round to the nearest
Inch.
The number b is irrational. Which statement about
41+b is true?
An irrational number is created by adding two rational numbers, according to the answer to the given question. If the oppositely irrational numbers a and b.
What is rational numbers?Rational numbers are those that may be written as a ratio (or fraction) of two integers. A fraction with a non-zero denominator is said to be rational.
A few instances of rational numbers are 1/2, 1/5, and 3/4. A rational number, “0,” can also be stated in a number of different ways, such as 0/1, 0/2, and 0/3. But 1/0, 2/0, 3/0, and so forth.
The number seven makes sense. A rational number is produced when two integers are split. To get the rational number 7, divide the whole number 7 by the whole number 1. Since 7 can be obtained by dividing two integers, it is referred to as a rational number.
Two rational integers added together yield an irrational number. Ab is irrational if and only if a and b are mutually exclusive irrational numbers.
Therefore, a = 2 and b = ab = 2 is an irrational number.
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At hannah’s school 3/5 of the school playground is covered with grass and 5/8 of the grassy area is a baseball field. How much of the school playground is taken up by the baseball field
The baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.
Hannah’s school playground is divided into two parts, with the majority of it being covered in grass. Specifically, 3/5 of the playground is grassy and the remaining 2/5 is taken up by other materials such as pavement or gravel. Of the grassy area, 5/8 is taken up by the baseball field. This means that the baseball field occupies a total of 15/40 or 3/8 of the entire playground.
In terms of proportions, if we consider the entire playground to be 100%, then the amount of the playground taken up by the baseball field is 3/8, or 37.5%. This means that 62.5% of the playground is taken up by the other materials and the remaining grassy area not occupied by the baseball field.In terms of area, the total size of the playground can be determined by multiplying the length of the playground by its width. If we assume that the length and width are equal, then the area of the playground can be calculated as the length squared. The area of the baseball field can then be calculated by multiplying 3/8 by the total area of the playground. This will give us the total area of the baseball field.
Overall, the baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.
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megan wants to test her assumption on the amount of sleep students are getting. she decides to focus her efforts on examining if students are getting less than eight hours of sleep. what should megan state for the null hypothesis and alternative hypothesis? a.) null hypothesis: alternative hypothesis: b.) null hypothesis: alternative hypothesis: c.) null hypothesis: alternative hypothesis: d.) null hypothesis: alternative hypothesis:
To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.
Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:
a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.
Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.
b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.
Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.
c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).
Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.
d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).
Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.
Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.
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The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane
and x represents the number of minutes the plane has been descending:
y=-5x + 100
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening
to the airplane at these time intervals.
Answer:
32x95%?
Step-by-step explanation:
Im so confused with this question statement.
what is the slope of the line that contains the points (-2,6) and (6,-3)?
PLEASE SHOW WORK
Answer: [tex]-\frac{9}{8}[/tex]
Step-by-step explanation:
If you are given two points of a line, the slope is defined as rise/run. Rise is the difference in y coordinates, (think about it, going UP is RISING), and Run is the difference in x coordinates, (again its pretty intuitive.)
So Slope = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]
This can be calculated with the coordinates of the two points, (order wont matter youll get the same answer).
Slope = (-3-6)/(6-(-2)) = -9/8
OR, (going the other way)
Slope = (6-(-3))/(-2-6) = 9/-8 = -9/8
Easy!
