Mr. Harrell has 64 feet of fencing that he will use to build a rectangular enclosement for chickens and he will use his barn as one of of the sides of the rectangle as seen in the image. Write a function A (x) relating the area of the enclosement A and the width of the rectangle x. Then, find the width that maximizes the area. Then state the maximum area.
Answers
Answer:
A = x(64 -x)/2x = 32 ft512 ft²Step-by-step explanation:
Given 64 feet of fencing that can be used for three sides of a rectangular enclosure next to a barn wall, you want a function for area in terms of enclosure width, the width that maximizes area, and the maximum area.
(a) FunctionIf we define the width (x) as the dimension parallel to the barn wall, then the fence available for the "height" (out from the barn wall) is (64-x) in length. Half that is used on either end of the enclosure, so the area is ...
A = WH
A(x) = x(64 -x)/2
(b) Best widthWe notice this function describes a parabola that opens downward, with zeros at x=0 and x=64. The vertex (maximum) is on the line of symmetry, halfway between the zeros:
x = (0 +64)/2 = 32
The width that maximizes area is x = 32 ft.
(c) Maximum areaUsing x=32 in the area formula, we find the maximum area to be ...
A(32) = 32(64 -32)/2 = 1024/2 = 512 . . . . square feet
The maximum area is 512 square feet.
__
Additional comment
Perhaps you can see that the best width is half the length of the available fence. The other half of the fence is used for the ends of the enclosure. This is the generic solution to this kind of problem.
Related Questions
jackson wants to test an assumption on the number of red candies in a bag of fruity tooty's candy. the company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims. what should jackson state for the null hypothesis and alternative hypothesis?
Answers
Jackson should correctly phrase both the alternative hypothesis and the null hypothesis as follows:
b. )
p = 0.20 indicates a null result.
A different result: p ≠ 0.20
What exactly is null hypothesis?
A specific type of statistical hypothesis known as a null hypothesis claims that no statistical significance can be established in a given set of facts. One can assess the truthfulness of a hypothesis through the use of sample data in hypothesis testing. It is represented by the letter H0 and is also sometimes referred to as the "null."
The conjecture, also known as the null hypothesis, is a tool used in quantitative analysis to examine the validity of beliefs about markets, economies, and investment strategies.
A null hypothesis is a form of speculation that asserts that specific characteristics of a population or data collection method are not distinct from one another in statistics.
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Which has a quotient of 1.66? Use number sense to find the answer. Select all that apply. A. 4.15÷2.5 B. 0.415÷0.25 C. 41.5÷0.25 D. 4.15÷0.25 E. 0 . 415 ÷ 2 . 5
help plssssssssssss
Answers
The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25
How to find which has a quotient?
Long division or repeated subtraction can be used to accomplish this.Finding the quotient of two integers, fractions, or algebraic words is achievable.Quotient * Dividend = Divisor
A. 4.15 ÷ 2.5
Quotient = 1.66
Divisor = Quotient * 2.5
= 1.66 * 2.5
= 4.15
So, Option A is a correct answer.
B. 0.415÷0.25
Divisor = Quotient * 0.25
= 1.66 * 0.25
= 0.415
So, Option B is a correct answer.
C. 41.5÷0.25
Divisor = Quotient * 0.25
= 1.66 * 0.25
= 0.415 ≠ 41.5
So, Option C is not a correct answer.
D. 4.15÷0.25
Divisor = Quotient * 0.25
= 1.66 * 0.25
= 0.415 ≠ 4.15
So, Option D is not a correct answer.
E. 0.415 ÷ 2
Divisor = Quotient * 0.25
= 1.66 * 2
= 3.32 ≠ 0.415
So, Option E is not a correct answer.
Hence, The option that has correct quotient is option A = 4.15 ÷ 2.5 and Option B = 0.415÷0.25
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The average test score of RSM students in September increased by 10%. In October it increased by another 15%. By what percent did the average score on the test increase during the two months? PLS PROVIDE SHOW OF STEPS!
Answers
The percent that the average score on the test increased during the two months is 12.5%.
By what percent did the average score on the test increase during the two months?It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..
The average of the increase will be:
= (10% + 15%) / 2
= 25% / 2
= 12.5%
The average is 12.5%.
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What is the vertex of the graph of f x )=[ x 5 ]- 6?
Answers
The vertex of the graph of f(x) = |x - 5| - 6 is (5, -6). It lies in the fourth quadrant.
Therefore the answer is (5, -6).
The graph f(x) = |x - 5| - 6 is symmetrical about the axis x = 5.
A vertex of a graph is a node of a graph. For a graph of the form f(x) = a|x - h| + k, the vertex is (h, k). So in this case where f(x) = |x - 5| - 6, a = 1, h = 5 and k = -6. Therefore the vertex of the given graph f(x) is
(5, -6)
--The question is incomplete, answering to the question --
"What is the vertex of the graph of f(x) = |x - 5| - 6?"
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can anyone help me?
Answers
Answer:
a. 648
Step-by-step explanation:
Deposit= Principal= p
Interest rate = R
Time= T
Simple Interest = P x T X R X 0.01
= 5400 x 6 x 2 x 0.01
=648
If - 4 ≤ x ≤2 and 5 ≤ y ≤ 12, what
is the largest possible value of (y - x)?
Answers
Answer:
16
Step-by-step explanation:
Since x is negative, lets instead thing of the problem as
y + (-x)
and find the bounds of -x to be
[tex] - 2 < = - x < = 4[/tex]
now, the max value of y is 12 and the max value of -x is 4
12 + 4 = 16
Two balls are to be pulled from a vase that contains 7 red balls, 9 green balls, and 2 black balls. After the first ball is drawn, it is
not replaced. What is the probability that two red balls are chosen from the vase?
Answers
The probability that two red balls are chosen from the vase would be = 1/9
What is probability?Probability is defined as the concept that proves that an event may occur or not.
The number of red balls = 7
The number of black balls = 2
The number of green balls = 9
The total number of balls in the vase = 18
The probability of getting 2 red balls = 2/18 = 1/9
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FILL IN THE BLANK. the area under the normal curve to the right of muμ equals _______.
Answers
Answer: One by two
Step-by-step explanation:
Because the mu is half or 0.5, so the word in the blank will be one by two!
In the first week of July, a record 1020 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 198 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answers
The percent decrease in the number of people who went to the pool over these four weeks is 15%.
What is the percent decrease in the number of people who went to the pool over these four weeks?The number of people in each week will be recorded below:
First week = 1020
Second week = 1020 - 100 = 920
Third week = 920 + 145 = 1065
Fourth week = 1065 - 198 = 867
The percent decrease in the number of people who went to the pool over these four weeks will be:
= (1020 - 867) / 1020 × 100
= 153 / 1020 × 100
= 15%
The percentage decrease is 15%.
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How do you solve an inequality on a calculator?
Answers
press menu and select option,press 2 to select to a polynomial degree of 2,select the number that matches the inequality u are about to solve and lastly input the values of coefficient of x into the expression and press equal to sign on the calculator
How do we solve inequality on a calculator?A relationship between two expressions or values that are not equal to each other is called 'inequality. '
Inequality can be greater than >, less than < , great than or equal to ≥ , less than or equal to ≤.
like other equations, inequality can be solved on a calculator. This process shows how inequality can be solved on a calculator. For example if 3x²+4x+5≥0 is to be solved on a calculator, the following steps are to be taken
Step 1 : press menu and select option B( inequality option)
Step2 : press 2 to select to a polynomial degree of 2
step 3 : select the number that matches the inequality u are about to solve
step 4: input the values of coefficient of x into the expression
step 5 : press the equal to sign on the calculator.
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Is the answer to this question A or B? I’m conflicted.
Would appreciate the reply!!
Answers
Answer: B
I have to add extra words to answer you but it’s B :))
a basketball player has a 25% accuracy rate at making three-point shots. mark thought it was reasonable that each attempt was independent and the probability stayed at 25% for this player. p (x equals k )equals (1 minus p )to the power of k minus 1 end exponent p using the geometric distribution formula, what is the probability that the basketball player makes his first three-point shot on the third attempt? answer choices are rounded to the hundredths place. a.) 0.56 b.) 0.25 c.) 0.38 d.) 0.14
Answers
The answer is c). The probability that the basketball player makes his first three-point shot on the third attempt is 0.38.
The geometric distribution is a probability distribution that describes the number of independent trials required to get a success. In this case, the basketball player has a 25% accuracy rate at making three-point shots, which means that the probability of success (making a three-point shot) is p=0.25 and the probability of failure (missing a three-point shot) is 1-p=0.75. Using the geometric distribution formula, the probability that the basketball player makes his first three-point shot on the third attempt is:
P(x=3) = (1-p)^(3-1) * p = (0.75)^2 * 0.25 = 0.38This means that there is a 38% probability that the basketball player will make his first three-point shot on the third attempt.
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How do you know if it's greater than or less than on a graph?
Answers
To determine whether an inequality represents a relationship of "greater than" or "less than" by looking at a graph, you can look at the direction of the solid line. If the line is pointing upwards towards the right, it represents a "greater than" relationship. If the line is pointing downwards towards the right, it represents a "less than" relationship.
For example, consider the graph of the inequality "y > x + 2." The points on the graph that satisfy this inequality are those that are above the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points above the line are greater than the values on the line, so the inequality "y > x + 2" represents a "greater than" relationship.
On the other hand, consider the graph of the inequality "y < x + 2." The points on the graph that satisfy this inequality are those that are below the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points below the line are less than the values on the line, so the inequality "y < x + 2" represents a "less than" relationship.
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Darcy is buying a new couch that cost $999.00. She has two payment options.
Option 1: Pay with credit card. The card charges 20.00% annual interest and Darcy expects to pay off the charge in 30 days.
Option 2: Take the store promotion of 15 monthly payments of $70 (including tax)
a) Calculate the total cost of each option
b) What is the annual interest rate being charged with Option 2?
Please show your work.
Answers
Answer:
Step-by-step explanation: a) To calculate the total cost of the couch when paid with a credit card, we need to calculate the amount of interest that will be charged. To do this, we first need to calculate the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 20/12 = 1.67%.
Next, we need to multiply the cost of the couch by the monthly interest rate to find the amount of interest that will be charged. In this case, the amount of interest is 999 * 1.67% = 16.67.
Finally, we need to add the amount of interest to the cost of the couch to find the total cost when paid with a credit card. In this case, the total cost is 999 + 16.67 = 1015.67.
To calculate the total cost of the couch when paid with the store promotion, we simply need to add up all 15 monthly payments. In this case, the total cost is 15 * 70 = 1050.00.
b) To calculate the annual interest rate being charged with Option 2, we need to divide the total cost of the couch by the number of monthly payments and then multiply by 12. In this case, the annual interest rate is (1050/15)*12 = 96%.
A pop quiz has 2 true/false questions. Paris used a 10-trial coin flip to simulate the results of guessing on the quiz. If t represents answering a question correctly, what is the experimental probability of correctly answering both questions by guessing? frequency of observed desired outcome: number of trials: experimental probability:.
Answers
Experimental probability of correctly answering both questions by guessing = 1/4 .
Tail (T) = True
Head (H) = False
Number of possible outcome = 2
Head (H) or Tail (T).
Probability = number of occurrence/number of possible outcome.
Since we can only have one T or F in a toss.
number of occurrence = 1
Probability of answering first question correctly = 1/2
Probability of answering second question correctly = 1/2
Probability of answering both questions correctly = Probability of answering first question correctly * Probability of answering second question correctly
Probability of answering both questions correctly = 1/2 x 1/2
Probability of answering both questions correctly = 1/4
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Answer:3 and 10 and 3/10
Step-by-step explanation:
What does the notation f/x y mean?
Answers
The notation f (x) = y means that the functional value at the point x is y.
In the notation f (x) = y, we understand that the value x is to be plugged in the function given to us (which is f here) which on solving gives y as the answer or solution 'y' of that function at a point x.
For example, let us consider the function f (x) = 2x + 3 = y
Then if we find f (2), then 2 will be plugged in the function 2x +3 such that
f (2) = 2(2) + 3 = 7,
which means that 7 is the functional value, 'y' at the point 2 which is considered as x.
The question is incomplete, the complete question is f (x) = y.
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How do you find the equation of a line with one point and slope of a fraction?
Answers
With the slope and one point of the line, Using the formula of equation of line with slope and a point, The answer is [tex](y-y_1)= m (x-x_1)[/tex] .
What do you mean by equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.
What do you mean by slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
points= ([tex]x_1 , y_ 1[/tex])
slope = m
Required equation,
[tex](y-y_1)= m (x-x_1)[/tex]
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HELP!!
An unsharpened pencil is in the shape of a
hexagonal prism with base area of 54 mm²
and length of 20 cm. Find the volume in
cubic millimeters. (1 cm = 10 mm)
Answers
10800 mm³ is the volume of the unsharpened pencil.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm².
The length of hexagonal prism is 20 cm.
Let us convert cm to mm
1 cm = 10 mm
20 cm =200 mm.
Volume of hexagonal prism V=Ah.
A is the base area and h is the height.
V=54×200
=10800 mm³.
Hence, volume of an unsharpened pencil is in the shape of a hexagonal prism with base area of 54 mm² and length of 20 cm is 10800 mm³.
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Match the histograms on the right to the summary statistics givern 20 Standard Deviation 1.6 9 10 21 Mean Median 56 65 56 56 56 65 56 56 51 5355 57 59 61 (a) IV 20 (b)I (d)II 40 50 60 70 80 90 10 4 16 36 56 76 96 116 20 26 36 46 56 66 76 86
Answers
The histograms is shown below.
What is Histogram?One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution.
Given:
The standard deviation for 4 we have the highest value and range for graph C have highest standard deviation.
and, the standard deviation for 1 have lowest deviation and range for graph A have lowest standard deviation.
and, for row 2 the second histogram is the answer and for row 4 the fourth histogram is the answer.
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Why might squaring a number and taking the square root of a number be thought of as opposite operations?
Answers
Therefore , squaring a number and taking the square root of a number is an opposite operation as we can see in the following explanation.
How is the square root defined?A number's square root, which is the result of multiplication by itself, yields the original number. Some examples of exponents are squares and square roots. Imagine the number twenty five. Additionally, this can be expressed as expression of 5x5.
Here,
In order to square an integer, you must multiply it by itself.
The opposite of squaring a number is the act of getting the square root.
Calculating the side length of a square whose area is a certain number can be compared to finding the square root of that number.
For example: √25= √5*5 = 5
where as square of 5 : 5*5 = 25
Therefore , squaring a number and taking the square root of a number is an opposite operation as we can see in the following explanation.
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Your mom wants to buy you a box of Squishmallows for $54.99. She has a 25% coupon.
a) What is the amount of discount? Make sure you round to the nearest cent.
b) What is the sale price?
Answers
Answer:
a) $13.75
b) $41.24
Step-by-step explanation:
Original price: $54.99
Discount: 25%
Amount of discount: 25% of $54.99 = 25/100 × $54.99 = 0.25 × $54.99 = $13.75
Sale price: $54.99 - $13.75 = $41.24
What is the relationship between the area of the base of a prism its height and its volume?
Answers
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.
What is area?The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
V=b*h
b=base area of prism
h=height of prism
The volume of a prism is calculated as V=Bh, where B is the base area and h is the height.
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What are the steps of copying?
Answers
The steps of copying involve selecting the text you want to copy, copying the text using the option from the right click menu or alternatively using the keyboard shortcut ctrl + c.
What is a clipboard?The clipboard is a section of memory that the computer temporarily saves data when you copy or cut it from its original location. When you paste something, the previously copied or cut data is retrieved from the clipboard and added to the new location.
What is the difference between copying and cutting the text?Text that is copied remains in its original location; a copy of the original text is created and kept in the clipboard. When you cut text, the original text is removed from its original location and put in the clipboard. When you copy or trim text, the original text is kept, but the original location is lost. In all cases, the copied or chopped text can be put into another location.
These steps can be used to copy text or other objects in a computer program:
By highlighting it with your pointer, you may choose the text or object that you wish to copy.
Use the keyboard shortcut "Ctrl+C" or the context menu when you right-click the highlighted text or object to choose "Copy" from the context menu.
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3/8 divided by 2/5 in fraction form and simplest form
Answers
Answer:
Step-by-step explanation:
for double fractions, invert the bottom one and then multiply them
[tex]\frac{3}{8}[/tex] * [tex]\frac{5}{2}[/tex]
= [tex]\frac{15}{16}[/tex]
= 0.9375
How can I get my SSS E1 number?
Answers
You can locate your SSS loan number scrawled on the upper right corner of your E-1 form if you applied for one in 2015 or earlier and still have a copy of it.
The personal information of an SSS member is contained on the SSS E1 form (also known as the E-1 form). Prior to receiving a social security number, a person must submit the E1 form to apply for membership in the Social Security System.
The applicant must complete the form with his personal data (such as name, date of birth, and home address), a list of dependents or beneficiaries, and, if self-employed, his profession or company.
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What is the use of median?
Answers
Median is the only average to be used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude,
e.g., to find the average intelligence among a group of people.
It is to be used for determining the typical value in problems concerning wages, distribution of wealth, etc.
It helps us to identify if the distribution is symmetric or not.
The mean and median of a symmetric distribution are close together.
If the distribution is exactly symmetric, the mean and median are exactly the same.
In a skewed distribution, the mean is farther out in the long tail than the median.
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What is the y-intercept of y=5x+3?
Answers
Answer:
Y-intercept: 3
Step-by-step explanation:
The equation is y = mx + b
m is the slope
b is the y-intercept
In this case, the y-intercept is 3
Equation would be y = mx + c
M (aka 5) is the gradient.
Hence why 3 should be the y intercept
witney peter, a professional dart player has a seventy percent chance of hitting the bull's eye on a dartboard with and throw. assume that that the throw of a dart is independent. what is the probability that pete hits five or fewer of his next ten shots?
Answers
Without spectacles, Witney Pete has a 5/10 chance of hitting the bullseye. Witney Pete could strike the bullseye with his spectacles 0.7 of the time. This likelihood is far higher than hitting the bullseye without glasses. the probability that Pete hits five or fewer of his next ten shots is approximately 2.487.
What is the probability that Pete hits five or fewer of his next ten shots?Generally, To find the probability that Pete hits five or fewer of his next ten shots, we need to find the probability that he hits exactly 0, 1, 2, 3, 4, or 5 bull's eyes.
The probability that Pete hits exactly k bull's eyes in n throws is given by the binomial distribution:
P(k bull's eyes in n throws) = (n choose k) * p^k * (1-p)^(n-k)
where p is the probability of hitting a bull's eye on a single throw and n choose k is the binomial coefficient, which is equal to n!/(k!(n-k)!).
Substituting the given values, we get:
P(0 bull's eyes in 10 throws) = (10 choose 0) * (0.7)^0 * (0.3)^10 = 0.028 P(1 bull's eyes in 10 throws) = (10 choose 1) * (0.7)^1 * (0.3)^9 = 0.189 P(2 bull's eyes in 10 throws) = (10 choose 2) * (0.7)^2 * (0.3)^8 = 0.462 P(3 bull's eyes in 10 throws) = (10 choose 3) * (0.7)^3 * (0.3)^7 = 0.605 P(4 bull's eyes in 10 throws) = (10 choose 4) * (0.7)^4 * (0.3)^6 = 0.501 P(5 bull's eyes in 10 throws) = (10 choose 5) * (0.7)^5 * (0.3)^5 = 0.302
The probability that Pete hits five or fewer bull's eyes in his next ten shots is the sum of the probabilities of hitting exactly 0, 1, 2, 3, 4, or 5 bull's eyes:
P(hitting 5 or fewer bull's eyes in 10 shots) = 0.028 + 0.189 + 0.462 + 0.605 + 0.501 + 0.302 = 2.487
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(17, 17) (0, 13) (19, –11) (14, –17) Is this relation a function?
Answers
The relation is not a function because the element 17 is paired with two elements in the range (17 and 0). Therefore, the relation is not a function.
What is relation and function ?A relation is a set of ordered pairs that represents a relationship between two sets of objects. For example, the relation {(1, 2), (3, 4), (5, 6)} represents a relationship between the sets {1, 3, 5} and {2, 4, 6}.A function is a special type of relation in which each element in the domain is paired with exactly one element in the range. A relation is a function if each element in the domain is paired with exactly one element in the range. In this case, the relation is not a function because the element 17 is paired with two elements in the range (17 and 0). Therefore, the relation is not a function.To learn more about function refer :
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What is the slope of y =- 4 5x 3?
Answers
The slope of the given line y = -(4/5)x + 3 is -(4/5).
What is the slope of the line?The slope of a line is defined as the gradient of the line.
The slope of a line is a measure of its steepness. It is defined as the change in y (the "rise") divided by the change in x (the "run") between two points on the line.
The equation is given in the question as:
y = - (4/5)x + 3
To find the slope of a line given by the equation y = mx + b, where m is the slope and b is the y-intercept, we can just take the coefficient of x, which is m.
As per the question, the coefficient of x is -(4/5), so the slope of the line is -(4/5).
Therefore, the slope of the given line is -(4/5).
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