The linear scan strategy for counting the number of negative values in an array involves sequentially going through each element of the array and checking if it is negative.
If the element is negative, the count is incremented. Once the end of the array is reached, the count is returned.
For example, consider an array A = [-2, 3, -1, 4, -7, 9]. The linear scan strategy would be as follows:
1. Initialize count to 0
2. Check if A[0] = -2 is negative, if yes, increment count. Count = 1
3. Check if A[1] = 3 is negative, if no, continue. Count = 1
4. Check if A[2] = -1 is negative, if yes, increment count. Count = 2
5. Check if A[3] = 4 is negative, if no, continue. Count = 2
6. Check if A[4] = -7 is negative, if yes, increment count. Count = 3
7. Check if A[5] = 9 is negative, if no, continue. Count = 3
8. Return count = 3.
Therefore, the linear scan strategy for counting the number of negative values in array A is 3.
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nondisclosure of the treatment an experimental unit is receiving
Blinding refers to the nondisclosure of the treatment an experimental unit is receiving in a controlled experiment.
Blinding is a technique used in experimental design to reduce bias and improve the validity of results. It refers to the practice of not revealing to the experimental units (e.g., participants, animals) or the experimenters which treatment they are receiving in a controlled experiment.
Blinding is used to eliminate potential sources of bias that might influence the results of the experiment. For example, if the participants are aware of the treatment they are receiving, they might behave differently and affect the results. Similarly, experimenters might unconsciously treat participants differently based on their knowledge of the treatment, which could also affect the results.
"
Complete question
________ refers to nondisclosure of the treatment an experimental unit is receiving.
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.................................................
12 mygs will cost 27, and 5 flasks will cost 30
how many steps in 1 mile
Generally speaking you can count on 2,000 steps equaling one mile.
How many steps in 1 mile?
The average person takes between 2,000 and 2,500 walking steps per mile as counted by a fitness band, or phone motion sensor. Running steps have a longer stride length, which means you may take between 1,000 and 2,000 steps per mile.A total of 10,000 steps equals 4 to 5 miles. The number of steps per mile varies from person to person and depends on your stride length. Knowing how many steps are typical for a mile, you can begin to envision how far you need to walk to log 10,000 steps per day.It also works in reverse. The miles might not seem so long if you realize how many you manage to log during your daily activities. Keep moving and you will make it to your daily goal.To learn more about mile refers to:
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Write a linear function f with the given values f(3)=-4f(5)=-4
The linear function that passes through the points f(3)= -4 and f(5) = -4 is:
f(x) = -4
How to write the linear function?A general linear function can be written as:
f(x) = a*x + b
Where a is the slope and b is the y-intercept.
Here we know the two pairs:
f(3) = -4
f(5) = -4
So for the inputs x = 3 and x = 5 we have the same output, then we have a constant linear function that can be written as:
f(x) = 0*x - 4
f(x) = -4
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
[tex] \sf \: x = 20[/tex]
Step-by-step explanation:
Given equation,
→ x - 18 = 2
Now the value of x will be,
→ x - 18 = 2
→ x = 2 + 18
→ [ x = 20 ]
Hence, the value of x is 20.
a couple planning their wedding offers four choices for meals: chicken, fish, steak, and vegetarian. the first 20 responses they receive are shown in the table below. meal choices chicken chicken fish steak fish chicken vegetarian vegetarian steak helpcopy to clipboarddownload csv create a relative frequency distribution for the data using excel. what is the relative frequency of responders that chose the vegetarian meal?
The relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.
The concept used in this problem is relative frequency, which is a measure of the number of times an event occurs in a data set, expressed as a fraction of the total number of events.
The relative frequency is a useful tool for summarizing and understanding the distribution of data, and provides a way to compare the relative frequencies of different events in a data set.
To create a relative frequency distribution in Excel, you would first create a table with the four meal options (chicken, fish, steak, and vegetarian) and count the number of times each option was selected. The relative frequency is calculated as the count of each meal option divided by the total number of responses (20 in this case).
Here is the frequency distribution as :
Meal Option → Frequency → Relative Frequency
Chicken → 6 → 0.3 (6/20)
Fish → 2 → 0.1 (2/20)
Steak → 2→ 0.1 (2/20)
Vegetarian → 10 → 0.5 (10/20)
Thus, the relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.
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The relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.
The concept used in this problem is relative frequency, which is a measure of the number of times an event occurs in a data set, expressed as a fraction of the total number of events.
The relative frequency is a useful tool for summarizing and understanding the distribution of data and provides a way to compare the relative frequencies of different events in a data set.
To create a relative frequency distribution in Excel, you would first create a table with the four meal options (chicken, fish, steak, and vegetarian) and count the number of times each option was selected. The relative frequency is calculated as the count of each meal option divided by the total number of responses (20 in this case).
Here is the frequency distribution as :
Meal Option → Frequency → Relative Frequency
Chicken → 6 → 0.3 (6/20)
Fish → 2 → 0.1 (2/20)
Steak → 2→ 0.1 (2/20)
Vegetarian → 10 → 0.5 (10/20)
Thus, the relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.
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Dijkstra: Strategy
Which algorithm design technique best describes Dijkstra's SSSP algorithm?
A) Exhaustive Search
B) Divide and Conquer
C) Greedy
D) Dynamic Programming
E) Randomized
The algorithm design technique best describes Dijkstra's SSSP algorithm is (c) Greedy.
Dijkstra's Single Source Shortest Path (SSSP) algorithm is considered a greedy algorithm because it makes locally optimal choices at each step in order to find the globally optimal solution. The algorithm starts from the source vertex and maintains a priority queue of vertices, where the priority of a vertex is determined by the length of the shortest path from the source to that vertex.
At each step, the algorithm chooses the vertex with the smallest priority, updates the distances of its neighbors, and adds them to the priority queue. This process continues until all vertices have been processed or a target vertex has been found. The algorithm always makes the choice that appears to be the best at the moment, with the goal of finding the shortest path from the source to all vertices.
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what is the slope and y-intercept of this equation?
y = -2x + 12 is the linear equation's slope intercept form.
How do you determine an equation's slope and y-intercept?In the form of a slope-intercept equation, the line's equation is stated as follows: y = mx + b, where m denotes the slope and b denotes the y-intercept.
Values for the slope and y-intercept describe the properties of the relationship between the two variables x and y.Slope is a measure of how quickly y changes for every unit change in x.
In the event that the x-value is 0, the y-intercept shows the y-value. An equation's slope intercept form is shown as follows:
y = mx + c
where
slope = m
y-intercept = c
Therefore,
4x + 2y = 24
2y = -4x + 24
multiply both sides by two.
2y / 2 = -4x /2 + 24 / 2
y = -2x + 12
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find the general solution to the following differential equation y'' 2y' y = 8e^-t
The general solution to the differential equation y'' - 2y' + y = 8e^-t is given by: y = c1e^(4t) + c2e^(-2t) + (4t + 1)e^-t.
The general solution to the differential equation y'' - 2y' + y = 8e^-t can be found using the method of characteristic equations.
The characteristic equation is obtained by substituting y = e^rt into the differential equation: r^2e^rt - 2re^rt + e^rt = 8e^-t
Expanding the left side:
r^2e^rt - 2re^rt + e^rt = 8e^-t
r^2e^rt - 2re^rt + (1-8)e^rt = 0
Solving for the characteristic equation:
(r-4)(r+2) = 0
The characteristic equation has two roots, r = 4 and r = -2. These roots correspond to the two linearly independent solutions of the differential equation:
y = c1e^(4t) + c2e^(-2t)
where c1 and c2 are arbitrary constants.
Therefore, The general solution to the differential equation y'' - 2y' + y = 8e^-t is given by:
y = c1e^(4t) + c2e^(-2t) + (4t + 1)e^-t
where c1 and c2 are arbitrary constants determined by initial conditions or boundary conditions.
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How are you supposed to tell even and odd functions apart?
Answer:A function f(x) is even if f(-x) = f(x). The function is odd if f(-x) = -f(x). An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.
Step-by-step explanation:
The function is even when f(-x) = f(x) and is odd when f(-x) = -f(x).This has been obtained using even-odd functions.
What are even-odd functions?
When the output value of a real-valued function, f(x), is equal to f(x), for all values of x inside the domain of f, the function is said to be an even function.
It is claimed that a real-valued function f(x) is an odd function when, for all values of x in the domain of f, the output value of f(-x) is equal to the negative of f(x).
We have an even function if we have an expression that is equivalent to f(x) and we have an odd function if we obtain an expression that is equivalent to -f(x).
If we take a function and substitute x for -x, simplify the result, and then compare it to what you started with, you can "determine algebraically" if the function is even, odd, or neither.
The function is even if you come out with exactly what you started with (i.e., if f (-x) = f (x), in which case all of the signs are the same. If you come out with exactly the opposite of what you started with (i.e., if f(-x) = -f (x), in which case all of the signs are switched), it is an odd function.
Hence, the function is even when f(-x) = f(x) and is odd when f(-x) = -f(x).
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Which phrase do we use to indicate that we are trying to study the relationship between two variables while the values of all other variables are held unchanged? A. Et ali B. Ceteris paribus C. Ad hominem D. E pluribus unum Why is this restriction so useful in economic analysis? A. If other variables that do not interact with these two variables are not held fixed, the true relationship between the two variables would be hidden. B. Lf every is allowed to change, it would be impossible to isolate the impact of one variable on another
Option B is the correct answer. Ceteris paribus is a phrase do we use to indicate that we are trying to study the relationship between two variables while the values of all other variables are held unchanged.
This is the most commonly-used phrase that defines 'all other things being unchanged or constant'. It is used in economics to rule out the possibility of 'other' factors changing, which is the specific causal relation between two variables is focused.
This is the Latin phrase that is generally used for saying 'with other things being the same'. It is particularly crucial in the study of cause and effect relationships between two specific variables such that other relevant factors influence.
The opposite word for this phrase is 'mutat's mutants, which defines changing some factors that are used to be changed. Ceteris paribus is often a fundamental assumption to the predictive purpose of scrutiny.
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Here is a composite function find an expression for m in terms of p give your answer in its simplest form
Question C)
The expression for m in terms of p will be m = 5p - 4
How to explain the functionA function shows the relationship between the variables that are provided or the data given regarding an information.
Function A x + 4 then × 2 = y
x = m
y = (m + 4) × 2 = 2m + 8
Function B x ÷ 5 Then + 1 = y
x = 2m + 8
y = 2p+1
(2m + 8) ÷ 5 + 1 = 2p+1
= (2m + 8) ÷ 5 = 2p
= 2m + 8 = 10p
= m + 4 = 5p
m = 5p - 4
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Here is a composite function find an expression for m in terms of p give your answer in its simplest form
Function A x + 4 then ×2 = y
Function B x ÷ 5 Then + 1 = y
m Function A then Function B = 2p+1
use the distributive property to remove the parentheses 2(3 + x)
Answer:
6 + 2x
Step-by-step explanation:
Distributive property is multiplying a number outside a parenthesis to those inside the parenthesis, thus:
2(3 + x)
(2(3) + 2(x))
[6 + 2x]
given a circle with the equation (x-7)^2+(y+3)^2=25 list the center and the radius of the circle
The required center of the circle is at (7, -3) and the radius of the circle is 5.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
Where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Here,
Given the equation of the circle:
(x-7)² + (y+3)² = 25
Compare the equation with the standard equation
Center of the circle
(-h, -k) = (-(-7), -(3))
(-h, -k) = (7, -3)
Radius,
r² = 25
r = 5
Thus, the required center of the circle is at (7, -3) and the radius of the circle is 5.
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A banker who has done several deals with Todd McFarlane and the McFarlane company and knew that the company tends to be
The correct option for the question is option d) Experience with the target
In the given example, a banker has done several transactions with Todd and found them to be economically prudent. Based on his interactions with Tedd, the lender is likely to categorize Todd as reckless and artsy. He was in this position to stereotype Todd because of the several dealings he had with him. As a result, it is an example of prior experience with the objective. As a result, the proper option is (d) Experience with the target. All other selections are inappropriate and incorrect.
The complete question is:
A banker who has done several deals with Todd McFarlane and the McFarlane Company and knew that the company tends to be fiscally conservative would be less likely to stereotype Todd McFarlane as a risky, artistic type. Which perceiver characteristic best explains this outcome?
a) Gender and emotional status
b) Needs and goals
c) Direction of glaze
d) Experience with the target
e) Cognitive load
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Rebecca has $128 on a gift card to spend. She spends $78 on running shoes. Tank tops cost $12. 50 each. How many tank tops can she buy?.
The manager of Lawn and Garden Services would like to estimate the proportion of her employees' time spent performing various gardening and lawn care activities. She has made 400 random observations of a typical worker, with the following results: Activity Time Observed Mowing 200 Trimming 80 Raking 40 Miscellaneous 80 If the manager wants to be 95. 44 percent confident that the true proportion of time spent mowing is within. 02 (plus or minus) of the sample proportion, what should be her sample size?
a. 400
b. 1,000
c. 1,600
d. 2,000
e. 2,500
The sample size should be e) 2,500.
To calculate the sample size needed for the manager's confidence interval, we need to use the formula for the margin of error:
Margin of error = z * (standard deviation of the sample proportion) / sqrt(sample size)
Given the sample data, the sample proportion of time spent mowing is 200 / 400 = 0.5.
Plugging in the values, we get:
Margin of error = 1.96 * sqrt(0.5 * 0.5 / 400) = 0.02
Rearranging the formula and solving for the sample size, we get:
Sample size = (z / margin of error)^2 * (sample proportion * (1 - sample proportion))
= (1.96 / 0.02)^2 * (0.5 * 0.5)
= 2500
So, the sample size needed for a 95.44 percent confidence interval with a margin of error of 0.02 is 2,500. The answer is option (e).
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How many centimeters are equal to 1 inch?
Answer:
multiply the length value by 2.54
so the answer is 2.54
2.54 centimeters are equal to 1 inch. The solution has been obtained by using the unit conversion.
What is unit conversion?
The same characteristic is stated in a different unit of measurement by using a unit conversion. If you want to represent time or distance, for example, you could use feet rather than hours to indicate the time or the distance, respectively. Measurements are frequently requested in a different set of units than those they are delivered in, such as chains, but are provided in a different set, such as feet.
We are given 1 inch which is to be converted into centimeters.
Since,
⇒1 inch = 0.0254 meters
So,
⇒1 inch = 2.54 centimeters
Hence, 2.54 centimeters are equal to 1 inch.
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Find the value of x.
A: 80 degrees
B: 40 degrees
C: 60 degrees
D: 140 degrees
Show work.
4: the diameter of a red blood cell is 6 x 10-6 m. how many red blood cells are needed to make a line 1 inch long?
42 red blood cells are needed to make a line 1 inch long
The diameter of a red blood cell is 6 x [tex]10^{-6}[/tex] m,
so we need to determine how many cells can fit in a
line 1 inch long (2.54 x[tex]10^{-5}[/tex] m).
Dividing the length by the diameter gives the number of cells:
2.54 x [tex]10^{-5}[/tex] m / 6 x [tex]10^{-6}[/tex] m = 42.33.
So, approximately 42 red blood cells are needed to make a line 1 inch long.
This highlights the small size of red blood cells and the remarkable ability of the human body to produce and maintain billions of these cells for proper blood circulation and oxygen delivery.
Red blood cells, also known as erythrocytes, are one of the main types of blood cells. They are biconcave discs with a diameter of about 7.5 micrometers, and their primary function is to transport oxygen from the lungs to the tissues and carbon dioxide from the tissues to the lungs.
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Refer to the system of linear equations shown below. Which of the following statements gives the best choice for multiplying to solve this system using the elimination method?
3x−6y=4
6x+11y=−2
1. Multiply the first equation by −11
and the second equation by 6
so the y-variables are eliminated.
2. Multiply the second equation by 1/2
so the x-variables are eliminated.
3. Multiply the first equation by −2
so the x-variables are eliminated.
4. Multiply the first equation by 2
so the x-variables are eliminated.
Answer:
3: Multiplying the first equation by −2 so the x-variables are eliminated.
Step-by-step explanation:
The elimination method is a strategy to solve a system of linear equations by eliminating one of the variables (usually the y variable) by adding or subtracting the equations. This can be done by multiplying one or both of the equations so that when added or subtracted, the y variable will cancel out.
In this case, the best option for multiplying to solve the system using the elimination method is to multiply the first equation by -2 so that the x-variables are eliminated. This is because when the first equation is multiplied by -2, it becomes -6x + 12y = 8, which has the same coefficient for x as the second equation. When the two equations are added, the x variable will cancel out, leaving us with an equation in terms of y, which can then be solved for x.
The equation after the elimination will look like this:
-6x + 12y + 6x + 11y = -2 + 8
6y = 6
y = 1
Finally, we can use this value of y to solve for x in one of the original equations:
3x - 6(1) = 4
3x = 10
x = 10/3 = 3.33
So the solution to the system is (3.33, 1).
What is the purpose of polynomials?
Answer: Polynomials are an important part of the "language" of mathematics and algebra. They are used in nearly every field of mathematics to express numbers as a result of mathematical operations. Polynomials are also "building blocks" in other types of mathematical expressions, such as rational expressions.
Step-by-step explanation:
The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with a standard deviation of 0. 1 ounces. What is the z-score corresponding to a weight of 8. 17 ounces? What percent of chocolate bars weigh less than 8. 17 ounces. Show and explain your work
95.54% of the chocolate bars at the factory weigh less than 8. 17 ounces
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that mean = 8, standard deviation = 0.1
For x < 8.17 ounces:
z = (8.17 - 8) / 0.1 = 1.7
From the normal distribution table:
P(z < 1.7) = 0.9554 = 95.54%
The probability that the chocolate bars weigh less than 8. 17 ounces is 95.54%
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Triangle RST is translated so that point R (-2, 1) is mapped to point R’ (2, -4). If point S is (-4, 3), what ordered pair best represents point S’?
The ordered pair (0, -2) best represents point S’ after the translation of triangle RST.
How to determine the ordered pair of SFrom the question, we have the following parameters that can be used in our computation:
R (-2, 1) is mapped to point R’ (2, -4).
This means that
(x, y) = (x + 2 - -2, y - 4 - 1)
This gives
(x, y) = (x + 4, y - 5)
For the point S, we have"
Substitute the known values in the above equation, so, we have the following representation
S' = (-4 + 4, 3 - 5)
Evaluate
S' = (0, -2)
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consider the following research scenario: ivan wants to research how the number of breaks throughout the day can impact fatigue. he gains permission from a local accounting firm and randomly assigns willing participants to take either ten or zero 5-minute breaks across the workday (in addition to regularly scheduled breaks). he then asks participants to complete a questionnaire to assess fatigue. in this study, what is the independent variable and what is the dependent variable? number of 5-minute breaks is the independent variable and fatigue is the dependent variable fatigue is independent variable and number of 5-minute breaks is the dependent variable the participant is the independent variable and number of 5-minute breaks is the dependent variable the participant is the independent variable and fatigue is the dependent variable
The independent variable is the number of 5-minute breaks, and the dependent variable is fatigue.
The cause is the independent variable. Its value is unaffected by the other study variables.
Effect is the dependent variable. Changes in the independent variable affect its value.
The independent variable is a variable in an experimental design that is manipulated or changed by the researcher to observe its effect on the dependent variable. It is also referred to as the "predictor variable" or the "explanatory variable". In the research scenario described, the independent variable is the number of 5-minute breaks (ten or zero) that are assigned to the participants.
The dependent variable is a variable in an experimental design that is being studied and measured to determine its relationship with the independent variable. It is also referred to as the "outcome variable" or the "response variable". In the research scenario described, the dependent variable is fatigue, as Ivan wants to study the impact of the number of 5-minute breaks on fatigue and will measure fatigue levels by using a questionnaire.
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The independent variable is the number of 5-minute breaks, and the dependent variable is fatigue.
The cause is the independent variable. Its value is unaffected by the other study variables.
Effect is the dependent variable. Changes in the independent variable affect its value.
The independent variable is a variable in an experimental design that is manipulated or changed by the researcher to observe its effect on the dependent variable. It is also referred to as the "predictor variable" or the "explanatory variable". In the research scenario described, the independent variable is the number of 5-minute breaks (ten or zero) that are assigned to the participants.
The dependent variable is a variable in an experimental design that is being studied and measured to determine its relationship with the independent variable. It is also referred to as the "outcome variable" or the "response variable". In the research scenario described, the dependent variable is fatigue, as Ivan wants to study the impact of the number of 5-minute breaks on fatigue and will measure fatigue levels by using a questionnaire.
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a cylinder jar is halfway full of baby food the volume of the baby food is 24 Pi cubic centimeters what is the height of the jar when the radius of the jar is 4 cm
please help
The height of the cylinder jar is 6/4 centimeters
How to determine the height of the cylinderThe formula for determining the volume of a cylinder is expressed with the equation;
V = πr²h
Such that the parameters are;
V is the volume of the cylinderπ takes the value of 3.14 or 22/7r is the radius of the cylinderh is the height of the cylinderFrom the information give, we have that;
Volume = 24π cubic centimeters
Radius = 4cm
Now, substitute the values into the formula
24π = π(4)²h
find the square
24π = 16πh
Make 'h' the subject of formula, we get;
h = 24π/16π
h = 24/16
h = 6/4
Hence, the value is 6/4
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Given that the point (-112, -15) is on the terminal side of an angle, θ, find the exact value of the following: sin(θ)= cos(θ)= tan(θ)= csc(θ)= sec(θ)= cot(θ)=
The value of the trigonometric functions given that the point (-112, -15) is on the terminal side of an angle, θ is sin(θ)= y/r = -15/ 113 cos(θ)= x/r = -112/ 113 tan(θ)= y/x = -15/ -112 csc(θ)= r/y = 113/ -15 sec(θ)= r/x = 113/ -112.
What is Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
The terminal points are given as follows:
x = -112 and y = -15
Using the Pythagorean theorem we have:
x^2 + y^2 = r^2
(-112)^2 + (-15)^2 = r^2
12544 + 225 = r^2
r = 113
Now, the trigonometric functions is given as:
sin(θ)= y/r = -15/ 113
cos(θ)= x/r = -112/ 113
tan(θ)= y/x = -15/ -112
csc(θ)= r/y = 113/ -15
sec(θ)= r/x = 113/ -112
cot(θ)= x/y = -112/ -15
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The density of solid fe is 7. 87 g/cm3. How many atoms are present per cubic centimeter (cm3) of fe?.
Assuming the solid Fe is pure iron, the atomic mass of iron is 55.845 g/mol. This means that in one cubic centimeter of iron there are 6.02 x 10²² atoms of Fe.
Solid iron has a density of 7.87 g/cm³. This means that in one cubic centimeter of iron, there are 6.02 x 10²² atoms of iron. This is calculated by taking the atomic mass of iron (55.845 g/mol) and dividing it by the density of iron (7.87 g/cm³). This gives us the number of atoms of iron in one cubic centimeter of iron, which is 6.02 x 10²² atoms.
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Solve the following linear system by elimination
so hmmm let's notice the denominators in each, so hmmm the 1st equation has an LCD of 6, so let's multiply both sides by that, and the 2nd equation has an LCD of 12, so let's multiply it by that to do away with the denominators, oddly enough, it gives us an elimination of a variable, so let's do so
[tex]\begin{array}{llll} \cfrac{1}{2}x-\cfrac{2}{3}y=6 \\\\\\ \cfrac{1}{4}x+\cfrac{1}{3}y=-1 \end{array}\hspace{5em} \begin{array}{llll} 6\left( \cfrac{1}{2}x-\cfrac{2}{3}y=6 \right) \\\\\\ 12\left( \cfrac{1}{4}x+\cfrac{1}{3}y=-1 \right) \end{array}\hspace{5em} \begin{array}{llll} ~~ 3x-4y&=36 \\\\\\\\\\ -3x-4y&=12\\\cline{1-2} ~\hfill -8y&=48 \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-8y=48\implies y=\cfrac{48}{-8}\implies y=-6 \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{3x-4y=36}\implies 3x-4(-6)=36\implies 3x+24=36 \\\\\\ 3x=12\implies x=\cfrac{12}{3}\implies x=4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (4~~,~-6) \end{array}}~\hfill[/tex]
The perimeter of a rectangle is 40 cm. The length is 14 cm.
Let x = width of the rectangle.
Ravi says he can find the width using the equation 2(x + 14) = 40.
Fran says she can find the width using the equation 2x + 28 = 40.
Answer the questions to solve the equations and to compare the steps and solutions.
1. Which of these is the most helpful first step for solving Ravi's equation, 2(x + 14) = 40? (1 point)
Circle the best answer.
Add 14 to both sides
Subtract 14 from both sides
Divide both sides by 2
Multiply both sides by 2
2. What would your next step be? (1 point)
3. Solve Ravi's equation, 2(x + 14) = 40, to find the width of the rectangle. Show your work. (1 point)
4. Which of these is the most helpful first step for solving Fran's equation, 2x + 28 = 40? (1 point)
Circle the best answer.
Multiply both sides by 2
Subtract 28 from both sides
Divide both sides by 2
Add 28 to both sides
5. What would your next step be? (2 points)
6. Solve Fran's equation, 2x + 28 = 40, to find the width of the rectangle. Show your work. (2 points)
7. The two equations have different solution steps. Do they have the same solution? Use the distributive property to show why this answer makes sense. (2 points)
Answer:2(x +14) = 40 (use the distributive property)2x + 28 = 40 (solve exactly like you did for Fran)2x = 12x = 6
Step-by-step explanation: