We have learned three methods for solving systems of equations - graphing, substitution, and elimination. Compare and contrast the three methods - how are they similar and how are they different? In what situations might each method be the most appropriate to use? When is it more convenient to use each method?
Answers
Graphing, substitution, and elimination are three methods for solving systems of equations. While they all aim to find the solution(s) to a system of equations, there are some important differences in how they work and when they are most appropriate to use.
Graphing involves plotting the equations on the same coordinate system and finding the point(s) where the graphs intersect. This method is visual and can be useful for understanding the overall behavior of the equations, but it can be time-consuming and inaccurate if the graphs are not precise enough. Graphing is most appropriate when the equations are simple and have integer solutions, or when a visual representation of the problem is necessary.
Substitution involves solving one of the equations for one variable, then substituting that expression into the other equation to create an equation with only one variable. This method is straightforward and can be done by hand, but it can be time-consuming and error-prone if there are many variables or the equations are complex. Substitution is most appropriate when one of the equations is already solved for a variable, or when the equations involve simple linear or quadratic forms.
Elimination involves adding or subtracting the equations to eliminate one of the variables. This method is efficient and can be done systematically, but it can be confusing if the equations are not balanced or there are many variables. Elimination is most appropriate when the coefficients of one of the variables are equal or opposite in both equations, or when there are many equations and variables.
In general, the choice of method depends on the specific equations and the preferences of the solver. Graphing is a good method to use when the equations are simple and easy to plot, substitution is useful when one equation is already solved for a variable or the equations involve simple forms, and elimination is a good choice when the equations have balanced coefficients or there are many equations and variables to consider. It is important to keep in mind the strengths and weaknesses of each method and to choose the most appropriate method based on the specific situation.
Note - While this answer may provide helpful information for your assignment, it is important to remember that using it verbatim could be seen as plagiarism. To avoid this, it is best to use your own words and properly cite any sources used. This will ensure that you are giving credit to the original author and presenting your own unique perspective on the topic.
Have a great Day!
~~~Harsha~~~
Related Questions
A new youth activity center is being built in pagosa springs. The perimeter of the rectangular playing field is 328 yards. The length of the field is 4 yards less than double the width. What are the dimensions of the playing field?
Answers
Answer: Width: 56 yards, Length: 108 yards
Step-by-step explanation:
What we know:
- Perimeter is 328 yards
- The length is 4 less than double the width
In this answer, I will use w as the variable for width.
Find the equation for the length.
The length of the field is double the width, 2w, minus 4.
We get: 2w - 4
A rectangle has four sides, two for width, two for length. So now we need to add width to width and length to length
Length: (2w - 4) + (2w - 4) = 4w - 8
Width: w + w = 2w
To find perimeter, you need to add all sides. So now we add our length and width
4w - 8 + 2w = 6w - 8
Now that we have our final equation, we need to solve for w.
6w - 8 = 328
Add 8 to both sides.
6w - 8 + 8 = 328 + 8
Combine like terms.
6w = 336
Divide 6 from both sides.
w = 56
The width is 56, now that we have solved w, we can plug it into our length equation
2(56) - 4 = 108
The length is 108.
Answer: 56 yards x 108 yards (width x length)
To check your work, you can easily add up all the sides and see if it matches the perimeter given.
108 + 108 + 56 + 56 = 328
I hope this helped!
15 pies a m regla de 3
Answers
Answer:
5m
Step-by-step explanation:
regla de 3:
1m = 3ft
15 pies ÷ 3 = 5m
With a coupon, a pair of shoes that normally costs $90 is only $72. Find the COP between $90 and $72.
Answers
Answer:
The discount rate operated by the coupon is 20%.
Step-by-step explanation:
Since the pair of shoes normally sells for $ 90, but through the application of a discount coupon it sells for $ 72, to determine the discount percentage made by this coupon it is necessary to perform the following calculation:
90 = 100
72 = X
(72 x 100) / 90 = X
7,200 = 90 = X
80 = X
100 - 80 = 20
Thus, the discount operated by the coupon is 20%.
Find the measure of angle 4
Answers
Answer:
38
Step-by-step explanation:
Notice that the first triangle is an isosceles triangle, meaning that the base angles are equivalent. Since one angle is 62, we know that the other is 62 as well, which makes 124. This means that angle 2 is 56 degrees. Since 2 and 3 are on the same 'line', they both add up to 180. If 2 is 56, then angle 3 is 124. So the three angles inside the triangle are 124, 18, and x. So, 124+18=142. 180-142= 38
What is the arc length of an arc with radius 15 inches and central angle 30°? Show your work.
Answer:
Answers
Step-by-step explanation:
the arc length of a while circle of 360° is the circumference of the circle, which is
2×pi×r
now, our radius r is 15 in.
and we are not dealing with the whole circle of 360° but only with a fraction of that : 30° out of the 360°
so, the arc length is
2×pi×15×30/360 = 2×pi×15×1/12 = pi×15/6 = pi×5/2 =
= 7.853981634... in
Full explanation and answers on these 2 questions please. Also only answer if u know what ur doing.
Answers
Step-by-step explanation:
Q3
25 - (x-8)²/4 = [100 - (x-8)²]/4
[100 - (x²- 16x + 64)]/4
(100 - x² + 16x - 64)/4 = (-x² + 16x + 36)/4
(36 + 16x - x²)/4 = (36 - 2x + 18x - x²)/4
[2(18 - x) + x(18 - x)]/4 = [(2 + x)(18 - x)]/4
....proved
Q4
3(ax + 7) - 2(x + b) = 4x + 29
expanding,
3ax + 21 - 2x - 2b = 4x + 29
3ax - 2x + 21 - 2b = 4x + 29
Comparing terms; x terms,
3ax - 2x = 4x
3a - 2 = 4
3a = 6
a = 6/3
a = 2
constant terms,
21 - 2b = 29
21 - 29 = 2b
2b = -8
b = -8/2
b = -4
.... proved
Select the law that shows that the two propositions are logically equivalent. -((w V p) ^(-91q1w)) -(w V p) v-(-91qAw) a. DeMorgan's law b. Distributive lawc. Associative law d. Complement law
Answers
The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).
What is meant by DeMorgan's law?By using their opposites, De Morgan's Laws explain how mathematical assertions and concepts are connected. The intersection and union of sets are connected by complements according to De Morgan's Laws in set theory. The De Morgan's Laws are rules of propositional logic that use negation to connect conjunctions and disjunctions of propositions.The complement of the intersection of the complements of two sets A and B is equal to the complement of the union of two sets A and B, according to De Morgan's first law. According to De Morgan's Law, "(P and Q)" and "not (not P or not Q)" are logically equal. If they are logically similar, then it should follow that "(P and Q)" implies "not (not P or not Q)," and "not (not P or not Q)" implies "(P and Q)".To learn more about DeMorgan's law, refer to:
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Activity
Harold and his friends combined all their jacks and balls while playing. Now they are wondering how to split the balls and jacks among themselves. The 6 friends have a total of 24 balls and 60 jacks. To solve this problem, answer each question below.
Part A
Express the total number of balls and jacks as a sum.
Answers
Answer:3 kilometers per hour.
Step-by-step explanation:
Harold and his friends combined all their jacks and balls while playing. Now they are wondering how to split the balls and jacks among ... The 6 friends have a total of 24 balls and 60 jacks.
Answer: The total number of jacks and balls is (24 + 60).
Step-by-step explanation: this was the answer edmentum gave me
At the Denver International Airport, planes must clear a mountain that is 1000 feet tall that is a horizontal distance of 2800 feet away. At what angle of elevation must the plane take off in order to safely clear the mountain ? Round your answer to the nearest WHOLE degree.
PLEASE i need help
Answers
Answer:
19 degrees
Step-by-step explanation:
Will have a triangle with horizontal distance being 2800, and vertical being 1000 feet. Angle between the horizontal and hypotenuse is what we are looking for.
Thus it's a tangent function.
SOH
CAH
TOA <-----
Tangent is the opposite / adjacent
So we will be looking at doing an Arctan to find the angle.
Arctan α = \(\frac{1000}{2800}\) = 19.29 degrees. Round to the nearest whole degree would be 19 degrees due to being less than .50
Your answer is 19 degrees
A=2 b=2 c=1 Find the value of 2abcosC
Answers
Answer:
\(2abCosC = 1\)
Step-by-step explanation:
The cosine rule is
=> \(a^2= b^2+c^2-2abCosC\)
For 2abCosC, it becomes
=> \(2abCosC = b^2+c^2-a^2\)
=> \(2abCosC = (2)^2+(1)^2-(2)^2\)
=> \(2abCosC = 1\)
HELP PLEASE NEED IT THANKS
Answers
Answer:
<
Step-by-step explanation:
1) Substitute 5 into the question
\(\frac{4(5)}{4}\)\(2(5)-3\)2) Work out the sides
\(\frac{4(5)}{4} =5\)\(2(5)-3=7\)3) Put it into an inequality
5 < 7
Hope this helps, have a great day!
use distributive property to rewrite this problem: -2(n-7)
Answers
To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:
a(b + c) = ab + ac
Applying this property to the given expression:
-2(n-7) = -2 * n + (-2) * (-7)
Simplifying further:
-2(n-7) = -2n + 14
Therefore, the rewritten expression is -2n + 14.
Find the remainder when f(x)=2x^3-x^2+x+1 is divided by 2x+1
Answers
Answer:
0
Step-by-step explanation:
By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.
On a test that has a normal distribution, a score of 29 falls three standard deviations above the mean, and a score of 23 falls one standard deviation above the mean. Determine the mean of this test.
Answers
The mean of the test is 20.
To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.
Let's denote the mean of the test as μ, and the standard deviation as σ.
We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:
29 = μ + 3σ
Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:
23 = μ + σ
Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.
From the second equation, we can isolate μ:
μ = 23 - σ
Substituting this value into the first equation, we have:
29 = (23 - σ) + 3σ
Simplifying the equation, we get:
29 = 23 + 2σ
2σ = 29 - 23
2σ = 6
σ = 3
Substituting the value of σ back into the second equation, we find:
μ = 23 - 3
μ = 20
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93 divided by 5932 long division
Answers
Answer:
63 73/93 (steps are in the attached file)
Step-by-step explanation:
Define an exponential function, f(x), which passes through the points (0,36) and(2,1). Enter your answer in the form a · b^xf(x) =
Answers
The general form of the exponential function is:
\(f(x)=a\cdot b^x\)we will find the equation of the exponential function which passes through the points (0, 36) and (2, 1)
So,
when x = 0, f(0) = 36
\(\begin{gathered} 36=a\cdot b^0 \\ 36=a\cdot1 \\ a=36 \end{gathered}\)and when x = 2, f(x) = 1
Using the substitution with a = 36
So,
\(\begin{gathered} 1=36\cdot b^2 \\ b^2=\frac{1}{36} \\ \\ b=\sqrt[]{\frac{1}{36}}=\frac{1}{6} \end{gathered}\)So, the answer will be the equation of the function is:
\(f(x)=36\cdot(\frac{1}{6})^x\)what is -3 (4n+2) = -4n + -2(4n-6)
Answers
Answer: There are no solutions.
Step-by-step explanation:
Can someone help with this
Answers
Answer:
The missing angle is 50 degrees.
Answer:
50°
Step-by-step explanation:
Knowing that this is a parallelogram, you can infer that the adjacent angles of the polygon must add up to 180 degrees by definition. Using what is given, you would take \(180 - 130\) to get your answer, \(50\)°.
Hoped this helped!
What is the quotient of 480 divided by -60
Answers
should be the answer
The quotient when 480 is divided by -60 is 8.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
The numbers given are 480 and -60.
Both are in opposite signs, that is one negative and other positive.
So the quotient will be negative.
Now divide 480 by 60.
Since both of the numbers contain 0 at the end, cancel it.
Then it becomes 48 divided by 6.
48 / 6 = 8
Hence the quotient is 8.
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Eric fell asleep at 3:15 pm he woke up after 2 hours and 35 minutes what time did eric wake up
Answers
2 hours and 35 minutes is equivalent to 2 hours + 35 minutes = 155 minutes
Since there are 60 minutes in 1 hour, we can convert the 155 minutes to hours by dividing it by 60:
155 minutes / 60 minutes/hour = 2.58 hours
Now, we can add this time to the time Eric fell asleep:
3:15 pm + 2.58 hours = 6:13 pm
Therefore, Eric woke up at 6:13 pm
Please help thank uuuuu
Answers
Answer:
12
Step-by-step explanation:
You simply add the coefficients together.
3 + 4 + 5 = 12
Help plzdsadsadsadsdsa
Answers
Answer:
Step-by-step explanation:
9b²c² = (3bc)²
100m²n⁶ = (10mn³)²
I hope I've helped you.
URGENT!!! Elementary school students were given a geometry assignment. They were to measure the area of several rectangles and to measure the diagonal of the rectangle as shown in the table.
The equation of the least-squares regression line is
ŷ = 3.6 + 0.113x, where ŷ is the diagonal and x is the area of the rectangle. Which shows the residual plot?
Answers
The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.
Please find attached the graph of the residual plot for the data created with MS Excel
What is a residual plot?A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.
The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158
The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;
Area (in²) \({}\) Residuals
x-value
5 \({}\) -1.0178
10 \({}\) -0.2718
24 \({}\) 0.605
46 \({}\) 0.7874
53 \({}\) 0.7018
78 \({}\) 0.0758
84 \({}\) -0.129
100 \({}\) -0.7538
The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option
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5x-5=3x +17
what is the answer?
Answers
Answer:
do 8x12 maybe
Step-by-step explanation:
im sorry i hope this helps
What is the probability of rolling a 3 and then rolling a 4 on a 6 sided cube?
1/6* 1/6 = 1/36
1/2*1/2 = 1/4
O1/6* 1/5 = 1/30
Answers
Answer: it is the 2 one
Step-by-step explanation:
Two functions, A and B, are described as follows: Function A y = 9x + 4 Function B The slope is 3 and the y-intercept is 4. How much more is the slope of function A than the slope of function B? 2 3 6 9
Answers
Answer:
6
Step-by-step explanation:
9 - 3 = 6
Answer: C
Step-by-step explanation:
What function is being described Justify each part of your function, explaining how you determined it.
My function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2. It has end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity. The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
Answers
The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.
What is the end behavior of a polynomial function?The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.
Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.
The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.
The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).
Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.
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if x k converges to x, and yk converges to y, does xk/yk converge to x/y math?
Answers
Yes, xk/yk converges to x/y. This can be proven mathematically using the definition of a limit.
If xk converges to x and yk converges to y, then the limit of xk/yk as k approaches infinity is equal to the limit of x/y. This can be expressed algebraically as limk→∞xk/yk = limk→∞x/y, which is equal to x/y. Thus, xk/yk converges to x/y.
To calculate this, we can take a sequence of xk an yk values, and divide every xk by its corresponding yk. For example, if xk = {2, 4, 8, 16, 32} and yk = {1, 2, 4, 8, 16}, then the sequence xk/yk = {2/1, 4/2, 8/4, 16/8, 32/16} = {2, 2, 2, 2, 2}. This sequence converges to 2, which is equal to x/y. Therefore, xk/yk converges to x/y.
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Suppose f(x) is continuous and defined for all real numbers. You are given that f(x) has critical points at x = -1 and x = 0. If f'(x) is positive in the interval x < -1, negative in the interval -1 < x < 0, and positive in the interval x > 0, is the point where x = -1 the location of a relative maximum, minimum, or neither? Maximum Minimum Neither
Answers
The point where x = -1 is the location of a relative maximum.
What is the critical point?
The concept of "critical point" is used in a lot of different ways, particularly, the most common way in which it is used is to describe the points where the slope of the tangent line is zero in continuous functions.
A critical point is a point where the first derivative of a function is equal to zero or is undefined.
A relative maximum occurs when the first derivative is zero and the second derivative is negative, while a relative minimum occurs when the first derivative is zero and the second derivative is positive.
The given information tells us that f'(x) is positive in the interval x < -1, negative in the interval -1 < x < 0, and positive in the interval x > 0.
This means that f'(x) is increasing in the interval x < -1, decreasing in the interval -1 < x < 0, and increasing in the interval x > 0. Therefore, at the critical point x = -1, f'(x) is zero and f''(x) is negative.
This means that the function changes from an increasing function to a decreasing function, indicating that the point where x = -1 is the location of a relative maximum.
Hence, the point where x = -1 is the location of a relative maximum.
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what is 1/3 multiply by 5
Answers
Answer: \(\frac{5}{3}\) or \(1\frac{2}{3}\) or \(1.6666...\) or \(1.67\)
Step-by-step explanation:
Since every whole number has a denominator of 1, we can "change" 5 into \(\frac{5}{1}\), and then multiply that by \(\frac{1}{3}\), which would give us \(\frac{5}{3}\). From there we can convert the \(\frac{5}{3}\) from an improper fraction into a mixed number. Hope this helps!
\(\frac{1}{3} *\frac{5}{1} = \frac{5}{3}\)
\(\frac{5}{3} = 1 \frac{2}{3}\)
\(1\frac{2}{3} = 1.67 (1.6666...)\)