Answer:
2080cm^3
Step-by-step explanation:
How to prove that C is a field? (I want detailed explanations.
Please list all the proofs of 11 axioms.)
To prove that C is a field, we need to show that it satisfies the following 11 axioms of a field:
C is closed under addition: For all a, b ∈ C, a + b ∈ C.
C is closed under multiplication: For all a, b ∈ C, ab ∈ C.
C is associative under addition: For all a, b, c ∈ C, (a + b) + c = a + (b + c).
C is associative under multiplication: For all a, b, c ∈ C, (ab)c = a(bc).
C has an additive identity: There exists 0 ∈ C such that for all a ∈ C, a + 0 = a.
C has a multiplicative identity: There exists 1 ∈ C such that for all a ∈ C, a1 = a.
C has additive inverses: For all a ∈ C, there exists b ∈ C such that a + b = 0.
C has multiplicative inverses: For all a ≠ 0 ∈ C, there exists b ∈ C such that ab = 1.
C is commutative under addition: For all a, b ∈ C, a + b = b + a.
C is commutative under multiplication: For all a, b ∈ C, ab = ba.
Multiplication distributes over addition: For all a, b, c ∈ C, a(b + c) = ab + ac.
Proofs of the 11 axioms:
To show that C is closed under addition, we can use the fact that the sum of two complex numbers is also a complex number. That is, for any a, b ∈ C, a + b = (a + bi) + (b + di)i, where i is the imaginary unit. This is clearly a complex number, so C is closed under addition.
To show that C is closed under multiplication, we can use the fact that the product of two complex numbers is also a complex number. That is, for any a, b ∈ C, ab = (a + bi)(b + di) = (ab - bd) + (ad + bc)i, which is also clearly a complex number, so C is closed under multiplication.
To show that C is associative under addition, we can use the associative property of addition for real numbers. That is, for any a, b, c ∈ C, (a + b) + c = a + (b + c).
To show that C is associative under multiplication, we can use the associative property of multiplication for real numbers. That is, for any a, b, c ∈ C, (ab)c = a(bc).
To show that C has an additive identity, we can use the fact that the real number 0 is also a complex number, and that for any a ∈ C, a + 0 = a.
To show that C has a multiplicative identity, we can use the fact that the real number 1 is also a complex number, and that for any a ∈ C, a1 = a.
To show that C has additive inverses, we can use the fact that for any a ∈ C, there exists a complex number -a such that a + (-a) = 0. This is because the real numbers have additive inverses, and the imaginary unit i has an additive inverse -i.
To show that C has multiplicative inverses, we can use the fact that for any a ≠ 0 ∈ C, there exists a complex number 1/a such that a(1/a) =
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Enter the value of n for the equation 35.3″ = 38.
The value of n for the given equation 3⁵. 3ⁿ = 3⁸ is n = 3.
What are laws of exponents?Several rules of exponents are presented according to the capacities they possess. The following rule governs multiplication: Add the exponents while maintaining the base's consistency.
When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.
Division Rule: When dividing similar bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the base constant.
The given equation is:
3⁵. 3ⁿ = 3⁸
Using the product rule for exponents we have:
3⁽⁵ ⁺ ⁿ⁾ = 3⁸
The above expression can be written as:
5 + n = 8
n = 8 - 5
n = 3
Hence, the value of n for the given expression 3⁵. 3ⁿ = 3⁸ is n = 3.
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The complete question is:
QUESTION 5 How many ways are there to construct a 3-digit code if numbers can be repeated?
There are 1,000 ways to construct a 3-digit code if numbers can be repeated. This is because there are 10 possible numbers (0-9) for each digit, and since numbers can be repeated, each digit has 10 options. So the total number of ways to construct a 3-digit code is 10 × 10 × 10 = 1,000.
Here is a step-by-step explanation:
1. Start with the first digit. There are 10 possible numbers (0-9) that can be used for this digit.
2. Move on to the second digit. Again, there are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
3. Finally, move on to the third digit. There are 10 possible numbers (0-9) that can be used for this digit, since numbers can be repeated.
4. Multiply the number of options for each digit together to get the total number of ways to construct a 3-digit code: 10 × 10 × 10 = 1,000.
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please help, i will give brainliest! please also explain how you got the answer!
Answer: 7.59
Step-by-step explanation: I added all of the miles he traveled up together. ( don't overthink questions like this)
Meg surveyed some students at her school about their favorite professional sports. Of the students surveyed, 2 said football was their favorite sport, while 8 of the students had other favorite sports. What is the experimental probability that the next student Meg talks to will pick football?
So, the experimental probability that the next student Meg talks will pick football is 0.2 or 20%.
What is Probability?Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.
Given by the question.
The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials or observations. In this case, the event is selecting football as the favorite sport, and the trials are the number of students Meg talks to.
Based on the information given in the problem, Meg surveyed a total of 10 students (2 who selected football and 8 who selected other sports). Therefore, the probability of the next student she talks to selecting football as their favorite sport is:
P (selecting football) = number of students who selected football / total number of students surveyed
P (selecting football) = 2 / 10
P (selecting football) = 0.2
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Dalton flies a plane against a headwind for 4661 miles. The return trip with the wind took 20 hours less time. If the wind speed is 10 mph, how fast does Dalton fly the plane when there is no wind?
Dalton flies the plane at a speed of 251 mph when there is no wind.
To solve this proble,m we can use the formula for distance, which is distance = speed × time. We can also use the fact that the speed of the plane with the wind is the sum of the speed of the plane without the wind and the wind speed, and the speed of the plane against the wind is the difference between the speed of the plane without the wind and the wind speed.
Let x be the speed of the plane without the wind, and t be the time it takes for the return trip with the wind. Then we can write the following equations:
4661 = (x - 10) × (t + 20) (1) for the trip against the wind
4661 = (x + 10) × t (2) for the return trip with the wind
Multiplying equation (2) by (t + 20) and subtracting equation (1) from it, we get:
4661t + 93220 = 4661t + 20x^2 + 200x - 200x - 200
20x^2 = 93220
x^2 = 4661
x = 251
Therefore, Dalton flies the plane at a speed of 251 mph when there is no wind.
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A triangle can be formed into a parallelogram as shown in the diagram below. Which equation can be used to find the area of the triangle in the diagram?
F.A = 4⋅6
G.A = 6÷2
H.A = 12
(2⋅6
)
J.A = 12
(4⋅6
)
Answer: J. A = 12 (4⋅6).
Step-by-step explanation:
Answer: J. A = 12 (4⋅6).
This equation can be used to find the area of the triangle in the diagram because it uses the formula for the area of a triangle, which is A = 1/2 * b * h, where b is the base and h is the height. Since the triangle in the diagram has a base of 4 and a height of 6, the equation A = 12 (4⋅6) can be used to find the area.
Answer:
The diagram is not provided, so it's difficult to determine the exact dimensions of the triangle and parallelogram. However, we can make some general observations to determine which equation can be used to find the area of the triangle.
First, we know that the area of a triangle is given by the formula:
A = 1/2 * base * height
We also know that the area of a parallelogram is given by the formula:
A = base * height
In the diagram, the triangle can be formed into a parallelogram by taking one of its sides and using it as the base of the parallelogram. The height of the parallelogram is the same as the height of the triangle.
Based on these observations, we can conclude that the equation that can be used to find the area of the triangle is:
A = 1/2 * base * height
where the base is one of the sides of the triangle, and the height is the height of the parallelogram (which is the same as the height of the triangle).
None of the answer choices provided match this equation, so the correct answer is not given.
If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative ..............of f.If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative ............ of f.
The function is relative minima
If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative maximum of f. If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative minimum of f.
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I need help with that
Answer:
Step-by-step explanation:
Multiply each then divide by the first number you started off with.
Marcus is painting all the walls in his apartment which she estimated to be a total of 1450 ft.² he computered that he has finished with 60% of the painting approximately how many square feet of of wall space or me remain to be painting
Answer:
580
Step-by-step explanation:
He painted 60/100 x 1450 = 870
Unpainted = 1450-870
Remaining = 580ft²
Darrell wants to see how much water is wasted by his leaky faucet. He put a 4 gallon bucket under the faucet. After 24 hours, the bucket was full.
The amount of water filled in bucket 6 hours is found as 1 gallon.
Explain about the proportion of the number?Mathematical proportions are comparisons of two numbers that categorize or persons. They are frequently expressed as fractions or with a colon. There are two ways to write mathematical proportions. You can use colons to compare the numbers, or you can use equivalent fractions to represent the proportion.
Darrell is interested in learning how much water his leaking faucet is wasting. Under the faucet, he positioned a 4 gallon bucket. The bucket was full after 24 hours.Now,
Let the amount of water filled in 6 hours be 'x'.
Using proportion:
4/24 = x/6
x = 4*6 / 24
x = 1 gallon
Thus, the amount of water filled in bucket 6 hours is found as 1 gallon.
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The complete question is attached.
Three numbers form a gp. If the first and third numbers are 5 and 245 respectively, find two possible values for the middle number. Showing the workings
The two possible values for the middle numbers in the geometric progression are +35 and -35.
We know that the three numbers form a geometric progression. Let the middle number be x:
5, x, 245
Since these numbers form a geometric progression, we know that:
x^2 = 5 * 245
So we have:
x = ± √(5 * 245)
x = ± 35
Therefore, the two possible values for the middle number are +35 and -35. To find the two possible values for the middle number in the geometric progression, we used the fact that the product of the first and third terms of a geometric progression is equal to the square of the second term.
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Demonstrate, using induction, that each of the equations
corresponding to the subsections are true for all n:
1) P(????) : 2 + 4 + 6 + ⋯+ 2????= ????(????+ 1), ∀ ????∈ℕ.
2) ∑????????= 1 �
This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n. To demonstrate the equations using induction, we need to follow three steps: the base case, the induction hypothesis, and the induction step.
1) P(n) : 2 + 4 + 6 + ⋯+ 2n= n(n+ 1), ∀ n∈ℕ.
Base case: For n = 1, the equation becomes 2 = 1(1+1), which is true.
Induction hypothesis: Assume the equation is true for n = k, that is, 2 + 4 + 6 + ⋯+ 2k= k(k+ 1).
Induction step: We need to show that the equation is also true for n = k+1. That is, 2 + 4 + 6 + ⋯+ 2k + 2(k+1)= (k+1)(k+2).
Using the induction hypothesis, we can substitute k(k+1) for 2 + 4 + 6 + ⋯+ 2k:
k(k+1) + 2(k+1) = (k+1)(k+2)
Distributing the (k+1) on the right side of the equation gives us:
k(k+1) + 2(k+1) = k(k+1) + 2(k+1)
This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n.
2) ∑i^2= n(n+1)(2n+1)/6, ∀ n∈ℕ.
Base case: For n = 1, the equation becomes 1^2 = 1(1+1)(2(1)+1)/6, which simplifies to 1 = 1, which is true.
Induction hypothesis: Assume the equation is true for n = k, that is, ∑i^2= k(k+1)(2k+1)/6.
Induction step: We need to show that the equation is also true for n = k+1. That is, ∑i^2 + (k+1)^2 = (k+1)(k+2)(2(k+1)+1)/6.
Using the induction hypothesis, we can substitute k(k+1)(2k+1)/6 for ∑i^2:
k(k+1)(2k+1)/6 + (k+1)^2 = (k+1)(k+2)(2(k+1)+1)/6
Multiplying both sides of the equation by 6 gives us:
k(k+1)(2k+1) + 6(k+1)^2 = (k+1)(k+2)(2(k+1)+1)
Distributing the (k+1) on both sides of the equation gives us:
k(k+1)(2k+1) + 6(k+1)^2 = k(k+1)(k+2)(2k+3)
This equation is true, so the equation is true for n = k+1. Therefore, by induction, the equation is true for all n.
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Help me pleaseeeeeeee
write the equation with both of them = 100
(3x + 50) + (2x + 15) = 100
combine like terms
5x + 65 = 100
subtract
5x = 35
x = 7
the question asks for <JTU = 2x + 15
plug in x = 7
x = 29
EDIT
Answer:
JTU = 29°
Step-by-step explanation:
I'm not sure if this is correct but I got 29°
(3x+50)° + (2x+15)° = 100°
x= 7°
(2x+15)°
((2x7)+15)° = 29°
what is the answer to 0.03 =
The answer to 0.03 as a fraction is 1/300. But as a percentage, it is 3%.
What is the difference between fraction and percentage?Fractions and percentages are both ways of expressing parts of a whole. A fraction represents a part of a whole, which is divided into equal parts, while a percentage is a fraction expressed as a number out of 100.
The main difference between fractions and percentages is their format. Fractions are typically written as a ratio of two numbers, with the numerator representing the part and the denominator representing the whole. Percentages, on the other hand, are typically written as a number followed by the symbol "%", which represents the part out of 100.
Full question "What is 0.03 as a fraction?"
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The coach for the Lady Bugs basketball team kept track of the scores of their games. Lady Bugs Game Scores
57
50
57
53
53
62
57
What is the range of the scores of the games?
A. 62
B. 50
C. 57
D. 12
The range of the scores of the basketball games played by the Lady Bugs basketball team is equal to option D. 12.
Scores of the games played by Lady Bugs basketball team is equal to
57, 50, 57, 53, 53, 62, 57
Arrange the scores of the team in ascending order we get,
50, 53, 53, 57, 57, 57, 62
Highest score of the team = 62
Lowest score of the team = 50
Range = highest score - lowest score
Substitute the value in the formula we get,
⇒ Range = 62 - 50
⇒ Range = 12
Therefore, the range of the score of the game played by basketball team is equal to option D. 12.
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I need some help please
Step-by-step explanation:
Option A is the right answer.
Solve using substitution.
Therefore, the solution to the system of equations is x = 7 and y = -2.
Answer: x = 7, y =- 2.
What does the meaning of this simple equation mean?a statement describing the relationship between the two phrases on either side of a sign. A single variable and an equal sign are typically present. Comparable is the equation 2x - 4 = 2. The variable x is present in the previous instance.
We are given the following system of equations:
-2x - 9y = 4 ---(1)
-5x - 10y = -15 ---(2)
We can use the method of substitution to solve this system of equations.
From equation (1), we can solve for x in terms of y:
-2x - 9y = 4
-2x = 4 + 9y
x = -2 - (9/2)y ---(3)
Now we can substitute this expression for x into equation (2) and solve for y:
-5x - 10y = -15
-5(-2 - (9/2)y) - 10y = -15
10 + (45/2)y - 10y = -15
12.5y = -25
y = -2
We have found the value of y to be 5. We can substitute this value back into equation (3) to find the value of x:
x = -2 - (9/2)y
x = -2 + (9/2)(2)
x = 7
Therefore, the solution to the system of equations is x = 7 and y = -2.
Answer: x = 7, y = -2.
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What is 98% of 349
so can you tell me what it is tell me once ya found out
Answer:
342.02
Step-by-step explanation:
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
please I need a solution
obtain the solution using the long division method
Stamps 380
Books 19 , 1 , 7 , 12
The number of stamps given for the books in question are :
1 book - 20 stamps 7 books - 140 stamps 12 books - 240 stamps How to find the number of stamps ?To find the number of stamps needed for 1 book, the formula is :
= Stamps needed for 19 books / Number of books
= 380 / 19
= 20 stamps
For 7 books :
= 7 books x 20 stamps per book
= 140 stamps
For 12 books :
= 12 books x 20 stamps per book
= 240 stamps
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Will a line passes through (2,2)if it is intersects the axes (2,0)and (0,2)
A line intersecting at the axes (2,0)and (0,2) will not pass through (2,2).
Given, a line intersects at the axis (2,0)and (0,2)
let the line intercept be expressed as
[tex]ax+by=1[/tex] where a and b are the x & y intercept.
since the intercept points are the axis (2,0)and (0,2)
a=2 and b=2
[tex]2x+2y=1[/tex]
when the point (2,2) is considered and put in equation
2(2)+2(2)=4≠1
Therefore, point (2,2) doesn't satisfy the equation and line doesn't pass through (2,2).
From the graph also, we can say that the line passing through (2,0) and (0,2) intersecting the axes do not pass through the point (2,2).
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How much water was in the cylinder before any marbles were dropped in
It is one of the most fundamental curvilinear geometric shapes, a cylinder has historically been thought of as a three-dimensional solid. It is considered a prism with a circle as its base in basic geometry.
What is Geometry?the area of mathematics that focuses on the characteristics and connections between points, lines, surfaces, solids, and their higher dimensional equivalents.
We can find the solution this way,
The volume of water in the Cylinder before marbles were dropped in =
The volume of water in the Cylinder After marbles were dropped in -
Volume of marbles
So, we can write it as,
Volume of water before = Volume of water after - Volume of Marbles
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Assume a triangle ABC has standard labeling. Determine whether the law of sines (LOS), law of
cosines (LOC) or neither should be used to begin solving the triangle.
a) ????,????,???????????? c
b) ????,????,???????????? ????
c) ????,????,???????????? c
d) ????,????,???????????? ????
The law of sines (LOS) or law of cosines (LOC) should be used to begin solving a triangle depending on the given information. The law of sines is used when we are given two sides and an opposite angle (SSA) or two angles and an opposite side (AAS). The law of cosines is used when we are given three sides (SSS) or two sides and the included angle (SAS).
a) ????,????,???????????? c: Use the law of cosines (LOC) since we are given two sides and the included angle (SAS).
b) ????,????,???????????? ????: Use the law of sines (LOS) since we are given two angles and an opposite side (AAS).
c) ????,????,???????????? c: Use the law of cosines (LOC) since we are given two sides and the included angle (SAS).
d) ????,????,???????????? ????: Use the law of sines (LOS) since we are given two angles and an opposite side (AAS).
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r division on the rational expressions and simplify. (mn)/(m^(2)+9m+18)-:(m)/(6m^(2)+13m-15)
The simplified result of is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).
To divide the rational expressions and simplify, we need to follow the steps below:
Step 1: Flip the second fraction:
(mn)/(m^(2)+9m+18) ÷ (m)/(6m^(2)+13m-15) = (mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)
Step 2: Change the division sign to multiplication:
(mn)/(m^(2)+9m+18) × (6m^(2)+13m-15)/(m)
Step 3: Multiply the numerators and denominators:
= (mn)(6m^(2)+13m-15) / (m^(2)+9m+18)(m)
Step 4: Simplify the result:
= (6m^(3)n + 13m^(2)n - 15mn) / (m^(3) + 9m^(2) + 18m)
= (mn)(6m^(2) + 13m - 15) / (m)(m^(2) + 9m + 18)
= (6m^(2) + 13m - 15) / (m^(2) + 9m + 18)
So the simplified result is (6m^(2) + 13m - 15) / (m^(2) + 9m + 18).
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The Lions won 35 out of 40 games this season.
1) What fraction of games played did the Lions win? Write your answer in simplest form.
2) Write a decimal and a percent equivalent to the fraction of games the Lions won. Show your work.
Answer:
35/40 = (7*5)/(8*5) = 7/8
So the Lions won 7/8 of the games they played.
2) To write a decimal equivalent to 7/8, we can divide 7 by 8 using long division:
0.875
___________
8 | 7.000
- 6.4
_______
60
-56
____
40
-40
____
0
So 7/8 is equivalent to the decimal 0.875.
To write a percent equivalent to 7/8, we can multiply the decimal equivalent by 100:
0.875 * 100 = 87.5%
So the Lions won 87.5% of the games they played.
A savings account balance is compounded annually. If the interest rate is 2% per year and the current balance is $1,932. 00, what will the balance be 7 years from now?
As per the concept of compound interest, the balance after 7 years will be $2,200.24.
In your case, you have a savings account balance that is compounded annually. The interest rate is 2% per year, which means that at the end of each year, the balance will increase by 2% of the previous year's balance. So, if your current balance is $1,932.00, the balance after one year will be:
Balance after one year = $1,932.00 + 2% of $1,932.00
= $1,932.00 + $38.64
= $1,970.64
After two years, the balance will be:
Balance after two years = $1,970.64 + 2% of $1,970.64
= $1,970.64 + $39.41
= $2,010.05
The formula for compound interest is:
A = P(1 + r/n)ⁿˣ
where:
A = the final amount
P = the principal amount (initial balance)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
ˣ = the number of years
In your case, the interest is compounded annually, so n = 1. The annual interest rate is 2%, which is equivalent to 0.02 as a decimal. The initial balance is $1,932.00, and you want to know the balance after 7 years, so t = 7. Using these values in the formula, we get:
A = $1,932.00(1 + 0.02/1)¹ˣ⁷
= $1,932.00(1.02)⁷
= $2,200.24
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A parabola has x-intercepts -2 and -8, and has vertex (-5,-18). Determine the equation of this parabola in the form y=a(x-r)(x-s)
The equation of the parabola in the form y = a(x - r)(x - s) is y = -2(x + 2)(x + 8).
To determine the equation of the parabola in the form y = a(x - r)(x - s), we need to find the values of a, r, and s. We are given the x-intercepts and the vertex, so we can use this information to find these values.
The x-intercepts are -2 and -8, so we know that r=-2 and s=-8. The vertex is (-5,-18), so we can plug these values into the equation and solve for a:
y = a(x - r)(x - s)
-18 = a(-5 + 2)(-5 + 8)
-18 = a(-3)(3)
-18 = 9a
a = -2
So the equation of the parabola is y = -2(x + 2)(x + 8).
In standard form, this equation is y = -2x² - 20x - 32.
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Someone please answer my question
Answer:
Point D is the solution to the system of equations.
Step-by-step explanation:
When asked for a solution involving 2 equations, the goal is to find a point (x,y) that would be a solution to both equations. Any point on a line that is defined by an equation is a solution to that equation. For an equation of y = 2x + 2, possible solutions are (1,4), (2,6), (5,12) etc. These points all lie on the line formed by that equation. There are an infinite number of possible solutions. If a second eqaution is added, there is now a constraint on the possible answers. The goal is to find a point that satisfies both equations.
If a seond equation of y = 1x + 3 were matced with y=2x+2, both are straight lines, but with different slopes. So they will intersect at some point. One may either solve mathematically using substitution, or by graphing, as was done here.
Matematically:
y = 2x + 2
y = 1x + 3
Rearrange either equation to isolate a variable, x or y. These are already isolated (since I made them up) so go to the next step of substituting one expression of y into the other:
y = 1x + 3
2x + 2 = 1x + 3
x = 1
Now use this value of x to find y:
y = 2x + 2
y = 2*(1) + 2
y = 4
The point these two lines intersect is (1,4) and is the "solution" to this series of equations.
See the attached graph.
green swam 2 laps every morning for 7 days.in addition to the laps he swam each morning, he swam 3 laps with his friends one Tuesday and Thursday.
The expression that shows the number of laps Glenn swam during the week is 2 * 7 + 3(2) = 20.
What distinguishes an equation from an expression?A mathematical expression is a grouping of numbers, variables, and operations without the equal sign. It may be condensed or given a single value. On the other hand, an equation is a declaration that employs the equal sign to demonstrate the equality of two expressions. To get the value of the variable that makes an equation true, equations can be solved.
Given that, 2 laps every morning for 7 days:
2 * 7
3 laps with his friends one Tuesday and Thursday.
3(2)
Total laps = 2( 7) + 3(2) = 20
Hence, expression that shows the number of laps Glenn swam during the week is 2 * 7 + 3(2) = 20.
Learn more about algebraic expressions here:
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