a. The series has form an where an = 1/n(n+1)
b. The first five terms in the sequence {an} are 1/2, 1/6, 1/12, 1/20, 1/30
c. The first five terms in the sequence of partial sums for this series are 1/2, 2/6, 3/12, 4/20, 5/30
d. The general formula for the partial sum Sn is Sn = 1 - 1/(n+1)
e. The sum of a series is defined as the limit of the sequence of partial sums, which means lim as n approaches infinity of Sn = 1.
f. True.
g. False.
a. Each term in the series is given by an = 1/n(n+1), which simplifies to an = 1/n - 1/(n+1). This form is a telescoping series.
b. The first five terms in the sequence {an} are obtained by plugging in n = 1, 2, 3, 4, 5 into the formula for an, respectively. Thus, we have a sequence of {an} = {1/2, 1/6, 1/12, 1/20, 1/30}.
c. The sequence of partial sums is obtained by summing the first n terms of the series. Thus, we have S1 = 1/2, S2 = 2/6, S3 = 3/12, S4 = 4/20, S5 = 5/30.
d. To find a general formula for the nth partial sum Sn, we can use the telescoping property of the series. We have:
Sn = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... - 1/(n+1) + 1/(n+1)
Simplifying, we obtain:
Sn = 1 - 1/(n+1)
e. The sum of the series is defined as the limit of the sequence of partial sums as n approaches infinity. Thus, we have:
lim as n approaches infinity of Sn = lim as n approaches infinity of (1 - 1/(n+1))
= 1 - 0 = 1
f. True, the sequence {an} converges to 0 since each term approaches 0 as n approaches infinity.
g. False, the sequence {an} converges to 0, not to 1.
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Brody made 7/8 lb of granola he puts 1/4 lb of granola into each bag how many bags will he be able to fill completely
3.52bags will be filled completely with 7/8 lb of granola and 1/4 lb of granola
What is word problems?
Word Problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols. Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.
To get the number of bags, we simplify and use the quotient, that is:
We divide the quantity of granola over the number of bags
=(7 / 8 pounds) / (1 / 4 pounds)
=0.88/0.25
= 3.52 bags
Hence, The number of bags that will be filled completely is 3.52 bags
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From Belmont, how much farther is it to riverside than yardley?
On solving the provide question, based on the congruent triangles properties, we got to know that x= 76° and 90°.
what are congruent triangles?Congruent triangles are two triangles that are identical in terms of their size and form. The two congruent triangles remain congruent whether you rotate, flip, or flip one of them. If two triangles have the same number of sides, then their angles and congruence must match.
As a result, we can determine that two triangles are congruent if all three of their sides are equal. We also understand that if there is a side, an angle between the sides, and a third side that is congruent, the three sides are congruent. which means sides, corners, and sides.
For green -
=> x = 76° ( both side are same)
For orange -=> x = 90°
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Solve the system of equations using elimination: x-3y=-14x−3y=−14 and x-7y=-26x−7y=−26.
Answer:
2x - 10y = - 40
Step-by-step explanation:
x - 3y = -14
x - 7y = -26
2x - 10y = - 40
Find the slope of the line through the pair of points: (7,5)(-8,4)
Answer:1/15
Step-by-step explanation
formula = y2-y1/x2-x1;
x1=7;y1=5; x2=-8;y2=4
4-5/-8-7=-1/-15
=1/15
The parallelogram has an area of 20 square inches. What are the dimensions of the parallelogram, to the nearest hundredth of an inch?.
The dimensions of the parallelogram to the nearest hundredth of an inch are 6.54 in and 3.06 in.
A Parallelogram is a flat shape with opposite sides parallel and equal in length.
properties of Parallelogram
The opposite sides are parallel and equal in lengthOpposite angles are equal, Angle A and angle B add up to 180°, so they are called supplementary angles.Trigonometry would be used to determine the base and the length of the parallelogram.
Base: cos 40 = adjacent /hypotenuse
0.7660 = adjacent / 4
adjacent = 4 x 0.7660
adjacent = 3.06 inch
Length = area/base
Length= 20/3.06
Length= 6.54 in
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A website charges $3 for each movie you download. They also charge a one-time sign-up fee of $14.99. What is the output variable?
The Output Variable is Total cost represented by c(m).
What is domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given:
A website charges $3 for each movie you download.
They also charge a one-time sign-up fee of $14.99.
So, the input variable will be m which shows the number of movies.
and, the output variable will be c which shows the total cost.
Then, the equation models the cost c(m), is c(m)=3m+14.99
Now, putting the values for m = 0, 1, 2, ....
c(0)= 4.99, c(1)= 17.99, c(2)= 20.99
Hence, the output variable is total cost.
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Help with question 3
The solution is [tex](27^2)^{ 1/5}[/tex] express as [tex]145 \frac{4}{5}[/tex] in simplest radical form.
How to calculate simplest radical form?A radical in mathematics is the opposite of an exponent, which is denoted by the symbol "√" and is also referred to as the root. It can either be a square root or a cube root, and the number before the symbol or radical is regarded as an index number or degree. This number cancels the radical and is represented as a whole number by an exponent.
step1:
extract form
27² =729
729/5= decimal form=145.8
step 2:
729/5=145.8
mixed form:
[tex]145 \dfrac{4}{5}[/tex]
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Find the product of 1/2a and -8/3b.
using distributive law
34. Apply Math Models Olivia makes and sells
bracelets and necklaces. She can make up to
60 pieces per week. Write and graph a system
of inequalities that shows the combination of
bracelets and necklaces that she can make if
she wants to sell at least 30 items per week.
If necklaces sell for $8 each and bracelets sell
for $5 each, what is the most money she can
make in a week? Explain.
The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).
what is unitary method ?The unitary technique is sometimes useful for multiplying and dividing by fractions because it makes sense immediately and can be done mentally if the numbers add up. This makes it a good method for defending or explaining frequently employed written fractional algorithms, like division by a fraction. The unitary technique has a formula that involves finding the value of a single unit, multiplying it by the quantity of units, and then finding the desired value.
given
Assume that y is the number of necklaces and x is the number of bracelets.
Up to (less than or equal to) 60 pieces (bracelets and necklaces) can be produced by Olivia each week:
x+ y ≤60
Up to (less than or equal to) 40 bracelets can be made by Olivia each week:
x≤40(2)
Up to (less than or equal to) 40 necklaces can be created by Olivia each week.
y≤40(3)
Olivia aims to sell at least 30 products per week, preferably more.
x+y≥30(4)
It is possible to write x+y60 as yx+60 with a boundary of y=x+60. Since is used, we shade below the line and draw the line as solid. (red)
The vertical boundary of x40 is defined by x=40. Because is employed,, after which we darken the line's left side and draw the line as solid. (orange)
The horizontal boundary of y40 is defined by y=40. Because is utilized, we shade below the line and draw a solid line over it. (green)
The expression x+y30 can be written as yx+30 has a limit of y=x+30.
Because is utilized, we shade above the line and draw the line as a solid. (blue)
The ordered pairings where the regions overlap are the answers to the linear inequality system (yellow).
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What is the solution to the system of linear equations x 3y =- 2?
The solution to the system of linear equations x 3y =- 2 is (x, y) = (6, -2).
The solution to the system of linear equations x 3y =- 2 can be found by using a method such as substitution or elimination.
One possible method is substitution, where we solve one equation for one variable in terms of the other, and then substitute that expression into the other equation.
For example, we can solve the equation x + 3y = -2 for x in terms of y: x = -3y - 2. Then we can substitute this expression into the second equation: -3y - 2 + 3y = -2, which simplifies to y = -2.
Then we can substitute this value back into the first equation to find x: x = -3(-2) - 2 = 6.
So the solution to the system of linear equations x 3y =- 2 is (x, y) = (6, -2).
In conclusion, The system of linear equations x + 3y = -2 can be solved by using the method of substitution. By solving one equation for one variable in terms of the other, and substituting that expression into the other equation, we find that the solution to the system is (x, y) = (6, -2).
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How do you find the perimeter of a concave pentagon?
The perimeter of a concave polygon may be calculated by summing the lengths of all its sides.
What is perimeter?A perimeter is a closed path that surrounds, encompasses, or outlines a two-dimensional shape or a one-dimensional length. The perimeter of a circle or ellipse is its circumference. The perimeter calculation has a variety of practical applications. The perimeter of an object is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length. A perimeter is the distance between the edges of a two-dimensional form. It is sometimes defined as the total of the object's side lengths. The perimeter of a shape is the algebraic sum of its side lengths. We have equations for the various forms in geometry.
Here,
The perimeter of a concave polygon may be calculated by summing the lengths of all its sides.
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Is 8 a factor of 63q + 15
Answer:
because it has many factors other than 1 and 18
Dante deposits $300 to open a savings account. He will earn 2% interest each year on his
money If he makes no deposits or withdrawals, how much money will Dante earn in interest
in 1 year? How much money will be in the account after 4 years?
When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.
what is amount ?aggregate attempting to determine the whole amount, time, or quantity. The amount at hand or under consideration is very active. the overall outcome, significance, or import. a third accounting, the principal, and the interest. There are word forms for quantities, amounting, and amounted. adaptable noun A thing's quantity is how much of it there is, how much you have, how much you need, or how much you can get. He needs that much money to make ends meet.
given
A= P( 1- rt )
A = 275 ( 1+ 300 )
A = 275( 1.4 )= $385
When Dante deposits $300 to create a savings account, $385 will be available in the account after 4 years.
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Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too.
Is this argument inductive or deductive?
If it is inductive, is it strong or weak?
If it is deductive, is it valid or invalid?
Annie loved the first novel she read by Danielle Steel. Ms. Steel has just published a new novel, and it got great reviews. Therefore, it is likely that Annie would like that novel too which means that the argument is inductive and it is a weak one.
What is an Inductive argument?This is a type of argument which is characterized by the arguer believing that the truth of the premises provides only good reasons to believe the conclusion is probably true.
In this scenario since Annie liked the author's previous books and the new one had great reviews then it is probably true that she would also like it and it is a weak one because assuming the premises are true,then it is probable for the conclusion to be false.
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Which of the following is a solution of the equation 2x 3y 13?
Step-by-step explanation:
Given equations are
2x+3y=13 ....(1)
4x+y=11 .....(2)
multiply the equation (2) by 3, we get
⇒12x+3y=33 .....(3)
Subtract equation (1) from (3) to eliminate y, we get
12x+3y=33
2x+3y=13
− − −
10x=20
⇒x=2
Put this value in equation (1), we get
⇒2(2)+3y=13
⇒4+3y=13
⇒3y=9
⇒y=3
∴ the solution is x=2,y=3.
Lian wants to place wood flooring in his rectangular-shaped laundry room with the dimensions
show below. How much flooring does Lian need?
The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.
what is rectangle ?A rectangle is a polygon with four right angles in Euclidean plane geometry. You may also refer to it as an equiangular quadrilateral, meaning that all of its degrees are comparable. A straight angle could also be present in the parallelogram. Rectangles with four evenly sized sides are called squares. Four 90-degree vertices with equal parallel sides make up a quadrilateral with the outline of a rectangle. As a result, it's also known as a georeferencing rectangle. A rectangle is also referred to as a parallelogram since its opposite sides remain parallel and equal.
given
are of floor = 12 * 12
= 144 ft2
The rectangle flooring needs to be installed in his rectangular laundry room, which has dimensions of = 12 * 12 and a floor area of = 144 ft2.
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What is a 1/3 scale factor?
A 1/3 scale factor is a constant of dilation that is used to change the size of a figure by a factor of 1/3. A dilation is a transformation that changes the size of a figure while preserving its shape.
In a dilation, the scale factor is multiplied by the coordinates of each point on the figure to determine the new coordinates of the dilated figure. If the scale factor is 1/3, then the coordinates of each point on the figure will be multiplied by 1/3, meaning that each point on the figure will be moved one-third as far from the origin as it was before the dilation.
The result of this is that the dilated figure will be smaller than the original figure and will have a scale factor of 1/3. It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.
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PLS HELP FAST! At what value of x does the function f(x)=2(3)^(x) overtake the function g(x)=2x^(2)+4x?
x=2 is value of x does the function f(x).
An easy definition of a function?
As a set of inputs with one output for each, a function is defined as a relationship between them.
In plain English, a function is an association between inputs in which each input is connected to precisely one output. a unique relationship in which each input only results in one outcome. Where x is the input value, it is frequently expressed as "f(x)". as in f(x) = x/2 ("f of x equals x divided by 2") Each input "x" yields a single output "x/2," indicating that it is a function: • f(2) = 1.
X f(x) g(x)
1 6 6
2 12 16
3 18 30
4 24 48
We can see from this table that f(x) is greater than g(x) starting from x=2
Therefore I think x=2 is your answer.
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What is the additive inverse of 7 by 8?
The additive inverse of 7/8 is -7/8.
This can be seen when using the additive inverse formula. The additive inverse formula states that if a number is denoted as x, then the additive inverse would be -x. Therefore, when applied to 7/8, it would be -7/8. This can also be seen when adding the two numbers together. When 7/8 is added to -7/8, the sum is 0. This can be seen in the calculation below:
7/8 + (-7/8) = 0
7/8 - 7/8 = 0
0/8 = 0
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a) What sum amounts to Rs. 3,600 in 2 years at the rate of 10% p.a.
At a 10% annual growth rate, the cash equals Rs. 3,600 in two years. Rs. 3960.
What does total principal amount mean?The principal is the sum you borrowed and are required to repay, while the interest is what you pay. For the majority of borrowers, the total monthly payment you make to your mortgage company includes additional expenses like homeowners taxes and homeowner's insurance that may be placed in an escrow account.
According to the given information:
here principal(P)=3600, R=10%, n= 2 year
amount A=p(1+R/100)ⁿ
3600(1+10/100)²
3600*11/10
=3690
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how old am i if 400 reduced byy one half must subtracted from 257
You are 57 years old if 400 reduced by one half must subtracted from 257 is your age in the given arithmetic problem.
What is arithmetic?Mathematical arithmetic, which includes operations on numbers, is its foundation. Addition, subtraction, multiplication, and division are among these operations. The foundation of the subject "Maths" is laid by one of the crucial branches of mathematics: arithmetic.
Despite the fact that the subject involves numerous other modified operations, addition, subtraction, division, and multiplication are the three basic operations under the heading of arithmetic.
Let your age be x
[tex]$x=257-400\frac{1}{2}[/tex]
x = 257 - 200
x = 57
Hence, your age is 57 years old.
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y-9+y-4 combining like terms (middle school)
By combining the like terms from the given expression we get 2y-13
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.
Given ,
The expression ,
=y-9+y-4
=y+y-(9+4)
=2y-13
Hence , By combining the like terms from the given expression we get 2y-13.
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An 9009h2
7 There are almost 40 thousand fourth graders in Mississippi and almost 400 thousand fourth graders in
Texas. There are almost 4 million fourth graders in the United States.
We write 4 million as 4,000,000. How many times more fourth graders are there in Texas than in
Mississippi? How many times more fourth graders are there in the United States than in Texas? Use the
approximate populations listed above to solve.
There are about 4 thousand fourth graders in Washington, D.C. How many times more fourth graders are
there in the United States than in Washington, D.C.?
There are about 1,000 times as many fourth graders in the US as there are in Washington DC.
what is an algebraic expression ?
Algebraic expression can be defined as the combination of constants , variables and operators.
We write 4 thousand as 4,000
We write 40 thousand as 40,000
We write 400 thousand as 400,000
The value of each place is ten times the value of the place immediately to the right.
So:
40,000 is 10 times 4,000
400,000 is 10 times 40,000.
4,000,000 is 10 times 400,000.
Thus, 400,000 = 10 *40,000, and there are about 10 times as many fourth graders in Texas as there are in Mississippi.
Also, 4,000,000 = 10* 400,000, and there are about 10 times as many fourth graders in the US as there are in Texas.
Finally, to go from 4,000 to 4,000,000, we have to multiply by 10 three times. We see that
10*10*10 = 10 * 100 = 1000
Hence, there are about 1,000 times as many fourth graders in the US as there are in Washington DC.
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Which of the following are quadratic equations? `(i)3x^2-5x+9=x^2-7x+3` (ii) `x+1/x=1` (iii) `x^2-3x=0`
Option (i) , (ii) and (iii) all represents quadratic equations as all of them is of degree 2 and coefficient of degree 2 is non-zero.
What is quadratic equation?Having the form a[tex]x^2[/tex] + bx + c = 0, quadratic equations are 2nd degree algebraic expressions. The meaning of the term "quad," is square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.
Option i
3x^2-5x+9=x^2-7x+3
so the coefficent of degree 2 is 3-1 which is 2 which is non - zero value so this expression is a quadratic equation.
Option ii
x+ [tex]\frac{1}{x}[/tex] =1
=> [tex]x^2[/tex] -x +1=0
so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.
Option iii
[tex]x^2[/tex] -3x=0
so the coefficent of degree 2 is 1 which is non - zero value so this expression is a quadratic equation.
so all the 3 option represents a quadratic equation.
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The two-way frequency table shows the number of blue and green parrots and parakeets in a rescue facility.
Green Blue Total
Parrot 17 16 35
Parakeet 20 28 48
Total 37 44 83
Find the probability that a randomly selected bird is a parakeet given that it is green.
The probability that a randomly selected bird is a parakeet given that it is green is 54.1%.
What is meant by probability?The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The likelihood that the coin will land with the heads side up after being tossed into the air is described using the word probability.
Let,
A be the Parakee
B be the Green
To find the probability that a randomly selected bird is a parakeet given that it is green.
That means P(A|B)
The number of birds that are both parakeet and green is n(A∩B)=20
The number of birds that are green is n(B)=37
Hence, using the conditional probability formula P(A∣B) = [tex]\dfrac{n(A\bigcap B}{n(B)}[/tex]
P(A∣B) = [tex]\dfrac{n(A\bigcap B)}{n(B)}[/tex]
P(A∣B) = 20/37
P(A∣B) = 20/37 × 100%
P(A∣B) = 54.1%
Thus, the probability that a randomly selected bird is a parakeet given that it is green is 54.1%.
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Find the area and perimeter of a triangle with ide length of 4 1/5 inche,and 4 2/7 inche
The perimeter of a triangle is about 18.77 inch and the area of a triangle is about 18 [tex]inch^{2}[/tex] .
What is triangle ?
A triangle is a three-sided polygon with three straight sides. The three sides of a triangle are called edges, and the three angles of a triangle are called vertices. The sum of the three angles of a triangle is always 180 degrees.
Have given ,
length of triangle [tex]4\frac{1}{5} ,4\frac{2}{7}[/tex],
perimeter of a triangle = [tex]4\frac{1}{5} +2*4\frac{2}{7}+6[/tex] = 18.77 inch.
Area of a triangle = [tex]\frac{1}{2}*2*4\frac{1}{5}*4\frac{2}{7}[/tex]
⇒ 18 [tex]inch^{2}[/tex].
Hence , The perimeter of a triangle is about 18.77 inch and the area of a triangle is about 18 [tex]inch^{2}[/tex] .
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What is the quotient of 3 divided by 8?
The quotient of 3÷8 is 0.375
The number 3 is called the numerator or dividend, and the number 8 is called the denominator or divisor.
The quotient of 3 and 8, the ratio of 3 and 8, as well as the fraction of 3 and 8 all mean (almost) the same:
3 divided by 8, often written as 3/8.
The result of 3/8 is a terminating decimal with 3 digits to the right of the decimal point.
3 divided by 8 in decimal = 0.375
3 divided by 8 in fraction = 3/8
3 divided by 8 in percentage = 37.5%
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I'LL DO ANYTHING FOR THE ANSWER!!!
Answer: 1. 55 sq inches
Step-by-step explanation:
add me and mark me brainlyest pls
Answer:
15.5 inches
Step-by-step explanation:
10cm = 3.93701 inches
3.93701 x 3.93701 = 15.50004774
15.50004774 to the nearest tenth is 15.5
Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
A) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
B) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
C) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
D) The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
please help me please
Michael and Ashley bought same amount of turkey and ham.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Michael and Ashley each buy x pounds of turkey and y pounds of ham.
Michael purchased from store A.
Cost of turkey per pound at store A = $3
Cost of ham per pound at store A = $4
Michael spends $18 at store A.
3x + 4y = 18
Ashley purchased from store B.
Cost of turkey per pound at store B = $4.50
Cost of ham per pound at store B = $6
Ashley spends $27 at store B.
4.5x + 6y = 27
We get two linear equations,
3x + 4y = 18
4.5x + 6y = 27
Multiplying the first equation throughout with 4.5 and the second equation throughout with 3, we get,
13.5x + 18y = 81
13.5x + 18y = 81
Since both the equations coincide, Michael and Ashley bought same amount of Turkey and Ham.
Hence Michael and Ashley bought same amount of turkey and ham.
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