The series is absolutely convergent, and by the Alternating Series Test, we can also conclude that it is conditionally convergent.
We can use the Alternating Series Test to determine whether the given series is convergent or divergent. However, before we apply this test, we need to check whether the series is absolutely convergent.
To do this, we will consider the series obtained by taking the absolute value of each term in the given series:
∞
∑[tex]|(-1)^n + n| / (n^3 + 2)[/tex]
n=1
Notice that [tex]|(-1)^n + n| = |(-1)^n| + |n| = 1 + n[/tex]for n >= 1. Therefore,
∞
∑[tex]|(-1)^n + n| / (n^3 + 2) = ∑ (1 + n) / (n^3 + 2)[/tex]
n=1
Now, we can use the Limit Comparison Test with the p-series [tex]1/n^2[/tex] to show that the series is absolutely convergent:
lim n→∞ [[tex](1 + n) / (n^3 + 2)] / (1/n^2)[/tex]
= lim n→∞ [tex](n^2 + n) / (n^3 + 2)[/tex]
= lim n→∞ ([tex]1 + 1/n) / (n^2 + 2/n^3)[/tex]
= 0
Since the limit is finite and nonzero, the series ∑ [tex](1 + n) / (n^3 + 2)[/tex]converges absolutely, and so the original series ∑ [tex]((-1)^n + n) / (n^3 + 2)[/tex]must also converge absolutely.
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The given series is absolutely convergent. This is determined by taking the alternating series test, and observing that the limit of the series as n approaches infinity is 0, and the terms decrease monotonically.
To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we'll first check for absolute convergence using the Absolute Convergence Test. If the series is not absolutely convergent, we'll then check for conditional convergence using the Alternating Series Test.
1. Absolute Convergence Test:
We take the absolute value of the terms in the series and check for convergence:
∑|((−1)^n + n) / (n^3 + 2)| from n=1 to infinity
We simplify this to:
∑|(n - (-1)^n) / (n^3 + 2)| from n=1 to infinity
Now, we'll apply the Comparison Test by comparing the series to the simpler series 1/n^2, which is known to converge (it is a p-series with p > 1):
|(n - (-1)^n) / (n^3 + 2)| ≤ |1/n^2| for all n
Since the series ∑|1/n^2| from n=1 to infinity converges, by the Comparison Test, the original series also converges absolutely. Therefore, the given series is absolutely convergent.
Your answer: The series is absolutely convergent.
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help is needed please
Answer:
A = 72 units²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
note that the middle section of the lower base = upper base = 6
here h = 8 , b₁ = 3 + 6 + 3 = 12 , b₂ = 6 , then
A = [tex]\frac{1}{2}[/tex] × 8 × (12 + 6) = 4 × 18 = 72 units²
Can you spot any mistakes below?
Q1. Make y the subject of the formula:
k=y(squared)+a
√k =y+a
√k - a=y
y=√k-a
Q2. Express in terms of t
t=v/4+1
t-1+v/4
t-1/4=v
Please help I do not know if there are any mistakes
In Q1, The equation k = y² + a is correct,
To make y the subject of the formula, √k = y + a is incorrect, it should be √k = y + √a
√k - √a = y
In Q2, t = v/4 + 1 is correct
t - 1 + v/4 is incorrect, it should be t - 1 = v/4
t - 1/4 = v
so the correct answer is t-1/4=v
Assume the two triangles shown are similar then the missing length
On solving the provided question, we can say that - Since the two triangle are similar and each sides are 3 times the others, so x= 3 X 4 = 12 cm
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Since the two triangle are similar
\and each sides are 3 times the other,
so x= 3 X 4 = 12 cm
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what is the coefficient of the x^4 y^3 term in the expansion of (x-2y)^7?
Help asap
2. A store sells two shades of purple paint. The tables show the number of gallons of blue paint and the number of gallons of red paint used to make each shade of purple paint.
Shade A
Number of Gallons of Blue Paint
8
12
16
24
Number of Gallons of Red Paint for shade A
12
18
24
36
Shade B
Number of Gallons of Blue Paint
5
7
9
12
Number of Gallons of Red Paint
10
14
18
24
Based on the tables, which statements are true? Choose all that apply.
A. The ratio of the number of gallons of red paint to the number of gallons of blue paint in
shade B is 2:1.
B. Shade B should be redder than shade A because shade B has 2 gallons of red paint for every 1 gallon of blue paint. Shade A has 13 gallons of red paint for every 1 gallon of blue paint.
C. Shade A should be bluer than shade B because shade A has 1 gallon of blue paint for every 2 gallons of red paint. Shade B has 1 gallon of blue paint for every 1/2 gallons of red paint.
D. Shade A should be bluer than shade B because shade A has gallons of blue paint for every 1 gallon of red paint. Shade B has gallon of blue paint for every 1 gallon of red paint.
E. If the store owner adds 1 gallon of blue paint to 20 gallons of shade A, she creates 21 gallons
of shade B.
Statement A is correct. The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 2:1.
What is the ratio?
Equivalent ratios are those that are the same when compared. Two or more ratios can be compared to determine whether or not they are equal. For example, the ratios 1:2 and 2:4 are equivalent.
Given that,
Shade A Total
Number of Gallons of Blue Paint: 8 12 16 24 60
Number of Gallons of Red Paint 12 18 24 36 90
Shade B
Number of Gallons of Blue Paint: 5 7 9 12 33
Number of Gallons of Red Paint 10 14 18 24 66
The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 66: 33 = 2:1.
It means for every 2 gallons of red paint for every 1 gallon of blue paint.
The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade A is 90:60 = 3:2.
It means for every 3 gallons of red paint for every 2 gallons of blue paint.
The total gallon in shade A is (60 + 90) = 150.
If she adds 1 gallon of blue paint to 20 gallons of shade A.
Then she creates 150/20 = 7.5 gallons of blue paint in shade B.
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gunnar's car get 22.4 miles per gallon, and his gas tank can hold 17.82 gallons of gas. how many miles can gunnar travel if he uses all of his gas tank
In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.
What is word problem?A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Gunnar's car travel using per gallon of gas = 22.4 miles.
According to the given question,
Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,
=> 22.4 × Car's total tank has hold
=> 22.4 × 17.82
=> 399.17 miles
Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.
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Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. How much did she earn last week if she sold $4,300 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Danielle earned a total of $1,058.25 last week.
What is Commission?A commission is a percentage of total sales as determined by the rate of commission. A commission is a profit paid due to making a sale.
commission=rate of commission⋅total sales.
To find the commission on a sale, multiply the rate of commission by the total sales.
commission = rate of commission⋅total sales.
commission = 7.75% x $4,300
commission = 0.0775 x $4,300
commission = $333.25
Danielle's earnings will be the addition of both her commission and base salary
Total = commission + base salary
Total = $333.25 + $725
Total = $1,058.25
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What is an algebraic expression for this word phrase? 7 more than the product of 5 and n
a. 5 + 7n is the algebraic expression for 7 more than the product of 5 and n
How is this determined?The expression needed to indicate the value of 5 added to the product of 7 and n is "5 greater than the product of 7 and n."
The equation 7n represents the product of 7 and n, and the expression 5 + 7n is obtained by adding 5 to 7n.
This is the proper algebraic expression for the phrase that was given.
It follows that 5 + 7n = 5 + 21 = 26, which is 5 more than the sum of the products of 7 and 3. As an illustration, if we substitute a value of 3 for n, the expression 7n would equal 21.
Because option b is a product of 5 and (7+n), which is not equivalent to 5 greater than the product of 7 and n, the other choices are incorrect.
The product of option c and (5+n) is 7, but it also does not equal 5 greater than the product of 7 and n.
A sum of 5, 7, and n makes up option d, which also does not equal 5 greater than the result of the product of 7 and n.
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Rachel took out a personal loan for $4,500 with a monthly payment of $173.06 for 36 months. determine the finance charge on rachel's loan if she takes all 36 months to pay it off. a. $48.06 b. $1,730.16 c. $4,500.00 d. $6,230.16 please select the best answer from the choices provided a b c d
Rachel's personal loan of $4,500 with a 12% annual interest rate for 36 months will have a finance charge of $6,230.16, meaning that she will need to pay a total of $10,730.16 to pay off the loan amount.
The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months).
Finance Charge = (Loan Amount x Interest Rate x Loan Term)
Finance Charge = ($4,500 x 0.12 x 36 months)
Finance Charge = $6,230.16
The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months). In this case, Rachel took out a $4,500 loan with a 12% annual interest rate for 36 months. The total finance charge for this loan can be calculated as follows: Finance Charge = ($4,500 x 0.12 x 36 months) = $6,230.16. This means Rachel will need to pay a total of $10,730.16 to pay off the loan, including the finance charge. This also means that Rachel's monthly payments of $173.06 will go towards the principle balance of the loan and the interest accrued during each month.
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What is the scale factor of the dilation in the similarity transformation?
The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.
What is scale factor?The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.
It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.
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Why is the center of dilation important?
A reference point used to appropriately scale the dilation of a figure.
Is the dilation center important?A dilation’s center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure. Scale Factor: In a dilatation, the scale factor is the amount by which the figure is stretched or shrunk. Dilation Center: The center of dilation is a reference point used to scale the dilation of a figure suitably.
Dilation of the pupil allows more light into the eye, much as opening a door allows light into a dark room. Dilation allows your eye doctor to examine for a variety of common eye issues, including diabetic retinopathy.
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Which of the following triangles is congruent to triangle PQR?
Third triangle is congruent to triangle PQR.
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
For triangles, there are five primary congruency rules:
Side-Side-Side is an SSS criterion.
The side-angle-side SAS criterion.
Angle, Side, Angle is an ASA criterion.
Angle-Angle-Side is an AAS criterion.
Right Angle Hypotenuse Side (RHS) Criteria
As Height of the triangle PQ is similar to triangle third
Angle 90° ≈ Angle 90° of third triangle
Angle 67° ≈ Angle 67° of third degree
So, By ASA, both the triangles are congruent.
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The future amount due on a compound interest loan of $12,000 at 7% compounded semiannually for four years is approximately ____. If the compounding period is increased to monthly, the amount due on the loan would be approximately ____
Part a: Future amount due on a compound interest loan is $12271.78.
Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.
Explain the term compounding?Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."The formula for compounding is:
A = P(1 + r/100n)∧nt
P = $12,000
r = 0.07
Part a: compounded semiannually.
t = 4 years.
n = 2
A = 12000(1 + 0.07/100*2)∧2*4
A = 12000*1.00280
A = 12271.78
Thus, future amount due on a compound interest loan is $12271.78.
Part b:
t = 4 years.
n = 12
A = 12000(1 + 0.07/100*12)∧12*4
A = 12000*1.0028038
A = 12033.64
Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.
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Answer: $15,802
$15,865
Step-by-step explanation:
V/-15=20 what does V equal?
Answer:
-300
just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)
solve for 20(-15) and you get -300
Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 50% end up investing in bonds, and 44% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?
Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks. The probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both) is 66%.
How to find the probability?60% invest in stocks
50% invest in bonds
44% invest in both bonds and stocks
Percent (only stock) = 60% -44%
Percent (only stock) = 16%
Percent (only bond) = 50% - 44%
Percent (only bond) = 6%
Percent (both) = 44%
Total = 16% + 6% + 44%
Total = 66%
Therefore the probability is 66%.
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PLEASE HELP I WILL GIVE BRAINLIST!
What is the length of the square’s side?
Answer:
x = 6 / sqrt(2)
Step-by-step explanation:
We are given the diagonal of a square
The side length is x
Using the Pythagorean theorem
x^2 + x^2 = h^2 where h is the length of the hypotenuse which is 6
x^2+x^2 = 6^2
2x^2 = 36
x^2 = 18
Taking the square root of each side
sqrt(x^2) = sqrt(18)
x = 3 sqrt(2)
This can be rewritten as
x = 3 sqrt(2) * sqrt(2)
------------------------
sqrt(2)
x = 3*2
-------
sqrt(2)
x = 6 / sqrt(2)
A box contains twelve 16 GB pen drives and eighteen 32 GB pen drives. Two 16 GB pen drives are defective, and four 32 GB pen drives are defective. If a pen drive is picked at random, what is the probability that it is a 16 GB pen drive or defective?
Therefore , the solution to the given problem of probability comes out to be P =0.6.
How are probabilities determined?Probability theory, a subfield of mathematics, calculates the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where 1 denotes certainty and around 0 denotes how probable the event is to occur. A likelihood is a numerical representation of the likelihood that a particular event will occur. Probabilities may alternatively be stated as percentages with a range of 0% to 100% or as a number between 0 and 1. the percentage of events over a wide range of comparably likely outcomes that happen in comparison to all other conceivable outcomes.
Here,
Given :
Twelve 16 GB and 18 32 GB pen drives are packaged together in a box.
To find the probability of 16gb pen drive is defective:
Thus,
Total pendrive = 30
Event = 16gb pen drive or defective:
The probability of it is 16gb pendrive = 12/30 = 0.4
The probability of it is defective pendrive = 6/30 = 0.2
thus,
total probability (16gb pen drive or defective) = 0.4 +0.2 =0.6
Therefore , the solution to the given problem of probability comes out to be P =0.6.
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aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. aidan can spend at most $50 dollars. write and graph an inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy
The inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy is,
⇒ 5x + 10y ≤ 50
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. Aidan can spend at most $50 dollars.
Now, Let the number of matinee tickets Aiden can buy = x
And, The number of evening tickets Aiden can buy = y
So, We can formulate;
The correct inequality is,
⇒ 5x + 10y ≤ 50
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Help with geometry similar triangles. Solve for x if ABC ~ JKL.
Amanda bought a dektop computer and a laptop computer. Before finance charge, the laptop cot more than the dektop. She paid for the computer uing two different financing plan. For the dektop the interet rate wa per year, and for the laptop it wa per year. The total finance charge for one year were. How much did each computer cot before finance charge?
The desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.
The discipline of finance is the study of money, money systems, and capital assets. It is associated with economics, which is the study of the production, distribution, and consumption of money, assets, products, and services, but is not the same thing
Let x be the cost of the desktop computer before finance charges.
We know that the laptop cost 150 more than the desktop, so the cost of the laptop is x+150
We also know that the total finance charge for one year is $303 and the interest rate of the desktop is 7% and the interest rate of the laptop is 9.5%
So we can set up the following equations using the information provided:
(x*0.07) + ((x+150)*0.095) = 303
Simplifying and solving for x:
0.07x + 0.095x + 14.25 = 303
0.165x = 288.75
x = $1750
Therefore, the desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.
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3. Norma has a collection of 80 books. 32 of the books are non-fiction. What percent of the books are non-fiction?
ر
A ratio or value that may be stated as a fraction of 100 is called a percentage.
How do you define percentages?A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it.
The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100.
Therefore, the answer is 25%.
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There are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.
A. Express y in terms of x
B. Make a table to show the relationship between y and x. Use values of x=10,20,30,40, and 50 in your table
We can write the linear equation:
y = x + 50
And evaluating it on the given values of x, we will get the table:
x y
10 60
20 70
30 80
40 90
50 100
How to express y in terms of x?We know that there are x sparrows in a tree, and there are 50 sparrows on the ground beneath the tree.
y represents the total number of sparrows, then y is equal to the number of sparrows on the tree (x) plus the ones beneath (50) then we will get:
y = x + 50
B) Now we want to make a table. To make that table, we need to evaluate the linear equation in different values of x.
if x = 10
y = 10 + 50 = 60
if x = 20
y = 20 + 50 = 70
if x = 30
y = 30 + 50 = 80
if x = 40
y = 40 + 50 = 90
if x = 50
y = 50 + 50 = 100
Then the table will be:
x y
10 60
20 70
30 80
40 90
50 100
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which is larger 7/12 or 2/3 with explanation
Answer:
2/3
Step-by-step explanation:
First divide the numerator by the denominator.
You then get the percentage and then you can judge from there.
Answer:
2/3
Step-by-step explanation:
first we have to equalise the denominators
we know 3 × 4 = 12 so we multiply both the denominator and the nominator by 4 which would give us 8/12
so the answer would be 2/3 since 8/12>7/12
Identify the initial amount a and the rate of decay r (as a percent) of the exponential function h(t)=1250(0.865)^t. Evaluate the function when t=3 . Round your answer to the nearest tenth.
When t = 3, the exponential function has a value of 809.0.
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.
Here,
Given the exponential function h (t) = 1250(0.865)^t
When t = 3
h(3) = 1250(0.865)^3
h(3) = 1250 (0.6472)
h(3) = 809.0
The exponential function when the value of t is 3 is 809.0.
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what is the equation of the line shown in the graph?
The equation for a horizontal line that passes through the points (a, b) is y = b, where b is constant because b is the y-intercept in the equation y = mx + b.
What is the equation for a horizontal line on a graph?As a result of the fact that in the equation y = mx + b, where 'b' is the y-intercept, there is no change in the value of y on the horizontal line and the slope is zero, the equation of a horizontal line is y = b, where 'b' is constant.A horizontal line's points all share the same y-coordinate.
When two points share the same y-coordinate, b, the line's equation is y=b. The coordinates (0,b) are known as the y-intercept of a horizontal line y=b. Horizontal lines are consistently perpendicular to the x-axis. The formula for the lines is always y = a y= a y= a, where a stands for a real number.
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What is the sum of additive inverse of 29 and 61?
The sum of the additive inverse of 29 and 61 is equal to -90.
The sum of the additive inverse of two numbers is equal to zero. The additive inverse of a number is the (opposite) number which when added to the original number yields zero. The formula for calculating the additive inverse of a number is additive inverse (x) = - x. The additive inverse of 29 and 61 can be calculated using the formula, additive inverse (29) = -29 and additive inverse (61) = -61.
Therefore, the sum of the additive inverse of 29 and 61 will be -29 + -61 = -90. This can be confirmed by adding 29 and 61 which will yield 90 and then subtracting 90 from zero to yield -90. In other words, the sum of the additive inverse of 29 and 61 is equal to -90.
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Shannon operates an orange juice stand. On Monday she used 1 1/2 bags of oranges. On Tuesday she used 2 times as many oranges as on Monday. How many bags of oranges did Shannon use on Tuesday?
The number of bags of oranges did Shannon use on Tuesday will be 3 bags.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Shannon operates an orange juice stand. On Monday she used 1 1/2 bags of oranges. On Tuesday she used 2 times as many oranges as on Monday.
The number of oranges will be calculated as,
⇒ 2 × (1 ¹/₂)
⇒ 2 × (1 + ¹/₂)
⇒ 2 + 2 × ¹/₂
⇒ 2 + 1
⇒ 3 bags
The number of bags of oranges did Shannon use on Tuesday will be 3 bags.
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Find an expression to present the area of the trapezoid below
Area of a trapezoid is found with the formula, A=(a+b)/2 x h. so the answer is 9(w-3) / (w + 7) (w + 2).
What is meant by trapezoid ?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.The trapezoid belongs to the category of shapes that only has one set of parallel sides. The isosceles trapezoid, which has two non-parallel sides of the same length, falls under a specific category. Although they are both quadrilaterals, a rhombus and a trapezoid are not the same thing.An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the place where the diagonals intersect.To learn more about trapezoid refer to
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Help with geometry similar triangles. Given AB || CD Find the length of BE.
Answer:
BE = 24
Step-by-step explanation:
These triangles are similar because of AA (Angle, Angle)
The given gives us a pair of parallel sides, allowing us to see that angles C and B are congruent due to being alternate interior angles.
Furthermore, we see that <AEB = <CEB due to vertical <'s being =
Next, we must set up a proportion;
If we create a proportion between the triangles, we must divide corresponding sides;
52/26 = 5x -7 / 2x+2 because we divided both triangles by using the same corresponding sides divided by the same corresponding side.
Simplify 52/26 to 2 and we get that 2 = 5x-7 / 2x+2
Multiply both sides by 2x+2 to get 4x+4 = 5x-7
Subtract 4x from both sides and add 7 from the right side to isolate x and get x=11
Finally, substitute the value of 11 for x into BE 2(11) + 2 and get 22 + 2 =24
What is the law of exponential change?
The law of exponential change states that when a quantity grows or decays at a rate proportional to its size, then the quantity changes exponentially over time. In other words, it follows an exponential function as opposed to a linear function.
The law of exponential changeThe law of exponential change describes the phenomenon of a quantity changing exponentially over time. This means that the rate of change is proportional to the quantity itself. For example, if a quantity increases by 10% each minute, then the quantity will double every 7.2 minutes. This is because each time the quantity increases by 10%, it is multiplying by 1.1. This process is ongoing and the rate of growth or decay will continue to increase exponentially.
The law of exponential change is used in many areas of science and mathematics, such as population growth and radioactive decay. It is also an important concept in economics, as it can be used to measure the growth of money over time.
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