The coordinates where the wood strips cross are (17.11,44). The solution is obtained using the concept of slope of line.
What is slope of line?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics.
The symbols delta y and delta x stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively.
We are given that Hana attaches thin strips of wood from each vertex perpendicular to the opposite edge.
Therefore, the point of concurrency will be in orthocenter.
We are given a triangle with coordinates X(0,0), Y(0,58), Z(36,44)
Now, we will find the slope
Slope(m) = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Slope of XY = (58-0)/0-0 = 0
Slope of YZ = (44-58)/(36-0) = -7/18
We know that slope of line perpendicular to XY is 0
Using point slope form, equation of the altitude perpendicular to XY is
⇒[tex]y-y_{1} = m(x-x_{1} )[/tex]
⇒y-44 = 0(x-36)
⇒y=44
Slope of line perpendicular to YZ is 18/7
Using point slope form, equation of the altitude perpendicular to YZ is
⇒y-0 = 18(x-0)/7
⇒y = 18x/7
Substitute the value of y in the above equation, we get
⇒44 = 18x/7
⇒x = 17.11
Hence, the coordinates where the wood strips cross are (17.11,44).
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please solve this for me :D
Multiplication fact is 4 x 4
Division fact is 16 ÷ 4
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
16
4 4 4 4
This means,
Multiplication facts = 4 x 4 = 16
Division facts = 16 ÷ 4 = 4
Thus,
The multiplication and division facts are:
4 x 4 and 16 ÷ 4.
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Afia entered this expression into her calculator at the shoe store:
`\frac{30}{100}\cdot56`
Write a question she could answer about prices at the shoe store using this expression.
What is the price of an item after a 30% discount if the original price of the item is 56 dollars?
How much is 8 cube?.
The value of 8 cube 512
As we know the cube of a number is the value that are obtained when a number is multiplied by itself three times.
If n be any real valued number then the cube of p is the product of number n three times.
i.e., n × n × n
The cube of number is represented by the third power (exponent = 3) of that number.
For above the cube of number 'n' is represented by n³
Here we need to find the cube of number 8.
From definition of cube of number,
8³ = 8 × 8 × 8
8³ = 64× 8
8³ = 512
Thus the cube of number 8 = 512
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Solve for n
n/5
+
0.6
=
2
5
n
+0.6=2
Pls help I need my ps4 back
The value of n in the equation n/5 + 0.6 = 2 is 7.
How to calculate the value of n in the equation?It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
In this case, n/5 + 0.6 = 2
0.2n + 0.6 = 2
Collect the like terms
0.2n = 2 - 0.6
0.2n = 1.4
Divide
n = 1.4 / 0.2
n = 7
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Complete question
Solve for n
n/5 + 0.6 = 2
How is the Declaration of Independence a reflection of the colonist’s motivations?
Answer: The Declaration of Independence, adopted by the Continental Congress on July 4, 1776, is a reflection of the colonists' motivations in several ways. Firstly, the Declaration states that the colonists believed that all men are created equal and have the right to life, liberty, and the pursuit of happiness. This reflects the colonists' belief in the Enlightenment principles of natural rights and individual liberty, which were influential in shaping their motivations for seeking independence from British rule.
Secondly, the Declaration cites a long list of grievances against King George III, accusing him of violating the colonists' rights and abusing his power. This reflects the colonists' growing frustration and anger towards British rule, which had been building for many years prior to the drafting of the Declaration.
Thirdly, the Declaration states that the colonists had attempted to resolve their differences with the British government through peaceful means, but that these efforts had been unsuccessful. This reflects the colonists' desire for a peaceful resolution to their issues, but their willingness to fight for their rights if necessary.
In summary, the Declaration of Independence reflects the colonists' belief in natural rights and individual liberty, their growing frustration and anger towards British rule, and their desire for a peaceful resolution to their issues but their willingness to fight for their rights if necessary.
Step-by-step explanation:
What is the product of two sets?.
The product of two sets is the set of ordered pair of elements from each set.
We know that the set is nothing but the collection of well-defined objects or elements or numbers.
The elements of sets are written in the curly brackets, seperated by comma.
A set is represented by a capital letter symbol.
For example., the set of natural numbers is denoted by N.
N = {1, 2, 3, 4, . . .}
As we know the Cartesian Product of sets M and N is defined as the set of all ordered pairs (x, y) such that x belongs to set M and y belongs to set N.
It is denoted as M × N = {(x,y) | x ∈ M and y ∈ N}
For example, consider a set P = {1, 2}
and set M = {3, 4, 5},
From the definition of the Cartesian Product of P and M,
P × M = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
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Write a function in terms of t that represents the situation.
A $900 sound system decreases in value by 9% each year.
y=
Answer:
y = 900(0.91^t)
Step-by-step explanation:
You want a function that describes the value of a $900 sound system that decreases in value by 9% per year.
Exponential functionWhen the amount of change is proportional to the amount, the amount is described by an exponential function:
y = ab^x
where 'a' is the initial value, and 'b' is the "growth factor."
ApplicationHere, the change is expressed as a "growth rate" of -9% per year. The growth factor is 1 added to the growth rate:
b = 1 +(-9%) = 1 -0.09 = 0.91
The initial value is given as ...
a = 900
So the function you want is ...
y = 900(0.91^t)
__
Additional comment
The independent variable in this case is time, and the problem statement tells you to use 't' to represent it. The decay rate is given as a percentage per year, so the units of t will be years.
pla shop mathematics
The number of trees more than 10m tall but not more than 20m tall is 18 trees.
How many of the trees are more than 10m tall but not more than 20m tall?0 < h ≤ 5 = 5
height greater than 0m less than or equal to 5m
5 < h ≤ 10 = 9
height greater than 5m less than or equal to 10m
10 < h ≤ 15 = 13
height greater than 10m less than or equal to 15m
15 < h ≤ 20 = 5
height greater than 15m less than or equal to 20m
20 < h ≤ 25 = 1
height greater than 20m less than or equal to 25m
The number of trees that are more than 10m tall but not more than 20m tall are;
10 < h ≤ 15 = 13
15 < h ≤ 20 = 5
So,
13 + 5 = 18 trees
Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.
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anaya is viewing her bank account online she sees 3 entries for monday each for -$10.50
We can see here that the expression that represents the total change in Anaya's account on Monday is: (- $10.5) x 3.
Note that Anaya sees 3 entries for Monday, each for - $10.50.
What is an expression?An expression is a combination of variables, operators, and/or values that can be evaluated to a single value. Expressions can be used in various programming languages or mathematical contexts to perform operations and make calculations. For example, in a programming language, an expression may be used in an assignment statement to assign a value to a variable, or it may be used in a control flow statement to determine which code block to execute.
We see here that since Anaya actually saw 3 entries that read -$10.50, it then means the expression as seen is above.
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You make 40 bracelets and sell them for C dollars each. The table to the right shows
the predicted sales for different prices, C. You use the expression C(40-5C) to
show your income from sales for the different prices.
Drag each term to its description in the table below.
According to the given statement In the given case- The correct answer the predicted sales for different prices is 180.
To calculate now How many bracelets must be sold for the company to turn a profit?Income = 34x
To break even, the company needs to sell 6 bracelets.
Given: C=4x+180 is the price (in dollars) of beads needed to make bracelets.
x is the quantity of bracelets.
The cost of each bracelet is $34.
To Locate:
A. Construct an equation that relates the revenue R to the quantity of bracelets.
B. How many bracelets must be sold for the company to turn a profit?
Given that the bracelet costs $34,
Let's say x bracelets are sold.
Revenue formula: Price * Quantity
Income = 34x
The revenue R in terms of the quantity of bracelets is equal to 34x.
How many bracelets must be sold for the company to turn a profit
⇒4x+180
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How do you describe the nature of the roots of 3x² 4x 5 0?.
D) The term "imaginary roots" describes the roots of the equation 3x2 - 4x + 5 = 0 the best.
The formula is the quadratic equation ax2 + bx + c = 0 in standard form.
x = [-b ± √(b2 - 4ac)]
/ 2a
It follows that
3x2 - 4x + 5 = 0
Here, an equals 3, b equals -4, and c equals 5.
Using these numbers as replacements in the formula
x = [-(-4) ± √((-4)2 - 4 × 3 × 5)]
/ (2 × 3)
By even more simplifying
x = [4 ± √(16 - 60)]
/6
x = [4 ± √-44]/ 6
As a result,
x = [4 ± 2√-11]/ 6
x = [2 ± I √11]/ 3
Additionally, b2 - 4ac = -44 0 is the discriminant. So, we have invented roots.
Therefore, the term "imaginary roots" is the best description of the roots of the equation 3x2 - 4x + 5 = 0.
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Full Question = Choose the best description of the roots of the equation 3x2 - 4x + 5 = 0.
Double root
Real and rational roots
Real and irrational roots
Imaginary roots
You had a bag of fruit snacks that you shared with 2 friends. Each of you got no fewer than 6 fruit snacks. The inequality x+326 models this situation.
Solve the inequality to find the number of fruit snacks that were in the bag.
There were no fewer than []
fruit snacks in the bag.
The inequality to find the number of fruit snacks that were in the bag is
x >= 15
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given ,
You had a bag of fruit snacks that you shared with 2 friends. Each of you got no fewer than 6 fruit snacks.
Given expression , x/3 >= 5
Multiply 3 on both sides
we get,
x/3 * 3 >= 5*3
x >= 15
So the inequality holds x >= 15 .
Hence, The inequality to find the number of fruit snacks that were in the bag is x >= 15
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How do you prove log2 7 is irrational?.
The log₂(7) is irrational, because if we assume that it is rational, we can reach a contradiction.
Assume that log₂(7) is rational. This means that it can be written as the ratio of two integers, a/b, where a and b are integers and b is not equal to zero.
Then, using the definition of a logarithm, we have: 2^(a/b) = 7
Multiply both sides by b, we have: 2^a = 7b
Now we have a problem, because 7b is not necessarily a power of 2. This means that our assumption that log₂(7) is rational leads to a contradiction, and therefore log₂(7) must be irrational.
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A stock investment is increasing by 5% each year. If the original investment was $2,125, how much will it be worth after 10 years?
Type your answer as a decimal rounded to the nearest cent.
Using exponential function, The value after 10 will be P(10) = 2125.0.05¹⁰.
The exponential function: what is it?A mathematical function with the following form is an exponential function: f ( x ) = an x. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
This is an exponential behavior expressed as:
P(t) = Abⁿ
P(t) = Ae^(n ln b)
Where P(t) is the worth after 10 years,
A is the original investment,
and b is the percentage (87% in this case).
From the problem, we identify:
A = 2125
b = 0.05
The final model is:
P(t) = 2125.0.05¹⁰
After 10 years (t = 10),
the investment will be (to the nearest whole number):
P(10) = 2125 ×0.05¹⁰
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Given the point (10,5) and the perpendicular line y = 1/2x - 4, write the equation of a line.
The linear equation perpendicular to the line y = 1/2x - 4 is:
y = -2x + 25
How to find the linear function?A general linear equation can be written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
And two lines are perpendicular if the product between the slopes is -1, then if we want to find a line perpendicular to:
y = 1/2x - 4
Then the slope m must be sch that:
m*(1/2) = -1
m = -2
Then the line is like:
y = -2*x + b
And we know that this passes through (10, 5), replacing these values:
5 = -2*10 + b
5 = -20 + b
5 + 20 = b
25 = b
So the linear equation is:
y = -2x + 25
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What is the rule for standard form?.
A fraction is said to be in standard form when both the numerator and denominator are co-prime numbers.
A well-known form of a range in Maths is largely cited for the illustration of large numbers or small numbers. We use exponents to symbolize such numbers in general shape. Any number that we can write as a decimal range, between 1. zero and 10.0, multiplied by means of a power of 10, is stated to be in general shape.
“ Standard form” is likewise known as “clinical Notation” depending on the mathematical lingo of the u. s. you are in. within the UK and the international locations that comply with the same conventions as the UK, the time period “medical Notation” is most typically used while in nations that comply with the usa conventions majorly talk to this shape of writing as the “fashionable form”.
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In a recent year 27.6 of doctors were female if. There were 52.500 female doctors registered what’s the total number
Answer:
190,217
Step-by-step explanation:
Let x = number of doctors.
27.6% of x is 52,500
0.276x = 52,500
x = 52,500/0.276
x = 190,217
A school sent registration of 150 students for grade IX in the board amounting Rs.45000 with an additional amount of 1.7 % for pay order. Find the total amount paid by the school and by each student.
Amount paid by each student = Rs.45765 / 150 = Rs.305
The school contributed an extra 1.7%. for the payment order on top of the registration fee of Rs. 45000.
To find the total amount paid by the school, we need to calculate the additional amount and add it to the registration fee:
Additional amount = (1.7/100) * 45000 = Rs. 765
Total amount paid by the school = registration fee + additional amount = 45000 + 765 = Rs.45765
To find the amount paid by each student, we need to divide the total amount paid by the school by the number of students:
Amount paid by each student = total amount paid by the school/number of students
Amount paid by each student = Rs.45765 / 150 = Rs.305
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The average price of a gallon of milk was $2.78 in 2000 and increased by about $0.11 per year. Write an inequality that could be used to determine the years, y, in which the price of a gallon of milk is between 3 and 4 dollars.
We know that the average price of a gallon of milk in 2000 was $2.78 and that it increased by about $0.11 per year. To find the years in which the price of a gallon of milk is between $3 and $4, we can use the following inequality:
2.78 + 0.11y < x < 4
Where x is the price of a gallon of milk in a given year y, and y represents the number of years since 2000.
The inequality can also be written as:
2.78 + 0.11y < x < 4
That can be simplified as
y > (3-2.78) / 0.11 = (0.22) / 0.11 = 2
y < (4-2.78) / 0.11 = (1.22) / 0.11 = 11
So, the years in which the price of a gallon of milk is between $3 and $4 are y > 2 and y < 11
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Can someone find the value of x?
9)The value of x is 26 degrees
10)The value of x is 13 degrees
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Vertical angles are equal
2x+1=53
=> 2x=53-1 = 52
x=52/2 = 26 degrees
similarly,
5x+1=66
=> 5x=66-1 = 65
=> x=65/5 = 13 degrees
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What are the solutions of the equation x4 5x2 14 0?.
The Equation is biquadratic , the four solutions of the equation x⁴ - 5x² - 14 = 0 are x = +√7 , x = -√7 , x = +√2i and x = -√2i .
The Biquadratic equation is given as : x⁴ - 5x² - 14 = 0 ;
to change the given equation to a quadratic equation ,
we substitute x⁴ = y² and x² = y .....equation(1)
the quadratic equation becomes as : y² - 5y - 14 = 0;
Now, we observe that to factor this expression, we find the two number whose product is 14 and whose difference is 5, such numbers are 7 and 2.
that means ⇒ y² - 5y - 14 = (y - 7)(y + 2);
from equation(1) ,
we get ; ⇒ x⁴ - 5x² - 14 = (x² - 7)(x² + 2) = 0;
Solving the two factors ,
we get ;
⇒ x² - 7 = 0 ⇒ x² = 7 ⇒ x = +√7 and x = -√7 ; and
⇒ x² + 2 = 0 ⇒ x² = -2 ⇒ x = +√2i and x = -√2i .
Therefore , the given equation has two Real Solutions and two Complex Solutions .
The given question is incomplete , the complete question is
What are the solutions of the equation x⁴ - 5x² - 14 = 0 ?
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Please find the measure of the unknown values. No links are allowed, and if used, your answer will be reported. The first person to answer correctly will be highly favoured to get marked as brainliest.
I would appreciate a detailed answer!
Thank you.
Answer:
x = 79
Step-by-step explanation:
Since PQ and RS are most likely parallel lines, we can consider the orange angles (image provided below) to be similar due to them being alternate interior angles.
Now that we know that one angle of the triangle given (orange) is 46 degrees, we can solve for the other angle of the triangle. A triangle adds up to 180 degrees, so we can find the missing angle by subtracting 180 from the given angles: 180-33-46 = 101 (marked in red).
With the red angle, we can find x by subtracting 180 from 101. Why you may ask? Because RS is parallel to PQ, so the degree will be 180. Therefore, the missing angle, x, will be 79.
Figure ABCDEF i hown on a coordinate grid. Figure ABCDEF i dilated with the orgin a the center of dialatiin to create figure a’b’c’d’e’f’ uing the rule
The correct answer is "Figure A’B’C’D’E’F’ is smaller than figure ABCDEF, because the scale factor is less than 1".
The Scale Factor is used to scale shapes in various dimensions. Geometry teaches us about various geometrical shapes in both two and three dimensions.
The scale factor is a measure for figures with similar appearances but differing scales or measures. Assume two circles appear identical but have different radii.
A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller).
Thus, the correct answer is "Figure A’B’C’D’E’F’ is smaller than figure ABCDEF, because the scale factor is less than 1"
Complete question:
Figure ABCDEF is shown on a coordinate grid. Figure ABCDEF is dilated with the origin as the center of the dilation to create figure A’B’C’D’E’F’ using the rule (x, y)—›(0.95x, 0.95y). Which statement is true?
Answer choices:
Figure A’B’C’D’E’F’ is smaller than figure ABCDEF, because the scale factor is greater than 1.
Figure A’B’C’D’E’F’ is larger than figure ABCDEF, because the scale factor is less than 1.
Figure A’B’C’D’E’F’ is smaller than figure ABCDEF, because the scale factor is less than 1
Figure A’B’C’D’E’F’ is larger than figure ABCDEF, because the scale factor is greater than 1.
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A’B’C’D’E’F’ is smaller than figure ABCDEF, because the scale factor is greater than 1.
A’B’C’D’E’F’ is larger than figure ABCDEF, because the scale factor is less than 1.
A’B’C’D’E’F’ is smaller than figure ABCDEF, because the scale factor is less than 1
A’B’C’D’E’F’ is larger than figure ABCDEF, because the scale factor is greater than 1.
Damon kayaks on a river near his home. He plans to kayak a total of 6.4 miles. Damon kayaks at an average speed of 1.6 miles per hour. How many hours will it take Damon to kayak the 6.4 miles?
Answer:
He plans to kayak a total of 6.4 miles. Damon kayaks at an average speed of 1.6 miles per hour. How many hours will it take Damon to kayak the 6.4 miles? It will take Damon 4 ‾ hours to kayak 6.4 miles.
Hello ixl. T and q are the midpoints of legs su and rv
RS is 75 units when T and q are the midpoints of legs SU and RV of a trapezoid.
What is a trapezoid?The bases are in step with one another. The median runs perpendicular to each bases, and its length will be determined by averaging the bases' lengths. 360° is the sum of all of the angles in a trapezoid. A aspect's angles upload as much as an entire one hundred eighty stages.
So, imagine cutting the trapezoid from half and and rotating and join it to became a long parallelogram
Now,
VR = UV + RS = 2QT
⇒ 35 + RS = 2 × 55
⇒ RS = 110 - 35
⇒ RS = 75
Thus, RS is 75 units when T and q are the midpoints of legs SU and RV of a trapezoid.
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The following T account how tranaction that were recorded by Reidential Relocator, a firm that pecialize in local houing rental
Cah
(a) 179,000 (b) 35,000
(d) 19,000 (e) 590
(g) 1,900 (h) 9,900
(i) 3,900
Equipment
(c) 69,000
Account Receivable
(f) 10,200 (g) 1,900
Account Payable
(c) 69,000
Supplie
(b) 35,000
Scott Hamilton, Capital
(a) 179,000
Fee Income
(d) 19,000
(f) 10,200
Telephone Expene
(e) 590
Scott Hamilton, Drawing
(i) 3,900
Salarie Expene
(h) 9,900
Required: Prepare a trial balance and an income tatement for Reidential Relocator. The trial balance i for December 31, 20X1, and the income tatement i for the month ended December 31, 20X1
Trial Balance as of December 31, 20X1:
Account Debit Credit
Cash: 179,000
Equipment: 69,000
Accounts Receivable: 11,100
Accounts Payable: 69,000
Supplies: 35,000
Scott Hamilton, Capital: 179,000
Fee Income: 29,200
Telephone Expense: 590
Scott Hamilton, Drawing: 3,900
Salaries Expense: 9,900
Total: 368,190 368,190
Income Statement for the month ended December 31, 20X1:
Revenue: 29,200
Expenses:
Equipment: 69,000
Supplies: 35,000
Telephone Expense: 590
Salaries Expense: 9,900
Total Expenses: 114,490
Net Income: (85,290)
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What is the value of 2x 3y 36 when Y 6?.
The value of x in equation 2x+3y=36, when y=6 is 9.
The replacement operation can be used in a variety of situations involving formal objects that contain symbols; it involves systematically replacing occurrences of a symbol with a particular value.
Substitution is a fundamental computer algebra operation.
Given equation 2x+3y=36 ; y=6
Solve the equation for given y.
Plugging y=6 in the given equation
We get 2x + 3(6) = 36
2x +18 = 36
2x = 36 - 18
2x = 18
x = 9
Therefore, the value of x in equation 2x+3y=36, when y=6 is 9.
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Max's dad bought his friends 5 bottles of water and 8 slices of pizza at the concession stand and spent $20.25. He had to go back and get 1 more bottle of water and 3 slices of pizza. This time the total was $6.50. What is the cost of one slice of pizza?
Step by step explanation please?!
Using simultaneous equations, the cost of one slice of pizza bought by Max's dad at the concession stand is $1.75.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently or simultaneously.
Simultaneous equations are also called a system of equations.
Bottles Slices of Total
of Water Pizza Cost
1st purchase 5 8 $20.25
2nd purchase 1 3 $6.50
Let the cost of bottles of water = b and the cost of slices of pizza = p
Equations:Equation 1: 5b + 8p = 20.25
Equation 2: b + 3p = 6.50
Multiply Equation 2 by 5:
Equation 3: 5b + 15p = 32.50
Subtract Equation 1 from Equation 3:
5b + 15p = 32.50
-
5b + 8p = 20.25
7p = 12.25
p = 1.75
The cost of one slice of pizza (p) = $1.75
Check:
b + 3p = 6.50
b + 3(1.75) = 6.50
b + 5.25 = 6.50
b = 1.25
= $1.25
Thus, the cost of one slice of pizza is $1.75.
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Answer this functions question
Answer:
[tex]\boxed{a = 4}[/tex]
Step-by-step explanation:
Note:
[tex]\fbox{\parbox{\textwidth}{%\textrm{\textsf{\textbf{Note:}}\\\textsf{This question is stated in a confusing manner and since I cannot see\\part a I am taking whatever I see on the screen as gospel truth\\\\From the question it appears that we are given gf(a) =3 and asked to solve for a.\\\\I am proceeding on that basis}}}[/tex]
We have the following functions
[tex]f(x) = \dfrac{2}{x}\\\\g(x) = \dfrac{x + 1}{x}\\[/tex]
[tex]gf(x) = g(f(x))[/tex]
[tex]\textrm{To find g(f(x)) wherever you see an x in gx), substitute the expression for f(x)}\\[/tex]
[tex]Since f(x) = \dfrac{2}{x}\\\\\textrm and}\\\\g(x) = \dfrac{x + 1}{x}\\[/tex]
[tex]\dfrac{\dfrac{{2}}{x}+1}{\dfrac{2}{x}}\\\\\\\\\left(\dfrac{{2}}{x}+1}\right) \div \dfrac{2}{x}\\\\= \left(\dfrac{{2}}{x}+1} \right) \times \dfrac{x}{2}\\\\[/tex]
[tex]\dfrac{2}{x} + 1} = \dfrac{2 + x}{x}\\[/tex]
[tex]\left(\dfrac{{2}}{x}+1} \right) \times \dfrac{x}{2}\\\\\\= \dfrac{2 + x}{x} \times \dfrac{x}{2}\\\\\\[/tex]
[tex]\textrm{The x's cancel out giving $\dfrac{2+x}{2}$}= 1 + \dfrac{x}{2}[/tex]
[tex]\textrm{For a specific value, a, if $g(f(a)) = 1 + \dfrac{a}{2}$ = 3}}[/tex]
[tex]\textrm{Then $\dfrac{a}{2}$ = 3-1 = 2}[/tex]
[tex]\boxed{a = 4}[/tex]
Your cla had an ant farm with 32 ant. If the number of ant increaed by a factor of 5 every week, how many ant would there be after 3 week? Write your anwer in numerical form
The ant population increases by factor of 5 every week. After 3 weeks, there will be 800 ants in the farm.
The problem can be solved by considering the ant population growth as a geometric sequence.
In a geometric sequence, a term is obtained by multiplying the previous term by a constant, which is called a common ratio. We can consider this common ratio as a growth factor.
In this case, the common ratio = 5
week 1 = 32 ants
week 2 = 32 x 5 ants = 160 ants
week 3 = 160 x 5 ants = 800 ants
We can also find the number of ants using the geometric sequence formula for the nth term:
a(n) = a . rⁿ⁻¹
Where:
a = first term = 32
r = common ratio = 5
Hence,
a(3) = 32 x 5² = 800 ants
Learn more about geometric sequence here:
https://brainly.com/question/28188245
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