The results of operations between the two functions f(x) = 2 · x + 1 and g(x) = 6 - x are listed below:
(f + g)(2) = 9 (f - g)(- 5) = - 20 (g - f)(4) = - 7 (f · g)(1 / 2) = 11 (f / g)(- 1) = - 1 / 7How to derive and evaluate a composite function
In this problem we have the definitions of two functions, linear equations on both cases. The procedure consists in using the definitions of operations between two functions and evaluate the resulting expression at a given value of x:
Addition
(f + g)(x) = f(x) + g(x)
Subtraction
(f - g)(x) = f(x) - g(x)
Multiplication
(f · g)(x) = f(x) · g(x)
Division
(f / g)(x) = f(x) / g(x)
Now we proceed to derive each expression and evaluate the resulting expression:
(f + g)(x) = (2 · x + 1) + (6 - x)
(f + g)(x) = x + 7
(f + g)(2) = 2 + 7
(f + g)(2) = 9
(f - g)(x) = (2 · x + 1) - (6 - x)
(f - g)(x) = 3 · x - 5
(f - g)(- 5) = 3 · (- 5) - 5
(f - g)(- 5) = - 20
(g - f)(x) = (6 - x) - (2 · x + 1)
(g - f)(x) = - 3 · x + 5
(g - f)(4) = - 3 · 4 + 5
(g - f)(4) = - 7
(f · g) (x) = (2 · x + 1) · (6 - x)
(f · g) (x) = 2 · x · (6 - x) + 6 - x
(f · g) (x) = 12 · x - 2 · x² + 6 - x
(f · g) (x) = - 2 · x² + 11 · x + 6
(f · g)(1 / 2) = - 2 · (1 / 2)² + 11 · (1 / 2) + 6
(f · g)(1 / 2) = 11
(f / g) (x) = (2 · x + 1) / (6 - x)
(f / g)(- 1) = [2 · (- 1) + 1] / [6 - (- 1)]
(f / g)(- 1) = - 1 / 7
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Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS
SSS
SAS
HL
Answer:
AAS
Step-by-step explanation:
BECAUSE OF THE QUESTION
ITS GIVEN IN QUESTION
it's congruent
Bill uses mirrors to augment the “laser experience” at a laser show. At one show he places three mirrors, A, B, C, in a right triangular form. If the distance between A and B is 20m more than the distance between A and C, and the distance between B and C is 20m less than the distance between A and C, what is the distance between mirror A and mirror C?
The distance between the mirrors A and C is 80 m.
What is Pythagoras theorem?The Pythagoras theorem tell the relation between the sides of a right triangle, in this we relate the hypotenuse to the other two sides of the triangle, mathematically expresses as- (hypotenuse)² = (Side1)²+(Side)²
Given that, Bill performed a show by placing three mirrors A, B and C in right triangular form, the distance between A and B is 20 m more than the distance between A and C, and the distance between B and C is 20 m less than the distance between A and C,
Let the distance between A and C be x,
AC = x
AB = x+20
BC = x-20
Using Pythagoras theorem,
AB² = AC²+BC²
x²+(x-20)² = (x+20)²
x²+x²+400-4x = x²+400+40x
x²-80x = 0
x(x-80) = 0
x = 0 or x = 80 (Neglecting x = 0 because distance between two sides of a triangle can't be 0)
Hence, The distance between the mirrors A and C is 80 m.
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Find the monthly payment on a VCR with an installment price of $994.01, 12 monthly payments, and a down payment of $200.
Answer:
62.16
Step-by-step explanation:
994.01 - 200.00 / 12
The perimeter of a rectangle is 20 ft. The length is 6 ft. Which equation can be
solved to find the width of the rectangle?
Answer: 20ft - 6ft
Step-by-step explanation:
j(m) = 2^m-1
What is j (4)?
Enter your answer in the box.
j(m) = 2ᵐ ⁻ ¹
for functions you will replace the number in the brackets with the letter! so:
j(4) = 2⁴ ⁻ ¹
= 2³
= 8
A falcon is flying at a speed of 107,360 yards per
hour. How fast is the falcon flying in miles per
hour? (Hint: A mile is equal to 1760 yards.)
Help
Help with this plsss !!!
Answer:
Just about 50%, depending on if the data set is a odd or even number
Step-by-step explanation:
At 45, is the median value. The median of a box plot is not necessarily 50% of the data. The median is the middle value in a dataset, or the value that divides the data into two equal halves. If the dataset has an odd number of values, the median will be one of the values in the dataset. If the dataset has an even number of values, the median will be the average of the two middle values.
PLEASE PLEASE HELP ME
make a list of at least 15 different phrases and expressions you can write using the variable y and the integer 2. Include all operations
I need this ASAP!!!
Answer:
y/2
y*2
y-2
y+2
y%2
y^2
Operations on Algebraic Expressions: The three major components of an algebraic expression are variables, constants, and coefficients. Addition, subtraction, multiplication, and division are the four fundamental operations. We solve both difficult and straightforward equations using operations on algebraic expressions.There are three categories of algebraic expressions: monomial, binomial, and polynomial or multi-term expressions.These are the algebraic terms: Alphabetic letters alone or in combination with numbers or fractions are the variables.The numbers that are connected to the variables in a single term are called coefficients.Constants: Single integers or numbers that are typically connected to other terms through elementary operations.Examples include 8xyz, 25x+12y+9, 2yz23zy, and 3a+2b+5c.Algebraic Expression Types
There are three different categories for algebraic expressions. As follows:
Expressions with a monomial or single word. For instance, 4xy2, 3ab, 7p, 5xyz, etc., where 3,4,5,7 are the coefficients and x, y, z, a, b, p are the variables.Expressions with two terms or a binomial. For instance, 2xyx, pq5p2, etc.Multi-term or polynomial expressions. as in 2x+5y4, 2xy2+3y+1, etc.To learn more about Operations on Algebraic Expressions refer to:
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"y/2," "y*2," "y-2," "y+2," "y%2," and "y". Constants, coefficients, and variables make up the three main parts of an algebraic expression.
Procedures for Algebraic Expressions:Constants, coefficients, and variables make up the three main parts of an algebraic expression. These four operations—addition, subtraction, multiplication, and division—are known as the fundamental operations.By performing operations on algebraic expressions, we are able to solve both complex and simple equations.Polynomial or multi-term expressions, binomial expressions, and monomial expressions are the three types of algebraic expressions.The variables are either alphabetic letters alone or in combination with numbers or fractions.The term "coefficients" refers to the numbers that link the variables in a single term.Single integers or numbers known as constants are those that are often connected to other terms through simple mathematical procedures. There are more examples, such as 8xyz, 25x+12y+9, 2yz23zy, and 3a+2b+5c.Monomial expressions or single-word phrases. For instance, 4xy2, 3ab, 7p, 5xyz, etc., where 3,4,5,7 are the coefficients and x, y, z, a, b, p are the variables. two-term or binomial expressions pq5p2, for instance, or 2xyx. such as 2x+5y4, 2xy2+3y+1, etc., are examples of multi-term or polynomial expressions.To learn more about Algebraic expressions refer to:
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Mohammad says that there is 5/8 of a ham sandwich left that he bought in LULU Supermarket and 1/2 of a turkey sandwich left. What is NOT a pair of equivalent fractions for 5/8 and ½.
The option that is not a pair of equivalent fractions for 5/8 and ½ is C. 3/8.
How to illustrate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
From the information, Mohammad says that there is 5/8 of a ham sandwich left that he bought in LULU Supermarket and 1/2 of a turkey sandwich left.
It should be noted that 3/8 is not an equivalent fraction. Therefore, the correct option is C.
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Mohammad says that there is 5/8 of a ham sandwich left that he bought in LULU Supermarket and 1/2 of a turkey sandwich left. What is NOT a pair of equivalent fractions for 5/8 and ½.
10/16
3/6
3/8
5/10
if n is an integer, what is the sum of the next three consecutive even integer great than 2n
The required sum is given as 6n + 12.
What are integers?Integers can be defined as the set of counting numbers and their negative values along with zero. An integer can be written in the form of a fraction by writing the denominator as 1.
The given problem can be solved as follows,
The consecutive three even integers greater than 2n can be written as,
2n + 2, 2n + 4 and 2n + 6
Now, the sum of these integers are given as follows,
2n + 2 + 2n + 4 + 2n + 6
= 6n + 12
Hence, the sum of the next three consecutive even integer greater than 2n is given as 6n + 12.
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help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
this is the same principle in every posted question.
I hope you understand this now.
if not please let me know what is still a "riddle" to you, so that I can explain it better.
remember, the inverse function of y = e^x is x = ln(y).
and the inverse function of y = ln(x) is x = e^y.
we want to find the value of x, where f(x) = 28.
28 = 0.48ln(x + 2) + 27
1 = 0.48ln(x + 2)
1/0.48 = ln(x + 2)
e^(1/0.48) = x + 2
x = e^(1/0.48) + 2 = 10.03119499... miles ≈ 10 miles
the pressure of 28 inches of mercury occurs about 10 miles from the eye of the hurricane.
What is positive [15]+ negative [-1]=
10. If m and n are positive integers and
2x(5x+3y) = mx² + nxy, what is the value
of m-n?
(A) -4
(B) -1
(C) 1
(D) 4
Answer:
D.)
Step-by-step explanation:
1.) Expand the expression with distributive property. If we expand, we get 10x^2+6xy.
2.) Figure out m and n based on the expression. Since m is in front of the x^2, that means that m=10, and since n is in front of the xy, that means that n=6.
3.) Compute based on m and n. Since m is 10 and n is 6, m - n = 10 - 6 = 4. Therefore, D.) is the answer.
6 -4 3
2 4 -2
Photo provided
The equations of the system would be 6x - 4y = 3 and 2x + 4y = -2.
What is the system of linear equations in matrices?
A system of linear equations in matrices is a set of linear equations that can be expressed in matrix form. In this form, the equations are written as a matrix equation of the form Ax = b, where A is an m × n matrix of coefficients, x is an n × 1 matrix of variables, and b is an m × 1 matrix of constants. The solution to the system of equations can be found by solving for the matrix x using the matrix equation Ax = b. This can be done using various techniques, such as Gaussian elimination or matrix inversion. Matrix equations can be used to solve systems of linear equations for which the traditional algebraic methods are difficult or impossible.
We can prepare the equations as:
Equation 1: 6x - 4y = 3
Equation 2: 2x + 4y = -2
Hence, the equations of the system would be 6x - 4y = 3 and 2x + 4y = -2.
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How many people Mark and Heather can invite to the party?
Evaluate the expression when y=6. y^2+5y+9
Answer:
75
Step-by-step explanation:
y² + 5y + 9
since y = 6 we will just substitute for y
= (6)² + 5(6) + 9
= 36 + 30 + 9
= 66 + 9
= 75
i hope this helps
URGENt please help me all I need is the answer of b
What is the 6th term in the Fibonacci sequence?
The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.. .
What is Fibonacci sequence?
One of the most well-known mathematical formulae is the Fibonacci sequence. Each number in the Fibonacci sequence is calculated by adding the two numbers that came before it. Typically, the Fibonacci series' first two terms are 0 and 1. Hundreds of years before Leonardo Pisano Bigollo was even aware of it, the Fibonacci sequence was well-known in India. Because the date November 23 contains the numbers "1, 1, 2, 3," which are a part of the sequence, it is recognized as Fibonacci Day.
The Fibonacci sequence is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946,….
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Which of the following interpretations of the mean is correct?
A. The observed number of hits per game ail be less than the mean number of hills per game for most games.
B. The observed number of hits per garret will bees equal to the mean number of hiss per game for most sties.
X C. In any number 0f game, one will expect the man number of hits per game to be its mean of the random variable
D. Chess the course of many games, one would expect the mean number of its per game to be the mean of the random variable.
Over the course of many games, one would expect the mean number of hits per game to be the mean of the random variable.
What is Mean?
A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilises the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.
There are two different types of means that can be calculated: the arithmetic mean and the geometric mean.
The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of numbers in the set.
Mean is the ratio of sum of observations to the total number of observation.
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Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair 3, 0, B at ordered pair 4, negative 2, C at ordered pair 1, negative 3. A triangle A prime B prime C prime has A prime at ordered pair negative 3, 0, B prime at ordered pair negative 4, negative 2, C prime at ordered pair negative1, negative 3. Which equation shows the correct relationship between the measures of the angles of the two triangles?
The measure of angle BCA = The measure of angle C prime A prime B.
How to calculate the measure of each angle in triangle ?Given that
Triangle ABC is transformed to triangle A′B′C′, as shown below:
A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes.
A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
According to the question
Triangle ABC is transformed to triangle A′B′C′, as shown below:
Here the triangle ABC is similar A'B'C' are similar triangles.
For similar triangles angles are congruent.
A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Therefore,
<BAC = <B'A'C'
<ABC = <A'B'C'
<ACB = <A'C'B'
Hence, The correct relationship between the measures of the angles of the two triangles is the measure of angle BCA = The measure of angle C prime A prime B.
The complete question is : Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime
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Determine the value of x, in dollars, that will make their weekly pay the same.
Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x)=185+.03x. Jim is paid $275 per week plus 2.5% of his total sales in dollars,x, which can be represented by f(x)=275+.025x.
The value of x, in dollars, so that they have equal weekly pay is $18,000.
Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is a set of values that have the potential of coming out as outputs of a function.
We are given that Guy and Jim earn the same weekly pay.
Then g(x) = f(x)
So, 185 + .03x = 275 + .025x
Rearranging terms so that the x's are together and the constants are together:
0.005x = 90
∴ x = 18,000
Thus, the value of x, in dollars, so that they have equal weekly pay is $18,000.
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When a local office supply store sells
5 packs of paper, it also sells 8 packs
of envelopes. How many packs of
envelopes would the store sell if it sold
15 packs of paper?
Answer:
If the local office supply store sells 5 packs of paper, it also sells 8 packs of envelopes. This means that the store sells 8 packs of envelopes for every 5 packs of paper.
If the store sells 15 packs of paper, it will sell 15 packs of paper * (8 packs of envelopes / 5 packs of paper) = <<15*(8/5)=24>>24 packs of envelopes.
Therefore, if the local office supply store sells 15 packs of paper, it will sell 24 packs of envelopes.
At December 31, the records of Nortech Corporation provided the following selected and incomplete data:
Common stock (par $1; no changes during the current year).
Shares authorized, 500,000.
Shares issued, 2; issue price $12 per share.
Common Stock account, $100,000.
Shares held as treasury stock, 2,000 shares, cost $10 per share.
Net income for the current year, $24,500.
Dividends declared and paid during the current year, $14,700.
Retained Earnings balance, beginning of the year, $145,000.
Required:
Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par
value per share. (Round "per share" answers to 2 decimal places.)
1-a. Shares authorized
1-b. Shares issued
1-c. Shares outstanding
2. The balance in Additional Paid-in Capital would be
3. Earnings per share is
4. Dividends paid per share of common stock is
5. Treasury stock should be reported in the stockholders' equity section of the balance
sheet in the amount of
6. Assume that the board of directors approved a 2-for-1 stock split. After the stock split,
the par value per share will be
500,000
290,000
A company's balance sheet is its financial statement at a given point in time and lists its assets, liabilities, equity capital, total debt, and other items.
What is meant by balance sheet?A balance sheet is a list of all your capital, obligations, and assets. The assets and liabilities of a firm are described in detail on a balance sheet, which is a financial statement.
The Equity Section of the Nortech Corporation's Balance Sheet exists as follows:
Common Stock:
500,000 shares, Authorized at $1 par value
200,000 Issued Shares at $1 = $200,000
Additional Paid-in Capital 4,143,000
3,000 shares, Treasury stock (3,000)
Retained Earnings 253,500
Total Equity $4,593,500
1c. Shares Outstanding = 197,000 (200,000 - 3,000)
2. Balance in Additional Paid-in Capital = $4,143,000
3. Earnings per share = $0.75 ($147,750/197,000)
4. Dividend per share = $0.25 ($49,250/197,000)
5. The Treasury stock is reported as $3,000 on the balance sheet.
6. With a 2-for-1 stock split, the par value becomes $0.50 ($1/2)
Data and Calculations:
Par value of Common Stock = $1
Authorized Shares = 500,000 shares
Issue price per share = $22
Common Stock Account = $200,000
Issued Shares = 200,000 shares ($200,000/$1)
Treasury Stock = $3,000 (3,000 x $1)
Additional Paid-in Capital = $4,200,000 (200,000 x $21)
Additional Paid-in Capital (Treasury Stock) = $57,000 ($19 x 3,000)
Balance of Additional Paid-in Capital = $4,143,000 ($4,200,000 - $57,000)
Retained earnings for the year:
Beginning Balance $155,000
Net income 147,750
Dividends paid (49,250)
Ending Balance $253,500
The complete question is:
At December 31, the records of Nortech Corporation provided the following selected and incomplete data: Common stock (par $1; no changes during the current year).Shares authorized, 500,000.Shares issued, ?; issue price $22 per share. Common Stock account, $200,000.Shares held as treasury stock, 3,000 shares, cost $20 per share. Net income for the current year, $147,750.Dividends declared and paid during the current year, $49,250.Retained Earnings balance, beginning of the year, $155,000.Required: Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par value per share. (Round "per share" answers to 2 decimal places.)
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Find the additive inverse of −9x+3
let additive inverse of it is y
So, y + (-9x+3) = 0
y = 9x-3
What is
17/11 times 6/10
Answer:
0.92727272727
Please vote for Brainliest and I hope this helps!
Answer:
38/22
Step-by-step explanation:
you multiply the first numbers and the last numbers and combine it
the difference of -2 and a number is -14. find the number
Answer
I think the number is -16, hope this helps!
Answer: the number is -12
Step-by-step explanation:
x-2=-14
x=-12
CAN SOMEONE PLEASE HELP ME WITH THIS GEOMETRY?
Answer:
x = -18
Step-by-step explanation:
Please tell me If I am wrong..
5 x 2 = 10 = numerator.
-9 x 2 = ? = denominator
? = -18
-9 x 2 = -18…
Follow me please. The answer is -18
How much should you invest at 4.6% simple interest in order to earn $55 interest in 14 months?
The required money that should have been invested to earn $55 is $1024.84.
Given that,
How much should you invest at 4.6% simple interest in order to earn $55 interest in 14 months is to be determined.
When some apply for their money on something so that they can get higher value in returns of their money.
Here,
SI = [p × r ×t]/100
55 × 100 = p × 4.6 / 12 × 14
p = $1024.84
Thus, the required money that should have been invested to earn $55 is $1024.84.
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Divide 2x^-13x+x^2+6 by x-4
The Quadratic Equation [tex]3x^{2}-13x+6[/tex] divided by [tex]x-4[/tex] for all the values of the x(except x=4).
Let us consider [tex]3x^{2}-13x+6[/tex] as equation→(1) of a Quadratic Equation assume some values for x which is satisfies the equation and doesn't satisfy equation by "hit and trail method".
x=1 substitute in the equation (1) we get ⇒ [tex]\frac{4}{3}[/tex]
x=2 we get [tex]3(2)^{2}-13(2)+6[/tex] [tex]=4[/tex]
x=4 we get[tex]3(4)^{2}-13(4)+6[/tex] ⇒ [tex]\frac{2}{0}[/tex] which is not defined.
x=6 we get [tex]3(6)^{2}-13(6)+6[/tex] [tex]= 12[/tex]
x= -2 we get [tex]3(-2)^{2}-13(-2)+6[/tex] ⇒[tex]\frac{22}{-3}[/tex]
And so on for the remaining values of x the equation will satisfy. Except for the value x= 4 the equation doesn't satisfy because if we substitute x=4 in x-4 we get 4-4 =0 anything divided by zero is not defined.
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Divide [tex]3x^{2}-13x+6 by x-4[/tex]
A rectangular piece of paper is twice as long as a square piece and 3 inches wider. The area of the rectangular piece is 108 in^2. Find the dimensions of the square piece.
The dimension of the square piece of paper is 6 inches.
How to find the dimension of the square piece?A rectangular piece of paper is twice as long as a square piece and 3 inches wider.
The area of the rectangular piece is 108 in².
A square has all its side equal to each other and a rectangle has two opposite sides equal to each other.
Therefore,
let
x = length of the square
Therefore,
length of rectangular piece = 2x
width of the rectangular piece = 3 + x
Therefore,
area of the rectangular piece = lw
where
l = lengthw = widthTherefore,
area of the rectangular piece = 2x(3 + x)
area of the rectangular piece = 6x + 2x²
108 = 6x + 2x²
2x² + 6x - 108 = 0
divide through by 2
x² + 3x - 54 = 0
x² - 6x + 9x - 54 = 0
x(x - 6) + 9(x - 6) = 0
(x + 9)(x - 6)
Therefore, we can only use positive numbers.
Hence,
x = 6
Therefore,
dimension of the square piece is 6 inches.
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