Answer: Y = 21
Step-by-step explanation:
What is the biggest prime number ever found?
As of 2021, the largest prime number ever found is a number with 24,862,048 digits, known as M77232917. It was found in December 2018 using a program called GIMPS (Great Internet Mersenne Prime Search).
Prime numbers are numbers that are divisible by only 1 and themselves. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.
Mersenne prime is a specific type of prime numbers that can be represented in the form Mp = 2^p -1 where p is a prime number. Mersenne primes are named after the French mathematician Marin Mersenne who studied them in the early 17th century.
The discovery of large prime numbers is a significant event in the world of mathematics, and it is an ongoing effort by many mathematicians and computer scientists. The Great Internet Mersenne Prime Search (GIMPS) is one such effort, it is a distributed computing project which allows anyone to participate in the search for large Mersenne primes by downloading a free program that runs in the background on a computer, searching for primes while the computer is idle.
The discovery of the largest prime number to date was a huge achievement in the field of mathematics and it was found using the GIMPS project, which is the most successful distributed computing project in the history of mathematics. The discovery of large primes has many implications in number theory, cryptography and computer science.
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Is 8 a multiple of 2 Yes or no?
Yes, number 8 is a multiple of 2 is a true statement.
As given in the question,
Given number is equal to :
2
Given multiple is equal to :
8
Multiple is the number which represents when we multiply the given number by any integers.
In standard form multiples of number 'n' is given by :
n × 1 = n
n × 2 = 2n
n × 3 = 3n
n × 4 = 4n
n × 5 = 5n
......... so on.
Multiple of 2 are as follow :
2 × 1 = 2
2 × 2 = 4
2 × 3 = 6
2 × 4 = 8
2 × 5 = 10
......... so on.
When we multiply 2 by 4 we get 8.
8 is the multiple of 2.
Therefore, yes the given statement 8 is a multiple of 2 is a true statement.
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the sum of twice a number, -1, 5 times the number, and -12
2x-1+5x-12
question says sum, so i know we are adding. 2 times a number means 2x (or other variable). i simplified plus negative one to minus one. add five times the number (x). and subtract 12.
Express each question as a single power. Then state the Exponent law used.
A) 2^4 x 2^7
Exponent Law(s)
B) (-3)^9 divided (-3)^5
Exponent Law(s)
C) (5^2)^-3 x 5^0
Exponent Law(s)
Please answer this math problem asap. Thanks!
Answer:
A) 2^4 x 2^7 = 2^(4 + 7) = 2^11
Exponent Law(s): Product Law
B) (-3)^9 divided (-3)^5 = (-3)^(9 - 5) = (-3)^4
Exponent Law(s): Quotient Law
C) (5^2)^-3 x 5^0 = 5^(-6) × 1 = 5^(-6)
Exponent Law(s): Power of a power rule; zero exponent rule
please help ASAP!!
Which of the following polynomial functions is graphed below?
A. f(x)=(x+5)(x+1)^2(x-1)
B. f(x)=(x-5)(x-1)^2(x-1)
C. f(x)=(x+2)^2(x-3)(x+1)
D. f(x)=(x-2)^2(x+3)(x-1)
Considering the graph shown, the polynomial represented is
A. f(x) = (x + 5) (x + 1)² (x - 1)How to determine the equation graphedThe x-intercept(s) of the function's graph, or the actual zero of a function, is the location on a graph where the function's graph crosses the x-axis.
Tracing the graph, the zeros or the x intercepts on the graph it can be traced to be:
x = -5x = -1x = 1solving the zeros
x = -5, x + 5 = 0
x = -1, x + 1 = 0
x = 1, x - 1 = 0
equating together
(x + 5)(x + 1)(x - 1) - these values are only present in option A. The effect in x = -1 will result to (x + 1)²
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3, 3/4, 3/16 find the 6th term
The sixth term is [tex]\frac{3}{1024}[/tex] .
Given series : 3, [tex]\frac{3}{4}[/tex] , [tex]\frac{3}{16}[/tex] and so on.
We need to find the sixth term, so n = 6.
The given series is in Geometric Progression.
To find the [tex]n^{th}[/tex] term of a Geometric Progression,
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
a is the first term of any series. Here, a = 3
r is common ratio. Here, r = [tex]\frac{1}{4}[/tex]
According to the question,
[tex]a_{6}[/tex] = 3[tex](\frac{1}{4} )^{6-1}[/tex]
⇒ [tex]a_{6}[/tex] = 3 × [tex](\frac{1}{4} )^{5}[/tex]
⇒ [tex]a_{6}[/tex] = 3 × [tex]\frac{1}{1024}[/tex]
⇒ [tex]a_{6}[/tex] = [tex]\frac{3}{1024}[/tex]
So, the sixth term is [tex]\frac{3}{1024}[/tex].
3x*2 -10x +7/ x +4 which of the following shows the division problem in synthetic division form?
We can write the given expression (3x² - 10x + 7/ x + 4) in synthetic form as :
- 4 |3 -10 7
What is Synthetic Division?In algebra, the synthetic division is one of the methods used to manually perform the Euclidean division of polynomials. The division of polynomials can also be done using the long division method. But, in comparison to the long division method of polynomials, the synthetic division requires lesser writing and fewer calculations. That means the synthetic division is the shorter method of the traditional long-division of a polynomial for the special cases when dividing by a linear factor.Given is the expression as -
(3x² - 10x + 7/ x + 4)
We can write the given expression in synthetic form as -
- 4 |3 -10 7
Therefore, we can write the given expression (3x² - 10x + 7/ x + 4) in synthetic form as :
- 4 |3 -10 7
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How to find mirror image of point with respect to line in 3d?
To find the mirror image of a point with respect to a line in 3D, you can use the projection of the point on the line, multiply it with the normal vector of the line, and then subtract the obtained vector from the position vector of the point twice.
To find the mirror image of a point with respect to a line in 3D, you can use the following method:
Write the equation of the line in the form ax + by + cz + d = 0, where (a,b,c) is a normal vector to the line and d is a constant.Find the projection of the point on the line by taking the dot product of the position vector of the point and the normal vector of the line, and dividing by the square of the length of the normal vector.Multiply the projection obtained in step 2 with the normal vector of the line.Subtract the vector obtained in step 3 from the position vector of the point twice, this will give you the position vector of the mirror image point.Express the obtained coordinates as (x',y',z') which are the coordinates of the mirror image point.To learn more about 3D images at
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Point B(4,-16) is dilated by a scale factor of 3/4 to create B'
Wrute a rule for the transformation
Give the locatiom of B'
The rule for the transformation, which is a dilation, is given as follows:
(x,y) -> (3x/4, 3y/4).
Hence the coordinates of B' are given as follows:
B'(3, -12).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The general rule is:
(x,y) -> (kx, ky).
In which k is the scale factor.
The scale factor for this problem is given as follows:
k = 3/4.
Hence the rule is:
(x,y) -> (3x/4, 3y/4).
The coordinates of B' are obtained multiplying each of the coordinates of B by the scale factor k = 3/4.
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A baseball is thrown upward in the air. The height of the baseball f seconds after it is released is approximated by the function.
h=-16t^2+64t+80
a. find the number of seconds that it takes for the baseball to reach the ground?
b. Find the number of seconds that it will take the baseball to be at its maximum height?
c. Find the maximum height of the baseball?
Show work!
The solution to the quadratic equations are
a) The number of seconds for the ball to reach the ground is t = 5 seconds
b) The number of seconds to reach the maximum height T = 2 seconds
c) The maximum height of the ball is h ( 2 ) = 144 feet
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as h ( t )
Now , the equation will be
h ( t ) = -16t² + 64t + 80 be equation (1)
a)
The number of seconds for the baseball to reach the ground be t
The height when the ball reaches the ground will be h = 0
Substituting the value of h ( t ) = 0 , we get
0 = -16t² + 64t + 80
On simplifying the equation , we get
16t² - 64t - 80 = 0
Divide by 16 on both sides of the equation , we get
t² - 4t - 5 = 0
On factorizing the equation , we get
t² + t -5t - 5 = 0
t ( t + 1 ) - 5 ( t + 1 ) = 0
( t - 5 ) ( t + 1 ) = 0
The value of t is time and it is not negative
So , when ( t - 5 ) = 0
Adding 5 on both sides of the equation , we get
t = 5 seconds
b)
The number of seconds the baseball to reach the maximum height be T
And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola
T = ( -b / 2a )
On simplifying the equation , we get
T = ( -64 / ( 2 ( 16 )
T = -64 / 32
T = 2 seconds
c)
The maximum height of the baseball is when T = 2
Substituting the value of t = 2 in the equation , we get
h ( t ) = -16t² + 64t + 80
h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80
On simplifying the equation , we get
h ( 2 ) = -64 + 128 + 80
h ( 2 ) = 64 + 80
h ( 2 ) = 144 feet
Hence , the equation is solved
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Admission to the state fair is $8 for adults and $7 for students. Write two equivalent expressions if two adults and two students go to the fair. Then find the total admission cost.
In linear equation, 44 is the total admission cost.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Linear equations with two variables, and so forth, are what the equation is known as if it has two variables.
Admission to the state fair = $8 .
adults and $7 = students
8 * 3 = 24
5 * 4 = 20
24 + 20 = 44
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If 1st number is a series of consecutive odd numbers is 6 less than the last one in the series, how many numbers are there is the series.
Let's call the first number in the series "x", and the last number in the series "y".
We know that the series is a consecutive series of odd numbers, and we also know that y is 6 less than the last number in the series.
Since the series is a consecutive series of odd numbers, we can say that the difference between any two consecutive numbers in the series is 2.
So, we can write an equation to represent this information:
y = x + (n-1) * 2
where n is the number of numbers in the series.
We also know that y is 6 less than the last number in the series, so we can add this information to our equation:
y = x + (n-1) * 2 - 6
To solve for n, we can rearrange the equation:
n = (y - x + 6) / 2 + 1
Now, if we know the value of x and y we can substitute them in the equation and find the number of terms in the series.
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Rewrite this series using Sigma notation:3+13+23*33+43
[tex]\begin{array}{llll} 3+10(1)\\ 3+10(2)\\ 3+10(3)\\ 3+10(4)\\ \end{array}\hspace{5em}\displaystyle\sum_{n=1}^{4}3+10n[/tex]
ITS COMPOUND INTERSET, ITS URGENT
a) The amount of money that Tony invested is; £1350
b) The rate of compound interest is; 4%
c) The graph that represents the growth in Toni's account is; Graph C
How to find the compound interest?The formula for the total value of her investment after t years is given by the formula; v = 1350 * 1.04^t
The general formula used to calculate the interest rate is given by,
a = p * (1 + r)^t
where;
a is amount
p is principal
r is rate of interest
t is time period
Comparing the given equation with standard equation, we have;
a = v
p = 1350
t = t
Now, 1 + r = 1.04
1 + r = 1 + 0.04
Thus;
r = 0.04 = 4%
Therefore, the money invested by tony P = £1350
The rate of compound interest is 4%
The graph that represents Toni's account is an exponential equation and since the initial amount is not zero, then the correct graph is graph C
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-1/3(12d+18) answer?
Answer:
-4d - 6
Step-by-step explanation:
-1/3(12d+18)
-4d - 6
That is the simplest we can simple the function
So, the answer is -4d - 6
Bianca deposits $3,000
in a savings account earning 4.25%
simple interest per year.
How much interest will Bianca earn for a period of 3
years?
Bianca will earn interest of $382.5 for a period of 3years.
What is simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same.
Simple interest is calculated with the following formula:
S.I. = P × R × T,
where P = Principal, R = Rate of Interest in % per annum, and T = Time
Given,
Principal P = $3000
Rate of interest R = 4.25% = 4.25/100 = 0.0425
Time T = 3 years
Simple interest S.I. = P × R × T
= 3000 × 0.0425 × 3
= 127.5 × 3
S.I. = $382.5
Hence, Interest Bianca will earn in 3 years = $382.5
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HELPPP THE QUARTER ENDS TOMORROW AND I MEED TO TURN IN THIS ASSIGNMENT PLEASE HELP ME TAKE MY POINTS JUST PLEASE HELP ME
The functions that are represented by WHO are 9/-5 and SEEM are -28, respectively.
what is function ?The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
as the function which is represented as WHO
= 9/ 7- 12
= 9 / -5
as the function which is represented as SEEM
= -4(-1 + 8)
= -4 ( 7)
= - 28
The functions that are represented by WHO are 9/-5 and SEEM are -28, respectively.
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The correct question is :- Transfer the word from the top box to the corresponding bottom box by function .
Is the midpoint method a stable?
Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.
what is order of rotation ?The maximum number of rotations that a geometry may accommodate is the order of rotational symmetry. The degree of rotational symmetry is denoted as 360°A°, where A° is the lowest angle that may be used to rotate a figure from its rotated shape back to its original shape. (170 degrees) How many times a perfect circle may be rotated while still preserving its appearance is a measure of a shape's rotational symmetry. The appearance of a full 360° revolution will be the same only when a triangle is placed back in its initial starting position.
given
Along with the second order backward differentiation formula (BDF2) for dissipative PDEs, the method (1.3), an implicit second-order.
A-stable time-stepping approach, is the recommended method for solving evolutive conservative systems of PDEs.
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What is the coefficient of the term in the expression 5xyz2 3zy?
So on solving the provided question we can say that coefficient of expression 5xyz2 is 5 and 3zy is 3
what is expression ?It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.
Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression Numbers, variables, and functions make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.
here,
coefficient of 5xyz2 is 5
and 3zy is 3
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Craig is considering four loans. Loan L has a nominal rate of 8.254%, compounded daily. Loan M has
nominal rate
of 8.474%, compounded weekly. Loan N has a nominal rate of 8.533%, compounded monthly. Loan O has a nominal
rate of 8.604%, compounded yearly. Which of these loans will offer Craig the best effective interest rate?
a. loan
b. loan M
C.
loan N
d
loan O
The loan that offers the best effective annual rate is loan N (option c)
What loan that offers the best effective annual rate?The effective annual rate is the actual interest rate that is earned on an investment after accounting for the number of compounding.
Effective annual rate = (1 + APR / m ) ^m - 1
Where M = number of compounding
Effective annual rate for loan L = (1 + 0.08254/365)^365 - 1=0.08603 = 8.603%
Effective annual rate for loan M = (1 + 0.08474/52)^52 - 1= 0.08836 = 8.836%
Effective annual rate for loan N = (1 + 0.08533/12)^12 - 1= 0.08875 = 8.875%
Effective annual rate for loan O=8.604%
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Initially, 80 bacteria are placed in a Petri dish. It is observed that the bacteria triple in population every 5 hours.
How can this information be interpreted?
Select True or False for each statement.
The scenario can be modeled by the function f(x)=80(3)x5, where f(x) represents the population of bacteria x hours after the bacteria are placed in the Petri dish.
After 13 hours, there are approximately 1592 bacteria.
The first statement is true and the second statement is false.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given that initial population of bacteria = 80
Bacteria triple in population every 5 hours.
Number of bacteria after the time 'x' hours is modeled as,
f(x) = [tex](80)(3)^\frac{x}{5}[/tex] which is given in the first statement.
So the first statement is true.
After 13 hours,
f(13) = [tex](80)(3)^\frac{13}{5}[/tex]
= 1391.89 ≈ 1392
But the second statement says the population is 1592 bacteria, which is false.
Hence the statement given first is true and the second one is false.
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[tex]18\frac{3}{4} - 5\frac{7}{8}[/tex]
What is 8÷1/2 i really need !help!
Answer:
4
Step-by-step explanation:
Answer: 4
Step-by-step explanation: Same thing as 8 / 0.5
30% of the money raised at every school bake sale goes to the 6th grade.$120 of the $250 raised goes to the 7th graders. What percent is this?
$ 286 is the percent.
What in mathematics is a percentage?
When the denominator is 100, percentages are really just fractions. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
30% * 120 = X
30/100 * 120 = X
36 = X
the $250 raised goes to the 7th graders.
250 + 36
= $ 286
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Dr. Goldsman is buying fertilizer for his lawn. - Xtra Green covers 1/20 of an acre with 1/2 of a pound of fertilizer granules. - Best Lawn covers 1/15 of an acre with 1/5 of a pound of fertilizer granules. If Dr. Goldsman wants to buy the brand that covers the most area per pound, which brand should he buy?
The Best Lawn covers the most area per pound is better choice to buy.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Xtra Green covers 1/20 of an acre with 1/2 of a pound of fertilizer granules.
So, area per pound covered by Xtra Green
= (1/20) /(1/2)
= 1/20 x 2/1
= 1/10
= 0.1
Best Lawn covers 1/15 of an acre with 1/5 of a pound of fertilizer granules.
So, area per pound covered by Best Lawn
= (1/15) /(1/5)
= 1/15 x 5/1
= 1/3
= 0.333
Hence, Best cover larger Area is better choice.
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how many total wholes are in 7/3.
Answer:
The fraction 7/3 cannot be expressed as a whole number. The fraction 7/3 can be expressed as a decimal, which is 2.3333.... and goes on forever, or as a mixed number, which would be 2 and 1/3.
It's important to note that when dividing two integers, the result is not guaranteed to be a whole number.
Step-by-step explanation:
O
-11-10-9-8
Select the values that make the inequality -s < 6 true.
Then write an equivalent inequality, in terms of s.
(Numbers written in order from least to greatest going across.)
0 -11
0-6
0 -1
05
6.1
0 -7
0 -5.9
D0
0.5-9
07
Equivalent Inequality: s
0-6.1
0-5
01
06
9 10 11
0 11
Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
9(x - y) = 30,
or (x-y) =30/9
To find :
a) 18(x - y) = ?
=> 2(9(x - y))
=> 2(30)
=> 60
b)6x - 6y = ?
=> 6(x-y) = 6(30/9)
=> 2*30/3
=> 20
c) 9(x-y)-9
=> 30 -9
=>21
Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.
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On solving the provided question, we can say that the inequality provided is -s < 6 he values that stratifies will be = 0-6
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
the inequality provided is
-s < 6
the values that stratifies will be = 0-6
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(question is in the image)
The pair of triangles are congruent. using the angle side angle (ASA) congruency theorem
What are congruent triangles?Two triangles are said to be congruent if all the three sides are equal to each other and all the three angles are equal to each other.
The angle side angle (ASA) congruency theorem states that two triangles are congruent if two angles and an included side of one triangle is equal to two angles and an included side of another triangle.
From the diagram, for both triangles, two angles and an included side is equal to that of the other triangle.
The pair of triangles are congruent.
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What is the minimum of the sinusoidal function?
Enter your answer in the box.
The minimum of the periodic sine function is - 4 and it's amplitude is |4|.
What are periodic functions?If there is a positive real number P such that f(x + P) = f(x), for all x being real numbers, then the function y= f(x) is said to be periodic. The fundamental period of a function is the least value of the positive real number P. The period during which a function repeats itself is also known as the fundamental period of the function.
f(x + P) = f(x).
From the graph, we conclude it is a sine function.
The amplitude of the graph is 4 units.
So, The graph reaches it's maximum and minimum at ± 4.
Therefore, The minimum of the function is - 4.
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Question content area top Part 1 a. Solve x+11=x+11 b. If you simplify an equation and get 0=0, what can you conclude about the solution(s) of the original equation? c. Write an equation for which every real number is a solution. Question content area bottom Part 1 a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x=enter your response here (Simplify your answer.) Your answer is not correct.B. The solution is the set of all real numbers. This is the correct answer.C. There is no solution. Part 2 b. If you simplify an equation and get 0=0, what can you conclude about the solution(s) of the original equation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is enter your response here. (Simplify your answer.) B. The solution is the set of all real numbers. Your answer is correct.C. There is no solution. Part 3 c. Write an equation for which every real number is a solution. Choose the correct answer below. A.3 left parenthesis x minus 2 right parenthesis equals 2 left parenthesis x minus 3 right parenthesis 3(x−2)=2(x−3) B.2 left parenthesis x minus 3 right parenthesis equals 2 left parenthesis x minus 3 right parenthesis 2(x−3)=2(x−3) C. x+2=x+3 VideoTextbook Get more help
Answer:
1a) x+11=x+11 becomes 0=0. What this means is that at all x values the y values are the same, in other words, they are the same line.
Please split up your questions as it is difficult to answer.