Therefore , the solution of the given problem of function comes out to be the limit may not exist, if the function is not continuous at x = 0.
What does the term function mean?The mathematical discipline encompasses arithmetic, symbols, and their divisions, as well as histology, construction, and both real and imagined geographic places. A function describes the connections between various elements, which all have an associated outcome. A function is composed of an array of different parts that, when combined, result in particular outcomes for each input.
Here,
We must be aware of the precise function or expression under consideration in order to respond to this query.
The action as x moves towards zero from the negative direction can change depending on the function.
If a function is continuous at x = 0, then in general, if the function has a limit as x gets smaller from the downward direction, however this limit will be the same as the limit as x reaches zero from the positive direction.
The limit as x approaches zero from the downward direction may vary from the limit as x approaches zero from the better way, or the limit may not exist, if the function is not continuous at x = 0.
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which side of figure wxyz corresponds with QR
The side of figure WXYZ corresponds with QR is XY
Mirror images:In mathematics, mirror images are often used in the study of symmetry and geometry. A mirror image, also known as a reflection, is a transformation that flips an object over a line called the mirror line.
An image appears to be reversed from left to right. Therefore, the left side of the object appears to be on the right side of the image, and the right side of the object appears to be on the left side
Here we have
Parallelogram PQRS and WXYZ which are two mirror images
Here the corresponding side of the two figures are
=> PQ and WX
=> QR and XY
=> RS and YZ
=> PS and WZ
Therefore,
The side of figure WXYZ corresponds with QR is XY
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Three variants of the gene encoding for the beta-goblin component of hemoglobin occur in the human population of the Kassena-Nankana district of Ghana, West Africa. The most frequent allele, A, occurs at a frequency of 0.83. The other two variants, S (sickle cell) and C, occur at frequency 0.04 and 0.13. Each individual has two alleles, determining the genotype of the beta-globin gene. Assume that the allele occur independently on one another.
a. What is the probability that a randomly sampled individual has two copies of the C allele?
b. What is the probability that a randomly sampled individual is a homozygote (two copies of the same allele)?
c. What is the probability that a randomly sampled individual is AS (one copy of A allele and one copy of S allele)?
d. What is the probability that a randomly sampled individual is AS or AC?
a. The probability that a randomly sampled individual has two copies of the C allele is 0.0169.
b. The probability that a randomly sampled individuTherefore, the answers are:
al is a homozygote is 0.7074.
c. The probability that a randomly sampled individual is AS is 0.0332.
d. The probability that a randomly sampled individual is AS or AC is 0.1411.
The probability of an individual having two copies of the C allele can be calculated using the formula for the probability of independent events: P(CC) = P(C) x P(C) = 0.13 x 0.13 = 0.0169.
The probability of an individual being a homozygote can be calculated by adding the probabilities of having two copies of each allele: P(AA) + P(SS) + P(CC) = (0.83 x 0.83) + (0.04 x 0.04) + (0.13 x 0.13) = 0.6889 + 0.0016 + 0.0169 = 0.7074.
The probability of an individual being AS can be calculated using the formula for the probability of independent events: P(AS) = P(A) x P(S) = 0.83 x 0.04 = 0.0332.
The probability of an individual being AS or AC can be calculated by adding the probabilities of each event: P(AS) + P(AC) = 0.0332 + (0.83 x 0.13) = 0.0332 + 0.1079 = 0.1411.
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What is the absolute deviant of 18, 13, 20, 14, 12, 6, 11, 5, 15, 10
1. APQR and ASTU are similar triangles. Prove that the slope of line segment PR and the slope of
line segment SU are equal.
Slope of PR = Slope of SU = rise / run = -3/2
How to Find the Slope of a Line?The slope of a line is the ratio of the rise over the run, which is m = change in y / change in x.
To prove that the slope of line segment PR and the slope of line segment SU are equal, find the slope of each of the line given that are similar triangles:
Slope of PR = rise / run = PQ/QR = -3/2
Slope of SU = rise / run = ST/TU = -6/4 = - 3/2
Therefore, both line segments have the same slope of -3/2.
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Please help will give brainilest
Step-by-step explanation:
The first step is to add 6 to both sides
3x =15+6
3x=21
Divide both sides by 3
X = 7
Divide 15x4 − 5x3 − 10x2 by −5x2.
−3x2 + x − 2
−3x2 + x + 2
−3x2 − 10x + 2
10x2 − 10x − 15
Answer: −3x^2+x+2
Step-by-step explanation:
Solution of the expression is,
⇒ - 3x² + x + 2
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
WE have to given that;
To divide 15x⁴ − 5x³ − 10x² by −5x².
Now, We can solve as;
⇒ (15x⁴ − 5x³ − 10x²) / −5x²
⇒ 5x² (3x² - x - 2) / - 5x²
⇒ - (3x² - x - 2)
⇒ - 3x² + x + 2
Thus, After divide we get;
⇒ - 3x² + x + 2
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so that \( i A_{1} \) is emalier than \( \left.A_{2} A_{2}\right) \) 7. [-81.19 Points] 5PRECALC7 6.5.023. so that \( A_{1} \) is smaller than \( A A_{2} \)-) \[ \begin{array}{l} b=27, c=33, \quad A=2
The answer to the question is that \( A_{1} \) is smaller than \( A_{2} \)
To begin, it is important to note that the terms "emalier" and "5PRECALC7" are not relevant to the question and can be ignored. Additionally, there are several typos and extraneous information that can also be ignored. The main focus of the question is to determine the relationship between \( A_{1} \) and \( A_{2} \).
From the information provided, it is clear that \( A_{1} \) is smaller than \( A_{2} \). This is because the value of \( A_{1} \) is given as 2, while the values of \( b \) and \( c \) are 27 and 33, respectively. Since \( A_{2} \) is the sum of \( b \) and \( c \), it is clear that \( A_{2} \) is larger than \( A_{1} \).
Therefore, the answer to the question is that \( A_{1} \) is smaller than \( A_{2} \).
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A village in alaska is sometimes visited by polar bears. In fact, bear visits form a poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equa
The probability for the bear visits using Poisson process of rate one visits per month is given by ,
P(X=i, Y=j) j=i j=2i j=3i
X=i e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i! 2/3^i× e^(-1)/i!
Bear visits form a Poisson process of rate 1 visit per month.
Number of visits in a month = Poisson distribution with parameter λ = 1.
Let X be the number of visits in a month.
And Y be the total number of bears in the month.
Probability of X and Y is equal to ,
P(X = i, Y = j), for i = 0, 1, 2, 3 and j = i, 2i, or 3i.
Law of total probability for P(X = i, Y = j) for each i and j.
P(X = i, Y = i)
= P(X = i) × P(Y = i | X = i)
= e^(-λ) × λ^i / i! × 1/3^i
= e^(-1) × 1^i / i! × 1/3^i
= e^(-1) (1/ i!) × 1/3^i
Now,
P(X = i, Y = 2i)
= P(X = i) × P(Y = 2i | X = i)
= e^(-λ) × ( λ^i / i!) × [(1/3)^i + 2(1/3)^(i-1)(2/3)]
= e^(-1) / i! × [1/3^i + 4/3^i-1]
For,
P(X = i, Y = 3i)
= P(X = i) × P(Y = 3i | X = i)
= e^(-λ) × λ^i / i! × (1/3)^i × 2
= 2e^(-1) / i! × 1/3^i
Therefore, the probability of the size of bears for given condition is equal to,
P(X=i, Y=j) j=i j=2i j=3i
X=i e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i! 2/3^i× e^(-1)/i!
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The given question is incomplete, I answer the question in general according to my knowledge:
A village in Alaska is sometimes visited by polar bears. In fact, bear visits form a Poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equal opportunity. Find the probability for each size.
solve it please
see the pic down and do it in a good way
Answer:
3/10
Step-by-step explanation:
0.3=30/100
30/100 simplyfied is 3/10
Therefore the answer is 3/10
hope this helped
show factorizing that 899 is not a prime number????
Answer:
The factors of 899 are 1, 29, 31, 899. Therefore, 899 has 4 factors.
Step-by-step explanation:
Therefore, 899 has 4 factors. And is not prime
Direction in your noteook solve following mindline theorem show your solution
The midline or midsegment theorem calculate the value of P. the value of the variable, P that base length in the trapezoid is equals to the 13.
A trapezoid is a 4-sided (square) shape in which some sides are parallels and others not. The midsection of a trapeze is the line that runs from the middle of one leg to the middle of the other. The midsection or Midsegment theorem of a trapezium states that if a line parallel to the two bases passes through the middle of one leg, it also passes through the middle of the other leg. Also, the length of the middle fragment is half the length of two bases. Now we see a trapezoid in the image above, the length of the midsegment = 25
One of the bases of the trapezium = 37
We need to calculate the value of the other base length P Using Midsigment or Midline Theorem, Midsigment = length of two bases/2
=> 25 = (37 + P)/2
=> 50 = 37 + P
=> P = 50 - 37
=> P = 13
Hence, required length is 13.
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Complete question:
Use the midline theorem to find the value of the variable in the trapezoid. See the above figure.
Malcolm is finding the solutions of this quadratic equation by factoring
3r²-24x=-45
Which of these is a correctly factored equation that can be used to find the solutions?
O 3(2-15)(x+1)=0
O 3(x-3)(x-5)=0
○ (3x - 5)(+9) = 0
O (3-3)(r-15) = 0
In a case whereby Malcolm is finding the solutions of this quadratic equation by factoring 3x²-24x=-45, the correctly factored equation that can be used to find the solutions is 3(x-3)(x-5)=0
How can the solution be found?The given equation is 3x²-24x=-45
The equation can be re written as;
3x²-24x=-45
3x²-24x+45 = 0
Then we can divide by 3 and have
x²-8x + 12= 0
thene if we factorize we have
x= 5, x= 3
Therefore, option B is correct. which is 3(x-3)(x-5)=0
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Translate the logarithmio statoment into an equivalent exponential statement. log_(4)(1)/(16)=-2
The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into the equivalent exponential statement [tex]4^(-2)=(1)/(16)[/tex].
The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into an equivalent exponential statement by using the definition of logarithms. The definition of logarithms states that if [tex]log_(b)(a)=c[/tex], then [tex]b^c=a.[/tex]
Using this definition, we can translate the logarithmic statement[tex]log_(4)(1)/(16)=-2[/tex] into an equivalent exponential statement by rearranging the terms.
The equivalent exponential statement would be[tex]4^(-2)=(1)/(16)[/tex]. This means that 4 raised to the power of -2 is equal to 1/16.
So, the logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex]can be translated into the equivalent exponential statement[tex]4^(-2)=(1)/(16)[/tex].
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what two situations involving rational exponents or radicals will never result in a negative real soltution
Answer:
There are two situations involving rational exponents or radicals that will never result in a negative real solution:
Even-indexed roots: If we take the square root, fourth root, sixth root, etc. of a non-negative real number, the result will always be non-negative. For example, the square root of 9 is 3, and the fourth root of 16 is 2, both of which are non-negative. This is because even-indexed roots always produce a non-negative result, regardless of the sign of the original number.
Exponents with even denominators: If we raise a non-negative real number to an exponent with an even denominator, the result will always be non-negative. For example, (4^2/4) is equal to 4, which is non-negative. This is because any negative base raised to an even power results in a positive number, and any positive base raised to an even power also results in a positive number. Therefore, any exponent with an even denominator will always produce a non-negative result, regardless of the sign of the original number.
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1) Identify the slope of the line y - 3 = 4(x + 1). Then use the equation to identify a point the line passes
through
Answer:
slope = 4 , point on line (- 1, 3 )
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y - 3 = 4(x + 1) ← is in point- slope form
with slope m = 4 and (a, b ) = (- 1, 3 )
The following table gives the frequency distribution of waiting
times (in minutes) for these customers.
The mean waiting time is:
The mean waiting time for these customers is 18.33 minutes.
The mean waiting time can be calculated by multiplying each waiting time by its frequency, summing up these products, and then dividing by the total number of customers.
In mathematical terms, the mean waiting time is:
Mean = (x1 * f1 + x2 * f2 + ... + xn * fn) / (f1 + f2 + ... + fn)
Where x1, x2, ..., xn are the waiting times, and f1, f2, ..., fn are the corresponding frequencies.
Using the data from the table, we can plug in the values and calculate the mean waiting time:
Mean = (5 * 2 + 10 * 4 + 15 * 6 + 20 * 8 + 25 * 10) / (2 + 4 + 6 + 8 + 10)
Mean = (10 + 40 + 90 + 160 + 250) / 30
Mean = 550 / 30
Mean = 18.33 minutes
Therefore, the mean waiting time for these customers is 18.33 minutes.
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Factor. 144p2−9q2 a. 9(p−q)2 b. (12p+3q)(12p−3q) C. (12p+3q)2 d. (12p−3q)2
The complete factorization of the expression 144p² - 9q² is (12p + 3q)(12p − 3q). The correct answer is B.
To factor 144p² - 9q², we can use the difference of squares formula, which states that:
a² - b² = (a + b)(a - b)
We can see that 144p² is a perfect square, as it is the square of 12p. Similarly, 9q² is a perfect square, as it is the square of 3q. So we can write:
144p² - 9q² = (12p)² - (3q)²
Now we can use the difference of squares formula to factor:
(12p)² - (3q)² = (12p + 3q)(12p - 3q)
Simplifying, we can also write this as:
144p² - 9q² = 3²(16p² - q²)
So, the factored form of 144p² - 9q² is:
144p² - 9q² = 3²(16p² - q²) = (12p + 3q)(12p - 3q)
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vocabalary Is the
expression 3x + 2x - 4 in
simplest form? Explain.
The terms 3x and 2x are
terms and
<>
in simplest form.
長
be combined. Therefore, the expression
The expression in simplest form is.
Answer:
Step-by-step explanation:
This expression isn't in simplest form. The terms 3x and 2x can be added, since they are like terms.
In simplest form, this expression would be 5x - 4.
Hope this helps!
Let R be a ring such that x = x2 for all x ∈ R. Prove that R is a ring commutative.
Yes, the given ring is commutative.We have that, a commutative ring in abstract algebra is a ring that satisfies a +b = b+a (for a defined operator).
Given: R is a ring such that [tex]$x = x^2$[/tex] for all [tex]$x\in R$[/tex].
To prove: R is a ring commutative.
Proof:
Let [tex]$a$[/tex] and [tex]$b$[/tex] be arbitrary elements in [tex]$R$[/tex].
[tex]$a+b = (a+b)^2 = a^2 + 2ab + b^2$[/tex]
[tex]$b+a = (b+a)^2 = b^2 + 2ab + a^2$[/tex]
Therefore, [tex]$a+b = b+a$[/tex]. Thus, R is a ring commutative.
Q.E.D.
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Math question 13 help
Answer:
This is an odd function
Step-by-step explanation:
Given a function f(x),
if f(-x) = f(x) then the f(x) is even
If f(-x) = -f(x0 then the function is odd
If neither of the above is true then the function is neither odd nor even
We are given
[tex]f(x) = 4x^3 - x^5 + 5x\\f(-x) = 4(-x)^3 -(x)^5 + 5(-x)\\\\(-x)^3 = - x^3\\(-x)^5 = -x^5\\\\\\\therefore\\f(-x) = 4(-x^3) - (-x^5) + 5 (-x)\\\\= -4x^3 + x^5 - 5x\\\\= -(4x^3 -x^5 + 5x)\\\\= -f(x)[/tex]
So the function is odd
When Veronica visit great Britain one British pound was worth US$1.40 while AU$1.00 was worth US$0.70 in this case how many AU$ was a British pound worth 
In the given question, 1 British pound will be equal to AU$2.00.
What is Algebra?Algebra is a common thread that runs through almost all of mathematics. It is the study of variables and the principles for manipulating them in formulas. Since all mathematical uses involve manipulating variables as though they were numbers, elementary algebra is a prerequisite.
The area of mathematics known as algebra aids in the representation of situations or issues as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z along with mathematical processes like addition, subtraction, multiplication, and division.
What is Transitive Property?A homogeneous relation R over the set A, which includes the elements x, y, and z, is what mathematicians refer to as a transitive relation. If R relates x to y and y to z, then R also relates x to z.
In this question,
1£ = US$1.40 (Equation 1)
AU$1 = US$0.70 (Equation 2)
Multiplying equation 2 by 2, we get
AU$2 = US$1.40
Using equation 1, we can say that,
1£ = AU$2
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Choose all of thr terms thag correctly complete the statement.
The set of all first components of the ordered pairs of a
function are called the ____
-Elements
-Relation
-Independent Variable
- Range
The set of all first components of the ordered pairs of a function are called the Independent Variable.
In a function, the first component of the ordered pairs is known as the independent variable, which is the input value of the function. The second component of the ordered pairs is known as the dependent variable, which is the output value of the function. The set of all first components is also called the domain of the function, while the set of all second components is called the range of the function.
Therefore, the correct term to complete the statement is the Independent Variable.
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Mrs Shepard rode her bike 5. 25 miles in 0. 7 hours how fast was she going in miles per hour
Mrs Sheperd was going 7.5 miles per hour
Let us assume that d represents the distance covered by Mrs Shepard, 't' represents the time required and 's' represents the speed of her bike.
Here, d = 5.25 miles
t = 0.7 hours
We know that the formula of speed is speed = distance/time
Using this formula we calculate the speed (s) of Mrs Shepard's bike.
speed = distance/time
⇒ s = d/t
⇒ s = 5.25/0.7
⇒s = 7.5 miles per hour
This means that the speed (s) of Mrs Shepard's bike was 7.5 miles per hour
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The function f(x) contains the point (4, −10). Show all calculations steps and state the image
(the new location) of point under each of the following general transformations:
a. = ( + 2) − 3
b. − 1 = 2( − 4)
c. − 1/3 = (−2)
d. 2 = ((+2)/3)
(the new location) of point under each of the following general transformations are as follows:
a. Image: (3, -10)
b. Image: (-1, -10)
c. Image: (-4/3, -10)
d. Image: (14/3, -10)
What is general transformations?
A transformation is a procedure that involves either changing an object's orientation to create an image or expanding or reducing its size to create a new one.
We'll use the given point (4, -10) as the input for each transformation, and apply the transformation to find the new location of the point.
a. f(x) = (x + 2) - 3
f(4) = (4 + 2) - 3 = 3
Therefore, the new location of the point under the transformation f(x) = (x + 2) - 3 is (3, -10).
b. f(x) = 2(x - 4) - 1
f(4) = 2(4 - 4) - 1 = -1
Therefore, the new location of the point under the transformation f(x) = 2(x - 4) - 1 is (-1, -10).
c. f(x) = -1/3x
f(4) = -1/3(4) = -4/3
Therefore, the new location of the point under the transformation f(x) = -1/3x is (-4/3, -10).
d. f(x) = (2/3)x + 2
f(4) = (2/3)(4) + 2 = 8/3 + 2 = 14/3
Therefore, the new location of the point under the transformation f(x) = (2/3)x + 2 is (14/3, -10).
In each case, the image of the point is the new location after applying the transformation.
a. Image: (3, -10)
b. Image: (-1, -10)
c. Image: (-4/3, -10)
d. Image: (14/3, -10)
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3. 1 130 points) Solve the following system of linear equations by the Matrix Inversion method using A' = ad/ ) det(A) 2x + 6y + 2z = 8 6x + 6y + 32-3 2x + 3y+z=3
So, the solution to the system of equations is:
x = -26/7
y = -25/7
z = -37/7
Solving a system of linear equations by the Matrix Inversion method involves finding the inverse of the coefficient matrix, multiplying it by the constant matrix, and solving for the variables.
First, we need to write the system of equations in matrix form:
[ 2 6 2 ] [ x ] [ 8 ]
[ 6 6 3 ] [ y ] = [ -3 ]
[ 2 3 1 ] [ z ] [ 3 ]
Next, we need to find the inverse of the coefficient matrix:
A = [ 2 6 2 ]
[ 6 6 3 ]
[ 2 3 1 ]
The determinant of A is:
det(A) = 2(6-9) - 6(2-6) + 2(18-6) = -6 + 24 + 24 = 42
The adjoint of A is:
adj(A) = [ (6-3) (-2+6) (-18+6) ]
[ (-6+3) (2-4) (12-6) ]
[ (6-18) (-2+12) (2-18) ]
= [ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]
The inverse of A is:
A' = (1/det(A))adj(A) = (1/42)[ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]
= [ 1/14 2/21 -4/7 ]
[ -1/14 -1/21 2/7 ]
[ -4/7 5/21 -8/21 ]
Now, we can multiply the inverse of A by the constant matrix to find the solution:
[ x ] [ 1/14 2/21 -4/7 ] [ 8 ]
[ y ] = [ -1/14 -1/21 2/7 ] [ -3 ]
[ z ] [ -4/7 5/21 -8/21 ] [ 3 ]
= [ (8/14) + (16/21) + (-32/7) ]
[ (-8/14) + (-3/21) + (-6/7) ]
[ (-32/7) + (15/21) + (-24/21) ]
= [ -26/7 ]
[ -25/7 ]
[ -37/7 ]
So, the solution to the system of equations is:
x = -26/7
y = -25/7
z = -37/7
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I need help determining the exponential function in the form of y=a(m) x
HELP PLS ☹️
Answer:
An exponential function in the form of y = a(m) x is of the form:
y = a * m^x
where "a" is a constant, "m" is a positive constant (the base of the exponential), and "x" is the independent variable.
To determine the exponential function in this form, you need to have some information about the function, such as its value at a particular point or its rate of growth.
Here are the general steps to determine the exponential function in the form of y = a(m) x:
Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.
Determine the value of "m" by solving for it using the given information.
For example, let's say you are given that the function passes through the point (2, 8) and has a growth rate of 3. To determine the exponential function in the form of y = a(m) x, you would follow these steps:
Plug in the values of x and y into the equation:
8 = a * m^2
Solve for "a" by isolating it on one side of the equation:
a = 8 / m^2
Use the given growth rate of 3 to find the value of "m":
m = 1 + r = 1 + 0.03 = 1.03
Plug in the value of "m" and the value of "a" you found in step 2 into the equation:
y = (8 / 1.03^2) * 1.03^x
Simplifying this equation gives:
y = 7.514 * 1.03^x
So the exponential function in the form of y = a(m) x that passes through the point (2, 8) and has a growth rate of 3 is y = 7.514 * 1.03^x.
Step-by-step explanation:
here is a more detailed explanation of the steps involved in determining an exponential function in the form of y = a(m) x:
Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.
In the equation y = a(m) x, "a" is a constant that represents the value of y when x is equal to 0. So to find the value of "a", we need to know the value of y for a specific value of x, other than 0.
Evaluate the following expression.
2
7/8 ÷ 1/8 + 2
Answer:
9
Step-by-step explanation:
7/8 divided by 1/8 is 7
7+2 = 9
Brainliest?
Write a polynomial f (x) that meets the given conditions. Polynomial of lowest degree with zeros of -2 (multiplicity 2) and 3 (multiplicity 2) and with f(0)=−108 Select one: a. f (x) = -3x4 + 6x3 + 33x2 - 18x - 108 b. f (x) = -3x4 + 6x3 + 33x2 - 36x - 108 c. f (x) = -3x4 + 6x3 - 111x2 - 36x - 108 d. f (x) = x4 - 2x3 - 11x2 + 12x - 108
f (x) = -3x4 + 6x3 + 33x2 - 18x - 108.
The correct answer is a. f (x) = -3x4 + 6x3 + 33x2 - 18x - 108, since this is a polynomial of the lowest degree (4) that has zeros of -2 (multiplicity 2) and 3 (multiplicity 2), as well as f(0)=-108. To solve this problem, use the Factor Theorem to determine the factors of the polynomial. Since the zeros are -2 and 3, the polynomial must factor into (x+2)2 and (x-3)2. This gives us the polynomial: f (x) = -3(x+2)2(x-3)2 - 108. Finally, expand the polynomial to get the answer: f (x) = -3x4 + 6x3 + 33x2 - 18x - 108.
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f(x) = x^2 - 4x - 1
Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.) I need the smaller
x
-value intercept and the larger
x
value intercept for this quadratic function. I have already determined that 2- sqrt of 5 and
2+
sqrt of
5,−0.267949
and
3.73205,−0.24,0
and
4.24,0
are not the correct answers so if that's what you get, please do not respond with those answers.
The vertex of the function is (2 , -5), the axis of symmetry is x = 2, and the intercepts are (2 + √(5) , 0), (2 - √(5) , 0), and (0 , -1).
To find the vertex, axis of symmetry, and intercepts of the function f(x) = x² - 4x - 1, we can use the following formulas:
Vertex: (-b/2a, f(-b/2a))
Axis of symmetry: x = -b/2a
Intercepts:
x-intercept: set f(x) = 0 and solve for x
y-intercept: set x = 0 and solve for y
Using these formulas, we can find the vertex, axis of symmetry, and intercepts of the function:
f(x) = x² - 4x - 1
a = 1, b = -4, c = -1
Vertex: (-b/2a , f(-b/2a)) = (-(-4)/(2)(1) , f(-(-4)/(2)(1))) = (2 , f(2)) = (2 , (2)² - 4(2) - 1) = (2 , -5)
Axis of symmetry: x = -b/2a = -(-4)/(2)(1) = 2
Intercepts:
x-intercept: 0 = x² - 4x - 1
use the quadratic formula to solve for x: x = (-b ± √(b² - 4ac))/(2a) = (-(-4) ± √((-4)² - 4(1)(-1)))/(2(1)) = (4 ± √(20))/2 = (4 ± 2√(5))/2 = 2 ± √(5)
so the x-intercepts are (2 + √(5) , 0) and (2 - √(5) , 0)
y-intercept: f(0) = (0)² - 4(0) - 1 = -1; so the y-intercept is (0 , -1)
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find the cosine of
I dont know what else it wants me to say because it says that its to short to ask.
well, for the cosine of G we'll need the hypotenuse GH, so let's get it, Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{GH}\\ a=\stackrel{adjacent}{\sqrt{6}}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ GH=\sqrt{ (\sqrt{6})^2 + 1^2}\implies GH=\sqrt{ 6 + 1 } \implies GH=\sqrt{ 7 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cos(G )=\cfrac{\stackrel{adjacent}{\sqrt{6}}}{\underset{hypotenuse}{\sqrt{7}}}\implies \cos(G )=\cfrac{\sqrt{6}}{\sqrt{7}}\cdot \cfrac{\sqrt{7}}{\sqrt{7}}\implies \cos(G )=\cfrac{\sqrt{42}}{7}[/tex]
