The inverse of the function f(x) =√x - 2 + 3 is (x - 3)² + 2 so, option B is correct.
What is the function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x)=√x - 2 + 3.
The inverse function can be found as shown below,
f⁻(x) = √(y - 2) + 3 (Replace x by y)
x = √(y - 2) + 3
solve the equation as shown below,
x - 3 = √(y - 2)
Squaring both sides,
(x - 3)² = [√(y - 2)]²
x² + 9 - 6x = y - 2
x² + 9 - 6x + 2 = y
y = x² - 6x + 11 or y = (x - 3)² + 2
Thus, the inverse of the function is (x - 3)² + 2.
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Why will the speedup of a parallel algorithm will eventually reach some limit?
The advantages of adding additional processors will decrease as more are added because some portions are always still sequential, and eventually the speedup approaches a limit.
What is a parallel algorithm's speedup factor?The ratio of the compute time for the sequential method to the time for the parallel algorithm represents the speedup of a parallel algorithm over a matching sequential algorithm. n-fold speedup is what we refer to if the speedup factor is n. For instance, if a sequential approach needs 10 minutes to compute while a parallel algorithm needs just 2, then the speedup is 5 times.
The observed speedup is dependent on every aspect of the implementation. For instance, more processors frequently result in speedups that are greater; but, if other programmer are running on the processors concurrently with a programmer using a parallel technique, the speedup may be reduced by those other applications.
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NEED HELP ASAP
PLEASE REFER TO PICTURE
Consider sequences of positive real numbers of the form , in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of does the term 3000 appear somewhere in the sequence ?
a. 1
b. 2
c. 3
d. 4
e. more than 4
No two values of x in the computation we just did are equal, there are 4 different values of x for which the sequence contains the value 2001.
What is meant by sequences?An ordered list of numbers is all that a sequence is. Number series are collections of numbers that adhere to a pattern or guideline. An arithmetic sequence is one where the rule is to add or take away a number each time.
To estimate a few terms of the sequence in order to obtain a feel how it looks like.
In our case, the definition is that [tex]$\forall$[/tex] (for all) [tex]$n > 1: a_n=a_{n-1} a_{n+1}-1$[/tex].
This can be rewritten as [tex]$a_{n+1}=\frac{a_n+1}{a_{n-1}}$[/tex].
We have [tex]$a_1=x$[/tex] and [tex]$a_2=2000$[/tex], and we estimate:
[tex]$& a_3=\frac{a_2+1}{a_1}=\frac{2001}{x} \\[/tex]
[tex]$& a_4=\frac{a_3+1}{a_2}=\frac{\frac{2001}{x}+1}{2000}=\frac{2001+x}{2000 x} \\[/tex]
[tex]$& a_5=\frac{a_4+1}{a_3}=\frac{\frac{2001+x}{2000 x}+1}{\frac{2001}{x}}=\frac{\frac{2001+2001 x}{2000 x}}{\frac{2001}{x}}=\frac{1+x}{2000} \\[/tex]
[tex]$& a_6=\frac{a_5+1}{a_4}=\frac{\frac{1+x}{2000}+1}{\frac{2001+x}{2000 x}}=\frac{\frac{2001+x}{2000}}{\frac{2001+x}{2000 x}}=x \\[/tex]
[tex]$& a_7=\frac{a_6+1}{a_5}=\frac{x+1}{\frac{1+x}{2000}}=2000[/tex]
At this point we see that the sequence will become periodic: we contain [tex]$a_6=a_1, a_7=a_2$[/tex], and each subsequent term exists uniquely determined by the previous two.
Hence 2001 appears, it contains to be one of [tex]$a_1$[/tex] to [tex]$a_5$[/tex].
As [tex]$a_2=2000$[/tex], we only have four possibilities left.
Clearly [tex]$a_1=2001$[/tex] for x = 2001, and [tex]$a_3=2001$[/tex] for x = 1.
The equation [tex]$a_4=2001$[/tex]
solves to [tex]$x=\frac{2001}{2000 \cdot 2001-1}$[/tex], and the equation [tex]$a_5=2001$[/tex] to [tex]$x=2000 \cdot 2001-1$[/tex]
There are four alternative values of x for which the sequence contains the value 2001 since no two values of x are equal in the computation we just performed.
Therefore, the correct answer is option (D) 4.
The complete question is:
Consider sequences of positive real numbers of the form x, 2000, y, ........ in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of x does the term 2001 appear somewhere in the sequence?
(A) 1
(B) 2
(C) 3
(D) 4
(E) more than 4
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The sum of two numbers is 50. the greater number is four less than five times the lesser number. Find the numbers
The required two numbers are 9 and 41.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Let x be the lesser number, and y be the greater number.
From the question, we know that:
x + y = 50 (Equation 1: The sum of the two numbers is 50)
y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)
The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.
Then, two numbers are x = 9 and y = 41.
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HELP ME NOW PLEASE DESCRIBE AND CREATE FRACTION PATTERNS
find the rule
1 3/8, 1 3/4, 2 1/8, 2 7/8
The missing term of the arithmetic sequence is 2 1/2
What is Arithmetic Progression?An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the arithmetic sequence be represented as A
Now , the equation will be
A = 1 3/8 , 1 3/4 , 2 1/8 , x , 2 7/8
The first term a₁ = 1 3/8
The second term a₂ = 1 3/4
The common difference d of the arithmetic sequence d = second term - first term
Common difference d = 1 3/8 - 1 3/4 = 3/8
Now , the fourth term of the arithmetic sequence is given by
Tn = a + (n - 1) d
Substitute the values in the equation , we get
a₄ = 1 3/8 + ( 4 - 1 ) ( 3/8 )
a₄ = 11/8 + 9/8
a₄ = 20/8
a₄ = 2 4/8
a₄ = 2 1/2
Therefore , the fourth term is 2 1/2
Hence , it is an arithmetic sequence and the fourth term is 2 1/2
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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys. 1/5=5 25/5=5 50/10=5 75/15=5. 5/1=5 20/5=4 40/10=4 69/15=4. These ratios are all equivalent. These ratios are not all equivalent. This relationship is proportional. This relationship is not proportional. Explain how you can tell whether a group of ratios represents a proportional relationship.
Even though this relationship is proportional, not all of these ratios are equal.
What is the solution to the 3 to 5 ratio?Verify that the ratios provided are equal. The ratios of 3:5 and 15:25 are both equal. Because the first ratio 3: 5 can be derived by multiplying the ratio 15: 25 by 5 on both the numerator and denominator. The initial ratio of 3: 5 can be multiplied by 5 to get the ratio 15: 25, and vice versa.
What is an illustration of a 4:1 ratio?This indicates that you would require an 8 fl oz can (a quarter of a quart) of Part B if you were ordering a quart of Part A. You will have 1.25 after combining Parts A and B.
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Mitchell made a scale drawing of a house. A rug in the hallway is 5 inches wide in the drawing. The actual rug is 3 feet wide. What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Answer:
Step-by-step explanation:
a.Scale factor = distance on the plot / actual distance
b.3 feet = 12 inchs.
so scale factor = 5/12
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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What is the length of the 3rd side?
The length of the 3rd side cannot be determined without at least one more side length.
In order to calculate the length of the third side of a triangle, we must also have the lengths of the other two sides. This is because the sum of the three sides of a triangle must equal 180°, so the length of one side can be determined from the other two. For example, if two sides have lengths of 4 and 8, then the third side must have a length of 8, as
4 + 8 + 8 = 180°.
Without knowing the lengths of the other two sides, it is impossible to calculate the length of the third side.
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Need the answer for these
Answer:
Step-by-step explanation:
2A. 3x=6 ⇒ x=2
2B. 3n=2(n-3) ⇒ 3n=2n-6 ⇒ n= -6
1. cross multiplication method
Select the correct answer. Which value in this data set is an outlier? 4, 5, 1, 7, 4, 5, 8, 9, 6, 5, 4, 9, 7 A. 1 B. 2 C. 3 D. 9
So, on solving the provided question, we can say that the outlier from the following data set will be 8.
What is outlier?Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater). For instance, both 3 and 85 are "outliers" when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc. Move away. Look for values that are significantly larger or significantly smaller than all other values to identify outliers. Because it is significantly smaller than all other values, Value 4 is an outlier. An observation that differs unusually from other values in a population sample taken at random is referred to as an outlier.
outlier = 4, 5, 1, 7, 4, 5, 8, 9, 6, 5, 4, 9, 7
outlier = 8
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Calculate the size of angle ABC
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
Describe trigonometry.Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.
Here,
There are two potential solutions because the supplied angle is opposite the given side that is the shortest.
Using the sine law,
B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)
Angle B may take on the following values:
B is equal to arcsin(9/14) = 40.0°.
B = arcsin(9/14) - 180° = 140.0°
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
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How do you find the y-intercept without a calculator?
In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y -intercept of the line.
Now, According to the question:
i) from the general equation of line we know that any line can be represented in the form y = mx + c , where m is a constant and is called the slope of the line and c is also a constant and is the y-intercept.
ii) In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept of the line.
iii) If for example we have the line 3y = 6x + 12 then we first get this equation of the line to match the general form of the equation of the line, that is y = mx + c. Therefore dividing both the left and the right sides of the given equation of the line by 3 we get y = 2x + 4 which matches with the general form of the equation for line and we see that the slope of the given line is m = 2 and the y intercept is given by c = 4.
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Multiply (x-3)(4x+2) using the FOIL method. Select the answer choice showing the FOIL method products
The result of (x-3)(4x+2) using FOIL method is 4x^2 -6x +2x -6.
The FOIL method is a technique used to multiply two binomials. It stands for "First, Outer, Inner, Last" and follows these steps:
First: Multiply the first term of the first binomial by the first term of the second binomial
Outer: Multiply the first term of the first binomial by the second term of the second binomial
Inner: Multiply the second term of the first binomial by the first term of the second binomial
Last: Multiply the second term of the first binomial by the second term of the second binomial
Applying FOIL method to (x-3)(4x+2) we get:
First: 4x * x = 4x^2
Outer: 4x * -3 = -12x
Inner: -3 * 4x = -12x
Last: -3 * 2 = -6
So the result of (x-3)(4x+2) is 4x^2 -12x -12x -6 = 4x^2 -24x -6.
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help please (photo attached)
Answer:
slope = -1
Step-by-step explanation:
any 2 points:
(2,2) (0,4)
to find the slope we use the formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
slope is:
2/-2 = -1
Answer:
The slope is =
2/-2 = -1
Step-by-step explanation:
Also i hope you have a wonderful day !
How do you know if 3 lengths will make a triangle?
If three lengths can make a triangle by using the Triangle Inequality Theorem which states . that any two triangle sides added together must exceed the third side If the sum of any two sides is equal to or less than the third side, then the lengths cannot make a triangle.
The Triangle Inequality Theorem can be used to determine if a triangle can be formed from three lengths. According to this theorem, any two triangle sides must add up to more than the third side. To put it to use, add up the lengths of the first two sides and compare them to the third side's length. The lengths cannot form a triangle if the total of the first two sides is more than or equal to the third side. The lengths can form a triangle if the product of the first two sides is bigger than the product of the third side.
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What is the sum of the positive integers that are solutions of -3n +3 >-11?
Step-by-step explanation:
-3n + 3 > -11
-3n > -14
3n < 14
n < 14/3
14/3 = 4.66666666...
the only positive integers that are smaller than 4.666666... are
4, 3, 2, 1
their sum is
4+3+2+1 = 10
Graph the line with 1 passing through the point (3, -4)
Answer:y=1x-7
Step-by-step explanation:
•35 POINTS• don’t explain.
SSS
SAS
ASA
SAA
HL
Reason:
The tickmarks tell us that the pair of hypotenuses are congruent.
The shared horizontal sides at the bottom are the pair of congruent legs of the right triangles. Therefore, we can use the hypotenuse leg (HL) theorem. This theorem only works for right triangles.
Given that K is the midpoint of segments RM and JL, and prove Δ RKJ ≅ Δ MKL.
Statements
Reasons
1. K is the midpoint of segments RM and JL
1. Given
2.
2.
3. and
3.
4. RK = MK and JK = LK
4. Definition of Congruent Segments
5. Δ EGF ≅ Δ EGH
5.
What is Reason #3?
a
Given
b
Definition of Midpoint
c
CPCTC
d
SSS Congruence Postulate
The complate table is,
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
What is Line segment?A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
K is the midpoint of segments RM and JL.
Now,
Since, K is the midpoint of segments RM and JL.
Hence, We get;
Statement Reasons
1) K is the midpoint of segments Given
RM and JL.
2) RJ ≅ ML SSS Congruence Postulate
3) RK ≅ MK , JK ≅ LK Definition of Midpoint
4) RK = MK , JK = KL Definition of Congruence
Segments
5) Δ EGF ≅ Δ EGH CPCTC
Thus, The complete table is shown above.
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A movie collection has 6 mystery, 10 comedy, 4 adventure, 9 drama, and 12 science fiction discs. How many 5-disc combinations can be made from the collection? (Hint: Divide the total combinations by 5. )
There are 749398 5-disc combinations that can be made from the collection.
Combination refers to the number of ways that a certain number of items can be selected from a larger set of items without regard to the order of the items. It is different from permutation, which takes into account the order of the items.
The number of combinations can be calculated using the formula:
nCr = n! / (r! x (n - r)!)
Where n is the total number of items in the collection, and r is the number of items in each combination
Since a movie collection has 6 mystery, 10 comedy, 4 adventure, 9 drama, and 12 science fiction discs, then the total number of discs in the collection is 41.
Plug in the values to the formula for combination.
nCr = n! / (r! x (n - r)!)
41C5 = 41! / (5! x (41 - 5)!)
41C5 = 41! / (5! x 36!)
41C5 = 749398
Therefore, there are 749398 5-disc combinations that can be made from the collection.
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How do you find the third side?
The third side of a triangle can be found using the Pythagorean Theorem.
This states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side (the hypotenuse).
Let's say you have a triangle with sides a, b, and c, where c is the longest side. To find c, you can use the following formula:
c = √(a2 + b2)
For example, if you have a triangle with sides a = 4 and b = 5, then c = √(42 + 52) = √41 = 6.4. Therefore, the third side of the triangle is 6.4.
To calculate this using steps, you would first square the two shorter sides of the triangle:
a2 = 4 x 4 = 16
b2 = 5 x 5 = 25
Then, add the two squares together:
16 + 25 = 41
Finally, take the square root of the sum to find the length of the third side:
√41 = 6.4
Therefore, the third side of the triangle is 6.4.
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You have an ant farm with 22 ants . The population of ants in your farm will double every 3 months
The number of ants in 6 months will be 88 ants.
How to calculate the value?The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this situation, in an ant farm with 22 ants and the population of ants in your farm will double every 3 months.
The number of ants in 6 months will be:
= 22 × (6/3)²
= 22 × 2²
= 88 ants
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Complete question
You have an ant farm with 22 ants . The population of ants in your farm will double every 3 months. What is the number of ants in 6 months.
Determine the prices for which quantity demanded is greater than quantity supplied.
The prices where the quantity demanded is greater than quantity supplied are :
$ 2$ 1$ 0When is quantity demanded greater than quantity supplied ?Quantity demanded refers to the amount of goods and services that people and businesses in an economy demand.
This amount of goods and services demanded will be more than the quantity supplied when the price of the good or service is less than the equilibrium price.
The equilibrium price here is $ 3 and so the prices less than $ 3 are $2, $1, and $ 0.
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How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2
On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735
what is mean absolute deviation?The average of the absolute deviations from the center point within a dataset is called the mean absolute deviation. This statistic summarizes the statistical spread or variability. Each data point's average distance from the mean is known as the dataset's mean absolute deviation. This gives a sense of the dataset's variability. To determine the absolute value, take the mean from each integer in the dataset and then subtraction. Take the total of the absolute values next. Subtract the aforementioned sum from the total number of items in the dataset to obtain the mean absolute deviation.
12,12,12,22,23,32,43
Mean Absolute Deviation (MAD): 8.8979591836735
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Answer:
On solving the provided question, we can say that 12,12,12,22,23,32,43 Mean Absolute Deviation (MAD): 8.8979591836735
Step-by-step explanation:
Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?
Answer:
$821.2
Step-by-step explanation:
cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2
Solve 3x^2 - 6x - 9?
Answer:
3(x+1)(x-3)
Step-by-step explanation:
Well, this isn't an equation, but we can factor it like this:
[tex]3x^2-6x-9=3(x^2-2x-3)=3(x+1)(x-3)[/tex]
The null and alternative hypotheses divide all possibilities in to:
a. two sets that may or may not overlap .
b. as many sets as necessary to cover all possibilities c. two non-overlapping sets d. two sets that overlap reset selection
Answer:
Step-by-step explanation:
b
Find the area of the right triangle below.
9m
4m
18 m²
Step-by-step explanation:The area is the size of a 2-dimensional shape.
Area of a Triangle
The formula for the area of a triangle is [tex]\frac{1}{2}bh[/tex], where b is the base and h is the height.
This formula comes from the fact that a triangle is half of a rectangle. Remember that the area of a rectangle is the base times the height, so a triangle would be half of this.
Solving for Area
The base of the triangle is 9 meters. Then, the height is 4 meters. So, we can plug these values into the formula.
[tex]A=\frac{1}{2}*4m*9m[/tex]So, A = 18. Then, since meters are being multiplied by each other, the units are meters squared. The final answer is 18 m².
Solve each system by graphing
I’m looking for the answer but also a explanation of how you solved it so I can solve the other 1s without help
Answer: its hard to give an answer but read explanation
Step-by-step explanation: so the first number (1/3x) is your slope and the second number is the y-intercept (5). so for example, you're going to put positive 5 on the y-axis and because you slope is a fraction, rise/run will make you go 3 to the right and 1 up. Then you do the same with the second equation except, the slop is negative and you'll have to go down.