Answer:
3/4
the other ones would be in improper form
Step-by-step explanation:
Answer:
three-fourths in standard form is 3/4
so D is the answer
If you have 24 square tiles, how many different rectangles can you make? Each rectangle must use all of the tiles and have no holes or gaps. Sketch each rectangle and label its length and width.
Answer:
4
Step-by-step explanation:
A rectangle has a shorter side and a longer side.
The longer side is called the length and the shorter side is called width.
with the 24 tiles you can make the following rectangles (consider the first number the length and the second number the width, and that each unit represents a tile):
24 x 1
12 x 2
8 x 3
6 x 4
A total of 4 different rectangles.
I am not counting the rectangles than have the same sides shifted, for example 2 x 12 because it is the same as 12 x 2 and we are asked for the rectangles to be different.
I attache an image of the sketch of each rectangle with the labels of length and width (not to scale).
How should this model be completed to represent 820 ÷ 17? Enter your answers by filling in the boxes. I'm in 5the BTW
Answer:
How should this model be completed to represent 820 ÷ 17? Enter your answers by filling in the boxes. I'm in 5the BTW
A software company is selling a new game in a standard edition and a collector's edition the box of the standard edition has a volume of 20 cubic inches and the box for the collector's edition has a volume of 50 cubic inches 30 cubic inches the company received an order for 75 copies
Answer:
option A is correct
75 − s = c
20s + 30c = 1,870
Step-by-step explanation:
The question is not complete.
Here is a complete form
"A software company is selling a new game in a standard edition and a collector's edition the box of the standard edition has a volume of 20 cubic inches and the box for the collector's edition has a volume of 50 cubic inches 30 cubic inches the company received an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, s, and collector’s edition games, c, that were ordered?"
s+c=75
75 − s = c
20s + 30c = 1,870
the options are
A. 75 − s = c
20s + 30c = 1,870
B. 75 − s = c
30s + 20c = 1,870
C. s − c = 75
25(s + c) = 1,870
D. s − c = 75
30s + 20c = 1,870
the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. after 3 hours it is observed that 500 bacteria are present. after 10 hours 5000 bacteria are present. what was the initial number of bacteria? (round your answer to the nearest integer.)
The initial number of bacteria in the culture was approximately 116. We can solve this using differential equation.
Let N(t) be the number of bacteria present at time t, and let k be the constant of proportionality for the growth rate. Then the differential equation that describes the growth of bacteria is:
dN/dt = kN
We can solve this differential equation to get:
N(t) = N0e\(^({kt)}\)
Where N0 is the initial number of bacteria at time t=0.
Using the given information, we can set up a system of two equations:
500 = N0e\(^{(3k)}\)
5000 = N0e\(^{(10k)}\)
Dividing the second equation by the first equation, we get:
10 = e\(^{(7k)}\)
Taking the natural logarithm of both sides, we get:
ln(10) = 7k
Solving for k, we get:
k = ln(10)/7
Substituting this value of k into either of the two equations above, we can solve for N0:
500 = N0e\(^{(3ln(10)/7)}\)
N0 = 116 (rounded to the nearest integer)
Therefore, the initial number of bacteria in the culture was approximately 116.
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Which of the following functions matches this graph?
Answer:
a. y=x^2
Step-by-step explanation:
desmos graphing calculator
What is the next fraction in this sequence? Simplify your answer. 1 4 , 3 10 , 7 20 , 2 5 , ...
The 5th term of the arithmetic sequence is a₅ = 9/20
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 first term of the AP a₁ = 1/4
The second term of the AP is a₂ = 3/10
So , the common difference is d = 3/10 - 1/4 = 1/5
Now , the arithmetic progression will be
The 5th term of the AP a₅ = a + ( n - 1 ) d
Substitute the values in the equation , we get
The 5th term of the AP a₅ = 1/4 + ( 5 - 1 ) ( 1/5 )
On simplifying the equation , we get
The 5th term of the AP a₅ = 1/4 + 4/5
The 5th term of the AP a₅ = 9/20
Hence , the 5th term of the AP 9/20
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Can someone help me with this? I’m genuinely confused it’s been three hours and no one helped me :(
Answer:
wddfgfgjgfccvnjjxcvbfx bff
Answer:
as attached image shows
Step-by-step explanation:
please help ill mark brilliant
Please select the correct answer from the group of answer choices for each part of the question:
1a. Consider the computing load of a sum of 100 scalar variables and one matrix subtraction of a pair of two-dimensional array with dimensions 100x100. Assume the matrix subtraction is fully parallelizable, calculate the speedup using 100 processors assuming 10 processors carry 20% of the load and the rest load is shared among the rest 90 processors evenly?
A: 101/3
B: 101/2
C: 101
D: 100
1b: For the following vector MIPS code DAXPY which performs Y=a x X+Y, fill the two blank instructions.
L.d $f1, a($sp) ;load scalar a
Lv $v0, 0($s0) ;load vector x
__________________ ;vector-scalar multiply
Lv $v2, 0($s1) ;load vector y
___________________ ;add y to product
Sv $v3, 0($s1) ; store the result
A:
mul.d $v1, $v0, $f1
add.d $v3, $v1, $v2
B:
mulvs.d $v1, $v0, $f1
addv.d $v3, $v1, $v2
C:
mul.d $v2, $v0, $f1
add.d $v3, $v1, $v2
D:
mulvs.d $v2, $v0, $f1
addv.d $v3, $v1, $v2
1c. Which of the following statement is incorrect?
A: Both multithreading and multicore rely on parallelism to get more efficiency from a chip.
B: In coarse-grained multithreading, switching between threads only happens after significant events such as last-level cache miss.
C: In fine-grained multithreading, switching between threads happens after every instruction.
D: Simultaneous multithreading (SMT) uses threads to improve resource utilization of statically scheduled processor.
1d. In the roofline model, the attainable GFLOPs/sec is set by _____?
A: Peak Memory BW x Arithmetic Intensity
B: Peak Floating-Point Performance
C: Min (Peak Memory BW x Arithmetic Intensity, Peak Floating-Point Performance)
D: Max (Peak Memory BW x Arithmetic Intensity, Peak Floating-Point Performance)
The correct answer is D: Max (Peak Memory BW x Arithmetic Intensity, Peak Floating-Point Performance).
1a. C: 101 to calculate the speedup, we need to consider the computing load distribution among the processors. In this case, 10 processors carry 20% of the load, which means each of these processors handles 2% of the load. The remaining 90 processors share the rest of the load evenly, so each processor among these 90 handles (100% - 20%) / 90 = 0.8889% of the load.
The speedup can be calculated using Amdahl's Law, which states that the speedup is limited by the portion of the program that cannot be parallelized. In this case, the matrix subtraction is fully parallelizable, so the only portion that cannot be parallelized is the sum of the scalar variables.
The speedup formula is given by: Speedup = 1 / [(1 - p) + (p / n)], where p is the portion that can be parallelized and n is the number of processors.
In this case, p = 0.02 (for the 10 processors) and n = 100. Substituting these values into the formula, we get: Speedup = 1 / [(1 - 0.02) + (0.02 / 100)] = 1 / 0.99 = 1.0101.
Therefore, the correct answer is C: 101.
1b. A:
mul.d $v1, $v0, $f1
add.d $v3, $v1, $v2
The code snippet performs the DAXPY operation, which multiplies a scalar value (a) with a vector (x) and adds the result to another vector (y). The blank instructions should be filled with the above choices.
1c. C: In fine-grained multithreading, switching between threads happens after every instruction.
In fine-grained multithreading, switching between threads happens after every instruction, which is an incorrect statement. Fine-grained multithreading allows switching between threads at a much finer granularity, such as cycle-by-cycle or instruction-by-instruction, to improve resource utilization.
1d. B: Peak Floating-Point Performance
In the roofline model, the attainable GFLOPs/sec is set by the peak floating-point performance of the processor. The roofline model is a performance model that visualizes the performance limitations of a system based on the memory bandwidth and arithmetic intensity of the code. The attainable performance is determined by the lower value between the peak memory bandwidth and the peak floating-point performance. Therefore, the correct answer is B: Peak Floating-Point Performance.
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(First-price procurement auction) We are used to auctions in which there is a single seller facing many potential buyers (i.e., the bidders). However, in many situations we have a single buyer who wants to buy a good (or service) from one of many sellers. In these situations, the buyer may want to run an auction. These are called procurement (or reverse) auctions and are very common both in the public and private world. In a procurement auction, sellers bid for the price at which they are willing to sell their item (or service). In this context, it is natural to talk about a bidder's cost (to provide a service or good) instead of a bidder's valuation. Let's consider a concrete example. Suppose your parents want to remodel their kitchen. They call two contractors (A and B) and ask them for quotes. Your parents tell them that they are going to run a sealed-bid first-price auction. That is, the contractors should email them their quotes, the contractor with the lowest quote wins, and gets paid her quote. Suppose that the contractors are symmetric and have private costs, and that their costs are independently drawn from a Uniform [0,1] distribution. In this simple 2-bidder procurement auction, the bidding strategy β ∗
(c)= 2
1
(1+c) is a (symmetric) Bayesian Nash Equilibrium. That is, in equilibrium, it is optimal for a contractor who anticipates a cost of completing the project of c to submit a quote equal to 2
1
(1+c) (a) If bidders follow the equilibrium bidding strategy, do they bid above or below their cost? How do you interpret the difference between a contractor's quote and their cost? (b) Write down the expression for the probability of contractor A winning when she submits a quote equal to b and contractor B submits a quote according to the equilibrium bidding function β ∗
(⋅). (c) Write down the expression for contractor A's expected payoff when she has a cost of completing the project equal to c and submits a quote equal to b, and her rival bids according to the equilibrium strategy β ∗
(⋅). (d) Show that the bidding strategy β ∗
(c)= 2
1
(1+c) is in fact a (symmetric) Bayesian Nash Equilibrium.
(a) In the equilibrium bidding strategy, bidders bid below their cost. The difference between a contractor's quote and their cost represents their strategic behavior in the auction.
By bidding below their cost, contractors try to increase their chances of winning the auction and securing the project.
This strategy allows them to potentially earn a higher profit if they win the auction and their cost turns out to be lower than their bid.
(b) The probability of contractor A winning when she submits a quote equal to b and contractor B submits a quote according to the equilibrium bidding function β(⋅) can be calculated as follows:
P(A wins) = P(A's bid ≤ B's bid)
Since the contractors' costs are independently drawn from a Uniform [0,1] distribution, the probability can be expressed as:
P(A wins) = P(A's cost + A's bid ≤ B's cost + B's bid)
Given that A's bid is b and B's bid is β∗(B's cost), the probability becomes:
P(A wins) = P(A's cost + b ≤ B's cost + β∗(B's cost))
(c) Contractor A's expected payoff when she has a cost of completing the project equal to c and submits a quote equal to b, while her rival bids according to the equilibrium strategy βx(⋅), can be calculated as follows:
Payoff(A) = P(A wins) × (b - c)
Using the probability expression from part (b), the expected payoff can be written as:
Payoff(A) = P(A's cost + b ≤ B's cost + βx(B's cost) × (b - c)
(d) To show that the bidding strategy βx(c) = 2/(1+c) is a (symmetric) Bayesian Nash Equilibrium, we need to verify two conditions:
(i) the strategy is optimal for a contractor given the strategies of other bidders, and
(ii) no bidder has an incentive to deviate from the equilibrium strategy.
(i) Optimality: Given the bidding strategy βx(c) = 2/(1+c), a bidder's expected payoff is maximized when they follow this strategy. This can be shown by calculating the expected payoff for a bidder who anticipates a cost of completing the project as c and submits a quote equal to βx(c). The expected payoff is maximized when the bidder follows the equilibrium strategy.
(ii) No incentive to deviate: Suppose a bidder deviates from the equilibrium strategy and chooses a different bidding strategy. In this case, the bidder's expected payoff would be lower than or equal to the expected payoff obtained by following the equilibrium strategy. Therefore, no bidder has an incentive to deviate from the equilibrium strategy, indicating that βx(c) = 2/(1+c) is a Bayesian Nash Equilibrium.
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what is the value of x in the equation, 5x - 7 = y, if y=8?
Answer:
The value of x is 3.
Step-by-step explanation:
5x-7=y
5x-7=8
5x=8+7
5x=15
x=15/5
x=3
Hey there!
5x - 7 = y
5x - 7 = 8
ADD 7 to BOTH SIDES
5x - 7 + 7 = 8 + 7
CANCEL out: -7 + 7 because it give you 0
KEEP: 8 + 7 because it help solve for the x-value
NEW EQUATION: 5x = 8 + 7
SIMPLIFY IT!
5x = 15
DIVIDE 5 to BOTH SIDES
5x/5 = 15/5
CANCEL out: 5/5 because it give you 1
KEEPs 15/5 because it give you the x-value
NEW EQUATION: x = 15/5
SIMPLIFY IT!
x = 3
Therefore, your answer is: x = 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Help me figure out where to plot these points.
Answer:
is there a graph or picture?
Step-by-step explanation:
i can try to help but what points do you need to plot?
SOMEONE PLEASE ANSWER THIS LAST QUESTION CORRECTLY :(
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
The requried, The range is the best measure of variability, and it equals 45. Option B is correct.
The appropriate measure of variability for the data shown is the range, which is the difference between the largest and smallest values in the dataset. From the stem-and-leaf plot, the smallest value is 20 and the largest value is 65. Therefore, the range is 65 - 20 = 45. Thus, the statement "The range is the best measure of variability, and it equals 45" is correct.
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Suppose a 5 × 8 coefficient matrix for a system has five pivot columns. Is the system consistent? Why or why not? Choose the correct answer below A. There is a pivot position in each row of the coefficient matrix The augmented matrix will have nine columns and will not have a row of B. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have C. There is a pivot position in each row of the coefficient matrix. The augmented matrix vill have six columns and will not have a row of the ○ D. *There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which wil have the form 0 000 0 o 0 0so the system is consistent. \
The system is consistent since it has an infinite number of solutions.
*There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have the form 0 000 0 o 0 0, so the system is consistent.
A coefficient matrix is a matrix that contains the coefficients of the variables in the linear equations of a system.
An augmented matrix is a matrix that contains the coefficient matrix's column and the constant vector's column.The system of equations has a unique solution if there is one pivot column for each row in the coefficient matrix.
In this case, a row echelon form can be used to convert the coefficient matrix. The augmented matrix will be used to identify whether a system of equations is consistent.
Suppose a 5 x 8 coefficient matrix for a system has five pivot columns. Then there is at least one row of the coefficient matrix that does not have a pivot position, as stated in option D. This implies that in the row echelon form of the coefficient matrix, there will be at least one row with zeros, indicating that there are an infinite number of solutions to the system.Therefore, the system is consistent since it has an infinite number of solutions.
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the function h is given by h(x)=∫x 1 ln(t sint 5)ⅆt for 1≤x≤7. on what intervals, if any, is h decreasing?
The intervals, if any, where h is decreasing will be B. 4.323 ≤ x ≤ 5.461.
How to calculate the valueA function simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Based on the information, function h is given by h(x)=∫x 1 ln(t sint 5)ⅆt for 1≤x≤7. It should be noted that x will give the range of 4.323 and 5.4613.
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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2≤x≤10
The average rate of change, in simplest form, of the function over the interval 2 ≤ x ≤ 10 is 9
How to find the average rate of change, in simplest form, of the function over the interval 2≤x≤10?The interval is given as:
2 ≤ x ≤ 10
From the table of values, we have
f(2) = 34
f(10) = 106
The average rate of change, in simplest form, of the function over the interval 2≤x≤10 is calculated as;
Rate = (f(10) - f(2))/(10 - 2)
This gives
Rate =(106 - 34)/(10 - 2)
Evaluate
Rate = 9
Hence, the average rate of change, in simplest form, of the function over the interval 2 ≤ x ≤ 10 is 9
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if y varies jointly as x and the inverse of z and y = -5 and x = -5 and z = 6, find y when x = 5 and z = -8
Step-by-step explanation:
y varies inversely as x=
y= k/xz
-5= k(-5)/6
k= 6
y=6/xz
y=6/5×-8
y= -3/20
Motor sold half of his comic books and then bought
seventeen more. He now has 33. With how many did he begin?
A digital thermometer costs $599.99. The company offers a $200 rebate. What percent of the cost is
the rebate?
Answer:
33.33%
Step-by-step explanation:
600/3 is 200 which means 1/3 of it is rebated
Mariam Estimated then Multiplied using these numbers 66 and 35. Her answer was 1,200. Was her solution correct?
Answer:
Her solution was or wrong
Step-by-step explanation:
Given:
Two numbers ;
66 , 35
Mariam product is 1,200
Find:
Her solution was right or wrong
Computation:
66 x 35
2,310
So,
Her solution was or wrong
there are six members on a student council. two of these members will serve on a spring formal committee. how many possible spring formal committees are there?
There are 30 different combinations of two members who can be selected to serve on the spring formal committee.
Permutation is the arrangement of elements in a specific order. In this scenario, the elements are the six members of the student council, and the order in which they are arranged is important.
To find the number of permutations, we use the formula nPk, where n is the number of elements and k is the number of elements we want to arrange.
In this case, n = 6 and k = 2,
so we have
=> 6P2 = 6!/(6-2)!
=> 6!/(4!) = 6 x 5/1 = 30.
So, there are 30 possible spring formal committees that can be formed from the six members of the student council.
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Which triangle would be impossible to create?
A. Right Isosceles
B. Acute Scalene
C. Obtuse Equilateral
D. Right Scalene
Or none of these
Obtuse equilateral, because an obtuse triangle needs one angle that is greater than 90 degrees, but in an equilateral triangle all the angles are 60 degrees because all the sides are equal.
If all sides are equal, then all their non-touching angles are equal.
Hope this helps!
Mark is a woodworker which means he builds structures out of wood. Mark can build 5 wooden entertainment stands in 8 days. At this rate, how many wooden stands can mark build in 30 days? Round to the nearest whole number of wooden entertainment stands
Answer:
your answer is 48
Step-by-step explanation:
8÷5=1.6
1.6×30=48
If the stream narrows from 30 feet to 20 feet, which of the following statments will be true. a. The width of the stream decreased and the velocity should decrease also. b. The width of the stream has narrowed and the velocity should increase. c. The width of the stream has narrowed and the velocity should stay the same.
If the stream narrows from 30 feet to 20 feet, the width of the stream has narrowed, and the velocity should increase. The correct answer is b.
According to the principle of conservation of mass, when the width of a stream narrows, the volume flow rate (the amount of water passing through a given point per unit time) must remain constant if there are no other factors involved.
The volume flow rate (Q) can be calculated as the product of the cross-sectional area (A) and the velocity (v): Q = A * v.
When the width of the stream narrows from 30 feet to 20 feet while the volume flow rate remains constant, the cross-sectional area decreases. To maintain a constant volume flow rate, the velocity must increase.
This is because the same amount of water is passing through a smaller cross-sectional area, requiring an increase in velocity to compensate for the reduced width.
Therefore, the correct statement is that the width of the stream has narrowed, and the velocity should increase.
The correct answer is b.
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HELP ASAP!!
Add. (5x + 8) + (2x + 5)
Answer:
7x + 13
Step-by-step explanation:
because the correct answer is 7x+13
How do you find the angle of a slope?
The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.
What is the angle of the slope?The angle of slope shows the departure of your climb from the idealistic flat surface of the course (remember, it's an idealized flat surface that ignores elevation change). In order to figure this out, divide the increase by the run and then find the inverse tangent of the outcome.The angle between a horizontal plane and a specific location on the land surface is known as the slope angle (degree).The term "slope" describes the incline's angle or grade. You might have an upward or downhill slope. The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.To learn more about angle of slope refer,
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the mass of a single bromine atom is 1. 327 × 10-22 g. this is the same mass as a. a) 1.327 × 10-16 mg. b. b) 1.327 × 10-25 kg. c. c) 1.327 × 10-28 μg. d. d) 1.327 × 10-31 ng.
Out of all the answer choices, d) 1.327 × 10-31 ng is the only one that matches the calculated value of the mass of a single bromine atom in nanograms. Therefore, d) is the correct answer.
To understand why, we need to convert the mass of a single bromine atom from grams to nanograms.
There are 10^9 nanograms in a single gram, so we can use this conversion factor to make the necessary calculation:
1.327 × 10-22 g x (10^9 ng/1 g) = 1.327 × 10-13 ng
However, none of the answer choices match this value. We need to use scientific notation to convert 1.327 × 10-13 ng into one of the given answer choices.
a) 1.327 × 10-16 mg = 1.327 × 10^-10 ng (since 1 mg = 10^6 ng)
b) 1.327 × 10-25 kg = 1.327 × 10^-4 ng (since 1 kg = 10^12 ng)
c) 1.327 × 10-28 μg = 1.327 × 10^-19 ng (since 1 μg = 10^3 ng)
d) 1.327 × 10-31 ng = 1.327 × 10-31 ng
Out of all the answer choices, d) 1.327 × 10-31 ng is the only one that matches the calculated value of the mass of a single bromine atom in nanograms. Therefore, d) is the correct answer.
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Help anyone can help me do 16 and 17 question,I will mark brainlest.The no 16 question is find the area of the shaded region
Answer:
Question 16 = 22
Question 17 = 20 cm²
Step-by-step explanation:
Concepts:
Area of Square = s²
s = sideArea of Triangle = bh/2
b = baseh = heightDiagonals of the square are congruent and bisect each other, which forms a right angle with 90°
Segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Question # 16
Step One: Find the total area of two squares
Large square: 5 × 5 = 25
Small square: 2 × 2 = 4
25 + 4 = 29
Step Two: Find the area of the blank triangle
b = 5 + 2 = 7
h = 2
A = bh / 2
A = (7) (2) / 2
A = 14 / 2
A = 7
Step Three: Subtract the area of the blank triangle from the total area
Total area = 29
Area of Square = 7
29 - 7 = 22
-----------------------------------------------------------
Question # 17
Step One: Find the length of PT
Given:
PR = 4 cmRT = 6 cmPT = PR + RT [Segment addition postulate]
PT = (4) + (6)
PT = 10 cm
Step Two: Find the length of S to PT perpendicularly
According to the diagonal are perpendicular to each other and congruent. Therefore, the length of S to PT perpendicularly is half of the diagonal
Length of Diagonal = 4 cm
4 ÷ 2 = 2 cm
Step Three: Find the area of ΔPST
b = PT = 10 cm
h = S to PT = 2 cm
A = bh / 2
A = (10)(2) / 2
A = 20 / 2
A = 10 cm²
Step Four: Find the length of Q to PT perpendicularly
Similar to step two, Q is the endpoint of one diagonal, and by definition, diagonals are perpendicular and congruent with each other. Therefore, the length of Q to PT perpendicularly is half of the diagonal.
Length of Diagonal = 4 cm
4 ÷ 2 = 2 cm
Step Five: Find the area of ΔPQT
b = PT = 10 cm
h = Q to PT = 2 cm
A = bh / 2
A = (10)(2) / 2
A = 20 / 2
A = 10 cm²
Step Six: Combine area of two triangles to find the total area
Area of ΔPST = 10 cm²
Area of ΔPQT = 10 cm²
10 + 10 = 20 cm²
Hope this helps!! :)
Please let me know if you have any questions
• Given: f (x) = ln (sin x²), decompose this function into functions g, h, and k such that g (h (k (x))) = f(x). For credit: Give each of the functions g, h, and k and show that they equal f (x).
The function f(x) = ln(sin(x^2)) can be decomposed into functions g, h, and k.
The innermost function k(x) is defined as k(x) = x^2, the intermediate function h(x) is defined as h(x) = sin(x), and the outermost function g(x) is defined as g(x) = ln(x). When we compose these functions as g(h(k(x))), we obtain ln(sin(x^2)), which is equal to the original function f(x). To decompose the function f(x) = ln(sin(x^2)), we break it down into three functions: k(x) = x^2, h(x) = sin(x), and g(x) = ln(x).
The innermost function, k(x), squares the input x. The intermediate function, h(x), takes the sine of the input x. Finally, the outermost function, g(x), computes the natural logarithm of the input x. When we compose these functions in the order g(h(k(x))), it results in ln(sin(x^2)), which matches the original function f(x). This decomposition allows us to express f(x) as the composition of simpler functions.
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graph the line that represents this equation
\(3x-4y=8\)
The graph of the line that represents the given equation, 3x - 4y = 8, is shown below
Graph of Linear equationsFrom the question, we are to graph the line that represents the given equation.
The given equation is
3x - 4y = 8
To graph the line, we will determine x-intercept and y intercept of the line.
The x-intercept in the point where y equals zero on the line
and
The y-intercept in the point where x equals zero on the line
Determining the x-intercept
3x - 4y = 8
Set y = 0
3x - 4(0) = 8
3x = 8
x = 8/3
The x-intercept is (8/3, 0)
Determining the y-intercept
3x - 4y = 8
Set x = 0
3(0) - 4y = 8
-4y = 8
y = 8/-4
y = -2
The y-intercept is (0, -2)
Using the x-intercept and y-intercept, the graph of the line is shown below
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