The use of prime factorization to find the exponents of the given numbers gives 625 = 5⁴, 343 = 7³, 216 = 6³, 169 = 13², 256 = 4⁴; 256 = 2⁸ and 729 = 9³; 729 = 3⁶
How to express numbers as a product of prime factors?
When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2
An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴
Thus, you can use prime factorization to find the exponent of the given numbers as follows:
625 as a power of 5
625 = 5×5×5×5 = 5⁴
343 as a power of 7
343 = 7×7×7 = 7³
216 as a power of 6
216 = 6×6×6 = 6³
169 as a power of 13
169 = 13×13 = 13²
256 as a power of 4; as a power of 2
256 = 4×4×4×4 = 4⁴
256 = 2×2×2×2× 2×2×2×2 = 2⁸
729 as a power of 9; as a power of 3
729 = 9×9×9 = 9³
729 = 3×3×3×3×3×3 = 3⁶
Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and 729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively
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X = 4/2, y=-3/4 find X+Y
x-y
Step-by-step explanation:
X+Y=4+2=6X-Y=4-2=2OR
X+Y=3+4=7X-Y=3-4=-1Arrange the pairs of points in increasing order of the slopes of the lines joining them.
(15, 30) and (20, 40)
(12, 32) and (18, 48)
(27, 12) and (72, 32)
(45, 15) and (60, 20)
(27, 2) and (243, 18)
(18, 63) and (24, 84)
(63, 9) and (84, 12)
↓
↓
↓
↓
↓
↓
The arrangement of the points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
How to Arrange the points in increasing order of the slopes of the lines joining them?
Slope is defined as the change in y divided by the change in x. Mathematically:
Slope = (y2 - y1) / (x2 -x1)
To arrange the pair of points. You need to find the slope:
For (15, 30) and (20, 40):
x1 = 15, y1 =30 and x2 =20, y2=40
slope = (40-30)/(20-15) = 10/5 =2
For (12, 32) and (18, 48):
slope = (48-32)/(18-12) = 16/6 = 2.67
For (27, 12) and (72, 32):
slope = (32-12)/(72-27) = 20/45 = 0.44
For (45, 15) and (60, 20):
slope = (20-15)/(60-45) = 5/15 = 1/3 = 0.33
For (27, 2) and (243, 18):
slope = (18-2)/(243-27) = 16/216 = 0.07
For (18, 63) and (24, 84):
slope = (84-63)/(24-18) = 21/6 = 7/2 = 3.5
For (63, 9) and (84, 12):
slope = (12-9)/(84-63) = 3/21 = 1/7 = 0.14
Therefore, the pairs of points in increasing order of the slopes are (27, 2) and (243, 18), (63, 9) and (84, 12), (45, 15) and (60, 20), (27, 12) and (72, 32), (15, 30) and (20, 40), (12, 32) and (18, 48), (18, 63) and (24, 84)
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A town has a population of 2.25 x 104 and grows at a rate of 5.1% every year. Which
equation represents the town's population after 2 years
Answer:
P=(2.25 x 10^4)(1 + 0.051)(1 +0.051)
Step-by-step explanation:
If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (10, 14)? −0.16 0.16 0.6 −0.6
The residual value is 0.6.
What is Residual?The estimated value of a fixed asset at the conclusion of its useful life or lease term is known as the residual value, also known as salvage value. In lease agreements, one of the lessor's main methods for figuring out how much the lessee must pay in periodic lease payments is the residual value.
Given:
y = 1.416x − 0.76
For (7, 8):
As, residual value = Measured value - Predicted value
or, residual value = (actual y-coordinate of the point) - (value of y from the
equation)
When x = 10:
So, the value of y from the equation,
[tex]y_1[/tex] = 1.416 x 10 - 0.76
[tex]y_1[/tex]= 14.16 - 0.76
[tex]y_1[/tex]= 13.4
and, actual y-coordinate of the point, [tex]y_2[/tex]= 14
Residual value = 14 - 13.4
Residual value = 14 - 13.4
Residual value = 0.6
Hence, the residual value is 0.6
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Answer:
0.6
Step-by-step explanation:
im taking the test rn
Express 60 as the product of its prime factors.
60 = (Answer here)
Answer:
2x2x3x5= 60
I hope you like it
Answer:
2 X 2 X 3 X 5
Step-by-step explanation:
We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.
help
If T=5n+2, which term will have a value of 52?
Answer:
T = 52
Step-by-step explanation:
y=– 3/7x+4. Perpendicular to line c is line d, which passes through the point (2,4). What is the equation of line d?
The equation of line d that is perpendicular to line c is: y = 7/3x - 2/3.
How to Find the Equations of Perpendicular Lines?Perpendicular lines have slope values, whose product is equal to -1, that is, they are negative reciprocals to each other. An equation in slope-intercept form is often written for a line as y = mx + b, where m = slope and b = y-intercept.
The slope of y - 3/7x + 4 is -3/7. The negative reciprocal of -3/7 is 7/3. Therefore, the slope (m) of the perpendicular line d is 7/3.
Substitute m = 7/3 and (x, y) = (2, 4) into y = mx + b to find the value of b (y-intercept of the line):
4 = 7/3(2) + b
4 = 14/3 + b
-14/3 + 4 = b
(-14 + 12)/3 = b
-2/3 = b
b = -2/3.
To write the equation of line d, substitute m = 7/3 and b = -2/3 into y = mx + b:
y = 7/3x - 2/3
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Which system of equations is represented by the graph ?
A. y=x^2+2x+1
2x+y=2
B. y=x^2-2x+1
2x+y=2
C. y=x^2+2x+1
2x+y=2
D. y=x^2-2x+1
2x-y=2
option D, y=x^2-2x+1 , 2x-y=2 represents system of equations .
Given:
points (1,0) and (3,4)
line equation is y - y1 = m(x-x1)
y - 0 = 4-0/3-1(x - 1)
y = 2(x-1)
y = 2x - 2
2x - y =2.
The vertex of the given upward parabola is in the first quadrant so the coefficient of [tex]x^{2}[/tex] must have positive values.
so y = [tex]x^{2} -2x+1[/tex]
Therefore option D y=x^2-2x+1 , 2x-y=2 is correct.
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lee went shopping with $60.50 . he bought 5 boxes of blue berries and 3 watermelons and had $16.50 left each watermelon cost $8.30
Assuming the question is : "how much does 1 box of blueberries cost?"
After he bought 5 boxes of blueberries and 3 watermelons, he was left with $16.50
Therefore, 5 boxes of blueberries and 3 watermelons cost $60.50 - $16.50 = $44
We are given the cost of 1 watermelon is $8.30
Therefore, 3 watermelons cost $8.30 x 3 = $24.90.
-> 5 boxes of blueberries cost $44 - $24.90 = $19.10
-> 1 box of blueberries cost $19.10 : 5 = $3.82
Answer:
If your trying to find the total of the 5 boxes of blue berries the answer is
$19.10
Step-by-step explanation:
60.50 - 16.50 = 44$ meaning he spent that much.
8.30 x 3 = 24.9
19.10 + 24.9 = 44
hope this helps
In 2005, there were 12,458 fish in Hound's Tooth
Lake. After years of drought, there were only
968 fish in 2010. Find the rate of change in the
population of fish for 2005–2010.
For the period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.
Define the term rate of change?The term "rate of change" (ROC) describes the rate at which an object changes over time. Thus, it is not the amount of specific changes themselves but rather the acceleration and deceleration all changes (i.e., the rate).According to the specified question-
Hound's Tooth Lake had 12,458 fish in it in 2005.In 2010, there were just 968 fish after years of drought.Rate of change = (final number - initial number)/(final year - initial year)
Rate of change = (12,458 - 968)/(2010 - 2005)
Rate of change = -11490/5
Rate of change = -2298 fishes per year.
Negative sign shows there is a decline in the number.
Thus, for the time period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.
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Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15. If
each bottle costs the same amount, how much is 8 bottles of juice?
As per the unitary method, the cost of 8 bottles is $6.48
Unitary Method:
Unitary method is the way of solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15.
Here we need to find the if each bottle costs the same amount, how much is 8 bottles of juice.
Let x be the cost of one bottle.
so, based on the unitary method we can written the situation as,
15 bottles = costs $12.15
Therefore, the cost of one bottle is.
x = 12.15/15
x = 0.81
So, the cost of 8 bottle is calculated by multiplying the cost of one bottle with 8,
Then we get,
=> 8 x 0.81
=> 6.48
Therefore, the cost of 8 bottles is $6.48
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GHLJ and GSTU are both parallelograms. Why is
∠L ≅ ∠T?
Parallelogram G S T U is inside of larger parallelogram G H L J. Side G S in on side G H, and side G U is on side G J.
The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that opposite angles of a parallelogram are congruent.
How to identify congruent angles?We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.
Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.
Thus, angle G is congruent to angle T and angle L .
Therefore, ∠L ≅ ∠T
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Answer:
By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation:
got it right on edge2
At the bowling alley kai rented shoes and purchased 3 games of bowling for $6.50.
Jack rented shoes and purchases 5 games of bowling for $9.50 Caelan has $17 if she rents shoes how many games of bowling can she purchase
Caelan must spend a total cost of $ 17 for 10 bowling games.
How many bowling games can Caelan purchase?
The total cost consists in the sum of a fixed cost, represented by rent of shoes, and a variable cost, represented by the number of bowling games, whose model is presented below:
c' = c + r · n
Where:
c - Fixed cost, in monetary units.r - Cost of each rent, in monetary units.n - Number of rented games.First, construct the system of equations related to Kai and Jack:
Kai
c + 3 · r = 6.50
Jack
c + 5 · r = 9.50
Second, solve the system of linear equations by numerical methods:
(c, r) = (2, 1.5)
Third, write the resulting function:
c' = 2 + 1.5 · n
Fourth, evaluate the function for the situation of Caelan:
17 = 2 + 1.5 · n
1.5 · n = 15
n = 10
Caelan rents 10 bowling games for $ 17.
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,
Admission to the art museum is $3 per person. When the museum opened this
there was $150 on hand in the ticket booth. At closing time, there was $1254. How many
people paid admission today?
Had:
Tickets:
Total:
Step-by-step explanation:
so the ticket booth had $150 so $1254 -$150=$1104
so $1104 ÷ by $3 each person = to 368 people paid the admission
Had: $150
Tickets :368
Total :$1254
a standard die is rolled three times. what is the probability of rolling a number less than 5 on the first two rolls, then an even number on the third roll?
2/216 or 1/108 is the probability of rolling a number .
How does probability explain work?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.The great thing about this question is that all three of those rolls are Independent Scenarios.
The probability of the first roll does not effect the outcome of the second or third roll
1/6 ( we want a 1, and there are 6 options.)
1/6 ( We want a 3, and there are 6 options
2/6 ( We want a 5 or 6, and there are 6 options)
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The distance from Jose’s home to school is 1. 85 miles. The school is 2. 34 miles from the local library, which is 1. 9 miles from Jose’s home. If Jose goes from his home to school, from school to the library, and then home, how far did he travel?
The Jose travels as he travels from his home to school, through school to the library, then finally back home is 4.19 miles.
Define the term total distance?Distance is defined as an object's entire movement without regard for direction. Distance can be defined as how much ground any object has covered regardless of its originating or ending place.The distance between Jose's house and school is 1.85 miles.
The school is 2.34 miles from the nearest library, which is 1.91 miles away from Jose's house.
Total distance = Jose’s home to school + school to library
Total distance = 1.85 + 2.34
Total distance = 4.19 miles.
Thus, the Jose travels as he travels from his home to school, through school to the library, then finally back home is 4.19 miles.
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Select the correct answer. There are three cell phone models in a store. When selecting a new cell phone, 25% of the customers choose model A, 33% choose model B, and 32% choose model C. The remaining customers buy from an old collection on which the average profit is $50. If the average profit earned on models A, B, and C is $60, $75, and $40, respectively, what is the expected value of the profit earned on all models?
Given the average profits on the different cell phone models, the expected value of profit to be earned on all models is $57.55
How to find the expected value?The expected value of the profit on these models of cell phones can be found based on the number of customers who choose the model and the profit of that model.
The expected value of the profit on all the models is:
= ∑ ( percentage of customers x Profit per model)
= (Percentage of customers model A x Profit from model A) + (Percentage of customers model B x Profit from model B) + (Percentage of customers model C x Profit from model C) + (Percentage of customers old collection x Profit from old collection)
= (25% x 60) + (33% x 75) + (32% x 40) + ( (1 - 25% - 33% - 32%) x 50)
= $57.55
Options for this question are:
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Suppose U = {2,3,6,9,10,13,14,17,19) is the universal set and A = {2,9,10). What is A'?
The complement of set A is { 3, 6, 13, 14, 17, 19}
What is the complement of a given set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
U = {2,3,6,9,10,13,14,17,19}, A = {2,9,10}
set A complement are all the elements in the Universal set U not contained in set A. Those elements are in set A' = { 3, 6, 13, 14, 17, 19}
In conclusion the complement of set A is { 3, 6, 13, 14, 17, 19}
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HELP PLS GIVING BRAINLIEST TO PERSON WHO ANSWERS FIRST
A rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven. Malik wants to rent a car, knowing that:
He plans to drive 250 miles.
He has at most $350 to spend.
Which inequality can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget?
The inequality that can be used to determine d, the maximum number of days Malik can afford to rent for while staying within his budget is 26.03d + 0.13m ≤ 350.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the rental car company charges $26.03 per day to rent a car and $0.13 for every mile driven
Let the number of days be d.
Let the number of miles be m.
The appropriate inequality to illustrate this is 26.03d + 0.13m ≤ 350.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.
Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read.
The total number of pages that he read will be 210 pages.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Based on the equation given, the equation to represent Amir's information will be:
y = 35 × x
y = 35x
Jesse's equation will be:
y = 30(x + 1)
Then, we'll equate both equations together. This will be:
35x = 30(x + 1)
35x = 30x + 30
35x - 30x = 30
5x = 30
x = 30/5
x = 6
Therefore, the number of pages read will be:
y = 35x
y = 35 × 6
y = 210 pages.
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how could we determine the input value of t when W(t)=15 and the rule for function w is 2t+5
ERROR ANALYSIS Describe and correct the error in identifying congruent triangles. TUV=XYZ by the SSS Congruence Theorem.
The letters for XYZ are in the wrong order.
The correct statement should be [tex]\triangle TUV \cong \triangle ZYX[/tex]
============================================
Further Explanation:
The order of the letters matters when writing congruence statements.
The claim is that [tex]\triangle TUV \cong \triangle XYZ[/tex]
The first two letters of each are "TU" and "XY" in that order.
But notice how TU has a single tickmark, while XY has a double tickmark. The two sides are clearly different.
--------
Instead, the statement should be: [tex]\triangle TUV \cong \triangle ZYX[/tex] because of the following three facts:
TU = ZY (single tickmark)UV = YX (double tickmark)TV = ZX (triple tickmark)Notice that:
TU and ZY are the 1st two letters of TUV and ZYXUV and YX are the last two letters of TUV and ZYXTV and ZX are the 1st and 3rd letters of TUV and ZYXGiven the speeds of each runner below, determine who runs the fastest.
i cant figure this out and its due soon pls help me
The person who runs fastest is Zach.
How to find the speed?Ron runs 9 feet per second: 9 ft/s
Zach runs 410 feet in 49 seconds:
410/49 ft/s
=8.36 ft/s
= 8.4 ft/s (Approximately)
Katie runs 1 mile in 412 seconds:
1 mile = 5280 ft
5280/412 ft/s
=12.8 ft/s
Noah runs 870 feet in 1 minute:
= 870/60 ft/s
= 14.5 ft/s
Hence,
Ron 9 feet per seconds
Zach 8.4 feet per seconds
Katie 12.8 feet per seconds
Noah 14.5 feet per seconds
So, Zach is the fastest.
Therefore the fastest is Zach.
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Write a linear function f with the given values f(0) = 2, f(3) = -1
The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
What is Linear Function?
A straight line on the coordinate plane is represented by a linear function.
The linear function formulas are:
y = mx + b (slope-intercept form)y−y1 = m(x−x1) (point-slope form)Ax + By = C (standard form)xa+yb = 1 (intercept form)Here, we have
The given functions are f(0)=2 and f(3) = -1
For f(0) = 2
Coordinate: (0,2)
y-intercept, c: 2
For f(3) = -1
Coordinate: (3,-1)
gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1
=( y₂-y₁)/(x₂-x₁)
= ( -1 -2)/(3 - 0)
= -3/3
= -1
The linear equation is in the slope-intercept form, y=mx+c
f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.
Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
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Help needed!!!
a) Convert the length and width of the swimming pool from centimetres to metres.
b) You’re thinking of laying bricks around the outside of the pool. Find the perimeter of the swimming pool, in metres.
c) You want to buy a pool cover. By rounding off your answers in a) to the nearest metre, estimate the area of the pool by multiplying the 2 numbers together.
d) Find the exact area of your new pool, in m2.
e) Was your estimate in d) reasonable?
f) Please explain why it was accurate or not
Answer:
Step-by-step explanation:
a) 100cm 1m so, 320/100=3.2m, 1200/100=12m
b) 3.2+3.2+12+12= 6.4+24=30.4
c) 3*12=36m squared
d) 3.2*12= 3*12+0.2*12=36+2.4=38.4m squared
e) My estimate in d) was reasonable
f) This is because 36 and 38.4 are really close to each other they only have a difference of 2.4 and that is because instead of multiplying the estimate with 3 and a 0.2 I just multiplied it with a 3. 0.2*12=2.4 so the difference is reasonable.
Helpppppppssssss ejejnee
Answer:
Step-by-step explanation:
Arithmetic Sequence
Answer:
(a) Arithmetic Sequence
Step-by-step explanation:
You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.
Arithmetic sequenceAn arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.
The graph shows an Arithmetic Sequence.
__
Additional comment
A graph of a geometric sequence would show points that lie on an exponential curve.
given the equation y(t)= -14t + 500, what is y (25)
The value of the equation y(t) at y(25) is 150
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Equations can be linear, quadratic or polynomials.
if y(t) = -14t + 500
The y(25) means substitute t = 25 into the equation
y(25) = -14(25) + 500
y(25) = -350 + 500
y(25) = 150
In conclusion, the value of y(25) is 150
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the product of three consecutive positive integers is times their sum. what is the sum of their squares?
77 is the sum of their integers squares .
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.Three types of integers exist: 0 (zero), positive integers (natural numbers), and negative integers.Let the numbers be ( n - 1 ), n , ( n + 1 )
according to question
( n - 1 ) (n) ( n + 1 ) = 8( n + n - 1 + n + 1 )
n( n² - 1 ) = 8(3n)
( n² - 1 ) = 24
n²= 25
n = 5
since n is positive integer n = 5
thus required numbers are 4,5,6
4² + 5² + 6² = 77
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Use the method of adding y-coordinates to graph the function.
f(x) = 3x - sin 4x
Graph of f(x) = 3x - sin 4x is using method of adding y-coordinates is attached below.
What is graphing method by adding ordinates?
The function y = 3x - sin 4x is actually the sum of two functions, y = 3x and y = - sin 4x.
For every value in the domain, there is a corresponding value in the range so that the point (x, 3x - sin 4x) is on the graph of y = 3x - sin 4x.
According to the given question:
Follow these steps to graphing the function:
1. Open an Excel file. Label the first column "x-coordinates," the second column "y = 3x," the third column "y = -sin 4x," and the fourth column "y = 3x - sin 4x." Set each column to round to four decimal places.
2. Set up the first column to range from -2pi to 2pi by intervals of pi/4.
3. Fill in the second and third columns by utilizing the equations y = 3x and y = - sin 4x, respectively.
4. Fill in the fourth column by simply adding the second and third columns.
5. Graph y = 3x - sin 4x by using the x-coordinates from column A and the y-coordinates from column D.
Check the attachment below for the required graph obtained after plotting the points.
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The identification of a relationship using
multiplication and the prediction of the value of one
quantity based on the value of another.
Utilizing multiplication to find relationships and predicting that value of one "Linear regression" is a quantity derived from the value of another.
Define the term Linear regression?The relationship in between magnitude of one parameter and that of a second is modeled by simple linear regression.
For instance, as X rises, Y also increases. or Y declines as X rises. 1 Regression defines the nature of the link, whereas correlation evaluates the strength of such a linking between two variables.Simple linear regression calculates the precise amount by which Y will alter when X alters by a specific amount. The variables X and Y remain interchangeable with the correlation coefficient. Regression uses a linear relationship, or a line, to try and predict any Y variable from the X variable:Y = b 0 + b 1 X.Thus, finding correlations via multiplication and assuming that the value of one "Linear regression" is a number obtained as from value of another
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