Answer:
Step-by-step explanation:
The expression representing the area covered by the pavilion can be found by multiplying the length by the width:
A = (x + 8) * (x - 4)
where A represents the area and x is the length of one of the sides.
during a short interval of time, the speed, , of an automobile is given by =2 3 where the time t is in seconds. the units of a and b are respectively
The units of a and b are m/sec³ and m/sec⁴
Given :v = at² + bt³
The dimension of velocity v = [L] [T]⁻¹
According to the Principle of Homogeneity of Dimension, "the terms combining the equation must have the same dimensions for the equation to have any physical meaning."
So, Dimensiona of v = Dimensions of at²
[L][T]⁻¹ = a[T]²
a = [L][T]⁻³ = m/sec³
Similarly, we can say
Dimension of v = Dimension of bt³
[L][T]⁻¹ = b[T]³
b = [L][T]⁻⁴ = m/sec⁴
Hence, the unit of a is m/sec³ and the unit of b is m/sec⁴
The question is incomplete, the complete question is
"During a short interval of time, the speed v in m/s of an automobile is given by v = at² + bt³ where the time t is in seconds the units of a and b are respectively:"
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Can anyone factor out the GCF of the 3 questions?
The GCFs of the given polynomials are 4, 7x² and 1
What are the greatest common factors?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Given are some polynomial, we need to find GCF,
a) 12x²-8x+4
12x² = 2×2×3×x×x
8x = 2×2×2×x
4 = 2×2
GCF = 2×2 = 4
b) 7x⁸-14x⁴+21x²
7x⁸ = 7×x×x×x×x×x×x×x×x
14x⁴ = 7×2×x×x×x×x
21x² = 7×3×x×x
GCF = 7×x×x
GCF = 7x²
c) 17x³+15x²-21x+3
17x³ = 17×x×x×x
15x² = 3×5×x×x
21x = 7×3×x
3 = 3×1
GCF = 1
Hence, the GCFs of the given polynomials are 4, 7x² and 1
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similar to the hospital schedule in example 2.9, suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries. a. how many different sequences are possible? b. how many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively? c. how many different schedules begin and end with a knee surgery?
a. The different sequences possible are 1200.
b. The different sequences have all hip, knee, and shoulder surgeries scheduled consecutively are 720.
c. The different schedules begin and end with knee surgery is 6.
(a) To find the number of different sequences, we can use the permutation formula n!/(n-r)!
where n is the total number of surgeries and r is the number of surgeries of each type that we need to schedule.
For knee surgeries, n = 5 (total surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 5!/(5-3)! = 5!/(2!) = 54 = 20.
Similarly, the number of different sequences for hip surgeries is 5!/(5-2)! = 5!/(3!) = 54*3 = 60.
Hence, the total number of different sequences is 20 * 60 = 1200.
(b) To find the number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively, we first need to find the number of sequences for each type of surgery.
For knee surgeries, n = 3 (number of knee surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 3!/(3-3)! = 3!/(0!) = 3! = 6.
Similarly, the number of different sequences for hip surgeries is 2!/(2-2)! = 2!/(0!) = 2! = 2.
For shoulder surgeries, the number of different sequences is 5!
Hence, the total number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively is 6 * 2 * 5! = 720.
(c) In order to find the number of different schedules that begin and end with knee surgery, we first need to find the number of sequences for the middle surgeries.
There are 2 hip surgeries and 2 knee surgeries left to schedule, so the number of different sequences for these surgeries is (2+2-1)!/(2!2!) = 3!/(2!1!) = 3.
Hence, the total number of different schedules that begin and end with a knee surgery is 3 * 2 * 1 = 6.
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The complete question is -
A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries.
(a) How many different sequences are possible?
(b) How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively?
(c) How many different schedules begin and end with knee surgery?
Use a calculator to find the approximate value of the expression. round the answer to two decimal places. the sine of the complementary angle to 75°.a. 0.65 b. 0.34 c. 0.57 d. 0.26
Answer: Option d. 0.26
Step-by-step explanation:
Since the addition of complementary angles = 90°
75° + x = 90°
x = 90° - 75 °
x = 15° ( the complementary angle )
sine 15° = 0.25882
= 0.26 correct to two decimal places
true or false? [1,5] = { 1, 2, 3, 4, 5 }.
The statement [1,5] = { 1, 2, 3, 4, 5 is False.
In mathematics, there are two ways of representing a set of elements: by using curly braces {} or square brackets []. The curly braces {} are commonly used to represent sets, while square brackets [] are used to represent lists or arrays.
[1,5] is a list, which means it is ordered and has duplicates allowed. On the other hand, {1,5} is a set, which means it is unordered and has no duplicates allowed.
Therefore, [1,5] is not equal to {1, 2, 3, 4, 5} because the former is a list of two elements, while the latter is a set of five distinct elements.
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If you invest $550.00 at a 4% interest rate, what will be the interest
Step-by-step explanation:
First, look at the amount of money. It's $550 so write that down on a piece of paper or something like that.The interest rate is 4%, so you have to times 1% 4 times to get the answer. Write it down.First, let's find 1% of 550.
---------------------------------------------
HOW TO FIND 1% OF 550:
Try to find the decimal point of 550. Since it's a full number, it'll be at the back. It looks like this: 550.00(see the point?)
Since behind the point there are 2 0's, round it back 2 times.It looks like this: 5.50(see it?)
---------------------------------------------
Now, let's multiply the "new" number amount we have. ($5.50)
5.50x 4-------------
22(yeah, I don't think I need to explain this but I did lol)
YAY!You got the answer! Congrats!
-eliana44ever
. imagine a hallway with 1000 doors numbered consecutively 1 through 1000. suppose all of the doors are closed to start with. then some dude with nothing better to do walks down the hallway and opens all of the doors. because the dude is still bored, he decides to close every other door starting with door number 2. then he walks down the hall and changes (i.e., if open, he closes it; if closed, he opens it) every third door starting with door 3. then he walks down the hall and changes every fourth door starting with door 4. he continues this way, making a total of 1000 passes down the hallway, so that on the 1000th pass, he changes door 1000. at the end of this process, which doors are open and which doors are closed?
A hallway having 1000 doors at the end of the process the doors which are open are all the factors of 24 i.e, 24,48,72,96,120,144...
A hallway has 1000 doors named 1 from 1000
So he opens all the doors of the hallway so all the doors are opened.
He decides to close every other door starting with door number 2 so 1st door is open and from 2nd door every alternate door is opened so factor of 2 is all close,
2, 4, 6, 8, 10, 12, 14, 16, 18, 20..................1000.
Then he decides to close very open door and open every close door from door three so,
3 is open it will be closed
6 was close so open
9 was open so it will be close
12 was close the it is open
so on 15,21, 27,33......999 will all be closed,
and all 18, 24, 30.....will be all open
then he walks down the hall and changes every fourth door starting with door 4
so 4 will be open so on
4, 8, 16,20, 28,32, 36,40........so on 1000 will all be open
and 12,24,48,60.............will be closed.
So all the door with factor of 12 i.e.12,24,36,48,60,72...will closed.
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using sequence, create numeric vector called grid containing n 1 equispaced points between 1 and 2 (inclusive) where n = 106.
grid <- seq(from = 1, to = 2, by = (2-1)/(106-1)). # Creates a numeric vector of 106 equispaced points between 1 and 2.
grid <- seq(from = 1, to = 2, by = (2-1)/(106-1)) #This will create a numeric vector called grid containing 106 equispaced points between 1 and 2 (inclusive). #The command takes three arguments. 'from' indicates the starting point for the sequence, in this case 1; 'to' indicates the ending point for the sequence, in this case 2; 'by' indicates the increment size between each number, which is calculated as (2-1)/(106-1). This is because there are a total of 106 numbers, so to get the distance between each number, we divide the total range (2-1) by the total number of points (106-1). This provides a numeric vector of 106 equispaced points between 1 and 2.
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a game is played by drawing four cards from an ordinary deck and replacing each card after it is drawn. find the probability of winning, if win comes with at least one ace among the four draws..
The probability of winning the game with at least one Ace among the four draws is 0.736.
The probability of winning in this game is calculated as,
There are 4 Aces in a standard deck of 52 cards, so the probability of drawing an Ace on one draw is 4/52.
The probability of not drawing an Ace in 4 draws is (48/52) * (47/51) * (46/50) * (45/49) = 0.264.
The probability of winning is the complement of not winning, which is 1 - 0.264 = 0.736.
So, the probability of winning the game with at least one Ace among the four draws is 0.736.
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25. A circle is inscribed in a square. Write a function for the area of the circle in terms of the side of the square.
A) A = πr² - S²
B) A = 1/4 πs²
C) A = s² - ππr²
D) A = 1/2 πs²
E) None of these
Correct option is B, function for the area of the circle in terms of the side of the square is A = [tex]\pi \frac{S^2}{4}[/tex].
What is the formula for calculating the area of an inscribed square in a square?Because the area of a square is one of its sides multiplied by itself, the area equals the square of the radius of a circle multiplied by two. Because the radius of the circle is a known quantity, the area of the inscribed square can be calculated numerically.
An “inscribed” square in a square is one in which all of the vertices of the smaller square are on the borders of the bigger square. To do this, the vertices of the smaller square will split each side of the bigger square into two segments, one on each side.
If a square is used to inscribe a circle, the square's side length will match the circle's diameter. As a result, the radius of an inscribed circle is S/2 for a square with length S. hence, the area of a circle is expressed as the square's sides,
= [tex]\pi \frac{S^2}{4}[/tex]
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Answer to [tex]9/10+3/1000[/tex]
(9 over 10 plus 3 over 1000)
A certain amount of two types of candy are mixed together. One candy is worth $1.05 a pound, one is worth $1.35 a pound. The mixture is worth $1.17 a pound. How much of each type is used to create 30 pounds of the mixture?
The number of candy that worth $1.05 per pound will be 5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Given that One candy is worth $1.05 a pound, one is worth $1.35 a pound. The mixture is worth $1.17 a pound.
Consider that x be the number of candy that worth $1.05 per pound.
Then the number of candy that worth $0.85 per pound will be (20 - x). Then the equation will be;
1.05x + 0.85(20 - x) = 0.90 × 20
105x + 85 × 20 - 85x = 90 × 20
20x = 5 × 20
x = 5 pounds
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At his job, the first 40 hours of each week that Thomas works is regular time, and any additional time that he works is overtime. Thomas gets paid $15 per hour
during regular time. During overtime Thomas gets paid 1.5 times as much as he gets paid during regular time. Thomas works 46 hours in 1 week and gets $117 in
deductions taken out of his pay for this week. After the deductions are taken out, how much of Thomas's pay for this week remains?
The total pay at the end of the week is $618.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
Thomas gets paid $15 per hour during regular time, hence for 40 hours he gets:
(15)(40) = 600
He works a total of 46 hours:
The additional time worked is 6 hours.
The payment for the additional hours is:
(1.5)(15) = 22.5
For 6 hours he gets:
(6)(22.5) = 135
Hence, the total income that he should get is 600 + 135 = 735.
He gets an deduction of $117, the final pay is:
735 - 117 = 618
Hence, the total pay at the end of the week is $618.
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let u=⟨4,2,−4⟩ . decompose f=⟨6,4,0⟩ into two vectors f1 and f2 , where f1 is parallel to u and f2 is orthogonal to u .
AS per the concept of vectors, two vectors f1 and f2 , where f1 is parallel to u and f2 is orthogonal to u .
In mathematics, vectors are quantities that have both magnitude and direction. They are often used to represent physical quantities such as forces and velocities.
In this case, we are given a vector u and another vector f, and we want to decompose the vector f into two separate vectors, f1 and f2. The first vector, f1, will be parallel to u, meaning that it will have the same direction as u but possibly a different magnitude.
The second vector, f2, will be orthogonal to u, meaning that it will be perpendicular to u.
Next, we will subtract the projection from f to find the vector f2.
This vector will be orthogonal to u because the projection is parallel to u, and the difference between the two vectors will be perpendicular to u.
The final answer will be the vectors f1 and f2, which together form the original vector f.
This process of decomposing a vector into its parallel and orthogonal components is an important tool in mathematics and physics.
Complete Question:
Let u=〈−6,2,3〉. Decompose F=〈4,0,6〉 into two vectors F1 and F2, where F1 is parallel to u and F2 is orthogonal to u and Prove it.
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a bee starts flying from point faces east, and flies a distance of 1 foot due east. for , once the bee reaches point , turns counterclockwise and flies two-thirds of the previous distance it flew to point . if the bee continuously flies this way for ever, it will approach a point that is feet away from , where are positive integers and is not divisible by the square of any prime number. what is ?
The bee's path can be modeled as a complex number sequence.
The bee started flying from the point facing east and flies a distance of 1 foot due east. For, once the bee reaches a point, turns counterclockwise, and flies two-thirds of the previous distance it flew to point
The first step is 1 + 0i. Each subsequent step is two-thirds of the previous step rotated by -90 degrees, which is equivalent to multiplying by -1/3 + i√3/3.
The bee's final position is the limit of this sequence, which is 0.5 + 0.5i√3. The distance from the starting point is |0.5 + 0.5i√3| = 0.5√(0.5² + (0.5√3)²) = √(0.25 + 0.75) = √(1).
Therefore, = √(1), and = 1.
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What is the area of triangle ABC?
two angles in the triangle are 60°, so the last one must be 60°, since all must add up to 180°, that means the triangle is equilateral
[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}~ ~~ units^2[/tex]
Answer:
C.
Step-by-step explanation:
It is an equilateral triangle.
DB = 6, AB = 12, DC = height
[tex]DC=\sqrt{(CB)^{2}- (DB)^{2} } =\sqrt{144-36} =\sqrt{108}=\sqrt{(36)(3)} =6\sqrt{3}[/tex]
[tex]A=\frac{(DC)(AC)}{2} =\frac{(6\sqrt{3})(12) }{2} =\frac{72\sqrt{3} }{2} =36\sqrt{3}[/tex]
Hope this helps
If WX = WZ, what theorem
can be used to show that
APXW = APZW?
Pls help asap
APX is congruent to WX and APZ is congruent to WZ
From step 2 and 3, we can conclude that APX is congruent to APZ.
What is transitive property prove the statement?One theorem that can be used to show that APXW = APZW when WX = WZ is the Transitive Property of Congruence.The Transitive Property states that if two figures are congruent to a third figure, then they are congruent to each other. In this case, WX and WZ are congruent because they are equal, and APX and APZ are congruent to WX and WZ, respectively. Therefore, APX and APZ are congruent to each other.Step by step explanation:Given WX = WZSince WX = WZ, we can say WX is congruent to WZ (Congruent figures have the same size and shape)APX is congruent to WX and APZ is congruent to WZFrom step 2 and 3, we can conclude that APX is congruent to APZ.Therefore, APXW = APZW (the sides of two congruent figures are equal)To learn more about transitive property refer:
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the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population. the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population. true false
The given statement "the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population." is FALSE
In inferential statistics, sample data is analysed as opposed to the entire population since, in some cases, it is impossible to analyse the population of an entire country. As a result, inferential statistics uses analysis of sample data to make conclusions about the entire population. The population's sample data are chosen, and after analysis, the results can be utilised to draw conclusions about the entire population.
Hence, the given statement "the branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population." is false
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A bushel of apples weight about 42 pound lthere are four packs in a bushel it takes 2 lb of apples to make one pie how much pie can you make with one pack of apples
We can make 5 pies with one pack of apples as the number of pies should be an integer.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A bushel of apples weighs about 42 pounds and there are four packs in a bushel.
So, The weight of one pack of apples is (42/4) = 10.5 pounds.
Now, It takes 2 pounds of apples to make one pie,
Therefore, We can make (10.5/2) = 5.25 pies but we can only make 5 pie from one pack of apples.
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Find the scale factor of figure A to figure B
Answer: 9:5
Step-by-step explanation:
What i a linear function in the form y=mxb for the line paing through (4. 5, -4. 25) with y-intercept of 2. 5
y=-1.5x+2.5 is the linear function with the y-intercept of 2. 5 for the line passing through (4. 5, -4. 25).
An expression that quantifies a line's direction and steepness is called its slope or gradient. This allows one to see how quickly the dependent variable is changing as the independent variable does. Given the points are (4. 5, -4. 25) and the y-intercept is 2.5.
First, find the slope of the equation. For this substitute (x₁, y₁) value and (x₂, y₂) values in the formula m=(y₂-y₁)/(x₂-x₁). We get,
[tex]\begin{aligned}m&= \frac{(y_2 - y_1)}{(x_2 - x_1)} \\&=\frac{(2.5 - (- 4.25))}{(0 - 4.5)}\\&= -1.5\end{aligned}[/tex]
Substitute, the value of slope and y-intercept in the general equation y=mx+c. We get, y=-1.5x+2.5.
The required answer is y=-1.5x+2.5.
The complete question is -
What is a linear function in the form y=mx+b for the line passing through (4.5, -4.25) with y-intercept 2.5?
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For f(x)=2/√10-6
Evaluate f (-6) = ?
The value of the function when evaluated is 1/2
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=2/√10-6
Express properly
So, we have the following representation
f(x)=2/√(10-x)
Substitute the known values in the above equation, so, we have the following representation
f(-6)=2/√10+6
Evaluate the like terms
f(-6)=2/√16
So, we have
f(-6) = 1/2
Hence, the function value is 1/2
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Question 8 of 10
A major arc will have a measure that is
OA. greater than 180°
B. less than 180°
C. equal to 180°
SUBMA
A. greater than 180°. A major arc is an arc of a circle that has a measure greater than 180°.
What is arc?Arc is a curved line which is part of the circumference of a circle or other curved shape. In mathematics, an arc is defined as a continuous segment of a circle. It is a line that joins two points on a circle's circumference. The length of an arc is proportional to the circle's circumference and is measured in radians or degrees. An arc can also be a part or section of a different type of curve such as an ellipse or parabola.
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find the product of (x+7)^2
Answer:
The product of (x+7)^2 is (x+7)(x+7) = x^2 + 14x + 49
Step-by-step explanation:
nine billion is how much greater than one hundred million? : * a) 8.9 x 10 9 b) 9.1 x 1 9 c) 8.999 x 10 9 d) 9.0 x 10 9
As per the given number nine billion is 8.9 x 10⁹ greater than one hundred million
Numbers are a fundamental part of our lives and the world around us. Understanding how to compare and perform arithmetic with large numbers is an important skill.
In this question, we are comparing two large numbers: nine billion and one hundred million.
The correct answer is (a) 8.9 x 10⁹.
The number nine billion can be written as
=> 9 x 10⁹,
where 10⁹ means 10 raised to the 9th power, or 10 multiplied by itself 9 times, which is equal to 1,000,000,000.
Meanwhile, one hundred million can be written as 100 x 10⁶, or 100 million.
To compare these two numbers, we subtract 100 million from nine billion, which gives us 8.9 x 10⁹.
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i just want to know the Answer for fun lol I will give brain list what is one third divided by seven with an explanation
Answer:
1/21
Step-by-step explanation:
1/3 divided by 7
= 1/3 x 1/7
= 1/21
Which statement explains how the lines x + y = 2 and y = x + 4 are related?
A. they are parallel
B. they are perpendicular
C. they are the same line
D. they are not related
Answer: B: They are perpendicular
Step-by-step explanation:
First, you have to convert the equations into y=mx+b form; thankfully, one is already done for us. x+y=2, to convert into y=mx+b form, you have to subtract x. then y=2-x, or in other words, y=-x+2. now that the equations are both in y=mx+b form, we can start graphing them. As I don't have a phone, I will try my best to explain how it is graphed rather than take a picture. For the first equation, y=-x+2, it will start at the height of 2 units. since we can substitute values for x, we can substitute x for 1, and immediately we have to multiply 1 by -1, which is -1. add 2 to -1, and you get 1. so when x increases by 1, y decreases by 1. This trend will continue with different numbers. The second equation, or y=x+4, is pretty straightforward. the y-value starts at a height of 4, and every time the x-value increases by 1, so does the y-value. Now notice how these equations have different meanings, and slopes. this means that they aren't parallel as they don't have the same slope, and they cannot be the same line as they are different equations. This only leaves B or D. When you graph it, you see that the two equations form two lines that cross together and form 4 90-degree angles, which is exactly what perpendicular means. Hope this helps!
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x ≈ 2.8
Step-by-step explanation:
using the sine ratio in the right triangle
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{PQ}{OQ}[/tex] = [tex]\frac{1.8}{x}[/tex] ( multiply both sides by x )
x × sin40° = 1.8 ( divide both sides by sin40° )
x = [tex]\frac{1.8}{sin40}[/tex] ≈ 2.8 ( to the nearest tenth )
Answer:2.8
Step-by-step explanation:
By using sine ratio , sine40°=opposite/hypotenuse
or, sine40°= 1.8/
or, x= 1.8/sine40°
or,x= 2.8003.......
or,x =2.8
how many free variables does each augmented matrix have?
The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an [tex]$m \times n$[/tex] matrix on the left side has n free variables.
An augmented matrix is composed of two parts, the left side and the right side. The left side is an [tex]$m \times n$[/tex] matrix, where m is the number of rows and n is the number of columns. The right side is a column of constants. The number of free variables in an augmented matrix is equal to the number of columns in the left side matrix, which is n.
The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an[tex]$m \times n$[/tex] matrix on the left side has n free variables.
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Which expression has a term with a coefficient greater than 1?
The expression that has a term with a coefficient greater than 1 is
3) 5 + 3m.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
We know a coefficient is a constant term that is with a variable.
By observing the given options we conclude that the expression
5 + 3m has a coefficient which is 3 and it is greater than 1.
Q. Which expression has a term with a coefficient greater than 1?
1) m -5×3.
2) 5 + m.
3) 5 + 3m.
4) 5/6m + 3.
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