Gauss-Seidel Method:
Iteration 1:
Starting with x(0) = [0, 0], we can substitute the initial values into the system of equations:
3(0) + 1(0) + 3x₂(1) + 6x₂(0) + 2x₂(0) = 0 -> 3x₂ = 0
3(0) + 3x₂(1) + 7x₂(0) = 4 -> 3x₂ = 4
Solving these equations, we find x(1) = [0, 4/3].
Iteration 2:
Using the updated values from the previous iteration, we have:
3x₁(1) + x₂(0) + 3x₂(1) + 6x₂(4/3) + 2x₂(4/3) = 0 -> 3x₁ + 16x₂ = -16/3
3x₁(1) + 3x₂(1) + 7x₂(4/3) = 4 -> 3x₁ + 19x₂ = 16/3
Solving these equations simultaneously, we obtain x(2) ≈ [-16/15, 8/15].
Iteration 3:
Using the updated values from the previous iteration:
3x₁(-16/15) + x₂(8/15) + 3x₂(-16/15) + 6x₂(8/15) + 2x₂(8/15) = 0 -> 3x₁ + 32x₂ = -16/5
3x₁(-16/15) + 3x₂(8/15) + 7x₂(8/15) = 4 -> 3x₁ + 19x₂ = 16/3
Solving these equations, we find x(3) ≈ [-16/35, 16/35].
After three iterations of the Gauss-Seidel method using the given initial value x(0) = [0, 0], we obtain an approximate solution of x(3) ≈ [-16/35, 16/35].
Jacobi's Method:
Iteration 1:
Starting with x(0) = [0, 0], we can update each component separately:
x₁(1) = (0 - (1(0) + 3x₂(0)) / 3 -> x₁ = 0
x₂(1) = (4 - (3x₁(0) + 7x₂(0))) / 3 -> x₂ = 4/3
Hence, x(1) = [0, 4/3].
Iteration 2:
Using the updated values from the previous iteration:
x₁(2) = (0 - (1(0) + 3x₂(4/3)) / 3 -> x₁ ≈ -16/15
x₂(2) = (4 - (3x₁(0) + 7x₂(4/3))) / 3 -> x₂ ≈ 8/15
Therefore, x(2) ≈ [-16/15, 8/15].
Iteration 3:
Using the updated values from the previous iteration:
x₁(3) = (0 - (1(-16/15) + 3x₂(8/15)) / 3 -> x₁ ≈ -16/35
x
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a30 arithmetic sequence of 1,-4,-9,-14
The 30th term a30 of the sequence is -1445
How to determine the value of a30?The definition of the function is given as
arithmetic sequence of 1,-4,-9,-14
The above definitions imply that we simply subtract 5 from the previous term to get the current term
Using the above as a guide,
so, we have the following representation
First term, a = 1
Common difference, d = 5
An arithmetic sequence is represented as
a(n) = a + (n - 1)d
For the 30th term, we have
a(30) = a + 29d
So, we have
a(30) = 1 + 29 * -5
Evaluate
a(30) = -144
Hence, the value of a30 is -144
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Determine whether the value given is a parameter or statistic In a sample of students who passed statistics, 70% used statistics in their future careers
Answer:
Statistic
Step-by-step explanation:
Statistic: numbers that summarize data from a sample
Parameter: numbers that summarize data for an entire population
a tank contains 1000 l of pure water. brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 lymin. brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 lymin. the solution is kept thoroughly mixed and drains from the tank at a rate of 15 lymin. how much salt is in the tank (a) after t minutes and (b) after one hour?
According to the information we can infer that the rate of salt in the water is: 0.65 Kg/min.
How to find the rate of salt in the water?To find the rate of salt in the water we must perform the following mathematical operation:
Rate in = 0.05lg/L * 5 L/min + 0.04 kg/L * 10 L/minRate in = 0.25 kg/min + 0.4 kg/minRate in = 0.65 kg/minAccording to the above, to find the amount of salt that is draining from the tank per minute we must multiply the value of 0.65kg/min. For example, in the case of being an hour (60 minutes).
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I need help this is due soon. Answers maybe...
Answer:
points you can use : (0,0), (1,4), (2,8)
Step-by-step explanation:
When 30 passengers, each with average mass of 80 kg , board the car, how much does the car move down on its spring suspension? assume that each wheel supports 1 / 8 the weight of the car.
The car move down on its spring suspension by the length of 0.0001501 m.
Define the term spring constant?The spring's stiffness is indicated by the spring constant, k. Higher spring constants are found in stiffer (harder to stretch) springs. An object's displacement is a distance calculation that expresses the deviation from its equilibrium or normal position.Acceleration due to gravity g = 9.81 m/s²
Spring constant k = 2.8×10⁷N/m.
Compression of spring x.
Force (F) = mg
Mass of the car is ;
m = 80 x 30
m = 2400 kg
Mass supported by the each spring,
m = 2400/8 = 300 kg
Put the value in force of spring;
F = kx
x = F/k = mg/k
x = (300 x 9.81)/ 2.8×10⁷
x = 0.0001501 m
Thus, the car move down on its spring suspension by the length of 0.0001501 m.
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The complete question is-
A passenger railroad car has a total of 8 wheels. Springs on each wheel compress--slightly--when the car is loaded. Ratings for the car give stiffness per wheel (the spring constant, treating the entire spring assembly as a single spring) as 2.8×10⁷N/m.
When 30 passengers, each with average mass of 80 kg, board the car, how much does the car move down on its spring suspension? Assume that each wheel supports 1/8 the weight of the car.
I toss a fair coin until it lands 15 heads in total. What is the probability that I make exactly 30 tosses altogether? Please express your answer in terms of factorials.
The probability of making exactly 30 tosses to obtain a total of 15 heads can be expressed in terms of factorials.
To find the probability, we need to consider the specific arrangement of heads and tails within the 30 tosses. In this case, we want exactly 15 heads out of 30 tosses.
The probability of getting a head in a single toss is 1/2, as the coin is fair. Therefore, the probability of getting exactly 15 heads in 30 tosses can be calculated using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Where:
- n is the total number of tosses (30 in this case),
- k is the number of successful outcomes (15 heads),
- (n choose k) is the binomial coefficient, calculated as n! / (k! * (n - k)!),
- p is the probability of a successful outcome (1/2 for a fair coin).
For this problem, the probability can be calculated as:
P(X = 15) = (30 choose 15) * (1/2)^15 * (1 - 1/2)^(30 - 15)
Using factorials, the calculation can be simplified. The binomial coefficient (30 choose 15) can be expressed as:
(30 choose 15) = 30! / (15! * (30 - 15)!)
By substituting the values and evaluating the expression, we can find the probability of making exactly 30 tosses and obtaining 15 heads.
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Please help quick will give brainliest!
============================================================
Explanation:
The information that b < d tells us that the degree of the numerator is smaller than the degree of the denominator. The denominator outgrows the numerator. I suggest looking at a table of values (select random positive integers for a,b,c,d where b < d).
So it's effectively similar to the end behavior of y = 1/x. As x gets larger, y approaches 0. Or you could look at something like y = (x^2)/(x^3) and it's the same idea.
Because r(x) approaches 0, this means we have a horizontal asymptote at y = 0.
what is the equation of y=x^3 with the given transformations
Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.
2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.
3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.
4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.
5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.
6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.
Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
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What is the rule for the line
Answer:
B
Step-by-step explanation:
the slope is negative and the y intercept is -1
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solve the equation |x|=3
Answer:
x= -3 or 3
Step-by-step explanation:
when a number is in those bars, it needs to find absolute value, and since we know the absolute value already, we can guess that its either -3 or 3.
PLS give me brainliest :(
____________________________->
Answer: 3
Step-by-step explanation: all its doing is asking for the positive of x which is 3
The population of a city is modeled by the function \(y = 35000(0.94) {}^{t} \)where y is the population of the city after t years starting in the year 2000 in what year will the population be 5,000
Solution
The population of a city is modeled by the function
\(y=35000(0.94)^t\)where y is the population of the city after t years starting in the year 2000
\(y=35000(0.94)^t\)In what year will the population be 5000
\(\begin{gathered} y=35000(0.94)^t \\ when\text{ y =5000} \\ t=? \end{gathered}\)\(\begin{gathered} y=35000(0.94)^t \\ 5000=35000(0.94)^6 \\ \frac{5000}{35000}=\frac{35000}{35000}(0.94)^t \\ \frac{1}{7}=0.94^t \end{gathered}\)\(\begin{gathered} ln0.1428=ln(0.94)^t \\ ln0.1428=tln(0.94) \\ -1.946=t(-0.06188) \\ t=-\frac{1.946}{-0.06188} \\ t=31.448 \\ t\approx32 \end{gathered}\)Therefore in 32 years time the population will be 5000
A furniture maker is gathering the supplies required to make 8 chairs and 1 table. The table will require 40 pounds of lumber. The furniture maker needs a total of more than 160 but less than 200 pounds of lumber. What is one possible value for the fraction of lumber required for each chair?
Answer:
To solve this problem, you can set up an equation using the given information. Let "x" be the fraction of lumber required for each chair.
We are told that the furniture maker needs a total of more than 160 but less than 200 pounds of lumber, and that the table will require 40 pounds of this lumber. Therefore, the chairs will require a total of more than 160 - 40 = 120 but less than 200 - 40 = 160 pounds of lumber.
Since there are 8 chairs, this means that each chair requires a fraction x of the total amount of lumber. We can write this relationship as:
8x > 120
8x < 160
To solve for x, you can divide both sides of both inequalities by 8:
x > 15
x < 20
Therefore, one possible value for the fraction of lumber required for each chair is any number between 15 and 20, including 15 and 20. For example, 18 is a possible value.
Answer:
20 pounds. Fraction can be 20/1.
If this help please set brainliest.
Step-by-step explanation:
We know that the furniture maker needs 40 pounds of lumber for the table and more than 160 pounds of lumber in total. This means that the furniture maker needs at least 40+160=200 pounds of lumber in total.
Since the furniture maker needs less than 200 pounds of lumber in total, the total amount of lumber needed for the chairs must be less than 200-40=160 pounds.
The fraction of lumber required for each chair is the total amount of lumber required for the chairs divided by the number of chairs. If the furniture maker needs less than 160 pounds of lumber for the chairs and is making 8 chairs, then the fraction of lumber required for each chair must be less than 160/8=20 pounds.
Therefore, one possible value for the fraction of lumber required for each chair is 20 pounds.
find the area of the triangle 18.94 ,67 9.32
Answer:
find the area of the triangle 18.94,67 9.32
Let f(x, y) = A(x2 + y2) in 0 < x < 1 and 0 Sy < 3.
(a) Determine the value of the constant A that makes f(x,y) a joint probability density function. (b) Compute P (x ≤ 1/2,Y≥2).
(a) To make f(x, y) a joint probability density function, we need to find the value of the constant A.
(b) To compute P(x ≤ 1/2, Y ≥ 2), we need to integrate f(x, y) over the given region and find the probability.
(a) For f(x, y) to be a joint probability density function, it must satisfy two conditions: non-negativity and total probability of 1.
The non-negativity condition implies that A(x² + y²) ≥ 0 for all values of x and y. Since x² and y² are always non-negative, we need A to be non-negative as well.
The total probability condition requires that the double integral of f(x, y) over the given region is equal to 1. The given region is 0 < x < 1 and 0 < y < 3.
∫∫R f(x, y) dA = 1
∫[0 to 1] ∫[0 to 3] A(x² + y²) dy dx = 1
Integrating with respect to y first:
∫[0 to 1] [Axy² + Ay³/3] evaluated from 0 to 3 dy dx = 1
∫[0 to 1] [3Ax + 9A/3] dx = 1
∫[0 to 1] (3Ax + 3A) dx = 1
[3A(x²/2) + 3Ax] evaluated from 0 to 1 = 1
3A(1/2) + 3A - 0 = 1
3A/2 + 3A = 1
Simplifying the equation:
9A/2 = 1
A = 2/9
Therefore, the value of the constant A that makes f(x, y) a joint probability density function is A = 2/9.
(b) To compute P(x ≤ 1/2, Y ≥ 2), we need to integrate f(x, y) over the given region.
P(x ≤ 1/2, Y ≥ 2) = ∫∫R f(x, y) dA
Here, R is the region where 0 < x < 1 and 2 < y < 3.
∫[0 to 1/2] ∫[2 to 3] A(x² + y²) dy dx
Integrating with respect to y first:
∫[0 to 1/2] [Axy² + Ay³/3] evaluated from 2 to 3 dx
∫[0 to 1/2] [Ax(3²) + A(3³)/3 - Ax(2²) - A(2³)/3] dx
∫[0 to 1/2] [9Ax + 27A/3 - 4Ax - 8A/3] dx
∫[0 to 1/2] [5Ax + 19A/3] dx
[5A(x²/2) + 19Ax/3] evaluated from 0 to 1/2
[5A(1/2²/2) + 19A(1/2)/3] - [0] = [5A/8 + 19A/6]
Simplifying the expression:
[15A/24 + 38A/24] = 53A/24
Substituting the value of A = 2/9:
53(2
/9)/24 = 53/108
Therefore, P(x ≤ 1/2, Y ≥ 2) is approximately equal to 0.4907.
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A small truck can hold a total of 40 crates and boxes. For every 3 crates the truck can hold, there is room for 5 boxes. How many crates and boxes are in the truck when it is completely full?
Answer: There are 25 crates and 15 boxes in the truck when it is full.
Step-by-step explanation:
Let c= Number of crates , b= Number of boxes.
As per given,
\(c+b = 40\) (i)
\(3c=5b\\\\\Rightarow\ c=\dfrac{5b}{3}\) (ii)
Put value of c from (ii) in (i)
\(\dfrac{5b}{3}+b = 40\\\\\Rightarrow\ \dfrac{5b+3b}{3}=40\\\\\Rightarrow\ \dfrac{8b}{3}=40\\\\\Rightarrow\ 8b=3\times40\\\\\Rightarrow\ 8b=120\\\\\Rightarrow\ b=\dfrac{120}{8}=15\)
put value of b in (ii),
\(c=\dfrac{5\times15}{3}=5\times5=25\)
Hence, there are 25 crates and 15 boxes in the truck when it is full.
25 boxes 15 crates
We would get this solution by adding up the two sides comparing the ratios, hence: we get room for 3 crates for every 5 boxes that we can hold in the truck.
What are ratios?A ratio is an ordered pair of numbers a and b, written a:b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. hence, if there is 3 crates and 5 boxes you could write the ratio as: 3 : 5 (for every 3 crates there are 5 boxes) 3 / 5 are boys and 5 / 3 are crates.
(b) Problem 15: Find the rate of change for this two-variable equation. y-x = 10
The rate of change for the equation y - x = 10 is 1.
To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.
We can rewrite the equation as y = x + 10 by adding x to both sides.
Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.
In other words, as x increases by 1 unit, y will increase by 1 unit as well.
As a result, 1 represents the rate of change for the equation y - x = 10.
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8. Given the following points, determine whether Triangle ABC is a right triangle. HINT use the distance formula!
A (0, 0)
B (-4,5)
C (3,-2)
Length of AB
Length of AC =
Length of BC =
Is triangle ABC right?
Which expression represents the volume, in cubic units, of the frustum? one-thirdπ(7.52)(11) – one-thirdπ(3.52)(8) one-thirdπ(7.52)(11) one-thirdπ(3.52)(8) one-thirdπ(7.52)(19) – one-thirdπ(3.52)(8) one-thirdπ(7.52)(19) one-thirdπ(3.52)(8)
The expression that represents the volume of the frustum, Volume of larger cone - volume of smaller cone, is: C. ⅓π(7.5²)(19) - ⅓π(3.5²)(8) .
What is the Volume of a Frustum?Volume of a frustum = Volume of larger cone - volume of smaller cone = ⅓π(R²)(H) - ⅓π(r²)(h)
Given the cone in the digram below with the following parameters:
R = 7.5 units
H = 8 + 11 = 19 units
r = 3.5 units
h = 8 units
Volume of the frustum = ⅓π(7.5²)(19) - ⅓π(3.5²)(8)
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Answer:
C. Edge
Step-by-step explanation:
Find the perimeter of the steel plate shown in the figure. Be sure to take into account allcircular cuts made.7"2"radiusradius10"-8"
To find the perimeter of the given steel plate:
1. Find the circular lengths; use the formula of the circumference of a circle and divide it in to 4 to find the length of those parts (those parts are quarter of circle):
Quarter circle part with radius 2"
\(\begin{gathered} C=2\pi r \\ C=2\pi(2") \\ C=4\pi \\ \\ Divide\text{ into 4:} \\ \frac{4\pi}{4}=\pi \end{gathered}\)Quarter circle part with radius 1"
\(\begin{gathered} C=2\pi(1") \\ C=2\pi \\ \\ Divide\text{ into 4:} \\ \frac{2\pi}{4}=\frac{1}{2}\pi \end{gathered}\)2. Add the lengths of each side of the plate to find its perimeter:
\(\begin{gathered} P=10"+7"+7"+6"+\pi"+\frac{1}{2}\pi" \\ \\ P=30"+\frac{3}{2}\pi" \\ \\ P\approx34.71" \end{gathered}\)Then, the perimeter of the plate is:Exact answer: 30"+3/2 π"Approximate answer: 34.71"Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make a 12% detergent solution. Which
equation can she use to find g, the number of gallons of water she should add?
Answer: 1.98/11+g = 12/100
Answer:
D \(\frac{1.98}{11+g} =\frac{12}{100}\)
Step-by-step explanation:
edge
Help please !!!????asap please
11 books
Step-by-step explanation:
I did 1,048-32x
What is the radius of the sector of the circle below, if the area is 30.39 m^2 and the central angle < AOB measures 43 °. (round answer to the nearest whole meter)
Answer:
a. 9m
Step-by-step explanation:
Pi = 3.14 = 22/7
formula :
Area of a Sector of a Circle = (central angle)/360 * πr² =
(central angle)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r^2 = 30.39
r^2 = (30.39 * 360) / (Pi * 43)
r^2 = (30.39 * 360) / (22/7 * 43)
r = √ (30.39 * 360 * 7) / (22 * 43)
r = √76582.8/946
r = √80.9543340381
8.99746264444 which is roughly
9
The radius of the sector will be 9m. The correct option is A.
What is the arc length of the circle?The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.
The radius will be calculated as below:-
Area of a Sector of a Circle = (central angle)/360 * πr² =
(Ф)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r²= 30.39
r² = (30.39 * 360) / (Pi x 43)
r²= (30.39 x 360) / (22/7 x 43)
r = √ (30.39 x 360 x 7) / (22 x 43)
r = √76582.8/946
r = √80.9543340381
r = 9
Therefore, the radius of the sector will be 9m. The correct option is A.
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4x-5y=23
y=-3x+3
how do i do this
final IXL question, I dont understand the topic so please provide a slight explination.
Answer:
5.4
Step-by-step explanation:
Set up a proportion for the large and small figure
\(\frac{Large}{Small}\) = \(\frac{Large}{Small}\)
\(\frac{3}{2}\) = \(\frac{j}{3.6}\) cross multiply and solve for j
3(3.6) = 2j
10.8 = 2j Divide both sides by 2
\(\frac{10.8}{2}\) = \(\frac{2j}{2}\)
5.4 = j
What is the RACI matrix?
a. Resource Allocation & Cost Inventory matrix
b. Matrix of Responsible and Certified Individuals
c. Responsible, Accountable, Consult & Inform matrix
d. Recently Added Control Incident reporting matrix
The RACI matrix is the Responsible, Accountable, Consult & Inform matrix. It is a tool used in project management to clearly define the roles and responsibilities of team members in relation to a project.
c. Responsible, Accountable, Consult & Inform matrix
The RACI matrix is a tool used in project management to clearly define roles and responsibilities. It stands for Responsible, Accountable, Consulted, and Informed. Assigning these roles to individuals or teams, it ensures efficient allocation of resources and effective communication throughout the project.
The matrix identifies who is Responsible for a task, who is Accountable for its completion, who needs to be Consulted before decisions are made, and who needs to be Informed about progress. This helps to avoid confusion and ensure that resources are allocated appropriately, which can ultimately impact the cost of the project.
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Show the calculating process by the restoring-division
algorithm for the following division case:
Divisor 00011
Dividend 1011
The quotient is 1111. The process continues until the result is less than the divisor.
To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:
Step 1: Initialize the dividend and divisor
Divisor: 00011
Dividend: 1011
Step 2: Append zeros to the dividend
Divisor: 00011
Dividend: 101100
Step 3: Determine the initial guess for the quotient
Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.
Step 4: Subtract the divisor from the dividend
101100 - 00011 = 101001
Step 5: Determine the next quotient bit
Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
Step 6: Subtract the divisor from the result
101001 - 00011 = 100110
Step 7: Repeat steps 5 and 6 until the result is less than the divisor
Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
100110 - 00011 = 100011
Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
100011 - 00011 = 100001
Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
100001 - 00011 = 011111
Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.
011111 - 00000 = 011111
Step 8: Remove the extra zeros from the result
Result: 1111
Therefore, the quotient is 1111.
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Quiz 3.1
What is the degree and leading coefficient of the function Y (2) = 7x4 – x6 +3?
Leading Coefficient : 7 and Degree: 4
O Leading Coefficient: 7 and Degree: 6
Leading Coefficient: -1 and Degree: 4
O Leading Coefficient: -1 and Degree: 6
Answer:
Leading coefficient -1 and Degree 6
Step-by-step explanation:
Leading coefficients mean the number associated with the variable that has the highest degree in your question
\(Y=7x^2-x^6+3\)
The highest degree is 6 and the leading coefficient would the number associated with x^6 which is -1 so the last option is correct
what is this??? 28÷7×4=?
Answer: 16
Step-by-step explanation: 28÷7=4
4×4 = 16
r = -5 + 19. r = ?
Please help me with this
Answer:
r = 14
Step-by-step explanation:
r = -5 + 19
Simplify the right side by subtracting 5 from 19
r = 14
Flooring costs £10 per m². How much will it cost to buy enough flooring for this room?
Check the picture below.
\(18m^2~~ + ~~10m^2\implies 28m^2\hspace{5em}(\stackrel{m^2}{28})(\stackrel{\pounds}{10})\implies \text{\LARGE \pounds280}\)