To solve the given linear system, we can use the Gaussian elimination method. This method involves reducing the given matrix to a row echelon form and then solving for the variables using back substitution.
Step 1: Reduce the given matrix to a row echelon form by performing elementary row operations.
\[ \left[\begin{array}{rrr|r} 6 & 2 & -3 & 0 \\ -5 & 3 & 9 & 0 \\ 2 & -7 & -1 & 0 \end{array}\right] \]
We can start by dividing the first row by 6 to get a leading 1:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ -5 & 3 & 9 & 0 \\ 2 & -7 & -1 & 0 \end{array}\right] \]
Next, we can add 5 times the first row to the second row and subtract 2 times the first row from the third row:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ 0 & \frac{16}{3} & \frac{17}{2} & 0 \\ 0 & -\frac{23}{3} & 0 & 0 \end{array}\right] \]
Finally, we can multiply the second row by $\frac{3}{16}$ and the third row by $-\frac{3}{23}$ to get a leading 1 in each row:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ 0 & 1 & \frac{51}{32} & 0 \\ 0 & 1 & 0 & 0 \end{array}\right] \]
Step 2: Use back substitution to solve for the variables.
From the third row, we have:
$x_2 = 0$
Substituting this into the second row gives us:
$x_3 = 0$
And substituting these values into the first row gives us:
$x_1 = 0$
Therefore, the solution to the given linear system is:
$x_1 = 0$, $x_2 = 0$, and $x_3 = 0$
This means that the given linear system has a unique solution at the origin.
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DBA QUESTION #3
How is the distributive property used when finding the product of two polynomials?
Give an example.
How are polynomials closed under multiplication?
Answer:
The distributive property is used when finding the product of two polynomials by distributing one polynomial to each term of the other polynomial. For example, if we wanted to multiply (3x - 4)(2x + 5), we would use the distributive property by first multiplying 3x(-4) and 2x(5) and then adding the results together.
Polynomials are closed under multiplication, meaning that when two polynomials are multiplied together, the result is always another polynomial. This is true because a polynomial is a combination of constants and variables raised to non-negative integer powers, and when two polynomials are multiplied, the result is a combination of constants and variables raised to non-negative integer powers, which is a polynomial.
I recently took a review test and it talked about amount of error (percent error) . The question said that , “the estimate number of balls in each bag was 86. It turned out to be 104. What is the percent of error? Round to the nearest tenth.” I wrote 17.3%. The teacher said it was wrong and claimed that you had to divide it by expected, not real. (Formula is (expected-real)/real.)) Can someone help me out, am I wrong or the teacher?
Percentage error is 17.30%, it can be said that the answer given by student is correct.
What is Percentage error?The percent error is the distinction between the estimated value and the actual value in relation to the actual value.
Estimated number of balls in each bag = 86
Real number of balls in the bag = 104
Percentage error = | ( estimated value - real value / real value ) | * 100
Percentage error = | ( 86 - 104 / 104 ) | * 100
Percentage error = | ( -18 / 104 ) | * 100
Percentage error = | - 17.30 | * 100
Percentage error = 17.30%
Thus, it can be said that the answer given by student is correct.
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Vinne Two weeks ago, the cost to fly from to was 210$. Now the cost is 300$. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Step-by-step explanation:
for % questions always find 100% and/or 1%.
everything else can be easily calculated out of these 2.
the original price of $210 = 100%, as we want to know how many % the new price is different from that.
100% = $210
1% = 100%/100 = 210/100 = $2.10
the new price is $300.
the difference is 300 - 210 = $90
how many % are $90 compared to the original price ?
well, as many as the times 2.1 (1%) fits into 90 :
90/2.1 = 42.85714286...%
that increase from $210 to $300 was 42.85714286...%.
an additional $50 baggage fee ?
we have to add this to the $300 and get $350 as new price.
that difference is now 350 - 210 = $140.
how many % are $140 compared to the original price ?
140/2.1 = 66.66666666...%
that increase from $210 to $350 was 66.66666666...%.
Please note that for 1 pound of bananas the cost is
$0.63/lb
(according to the US Bureau of Labor Statistics.) In 1939 , the cost of bananas was
14%
lower. Pam buys 5 pounds of bananas for children at the camp she works for. What would these bananas have cost in 1939?
The cost of 5 pounds of bananas in 1939 would have been $2.709.
According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.
Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb
Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb
Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709
Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.
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Create utilities for location and price combinations considering restrictions listed on the case study (200-level seats cannot be less than $60, 300-midcourt seats cannot be less than $35).
Based on the results,
1.which location & price combination is the best alternative to raise prices? Which location & price combination is the best alternative to lower prices?
2. How much could administration raise 300 mid-level seat prices to give them the same level of attractiveness as the next best alternative? Should they raise the prices to the calculated level? Please explain.
1. To raise prices, the best alternative is to increase the price of 200-level seats to $60 or higher. To lower prices, the best alternative is to reduce the price of 300-midcourt seats to $35 or lower.
2. Administration could raise 300 mid-level seat prices to make them as attractive as the next best alternative. To calculate the optimal level, the cost of the next best alternative (200-level seats) needs to be compared with the cost of the 300-midcourt seats. If the cost of the 300-midcourt seats is lower than the cost of the 200-level seats, administration should raise the price of the 300-midcourt seats to match the cost of the 200-level seats. The attractiveness of the two options should be assessed to determine if the 300-midcourt seats should be priced at the calculated level.
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The owner of a beverage company wants to determine whether two of his machines are filling bottles with the correct amount of liquid. He randomly selects 20 bottles filled by each of the two machines and measures the number of ounces that the bottles contain. The histograms below show the data. If the machines are designed to dispense between 5 and 6 ounces into a bottle, which machine appears to be doing a better job? Explain how you determined your answer.
Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.
What is histogram?The most common graph for displaying frequency distributions is a histogram.
To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.
Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.
Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.
This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.
Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.
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Your question seems incomplete, the probable complete question is:
A table of values for a one-to-one function is given. Find the
indicated value.
x
1
2
3
4
5
6
f(x)
7
9
3
0
4
1
f −1(0) =
The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. In other words, if f(x) = y, then f^-1(y) = x.
To find the inverse of a function from a table of values, we simply switch the x and y values. So, for the given table of values:
x | 1 | 2 | 3 | 4 | 5 | 6
---|---|---|---|---|---|---
f(x) | 7 | 9 | 3 | 0 | 4 | 1
The inverse function f^-1(x) would have the table of values:
x | 7 | 9 | 3 | 0 | 4 | 1
---|---|---|---|---|---|---
f^-1(x) | 1 | 2 | 3 | 4 | 5 | 6
Now, to find f^-1(0), we simply look for the value of x that corresponds to f^-1(x) = 0. From the table, we can see that f^-1(0) = 4.
Therefore, the answer is f^-1(0) = 4.
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Prove that these two statements have the same slope: y = -3x - 8 and 3x + y = -8
Answer:
When you make 3x + y = -8 into a slope intercept equation it will become the same question
3x + y = -8
-3x | -3x
y = -3x - 8
What is the future value of $2000 earning 18% interest,
compounded monthly, for 4 years? (Round your answer to two decimal
places.)
The future value of $2000 earning 18% interest, compounded monthly, for 4 years is $6,116.23.
To calculate the future value, we use the formula:
[tex]FV = P(1 + r/n)^{nt}[/tex]
Where:
FV is the future value
P is the principal amount ($2000)
r is the annual interest rate (18%)
n is the number of times the interest is compounded per year (12 for monthly compounding)
t is the number of years (4)
Plugging in these values, we get:
[tex]FV = 2000(1 + 0.18/12)^{12*4}[/tex]
FV = 6116.23
Therefore, the future value of $2000 earning 18% interest compounded monthly for 4 years is approximately $6,116.23. This means that if you invest $2000 today and earn 18% interest compounded monthly for 4 years, your investment will grow to $6,116.23 at the end of the 4-year period. It's important to note that the actual value may vary depending on the exact compounding method used by the bank or financial institution.
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Hellllllllllllllllp meeeeeeeeeeeee
Answer: Option B is the correct answer
Step-by-step explanation:
Area of lateral surface = 3 x Area of rectangle
The rectangle is of 5 inches wide and 14 inches long.
Area of rectangle = 5 x 14 = 70 square inches
Area of lateral surface = 3 x Area of rectangle
Area of lateral surface = 3 x 70 = 210 square inches
Option B is the correct answer.
Use the equation to complete an algebraic proof that proves the answer is x = 7/6. Write your proof in your journal and upload your answer. You will be awarded 5 points for the statements and 5 points for the reasons.
2x+6/5= 4x-3
Proofs
The given statement [tex]x = \frac76[/tex] can be proved by using the given equation.
What is Algebra?Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. tries to find solutions to equations that contain one or more unknown quantities. Although early mathematicians would not have been familiar with such a concept, the word "equation" is frequently employed to conveniently represent these operations when discussing the early history of algebra.
As per the given data:
[tex]\frac{2x+6}{5} = 4x -3[/tex]
Simplifying to evaluate the expression:
[tex]\frac{2x+6}{5} = 4x -3[/tex]
[tex]= 2x+6 = 5(4x -3)\\= 2x + 6 = 20x - 15\\= 18x = 21\\= x = \frac{21}{18}\\\\= x = \frac76[/tex]
Hence, the given statement [tex]x = \frac76[/tex] can be proved by using the given equation.
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Course... Penn State World... Dashboard (5) APA References P... FACTORING POLYNOMIALS Greatest common factor of three univariate monomials Find the greatest common factor of these three expressions. 28w,8w^(5), and 20w^(4)
The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.
The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.
First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.
Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.
Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.
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# 20 i
STRUCTURE Find the value of x for which PQ|| RS
P 2x + 4
Q
x =
3x + 5
Previous
13
R
14
S5
7
15
T
16
The value of the variable x for the similar triangles is equal to 3
How to evaluate the value of x for the similar trianglesThe triangles PTQ and STR are similar, this implies that the length ST of the smaller triangle is similar to the length PT of the larger triangle
and the length RT of the smaller triangle is similar to the length QT of the larger triangle
so;
5/(2x + 9) = 7/(3x + 12)
5(3x + 12) = 7(2x + 9) {cross multiplication}
15x + 60 = 14x + 63
15x - 14x = 63 - 60 {collect like terms}
x = 3.
Therefore, the value of the variable x for the similar triangles is equal to 3
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david is filling five 3/4 quart bottles wich a sports drink his measuring cup only holds 1/4 quart. how many times will david need to fill the measuring cup in order to fill the 5 bottles
David will need to fill the measuring cup 15 times in order to fill the 5 bottles.
What does measurement mean?An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.
Each bottle holds 3/4 of a quart, and his measuring cup holds 1/4 of a quart.
David will have to fill his measuring cup 3 times in order to fill 1 bottle of capacity 3/4 quarts.
For 5 bottles, it will be 3*5 times which results in 15 times.
Thus, David will need to fill the measuring cup 15 times in order to fill the 5 bottles.
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need help finding side length. asap pls
The missing side in the triangle has a length of 9.899.
What is the property of an isosceles triangle?In an isosceles triangle, the two sides are equal and the angles opposite to the two equal sides are also equal.
In the figure, ∠RQS = ∠RSQ =45°
Thus, it is an isosceles triangle with sides RQ=RS= 7
What is Pythagoras' theorem?
According to Pythagoras' theorem for a right-angled triangle:
Base² + Height²= Hypotensuse²
In the given figure: Base = 7 and Height = 7,
Thus, QS²= RQ² + RS²
QS² = 7² + 7²
QS = √98
=9.899
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Kendra’s water bottle contains 2 quarts of water.she wants to add drink mix to it, but he directions for the drink mix give the amount of water in fluid ounces.how many fluid ounces are in her bottle
By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:
64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.
So Kendra's water bottle holds 64 fluid ounces.
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Suppose g(x)=x+3/2. Evaluate g(g(1)) and g(g(g(1)))
Answer: g(g(1)) = 4 and g(g(g(1))) = 5 1/2
Step-by-step explanation:
We will first find g(1). To do so, we plug 1 in for x.
g(1) = (1) + 3/2 = 5/2 = 2 1/2
To find g(g(1)) we will plug in 5/2 for x.
g(g(1)) = (5/2) + 3/2 = 8/2 = 4
To find g(g(g(1))) we will plug in 4 for x.
g(g(g(1))) = (4) + 3/2 = 11/2 = 5 1/2
Hope this helps!
estimate the product of 3.8 and 11.9 by rounding
The product or multiple of 3.8 and 11.9 by rounding off (simplification) is equal to 45.22.
What is simplification in mathematics?Simplification means keeping it simple. In mathematics, it simplifies or simplifies formulas/fractions/problems into simpler forms. Simplify the problem with calculations and solutions.
Simplification generally means finding answers to complex calculations involving division, multiplication, square roots, cube roots, plus and minus numbers.
Why do we use simplification?Simplicity complicates deadpan, making it easier to understand and solve. Here are some advantages of solving a problem or equation by simplification.
It helps you solve your problem in fewer steps. Complex problems can be reduced to simpler forms by following the rules of simplification
According to the question:
3.8×11.9 = (38/10)×(119/10)
= 4522/100
= 45.22
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the two triangles in the diagram are similar there are 2 possible values for x
The possible values of x are 2 and 17
How to determine the possible values of xThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Similar triangles
In the triangles, we have the following possible equations
15/18 = 10/(10 + x)
10/18 = 15/(10 + x)
Solving the equations, we have
15/18 = 10/(10 + x)
150 + 15x = 180
15x = 30
x = 2
10/18 = 15/(10 + x)
100 + 10x = 270
10x = 170
x =17
Hence, the values of x are 2 and 17
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Complete Question
The two triangles in the diagram are similar there are 2 possible values for x
See attachment for image of the triangle
The median stock price for firms in the Camaro Stock Market is $30, and the standard deviation is $8.20. Assume that the stock prices are normally distributed.
(i) What is the probability a firm will have a stock price of at least $40?
(ii) How high does a stock price have to be to put a firm in the top 10%?
Do NOT use EXCEL
a) (i) 0.3112
(ii) 20.50
b) (i) 0.2112
(ii) 50.50
c) (i) 0.1112
(ii) 40.50
d) (i) 0.6112
(ii) 30.50
e) None of the answers are correct
The probability a firm will have a stock price of at least $40 is 0.1112. There should be 40.50 stock price have to be to put a firm in the top 10%. The correct answer is e) None of the answers are correct.
(i) To find the probability that a firm will have a stock price of at least $40, we need to find the z-score for $40 and use the standard normal table to find the corresponding probability. The z-score is calculated as (x - μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this case, the z-score for $40 is (40 - 30)/8.20 = 1.22. Using the standard normal table, we find that the probability of a z-score less than 1.22 is 0.8888. Therefore, the probability of a stock price of at least $40 is 1 - 0.8888 = 0.1112.
(ii) To find the stock price that puts a firm in the top 10%, we need to find the z-score that corresponds to the 90th percentile in the standard normal table. The z-score for the 90th percentile is 1.28. We can then use the formula x = μ + zσ to find the stock price that corresponds to this z-score. In this case, the stock price is 30 + 1.28(8.20) = 40.50.
Therefore, the correct answer is (i) 0.1112 and (ii) 40.50.
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Rewrite the expression in terms of ln 3 and ln 4.
ln(144)
ln(144) can be written in terms of ln(3) and ln(4) as:
ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)
We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).
First, we can find the prime factorization of 144:
[tex]144 = 2^4 * 3^2[/tex]
Using the property above, we can rewrite ln(144) as:
[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]
Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):
ln(144) = 4 ln(2) + 2 ln(3)
Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:
ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)
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For the points(2,73)and(−22,3), (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Part 1 of 2 (a) The exact distance between the points is Part 2 of 2 (b) The midpoint is
For Part 1 of 2 (a): The exact distance between the points (2,73) and (-22,3) is 74.
For Part 2 of 2 (b): The midpoint of the line segment whose endpoints are the given points is (−10,38).
(a) The exact distance between the points is found using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:
d = √[(-22 - 2)² + (3 - 73)²]
Simplifying:
d = √[(-24)² + (-70)²]
d = √[576 + 4900]
d = √[5476]
d = 74
Therefore, the exact distance between the points is 74.
(b) The midpoint of the line segment whose endpoints are the given points is found using the midpoint formula:
M = [(x1 + x2)/2, (y1 + y2)/2]
Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:
M = [(2 + (-22))/2, (73 + 3)/2]
Simplifying:
M = [(-20)/2, (76)/2]
M = [-10, 38]
Therefore, the midpoint is (-10, 38).
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The graph of f(x)=x^2 was transformed to create g(x)=2/3x^2 Mark the statement. True or False
The graph of g(x) will be wider than f(x)
Graph of g(x) will be wider than f(x) is false.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The graph of f(x)=x² was transformed to create g(x)=2/3x².
The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.
This means that the graph of g(x) will be narrower than the graph of f(x), not wider.
Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).
Hence, graph of g(x) will be wider than f(x) is false.
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You have $109 in the bank and your parents just gave you $281 for your birthday. Now you have exactly enough money to buy a laptop. How much does the laptop cost? Write an equation to represent the question. Use x as the variable.
Answer:
$109+$281=x when x=391
so that means a laptop equals $391 dollars
Are the ratios 3:6 and 2:4 equivalent? ) yes no
Answer:
Yes, the ratios 3:6 and 2:4 are equivalent because they represent the same proportion. To confirm, we can simplify both ratios to their simplest form:
3:6 can be simplified by dividing both terms by 3: 3/3 : 6/3 -> 1:2
2:4 can be simplified by dividing both terms by 2: 2/2 : 4/2 -> 1:2
Since both ratios simplify to the same ratio, 1:2, they are equivalent.
Answer: yes !!
Step-by-step explanation: 3:6 and 2:4 are equivalent b/c of their common factors.
18. To find the perimeter of a regular octagon, use the
expression 8s, where s represents side length. If the
side length of a regular octagon is 1. 5 feet, what is
its perimeter in feet?
The perimeter of a regular octagon, we use the expression 8s, where s represents side length. The perimeter of a regular octagon with side length 1.5 feet is equals to the 12 feet.
Regular octagon is a polygon with eight sides. The perimeter of a polygon is equals to the sum of all its sides. All eight sides of regular octagon are same measure. So, in other words the perimeter of Regular octagon is equal to eight times the length its side. Here,
Side length of a regular octagon
= 1.5 feet
=> Perimeter = 8 × 1.5 feet [An octagon has 8 sides]
=> Perimeter = 12 feet
Hence, required perimeter is 12 feet.
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area of a triangle that is 34in base. and 14in height.
Answer:
Step-by-step explanation:
A=[tex]\frac{1}{2}[/tex]bh
=[tex]\frac{1}{2}[/tex]×34×14
=238 in²
For each of the following statements, indicate if it is true or false. Write T for a true statement, and F for a false statement. You will receive 1 point for every correct answer and .5 negative points for every incorrect answer (but you cannot receive a negative mark on this question). (a). If A is an m x n matrix and B is an n x n matrix, where m
The given statement " If A is an m x n matrix and B is an n x n matrix, then A × B is an m x n matrix" is True. Correct answer of (a) is T.
This statement is definately true because, it helps to consider the dimensions of a matrix. The dimensions of a matrix refer to the number of rows and columns it contains. In the case of an m x n matrix (A) and an n x n matrix (B), the dimensions of A are m rows and n columns, while the dimensions of B are n rows and n columns.
When A is multiplied by B, the result is an m x n matrix, meaning it contains m rows and n columns. This is due to the fact that the number of columns of the first matrix (A) must equal the number of rows of the second matrix (B) in order for the matrices to be compatible for multiplication.
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the base of a parallelogram is one third its height if the area is 768 square cm find the base and height
The base and height of the parallelogram is B = 16 cm and H = 48 cm
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be represented as A
Now , area of parallelogram A = bh
And , base of a parallelogram is one third its height
So , B = ( 1/3 )H
And , area of parallelogram is A = 768 cm²
On simplifying , we get
768 = ( 1/3 )H²
Multiply by 3 on both sides , we get
H² = 2304
Taking square roots on both sides , we get
H = 48 cm
So , the height of the parallelogram is 48 cm
And , the base of the parallelogram is 16 cm
Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively
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Equation: 4P + 5O2 → 2 P2O5
How many moles of P2O5 are formed from 3.4 grams of O2? Show the math
90 POINTSSSS!!! :)
The mass of the P₂O₅ formed from 3.4 moles of O₂ gas is equal to 386.1 g.
What is a mole?A mole can be described as a unit for measurement of a huge number of quantities of atoms, molecules, ions, or other particles. The atomic mass can be expressed as the one mole of any element.
The number of particles present in one mole was to be equal to 6.023 × 10 ²³ which is Avogadro’s constant.
Given, the number of moles of O₂ gas = 3.4 moles
The balanced chemical reaction of phosphorous and oxygen gas can be given as:
4 P + 5 O₂ → 2 P₂O₅
5 mol of Oxygen reacts with moles of P₂O₅ = 2 mol
3.4 mol of O₂ gas reacts with moles of P₂O₅ = (2/5) × 3.4 = 1.36 mol
The mass of the 1.36 mol of P₂O₅ = 1.36 × 283.89 = 386.1 g
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