The final equation in the system, and it can be used to solve for either x or y is x + 1.5y = 3
The pivot operation is used to solve linear equations. The operation starts by selecting a pivot element from a matrix. This pivot element is usually the first non-zero element in the first column of the matrix. The pivot element is then multiplied by a scalar to create a new equation. This new equation is then added to or subtracted from the other equations in the system to eliminate the coefficient of the pivot element. This process is repeated until the system of equations is solved.
For example, consider the following system of equations:
2x + 3y = 6
4x + 6y = 12
The first non-zero element in the first column is 2, so this will be our pivot element. To use the pivot operation, we multiply 2 by a scalar and add this new equation to the other equation. Let's use the scalar 4. This gives us:
8x + 12y = 24
Now we subtract this equation from the other equation to eliminate the coefficient of the pivot element:
2x + 3y = 6 - 8x - 12y = 24
This leaves us with:
-6x - 9y = 18
We now have an equation with only one variable. To solve for this variable, we can divide both sides by -6, giving us:
x + 1.5y = 3
This is the final equation in the system, and it can be used to solve for either x or y.
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Find the surface area of the equilateral triangular pyramid base is 16 height is 20
The surface area of a pyramid with a base equilateral triangle is 480 + 100√3 square inches.
What is the surface area of a pyramid?The total surface area (S) of a regular pyramid is given by the formula as
1/2 Pl + B ...... (i)
Here, p represents the perimeter of the base, l is the slant height, and B is the base area of the pyramid.
As per the question, we have
Side of equilateral triangle = 20 inches
The slant height of the pyramid(l) = 16 inches.
First, we have to determine the perimeter and Area of the base pyramid.
The perimeter of an equilateral triangle (p):
= 3 × side
= 3×(20)
= 60 inches
Area of an equilateral triangle (B):
= (√3/4) × side²
= (√3/4) × (20)²
= 100√3 square inches.
Substitute the above values in equation (i), and we get
The total surface area (S):
= 1/2 x 60 x 16 + 100√3
= 480 + 100√3 square inches
Hence, the surface area of the given pyramid is 480 + 100√3 square inches.
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Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19 ∘ ∘ to the plane at point � A. At some later time, she measures an angle of elevation of 37 ∘ ∘ to the plane at point � B. Find the distance the plane traveled from point � A to point � B. Round your answer to the nearest foot if necessary.
The plane travels a distance of 11710 feet from point A to point B.
What is Tangent function?Tangent function of an angle in a right angled triangle is defined as the ratio of the opposite side to the adjacent side.
The figure representing the situation is given below.
From triangle AOC,
tan 19° = AC / OC
tan 19° = 7425 / OC
OC = 7425 / tan 19°
OC = 21563.77 feet
Similarly for triangle BOD,
tan 37° = BD / OD
tan 37° = 7425 / OD
OD = 7425 / tan 37°
= 9853.31 feet
AB = CD
= OC - OD
= 21563.77 feet - 9853.31 feet
= 11,710.46 feet
≈ 11710 feet
Hence the distance plane travelled from point A to point B is 11710 feet.
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Convert the following decimal number to a fraction or mixed number: 6.4
Answer:
Step-by-step explanation:
well 6.4 converted to a fraction is 32/5 so i hope this helps.
6 ln(8x+1)-14=28 solve for the exact value of x
ln(8x+1) = (28+14)/6 = 7
8x+1 = e^7
8x = e^7 - 1
x = (e^7 - 1)/8
Answer:x=e^7-1/8
Step-by-step explanation:
6 ln(8x+1)-14=28
+14 +14
6 ln(8x+1) =42
6 ln(8x+1)/6 42/6
log e (x) = a-->e^a=x
8x+1=e^7
8x/8 =e^7-1/8
x=e^7-1/8
stephanie is drawing the layout of a parking lot on a coordinate grid and needs to verify that two sides meet in a right angle. in her sketch, one side of the parking lot has endpoints a(18,24) and b(50,0) . the second side of the parking lot has endpoints b(50,0) and c(0,0) . how can stephanie prove that the two sides of the parking lot meet in a right angle? select all that apply.
If Stephanie need prove that two sides of the parking lot meet in a right angle , then the options that apply are :
(a) Find the slopes of AC and CB. If the product of the slopes is -1, then the sides meet in a right angle. and
(e) Find AB, BC, and AC. If AB²+ BC² = AC² then the sides meet in a right angle.
The endpoints of the triangle parking are : A(0,0) , B(50,0) and C(18, 24) .
Option (a) : The slope of AC = (24-0)/(18-0) = 24/18 = 4/3 .
slope of CB = (0-24)/(50-18) = -24/32 = -3/4 .
the product of slope of AC and CB = -1 , hence the triangle is Right Triangle .
Option (e) : The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, the hypotenuse.
In this case, AB and BC would represent the two shorter sides and AC would represent the longest side. If AB² + BC² = AC², then the three sides form a right triangle and the two sides meet in a right angle.
Stephanie is drawing the layout of a parking lot on a coordinate grid and needs to verify that two sides meet in a right angle. In her sketch, one side of the parking lot has endpoints A(0,0) and B(50,0). The second side of the parking lot has endpoints B(50,0) and C(18, 24). How can Stephanie prove that the two sides of the parking lot meet in a right angle? Select all that apply.
(a) Find the slopes of AC and CB. If the product of the slopes is -1, then the sides meet in a right angle.
(b) Find the slopes of AB and AC. If the product of the slopes is -1, then the sides meet in a right angle.
(c) Find the slopes of CB and AB. If the slope of AB is the opposite of the slope of AC, then the sides meet in a right angle.
(d) Find AB, BC, and AC. If AB + BC = AC, then the sides meet in a right angle.
(e) Find AB, BC, and AC. If AB² + BC² = AC² then the sides meet in a right angle.
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Please help me on this question.
For what value of x is line m parallel to line n?
Answer:
x=42
Step-by-step explanation:
Step 1) 105=3x-21
Step 2) 126= 3x
Step 3) 42=x
Amir buys a car for £15095 which depreciates in value at a rate of 2.75% per year
Work out how much Amir's car will be worth in 4 years.
Answer: £13,741.69 will be the value in 4 years
Step-by-step explanation:
formula: present value * (1-depreciation rate)^years
15095*(1-0.0275)^4
=13,741.69
Determine all intervals on which the graph of f is decreasing.
f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
How do you find the decreasing interval on a graph?To find when a function is decreasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.
The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
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Using division, what is the quotient (3x³ + 4x - 32) = (x - 2)?
O 3x² + 6x - 16
O 3x² - 6x + 16
O 3x² + 6x + 16
O 3x² - 6x - 16 +
1
(x-2)
Answer:
3x² + 6x + 16
Step-by-step explanation:
Please answer number number 3 please :)
Answer:
3
negative infinity
negative infinity
Step-by-step explanation:
Real zeros are x values where the graph f(x) crosses the x-axis. Basically what values will you put in to get 0. There are 3 such values where the graph crosses the x axis.
You can see at we move right along the x -axis (x values towards infinity) the graph goes down and keeps going down, so we can say that it is going towards negative infinity in y direction because down is negative and up is positive. Same with the other side, as x values move towards left, graph moves down.
someone rolls a fair six-sided die and you win points equal to the number shown. what is the expected number of points after one roll? after 2 rolls? after 100 rolls?
All parts of the problem regarding die rolls have been solved and explained below.
In order to find the probability of getting any one point out of the 6 after rolling the die, we first need to Add up all of the number of points in the die, that is -
= 1+2+3+4+5+6
= 21.
We also know that after any roll of one die, the probability of getting about one particular point is 1/6.
So, the expected number of points after one roll can be calculated is-
= 21/6= 3.5
After two rolls, we can just twice the probability of it happening before-
= (2 x 21)/6 = 7.
Similarly, after 100 rolls = 350, and after N rolls, 3.5(N).
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assuming we know σ=5.5, construct a 85.0 percent confidence interval for the true population mean, μ, given that a random sample of 94 values was noted to have x¯=85.0.
The confidence interval is (84.41, 85.59), meaning that we are 85.0% confident that the true population mean, μ, lies between 84.41 and 85.59
How to construct the confidence intervalA 85.0% confidence interval for the true population mean, μ, can be constructed using the following formula:
x¯ ± (Zα/2 * σ/√n)
where
x¯ is the sample mean (85.0), Zα/2 is the critical value for a given confidence level σ is the population standard deviation (5.5)n is the sample size (94).Using the Z-score table for a confidence level of 0.85, we have
Zα/2 = 1.040.
Substitute the known values in the above equation, so, we have the following representation
CI = 85.0 ± (1.040 * 5.5/√94)
Evaluate
CI = 85.0 ± 0.59
This gives
CI = 84.41 to 85.59
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Does anyone know the answer to this question?
Express 220 as the product of its prime factors write the prime factors in ascending order and give your answer in ascending order
Answer:
Below
Step-by-step explanation:
220 = 2 x 110
= 2 x 2 x 55
= 2 x 2 x 5 x 11
Would appreciate a help with this question on how to do it. thanks :)
Which expression is equivalent to
Answer:
i believe it is the second answer choice
Step-by-step explanation:
An oven used 8.24 units of electricity over
5 hours.
What is the rate of electricity usage for this
oven in units per hour?
Give your answer to 1 d. p
The number of units of electricity used in one hour is 1.6
How to calculate the number of electricity used in one hour?An oven uses 8.24 units of electricity in 5 hours
The number of unit used in one hour can be calculated as follows
= 8.24/5
= 1.6
Hence 1.6 units of electricity was used in one hour
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however sums between 10 and 19 inclusive are forbidden
The result is true, the number is forbidden.
This rule can be expressed mathematically as:
10 ≤ x < 19
This statement is saying that any number x must be greater than or equal to 10, but less than 19. So if x is set to any number between 10 and 19, the statement will be false. For example, if x is set to 15, the statement becomes:
10 ≤ 15 < 19
Which is false. So any number between 10 and 19 is forbidden.
This can be calculated by first subtracting 10 from the number. For example, if the number is 17, we would subtract 10 to get 7. Since 7 is less than 19, the number is forbidden. We can also use this equation to check any given number:
x − 10 < 19
If the result is true, then the number is forbidden. For example, if x is set to 17, the equation becomes:
17 - 10 < 19
Which is true, so 17 is forbidden.
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Complete question:
What is the sum of any two numbers between 10 and 19?
you have 10 pairs of socks, five black and five blue, but they are not paired up. instead, they are all mixed up in a drawer. it's early in the morning, and you don't want to turn on the lights in your dark room. q1.1 sock drawer i 5 points grading comment: how many socks must you pull out to guarantee that you have a pair of one color?
The number of socks you pull out to have two black socks is 3 socks
Total number of pairs of socks in a drawer = 10
Number of black pairs of socks = 5
Number of blue pairs of socks = 5
A. If you picked 2 socks [black] and [blue] 3rd pick guarantees you will have one pair of either blue or black
The number of socks you pull out to guarantee that you have a pair of one color is 3 socks
B. If you want to pick 2 good pairs and your 6 picks are the worst case, so 7th pick of the socks will give you good pair of two colors.
The number of socks you pull out to have two good pairs is 7 socks
C. If you want to have a pair of black socks your worst case will be you pick all 10 blue socks so another 2 socks must be black.
Therefore, the number of socks you pull out to have two black socks is 12 socks.
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T varies s/t when
S =36, t =16, T=18
Find T when s=33, t=18
Answer:
Step-by-step explanation:
We are given that T varies as the square root of the ratio of s and t, and we are trying to find the value of T when s=33 and t=18.
The relationship between T, s and t can be represented by the following equation:
T = k * √(s/t)
Where k is a constant.
We are given that when S=36, t=16, T=18. We can use this information to find the value of k.
We know that T = k * √(s/t)
and, T = 18 when s=36, t=16.
So we can substitute these values in the equation
18 = k * √(36/16)
Solving for k, we get:
k = 18/2 = 9
Now that we know the value of k, we can use it to find the value of T when s=33 and t=18.
T = k * √(s/t) = 9 * √(33/18) = 9 * √(11/6) = 9 * √(11/6)
The value of T when s=33, t=18 is 9 * √(11/6),
It is not possible to give the exact value of T because the value of the square root of (11/6) is not a whole number.
PLEASE HELP! Based on the graph shown, which of the following statements is true?
Median is defined as the middle value in a given set of numbers or data. ... defined by a median. The repeated value of the given data is defined by mode.
Define median?
The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points.The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.Find n/2. Then find the class whose cumulative frequency is greater than and nearest to n/2. This is the median class.To learn more about median refers to:
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Correct option is C, The median 300, is the middle number.
The x-axis in the graph below depicts the numbers, and the y-axis the frequency.
Total = 72
The most frequent number is called the mode. The frequency that appears most frequently in the table above is 18 at 300. As a result, the data's mode is 300.
The frequency sum is 72, an even number.
N/2th term median
Mean = 72 / 2
average 36th term
We need to identify the number whose cumulative frequency is greater than 36 but less than 36 before it.
The graph's median value is 300.
Since the values of the median and mode are equal, median equals mode.
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what is the big-oh order of the following growth expression? f(n)=24n 2nlg(n) 280
The big-Oh order of the expression f(n) = 24n²nlogn + 280 is O(n²), which means that the time complexity of the algorithm is proportional to n².
The big-Oh order is a way of measuring the growth of a mathematical expression in terms of time complexity. It is used in computer science to analyze algorithms and to predict their performance.
In this case, we are looking at the big-Oh order of the expression f(n) = 24n²nlogn + 280.
To determine the big-Oh order, we need to find the dominant term in the expression, or the term that grows the fastest as the input size (n) increases.
In this expression, the dominant term is 24n²logn, since it grows much faster than the constant term 280.
Now, we can simplify the expression further. The logarithmic term is a much slower growing term compared to the polynomial term, so we can ignore it.
This means that the big-Oh order of the expression is O(n²), which means that the time complexity of the algorithm represented by the expression is proportional to n².
This means that the time taken by the algorithm will increase rapidly as the input size (n) increases.
Complete Question:
What is the Big-Oh order of the following growth expression?
f(n)=24n+2nlg(n)+280
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Which two statements can you use to distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words “east” and “west”?
Answer:
We can solve this by giving the velocities opposite signs.
Step-by-step explanation:
Traveling west at 5 miles per hour can be given a positive sign and traveling east is opposite to west on a straight line, so we can denote that with a negative sign.
Hence, we can distinguish the velocities without using the words "east" and "west" by giving the velocities opposite signs.
simplify (4/5a - 8) + ( -2/5a - 2/3)
Mrs. Ramirez is planning a family reunion and deciding where to buy food and drinks. She considers the information below. She expects 96 family members to attend. How much would it cost to buy 96 hotdogs purchased from Value Market? Show your work.
b) How much would 96 hotdogs cost from Sammy's Bulk Store? Show your work.
a) 96 hotdogs purchased from Value Market would cost $96. This is because Value Market sells hotdogs for $1 each. Therefore, 96 hotdogs would cost $96.
What is Value Market?Value Market is an investment approach that focuses on buying assets that have the potential to generate returns that exceed the market average over the long term. It involves buying stocks or other assets at a price lower than their intrinsic value, or the stock's true underlying worth. This approach requires investors to do extensive research and analysis to identify undervalued assets and purchase them at prices that are below their true worth.
b) 96 hotdogs purchased from Sammy's Bulk Store would cost $48. This is because Sammy's Bulk Store sells hotdogs in packs of 8 for $4 each. Therefore, 96 hotdogs would cost $48 (96/8 = 12 packs of 8 hotdogs, 12 x $4 = $48).
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increase £102 by 15%
£117.3
Step-by-step explanation:To increase an amount by a certain percentage, you can use the following formula:
New amount = original amount + (percentage increase x original amount)/100
In this case, to increase £102 by 15%:
New amount = 102 + (15/100) x 102 = 102 + 15.3 = £117.3
yeah that's it...
102 + 102 × 15/100 = £117.3
in exercises 35–38, are and parallel? and if so, do they point in the same direction?
Yes, the lines AB and PQ are parallel lines and have same direction.
Coordinates of the line AB and PQ :
A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)
Slope = (y₂ - y₁)/ (x₂ -x₁)
Substitute the value in the formula:
Slope of the line AB = ( 4 - 1 )/ ( 3 - 1 )
⇒ Slope of the line AB = 3 /2
Slope of the line PQ = ( 10 - 1 )/ ( 7 - 1 )
⇒ Slope of the line PQ = 9 /6
⇒ Slope of the line PQ = 3 /2
Slope of line AB and PQ are equal it implies they are parallel lines.
Therefore, both the lines AB and PQ are parallel lines to each other and are in the same direction.
The above question is incomplete , the complete question is:
Are lines AB and PQ parallel? And if so, do they point in the same direction? A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)
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if i subtract 20 from my number, then square the result, i get the same answer as, if i square my number, then subtract 20 from the result
Answer:
The number is 10.5.
Step-by-step explanation:
Let x be your number.
"i subtract 20 from my number,:" (x-20)
"square the result" : (x-20)^2
-------
"i square my number": x^2
"subtract 20 from the result": x^2 - 20
-----
The results are equal:
(x-20)^2 = x^2 - 20
x^2 -40x + 400 = x^2 - 20
-40x = -420
x = 10.5
==================
CHECK:
1) (x-20)^2 = ?
(10.5-20)^2 = 90.25
2) x^2 - 20 = ?
(10.5)^2 - 20 = 90.25
x=10.5 is correct
Answer:
[tex]\textrm{The number is: }\\\\\\ \rm{\boxed{\dfrac{21}{2}}\; or\; \boxed{10.5} \;in \;decimal}}[/tex]
Step-by-step explanation:
Let x be the number we have to determine
From the question description
[tex]\left(x-20\right)^2=\:x^2-20[/tex]
[tex]\mathrm{Expand\:}\left(x-20\right)^2:\quad x^2-40x+400[/tex]Answer:
[tex]\rm{\boxed{x = \dfrac{21}{2}}\; or\; \boxed{x = 10.5} \;in \;decimal}}[/tex]
Directions: Simplify by multiplying the expressions.
1. (X + 8) (x-8)
2. (y + 10) (Y-10)
3. (m-4)(m + 4)
4. (n - 9) (n + 9)
5. (3x + 1)(3x - 1)
6. (5c+4)(5c - 4)
7. (11z-7)(11z + 7)
8. (20x + 9) (20x-9)
9. (8x + 3y)(8x - 3y)
Answer:
[tex] 1.{x}^{2} - 64[/tex]
[tex]2. {y}^{2} - 100[/tex]
[tex]3. {m}^{2} - 16[/tex]
Answer:
1. (x + 8) (x - 8) = x^2 - 64
2. (y + 10)(Y - 10) = y^2 - 100
3. (m - 4)(m + 4) = m^2 - 16
4. (n - 9)(n + 9) = n^2 - 81
5. (3x + 1)(3x - 1) = 9x^2 - 1
6. (5c + 4)(5c - 4) = 25c^2 - 16
7. (11z - 7)(11z + 7) = 121z^2 - 49
8. (20x + 9)(20x - 9) = 400x^2 - 81
9. (8x + 3y)(8x - 3y) = 64x^2 - 9y^2
Step-by-step explanation:
:)
191. ∭ e ⎛ ⎝2x 5y 7z ⎞ ⎠dv, where e = ⎧ ⎩ ⎨(x, y, z)|0 ≤ x ≤ 1, 0 ≤ y ≤ − x 1, 1 ≤ z ≤ 2⎫
The solution of the integral operation is [tex]e^{2x - 5y + 7z}[/tex]
The integral is a concept in mathematics that involves finding the total amount of a quantity that changes continuously over a given region.
In this case, we are calculating the triple integral of the function [tex]e^{2x - 5y + 7z}[/tex] over a region defined by the conditions 0 ≤ x ≤ 1, 0 ≤ y ≤ −x + 1, and 1 ≤ z ≤ 2.
In order to start solving the integral, we need to first visualize the region defined by the conditions in 3D space.
This region can be seen as a triangular prism with vertices at (0,0,1), (1,0,1), and (1,1,2).
Next, we need to break down the integral into smaller parts. We will use cylindrical coordinates, where x = rcosθ, y = rsinθ, and z = z, to simplify the calculation of the integral.
The triple integral can then be written as
=> [tex]\int\int\int e^{(2rcos\theta - 5rsin\theta + 7z)} r dr d\theta dz,[/tex]
where the limits of integration for r, θ, and z are defined by the conditions stated above.
The final result will be the total amount of the function is
=> [tex]e^{2x - 5y + 7z}[/tex]
over the region defined by the conditions.
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