Answer:
Step-by-step explanation:
To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin, you would need to double the x and y-coordinates of each vertex of the square.
Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:
(2a, 2b)
(2a, 2b + 2)
(2a + 2, 2b + 2)
(2a + 2, 2b)
So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.
To graph the image, you would plot each of the new vertices and connect them to form the image square.
The solution is given below.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin,
we would need to double the x and y-coordinates of each vertex of the square.
Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:
(2a, 2b)
(2a, 2b + 2)
(2a + 2, 2b + 2)
(2a + 2, 2b)
So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.
To graph the image, we would plot each of the new vertices and connect them to form the image square.
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Suppose that the world's current oil reserves is R = 2090 billion barrels. If, on average, the total reserves is decreasing by 18 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R , in terms of t , the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R = B.) 15 years from now, the total oil reserves will be billions of barrels. C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)
a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.
b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.
c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.
What is a linear equation?A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.
A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.
The current total world oil reserves, R = 2,090 billion barrels
Average decrease per year = 18 billion barrels
a) Linear equation for R is 2,090 - 18t
b) In 15 years, the total oil reserves = 2,090 - 18(15)
= 2,090 - 270
= 1,820
c) The constant rate of decrease = 18 billion barrels per year
The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).
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Need help on algebra please
Answer:
Step-by-step explanation:
Solve the question with Steps
The solution of the question sin(50)sin(80)cos(50)cos(80) is cos^2(80o), the correct option is D.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot. Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
Given;
sin(50)sin(80)cos(50)cos(80)
Now,
=sin(20°)cos(80°) – cos(20°)sin(80°)
=sin(A-B) = sinA.cosB – cosA.sinB
=sin(20°-80°)
=sin(-60°)
=cos^2(80o)
Therefore, by trigonometry the answer will be cos^2(80o).
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Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the greatest measure
• B. second-longest side
• C. shortest side
• D. angle with the smallest measure
The longest side of a triangle is always opposite the,
A. angle with the greatest measure.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
We know, The length of the largest side in a triangle is opposite to the largest angle.
The statement, The longest side of a triangle is always opposite the
angle with the greatest measure.
Because A longer angle will be more spread out and hence the opposite side will be longer too.
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Help me with this question…..
The volume of the cone shown can be described to be A. 513 π cubic units
How to find the volume of a cone ?The volume of a cone can be found by the formula :
= π x radius ² x height / 3
The radius of this cone is 9 units and the height is 19 units.
The volume of this cone then is :
= π x radius ² x height / 3
= π x 9 ² x 19/ 3
= π x 81 x 19/ 3
= π x 513
= 513 π cubic units
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-2√x+5 +1
End behavior
Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.
For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:
lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞
As x approaches negative infinity, the square root of x approaches 0, so the function approaches:
lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7
Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.
Step-by-step explanation:
PLEASE HELP ME ASAP
5. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.
Convert 40 fluid ounces to pints.
Answer:The answer is 2.5 pints.
Distance formula is D=~^ (X2-X1)*2 + (Y2- Y1)*2
pls help!
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad P2(\stackrel{x_2}{-3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~-3 - 6~~)^2 + (~~5 - 3~~)^2} \implies P1P2=\sqrt{( -9 )^2 + ( 2 )^2} \\\\\\ P1P2=\sqrt{ 81 + 4 } \implies P1P2=\sqrt{ 85 }[/tex]
What is the correct answer answer asap for brainlist
According to the information, it can be inferred that the option that the quote explains is: The outcome... is situational irony because the opposite of what was expected is what happening.
How to identify the correct option that explains the quote?To identify the correct option that explains the quote we must read the text carefully and the options. Once we have read and understood this information, we can infer which option explains the quote.
In accordance with the above, option A would be the one that explains the quote because options B and C by discarding are fragments of the quote. So these fragments could not explain the same quote that is being used in the text. On the contrary, the paragraph of option A does explain the situation clearly.
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Consider a lease for 120,000 square feet of space and specifies base rent of $5 psf. In addition, the lease provides for percentage rent of 3% of sales in excess of the natural breakpoint. a) Calculate the natural breakpoint for this lease.
Answer:
$20M
Step-by-step explanation:
You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.
Minimum rentThe minimum rent is ($5/ft²)×(120000 ft²) = $600,000.
BreakpointThe amount of sales that makes $600,000 equal to 3% of sales is ...
$600000 = 0.03s
s = $600000/0.03 = $20,000,000
The "natural breakpoint" is $20M in sales.
__
Additional comment
When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.
PLEASE HELP!!! VERY URGENT
A person walks due south from point A for 500 yards and then due west for 300 yards, arriving at point B. Answer the following questions using complete sentences. 2 points for each correct answer and 2 points for each correct explanation.
i. What is the person's displacement from the starting point? How did you calculate this? Be sure to round to the nearest hundredth.
ii. From point B, in what direction would the person have to look in order to be looking back at point A (the starting point)? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
iii. A friend is standing at point A looking at point B. In what direction would that friend be looking? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
The answers are mentioned below.
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).
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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.
Therefore, the displacement can be calculated as the
√(500² + 300²)
= 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.
Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be
360 - 31.39
= 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.
However, the true bearing is measured from the north and therefore, the true bearing would be
90 + 59.04
= 149.04 degrees (rounded to the nearest hundredth).
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Q.Find the mistake made in the steps and justifications for solving the equation below.
Picture attached?
A. The justification for step 1 is incorrect and should be the multiplication property of equality.
B. The justification for step 3 is incorrect and should be the addition property of equality.
C. Step 5 is incorrect and should show be x=10/16.
D. Step 4 is incorrect and should be 10x = 24.
Answer:
The correct answer is D. Step 4 is incorrect and should be 10x = 24.
A rectangular field is four times as long as it is wide. If the perimeter of the field is 400 yards, what are the field’s dimensions?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note the perimeter of the rectangle is:
2 x Length + 2 x Width.
Answer:
2 x Length + 2 x Width.
Step-by-step explanation:
Graph the function y=x/4
Answer:
Step-by-step explanation:
Find dy/dx by implicit different iation xy^2= 4.
The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).
What is differentiation by parts?By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.
Given function is xy²= 4. The given expression will be different as below,
dy / dx ( xy² ) - 4 = 0
2xy( dy / dx) + y² = 0
dy / dx = -y / 2x
Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).
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If it takes 6 people 8 hours to finish the job, how long would it take 4 people?
12 hours
If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours
Answer:
5.333 hours.
Step-by-step explanation:
Put this on a chart:
6 people = 8 hours
4 people = ? hours
To find ? Use crisscross multiplication and solve:
? = (4 * 8) / 6
? = 32 / 6
? = 5.333
Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.
Fill in the table for y = 3x - 1
Answer:
1. -7
2. -1
3. 5
Step-by-step explanation:
Substitute the value given into the equation
5.3A Find Two Numbers Whose Product and Sum is as Indicated
Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.
How to find a set of two real numbers
In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:
x₁ + x₂ = b
x₁ · x₂ = c
Whose solution can be found by numerical methods.
Now we proceed to determine the values for each cases:
(x₁, x₂) = (6, 1)(x₁, x₂) = (4, 9)(x₁, x₂) = (3, - 2)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (- 8, 2)(x₁, x₂) = (2, - 2)(x₁, x₂) = (4, - 2)(x₁, x₂) = (- 4, 3)(x₁, x₂) = (- 5, - 4)(x₁, x₂) = (5, - 3)(x₁, x₂) = (6, 2)(x₁, x₂) = (- 2, - 3)(x₁, x₂) = (- 2, - 7)(x₁, x₂) = (2, 8)(x₁, x₂) = (11, - 2)(x₁, x₂) = (5, - 4)(x₁, x₂) = (- 8, 1)(x₁, x₂) = (8, - 3)(x₁, x₂) = (7, 8)(x₁, x₂) = (8, 8)(x₁, x₂) = (6, 4)(x₁, x₂) = (6, 9)(x₁, x₂) = (3 - 2√2, 3 + 2√2)(x₁, x₂) = (9, - 4)(x₁, x₂) = (8, - 7)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (8, - 2)(x₁, x₂) = (- 9, - 9)(x₁, x₂) = (- 15, 3)(x₁, x₂) = (7, - 6)(x₁, x₂) = (- 7, - 7)(x₁, x₂) = (- 8, - 8)(x₁, x₂) = (12, - 3)(x₁, x₂) = (- 3, - 8)(x₁, x₂) = (4, - 3)(x₁, x₂) = (- 12 - √119, - 12 + √119)(x₁, x₂) = (7, - 4)(x₁, x₂) = (- 6, - 9)(x₁, x₂) = (5, 7)(x₁, x₂) = (- 8, 4)(x₁, x₂) = (- 7, 6)(x₁, x₂) = (5 / 2 + √73 / 2, 5 / 2 - √73 / 2)(x₁, x₂) = (5, 6)(x₁, x₂) = (- 10, 4)(x₁, x₂) = (- 9, 4)(x₁, x₂) = (- 9, 7)(x₁, x₂) = (6, 8)(x₁, x₂) = (- 7, 3)To learn more on real numbers: https://brainly.com/question/24908711
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(1 point) Find an equation of a line perpendicular to 2 = 10 and passing through the point (3,2). The line is
An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.
The equation of a line with slope m passing through the point (x1, y1) can be written in the form:
y - y1 = m(x - x1)
Since the slope of the line is undefined, the equation of the line would be in the form:
x - x1 = constant
To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:
x - 3 = constant
So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:
x - 3 = constant
or simply:
x = 3.
Suppose a biologist tagged 53 penguins in antarctica during mating season. The next year, they caught 82 and found that 11 of them had tags. Estimate the total number penguins in the area.
It can be estimated that there are 395 penguins in the area.
What is Proportion ?Proportion is a mathematical comparison between two numbers. According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".
We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.
The proportion should therefore be [tex]x:53=82:11[/tex] where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:
[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]
Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.
395 penguins are in the area according to our estimation.
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(1) Find the temperature at 8:00 pm and midnight in your town. Then find the find the Difference between the two Temperatures.
(2) Clear Parenthesis and combine like terms, 12-3(x+2y-5).
1. The difference between the temperature is 14°C.
2. The value of the expression will be -3x - 6y + 27.
How to calculate the valueThe difference between the temperature will be:
= -10 + 24
= 14°C.
For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:
x + 2y - 5
Next, multiply this expression by 3:
3(x + 2y - 5) = 3x + 6y - 15
Finally, substitute this back into the original expression:
12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27
So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.
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A differentiable function f(x,y) has the property that f(5,4)=7 and fx(5,4)=-3 and fy(5,4)=7. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=5, y=4
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.
In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:
z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])
where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).
In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:
z - 7 = (-3)(x - 5) + (7)(y - 4)
Simplifying this equation, we get:
z = -3x + 7y + 8
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PLS help fast this is the last day for my test solve the system of linear equations. check your solution. 3y+4y=-10 y=-3/4x - 5/2
This equation has infinitely many solutions.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: 3x+4y = -10...(1),
y = -3/4x - 5/2....(2)
We solve this linear equation and we get
We multiply equation (2) by 4 and we get
4y + 3x = -5(2)
4y + 3x = -10
Hence, this equation has infinitely many solutions.
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Answer Quick
Factor what the image says
Answer:
49u² - 154u + 121 factored is (7u - 11)²
Step-by-step explanation:
To factor the given quadratic expression, 49u² - 154u + 121, rewrite in the form a² - 2ab + b².
Rewrite 49 as 7² and 121 as 11²:
[tex]\implies 7^2u^2-154u+11^2[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^n \cdot c^n=(ac)^n:[/tex]
[tex]\implies (7u)^2-154u+11^2[/tex]
Rewrite 154u as 2 · 7u · 11 :
[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2[/tex]
Compare with the form a² - 2ab + b²:
a = 7ub = 11Apply the perfect square formula: a² - 2ab + b² = (a - b)²
[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2=(7u-11)^2[/tex]
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales orice Zion Sun
Chairs must sell each chair for to earn a monthly profit of $65,000, if of the total monthly fixed costs are $17,363.50
and the variable cost per chair is $52.17.
• $71.49
• $75.21
O $23.04
O $25.67
Zion Sun Chairs must sell each chair for at least $75.21 to earn a monthly profit of $65,000.
To determine the minimum sales priceTo determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $65,000, we can use the following formula:
Total Profit = Total Revenue - Total Cost
We know that the monthly fixed costs are $17,363.50, and the variable cost per chair is $52.17. Therefore, the total cost to produce 3,575 beach chairs each month can be calculated as follows:
Total Cost = Fixed Cost + (Variable Cost per Chair x Number of Chairs)
Total Cost = $17,363.50 + ($52.17 x 3,575)
Total Cost = $203,871.25
To earn a monthly profit of $65,000, we can set up the equation as follows:
$65,000 = Total Revenue - $203,871.25
Total Revenue =$268,871.25
To find the minimum sales price per chair, we can divide the total revenue by the number of chairs:
Minimum Sales Price per Chair = Total Revenue / Number of Chairs
Minimum Sales Price per Chair = $268,871.25 / 3,575
Minimum Sales Price per Chair ≈ $75.208
Therefore, Zion Sun Chairs must sell each chair for at least$75.21 to earn a monthly profit of $65,000, given the monthly fixed costs, variable cost per chair, and production quantity.
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Bodmas sums
2.4of4.5-5.6/1.4+3.8*2
On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4
what is BODMAS ?The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.
By BODMAS
2.4of4.5-5.6/1.4+3.8*2
10.8-5.6/1.4+3.8*2
10.8-4+3.8*2
10.8-4+7.6
14.4
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Find the echelon form of this augmented matrix, written so there are 1's on the diagonal. 1 - 1 2 400 100 900 1 -3 7 - 300
To find the echelon form of the augmented matrix, we will use row operations to transform the matrix into a triangular form.
How to solve for the matrix
Starting matrix:
[ 1 -1 2 | 400 ]
[100 900 1 | -3 ]
[ 1 -3 7 | -300 ]
Subtracting the first row from the second and third rows, respectively:
[ 1 -1 2 | 400 ]
[ 0 901 -199 | -403 ]
[ 0 -2 5 | -700 ]
Dividing the second row by 901 to get a leading 1:
[ 1 -1 2 | 400 ]
[ 0 1 -199/901 | -403/901 ]
[ 0 -2 5 | -700 ]
Adding 2 times the second row to the third row:
[ 1 -1 2 | 400 ]
[ 0 1 -199/901 | -403/901 ]
[ 0 0 5 - (2*199/901) | -496/901 ]
Dividing the third row by 5 to get a leading 1:
[ 1 -1 2 | 400 ]
[ 0 1 -199/901 | -403/901 ]
[ 0 0 1 - (2*199/901) | -496/901 * (1/5) ]
Subtracting 2 times the third row from the second row:
[ 1 -1 2 | 400 ]
[ 0 1 0.12985349611 | -1.45323773515 ]
[ 0 0 1 - (2*199/901) | -0.21964542252517706 ]
Subtracting 2 times the third row from the first row:
[ 1 -1 0.640177312 | 1.82816635434407 ]
[ 0 1 0.12985349611 | -1.45323773515 ]
[ 0 0 1 - (2*199/901) | -0.21964542252517706 ]
This is now in row echelon form with 1's on the diagonal. Therefore, the echelon form of the given augmented matrix is:
[ 1 -1 0.640177312 | 1.82816635434407 ]
[ 0 1 0.12985349611 | -1.45323773515 ]
[ 0 0 1 - (2*199/901) | -0.21964542252517706 ]
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Find the dimensions of a rectangular Persian rug whose perimeter is 22 ft and whose area is 10 ft squared
rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
How to calculated dimensions of a rectangular Persian rug?Let's say that the Persian rug is rectangular, with length "l" and width "w".
The total of a rectangle's four sides is known as the perimeter, and it can be calculated as follows:
Perimeter = 2l + 2w
Given that the distance around it is 22 feet, we can write:
2l + 2w = 22
When we simplify this equation, we obtain:
l + w = 11
A rectangle's area is determined by the product of its length and breadth, which may be written as follows:
l x w = area
Given that the space is 10 square feet, we can write:
l x w = 10
Two equations with two variables are now available:
L+W = 11, and L x W = 10.
To find l and w, we can utilise substitution or elimination. For instance, we can solve for w from the first equation in terms of l:
w = 11 - l
Using this expression as w's replacement in the second equation, we obtain:
l x (11 - l) = 10
The result of expanding and rearrangement is a quadratic equation:
l² - 11l + 10 = 0
Using the quadratic formula or factoring, we can solve this quadratic problem. Factoring results in:
(l - 10)(l - 1) = 0
so either l = 10 or l = 1 is true.
w = 1 if l = 10, otherwise. w equals 10 if l = 1.
As w is always smaller than l, we have
The rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
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A train travelling at 105km/hr goes through a tunnel 1575m long. Calculate in seconds,the time a passenger on the train spends in the tunnel
Correct me if im wrong :)
