Answer:
4 hrs
Step-by-step explanation:
let x = # of hours he rented the unicycle
$15 + ($2/hr)x = $23
($2/hr)x = $23 - $15 = $8
x = ($8) / ($2/hr) = 4 hours
Select the correct answer from each drop-down menu.
Robbie wants to construct an equilateral triangle. He draws diameter AB of circle O and constructs the perpendicular bisector of
diameter AB, find the points X and Y. Then he draws the triangle AXB. What error did he make?
The first mistake Robbie made was
Submit
.He should have
Reset
The first mistake Robbie made was, take improper lengths. AB is the diameter; its length is longer than the sides AX and XB. So, the triangle formed will not be an equilateral triangle.
What is an equilateral triangle?An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposing the three equal sides are equal in size because the three sides are equal.
The first mistake Robbie made was, take improper lengths. AB is the diameter; its length is longer than the sides AX and XB. So, the triangle formed will not be an equilateral triangle.
He should have, after drawing the diameter AB, construct a circle with point A as the center and AO as the radius. Mark the point of intersection as X. Then, AO, AX and OX would form an equilateral triangle.
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Answer:
1. constructing the perpendicular bisector of AB
2.
Step-by-step explanation:
an adventurous dog strays from home, runs five blocks east, four blocks north, five blocks east, two blocks north, and three blocks west. assuming that each block is about 100 m, how far (in m) from home and in what direction (in degrees counterclockwise from the east axis) is the dog? use a graphical method.
The distance between the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.
In the inquiry,
The daring dog begins, let's say, at O.
He walks 300 meters east by 3 blocks.
then,
200 m / 2 blocks north
100 m East of 1 block
Block North = 100 meters.
200 m = 2 blocks west
So,
the separation between the Dog's initial location and ending position.
OE is supplied by,
By using Pythagoras' theorem to triangle OLE,
OE²=OL²+LE²
OE²=200²+300²
OE²=40000+90000
OE=360.55m
Therefore, the distance of the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.
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Drag numbers to complete a function in terms of x and y for the line that contains the points (2, 4) and (6, 16). Numbers may be used once, more than once, or not at all. 12346 y = x –
The function in terms of x and y for the line that contains the points (2, 4) and (6, 16) would be; y=3x-2
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The slope of the line is calculated as follows:
m = Δy/Δx
Given that the line that passes through the points (2, 4) and (6, 16)
To find the function of the line that passes through points (2, 4) and (6, 16)
Therefore, the slope of the line is;
m = Δy/Δx
m = 3
The equation is;
y = mx + c
y = 3x - 2
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The correct statement for the given diagram are-
m∠5+m∠6=180°m∠2+m∠3=m∠6m∠2+m∠3+m∠5=180°Define the term supplementary angles?Two angles are said to be supplementary if their sums total 180 degrees.
case A: m∠5+m∠3=m∠4 ...eq A
From the definition of supplementary angles
m∠3+m∠4=180°
m∠4=180°-m∠3 ....eq B
Put eq B in eq A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
The result is true for m∠2=m∠3
Thus,
The case is not always true.
case B: m∠3+m∠4+m∠5=180° ...eq A
From the definition of supplementary angles
m∠3+m∠4=180°
m∠4=180°-m∠3 ....eq B
Put eq B in eq A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
The case is not true.
case C: m∠5+m∠6=180°
From the definition of supplementary angles
m∠5 and +m∠6 = 180
The case is always true.
case D: m∠2+m∠3=m∠6 ...eq A
From the definition of supplementary angles
m∠5+m∠6 = 180°
m∠6=180°-m∠5 ....eq B
Put eq B in eq A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Sum of interior angles of triangle equals 180 degrees
Thus,
This option will always be true.
case E:
m∠2+m∠3+m∠5=180°
Sum of interior angles of triangle equals 180 degrees
Thus,
This option will always be true.
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The correct question is attached.
The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t
The total profit as the subject of formula is t = 3p
How to make the total profit the subject of formulaFrom the question, we have the following parameters that can be used in our computation:
p = t/3
Where
Individual Profit = p
total profit = t
Recall that, we have
p = t/3
Multiply both side of the equation by 3
So, we have
3p = t
Rewrite as
t = 3p
Hence, the solution is t = 3p
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Complete question
The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t
make t the subject
Consider the weighted voting system [13: 14, 6, 4, 2]
Are dummies
The number of sequential coalitions is 13!
How to determine the number of sequential coalitions?From the question, we have the following parameters that can be used in our computation:
System = [13: 14, 6, 4, 2]
This means that
n = 13
The number of sequential coalitiions is calculated as
Coalition = n!
substitute the known values in the above equation, so, we have the following representation
Coalition = 13!
Hence, the coalition is 13!
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Complete question
Consider the weighted voting system [13: 14, 6, 4, 2]
How many sequential coalitions are there?
Please help, I cannot figure out how to do this for the life of me -number 15
The bottom of a deep trench in an ocean is estimated to be 12,731 feet below sea level.
The corresponding integer is?
please help
Answer:
-12,731
Step-by-step explanation:
You want to know what integer would be used to represent the value 12,731 feet below sea level.
Signed valuesUsually we measure elevation up from sea level. So, distances below sea level are usually represented with negative numbers. The integer corresponding to 12,731 feet below sea level would be ...
-12,731 . . . . feet
Two restaurants offer customers large pizzas using different measurements for diameter. Restaurant 1: One large 14-inch pizza for $12.99 Restaurant 2: One large 36.83-centimeter pizza for $12.99 If 1 inch = 2.54 centimeters, what is the length of the crust around the larger pizza, using π = 3.14?
A. 115.65 inches
B. 22.77 inches
C. 43.96 inches
D. 45.53 inches
Answer:
D. 45.53 inches
Step-by-step explanation:
Restaurant 1: diameter = 14 inches
Restaurant 2: diameter = 36.83 inches × (1 inch)/(2.54 cm) = 14.5 inches
The larger pizza is from Restaurant 2, and its diameter is 14.5 inches.
circumference = πd = 3.14 × 14.5 inches = 45.53 inches
Answer: D. 45.53 inches
Answer:it is d 45.53
Step-by-step explanation:becuase I did the test
En la frutería “Todo barato”, 2 kg de tomates cuesta $ 38.00. ¿Cuánto debe de pagar Karla si compra 9 kg de tomates
Answer: hi
Step-by-step explanation: hi
The admission fee at an amusement park is $1.25 for children and $7.20 for adults. On a certain day, 253 people entered the park, and the admission fees collected totaled $1060. How many children and how many adults were admitted?
There were _______ children admitted.
There were _______ adults admitted
This is a system of equations problem. We can set up the following equations:
x = number of children admitted
y = number of adults admitted
1.25x + 7.20y = 1060 (the total amount of money collected)
x + y = 253 (the total number of people admitted)
To find the number of children admitted, we can use the second equation to solve for one of the variables in terms of the other.
x + y = 253
x = 253 - y
Now we can substitute this expression into the first equation:
1.25(253 - y) + 7.20y = 1060
Solving for y we get
y = 120
So there were 120 adults admitted.
We can use the second equation to find the number of children admitted:
x + y = 253
x = 253 - y
x = 253 - 120
x = 133
So there were 133 children admitted.
Therefore,
There were 133 children admitted.
There were 120 adults admitted.
Answer:
128 children, 128 adults
Step-by-step explanation:
1.25 per child (c)
7.2 per adult (a)
a+c = 253 so c = 253-a
1.25c+7.2a=1060
2 equations 2 variables, solve
1.25 (253-a) + 7.2*a = 1.25*253 -1.25a + 7.2a =1060
sp 5.95a =1060- 1.25*253
so a =125
c = 253-125 = 128
A graphing calculator is recommended. Use technology to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. (Round your answers to five decimal places.) y = e−x2, y = 0, x = −5, x = 5. a) about x-axis. b) about y= - 1
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740
We have to find the volume of given curve about x-axis
we have [tex]$\mathrm{y}=\mathrm{e}-\mathrm{x}^2,[/tex] y=0, x=-5, x=5
(a).
The volume of solid of revolution about the x-axis using disk method is evaluated as:
The disk method is the process of finding the volume of an object by dividing that object into many small cylinders/disks and then adding the volumes of these small disks together.Volume V=[tex]\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$[/tex]
[tex]$$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$[/tex]
V=3.93740
we use the formula
[tex]$$\int_{-\mathrm{n}}^{\mathrm{n}} \mathrm{e}^{-\mathrm{a} \mathrm{x}^2} \mathrm{dx}=\frac{\sqrt{\pi} erf \sqrt{a} n }{\sqrt{a} }[/tex](b). The volume of solid of revolution about the y= - using washer method is:
This particular shape is called a washer, or a disk. This shape is obtained by rotating two functions around the x-axis or the y-axis. To find the volume of this shape, create slices of the shape and subtract the missing middle space after finding the total volume. This method is called the washer method.[tex]$$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$[/tex]
Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740
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define the least common multiple of a and b to be the smallest positive number which is divisible by both a and b. prove that the least common multiple of a and b is ab precisely when a and b are coprime 6
The least common multiple(LCM) of two coprime numbers is their product, ab.
Let a and b be two positive integers, and let LCM(a,b) be the least common multiple of a and b.
By definition, LCM(a,b) is the smallest positive number which is divisible by both a and b.
Now, suppose that a and b are coprime, meaning that there are no positive integers other than 1 that divide both a and b.
Since 1 divides both a and b, and 1 is the smallest positive integer, we know that 1 is the only positive integer that divides both a and b.
Therefore, LCM(a,b) must be divisible by both a and b, and 1 is the only positive integer that divides both a and b.
Thus, LCM(a,b) = ab.
This proves that the least common multiple of a and b is ab precisely when a and b are coprime.
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Which one is correct?
A
B
C
D
Answer: C
Step-by-step explanation: TYSM if you give me a brainly... ps love you
Answer:
B.
A trapezoid looks like the following in the image, and B is the same but flipped.
Step-by-step explanation:
Hope it helps! =D
consider a circle of radius 2 centered at the origin. find parameterizations of this curve under the following assumption. clearly state any restriction on the variable of parametrization
As per the given radius, the parameterizations of this curve is 4
The term curve in math is defined as an abstract term used to describe the path of a continuously moving point
Here we have given that consider a circle of radius 2 centered at the origin.
And we have to find the parameterizations of this curve under the following assumption.
Here we have know that we need to find a parameterization for the circle of radius 2 in the xy-plane that one is centered at the origin at the direction of clockwise.
=> x(t) = 2cos(t) ------------------(1)
and
=> y(t) = −2sin(t) -----------------(2)
Here we have to note that the given expression is written as,
=> x²(t) + y²(t)
When we apply the values on it then we get
=4cos²t + 4sin²t
Then it can be written as,
=> 4(cos²t + sin²t)
=> 4
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2023 1-100 math challenge answers
Answer:
Step-by-step explanation: 1*23= 23 because anything times one is equal to itself
Solve for x. *
A. 180
B. 50
C. 130
D. 138
Answer: c) 130
Step-by-step explanation:
x+8+42=180
x=180-50
x=130
All the questions answered
The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 = (x+7)(x+7)
What is Quadratic equation?Any equation using the formula ax² + bx + c = 0 is a quadratic equation.
where a, b and c are constants, and x is an unknown variable.
It is called "quadratic" because the variable is squared (in other words, raised to the power of 2).
The most common way to solve a quadratic equation is to factor it into two linear equations, which can then be solved using the methods of linear algebra.
Another way is to use the quadratic formula, which expresses the roots of the equation in terms of the coefficients a, b and c.
It is called a quadratic equation because it can be written in the form
ax² + bx + c = 0
which is the standard form for a quadratic equation.
Examples:
1) x² + 4x – 5 = 0
2) 4x² – 7x + 3 = 0
3) 2x² + 3x – 4 = 0
Therefore , The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 = (x+7)(x+7)
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Coding languages communicate information that is key to which of the following aspect(s) of the health care system?
code, in communications, a dull rule for replacing a piece of information such as a letter, word, or phrase with a casually selected equivalent.
The term has been frequently exploiting and used as a synonym for cipher, which is a method for transforming a message according to a rule to cover its meaning.
In the past this hazy of the distinction between code and cipher was rather inconsequential; in fact, many historical aught would be more properly classified as codes according to present-day criteria.
In modern communications systems, information is frequently both encoded and encrypted (or enciphered), and so an understanding of the variation between the two is important.
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Draw the graph of y=f(x) and y= 1/f(x) on the same axes.
f) f(x) = -(x+4)²+1
are there any specific steps to get the answers here?
Answer: To graph y = f(x) and y = 1/f(x) on the same axes, you can follow these steps:
First, graph y = f(x) by plotting a few points, such as (-5, -19), (-3, -1), (0, 1) and (5, 19), and then connecting them with a smooth curve.
Then, graph y = 1/f(x) by finding the inverse function of f(x) which will be
1/f(x) = -1/(x+4)²+1
Next, plot a few points on this new function, such as (-5, -1/19), (-3, -1), (0, 1) and (5, 1/19), and then connecting them with a smooth curve.
Finally, make sure that the same x and y scales are used for both graphs, and label the axes and the functions clearly.
It is important to note that as f(x) = -(x+4)²+1, the domain of f(x) is all real numbers but the range is (1, infinity) so the reciprocal will be defined only for the range of f(x) and the domain of 1/f(x) will be (1, infinity)
Also, the graph of y = f(x) will be a parabola opening upwards and y = 1/f(x) will be a parabola opening downwards, both with vertex (-4,1)
The graph of y = -(x+4)²+1 will be a parabola opening upwards and the graph of y = -1/(x+4)²+1 will be a parabola opening downwards.
Step-by-step explanation:
show that {1,2,3} under multiplication modulo 4 is not a group but that {1,2,3,4} under multiplication modulo 5 is a gruoup.
The set {1,2,3} is not a group under multiplication modulo 4, as it does not contain an identity element. However, the set {1,2,3,4} is a group under multiplication modulo 5.
A group is a set of elements which is closed under an operation and contains an identity element. In order to be a group, the set must satisfy the four group axioms: closure, associativity, identity, and invertibility. The set {1,2,3} does not satisfy the group axioms under multiplication modulo 4, since it does not contain an identity element, and thus is not a group.
On the other hand, the set {1,2,3,4} is a group under multiplication modulo 5, since it contains an identity element (1) and is closed under multiplication. The other group axioms are also satisfied, as the operation is associative, and each element has an inverse (for example, the inverse of 1 is 4). Therefore, {1,2,3,4} is a valid group under multiplication modulo 5.
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let f(x)=3x-1.then find g(x):if f(g(x))=9x the power of 2+12x+8
Answer:
3x^2 + 4x + 3
Step-by-step explanation:
we can use this information to find g(x) in terms of f(x).
substitute f(x) = 3x-1 into f(g(x)) = 9x^2 + 12x + 8, we get:
3g(x) - 1 = 9x^2 + 12x + 8
Now, we can solve for g(x) by isolating it on one side of the equation:
3g(x) = 9x^2 + 12x + 9
g(x) = 3x^2 + 4x + 3
therefore g(x) is equal to 3x^2 + 4x + 3
Find the volume of the solid of revolution obtained by rotating the region bounded by the curves x=0
, y=0
The volume of the solid of revolution is 0
The volume of the solid of revolution obtained by rotating the region bounded by the curves x=0 and y=0 is zero since the area of the region is zero.
To calculate the volume of a solid of revolution, we use the formula V = ∫2dx, where r is the radius of the circle obtained by rotating the curve about the x-axis. Since the region bounded by the curves x=0 and y=0 has an area of 0, the radius r is also 0 and the integral becomes 0. Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=0 and y=0 is 0.
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Use a graphing calculator to graph f(x)=-x^3+3x²-2 and find the following features of the graph. Round answers to the nearest hundredth, if necessary.
The x-intercepts of this graph from least to greatest are x = -0.73, x = 1, and x = 2.73.
The local minimum of this graph is (0, -2).
The local maximum of this graph is (2, 2).
The intervals on which the function is decreasing are x < -0.73 and x > 1.
The intervals on which the function is increasing are 1 < x < 2.73.
What is the local minimum of a graph?The local minimum of a graph can be defined as the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (0, -2).
Conversely, the local maximum of a graph can be defined as the point on the graph of a function where it changes from an increasing function to a decreasing function, which is given by this ordered pair (2, 2).
For any given function, y = f(x), if the output value is decreasing when the input value is increased, then, the function is referred to as a decreasing function.
In conclusion, we would use an online graphing calculator to plot the given function f(x) = x³ + 3x² - 2 in order to determine its key features.
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the 1x8 vector resulting from multiplying each entry of x by 4. do this in one line! store the result as x4.
The 1x8 vector resulting from multiplying each entry of x by 4.x4 = [4*x1, 4*x2, 4*x3, 4*x4, 4*x5, 4*x6, 4*x7, 4*x8]
For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], x4 would be [4, 8, 12, 16, 20, 24, 28, 32]. This can be represented mathematically as x4 = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8] which is the same as 4*x = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8]. By multiplying each entry of x by 4, we can create a new vector x4 with every entry multiplied by 4.Multiplying each entry of a 1x8 vector x by 4 can be expressed as multiplying the vector by the scalar 4, resulting in a 1x8 vector x4. For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], then x4 = [4, 8, 12, 16, 20, 24, 28, 32].
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The value of x that makes the equation true is ____
The value of x that makes the equation true is 12°. The solution has been obtained using angle sum property of triangle.
What is Angle Sum Property?
The Angle Sum Property states that the sum of the measures of the angles of a triangle is 180°. This means that if you add up all three angles of a triangle, the total measure will be 180°. This property is true for all triangles, regardless of the size or shape. It is one of the most important properties in geometry and is used to solve problems involving angles in triangles.
We are given two angles as (2x)° and (5x+18)°
Also, we are given two sides of the triangle are same.
This means that the angles opposite to the sides are also same.
Thus, the angles of the triangle are (2x)°, (5x+18)° and (5x+18)°
Using angle sum property,
⇒ (2x)° + (5x+18)° + (5x+18)° = 180°
⇒ (2x)° + 2 * (5x+18)° = 180°
⇒ (2x)° + (10x+36)° = 180°
⇒ (12x + 36)° = 180°
⇒ (12x)° = 144°
⇒ x = 12°
Hence, the value of x that makes the equation true is 12°.
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If I go to the store to buy 6 packages of sausages ( each package has 2 1/2 sausages ) and my dog eats 2 sausages every day in total
How many days until I need to go to the store for sausages again?
The number of days until I need to go to the store for sausages again is
7.5 days.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of packages = 6
Number of sausages in each package = 2(1/2)
Total sausages.
= 6 x 2(1/2)
= 6 x 5/2
= 3 x 5
= 15
Number of sausages the dog eats each day = 2
The number of days the sausages will be used.
= 15/2
= 7.5
Thus,
The number of days is 7.5 days.
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A scientist records the temperature of three different mixtures as -33.625℉, -33 5/6℉, and -33 6/25℉. What is the order from least to greatest temperature of the mixtures?
Answer: To determine the order of the temperature of the mixtures from least to greatest, we need to compare the values of the temperatures in their simplified fractional forms.
-33.625℉ = -33 5/8℉
-33 5/6℉ = -33 5/6℉
-33 6/25℉ = -33 24/100℉
We can compare the fractions by comparing the numerators, if they are the same we can compare the denominators.
So, the order from least to greatest temperature of the mixtures is:
-33 6/25℉ < -33 5/6℉ < -33 5/8℉
It's important to notice that these temperatures are negative.
Step-by-step explanation:
s for each matrix below, apply the given row operation(s) to the matrix in order, and give the resulting matrix.
The resulting matrix by applying the given row operations −2R2+3R1 →R1 is given by [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .
Matrix A is equal to :
A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]
Now replace the row R1 by applying the row operations -2R2 + 3R1 on the given matrix we get ,
First element of row 1 is replaced by :
-2(8) + 3(-3)
= -16 -9
= -25
Second element of row 1 is replaced by :
-2(5) + 3(5)
= -10 + 15
= 5
Third element of row1 is replaced by :
-2(6) + 3(2)
= -12 + 6
= 6
Therefore, the resulting matrix after applying the row operation is given by : [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .
The above question is incomplete , the complete question is :
Consider matrix A.
What matrix results apply the given row operation(s) R1 to the matrix in order, and give the resulting matrix represented by −2R2+3R1?
A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]
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Projects that adopt agile methodology are not prone to the typical rapid changes that occur throughout the system development lifecycle.
False
True
Projects that adopt agile methodology are not prone to the typical rapid changes that occur throughout the system development lifecycle, The statement is False.
The methodology is defined as to the overarching strategy and rationale of your research project.
It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.
Agile project management methodology is commonly used for software development projects. It has greater adaptability to frequently changing scopes. Adopt Agile because they want to increase speed to market, meet customer demand, or increase team productivity.
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