According to the given statements regarding matrix and vectors, we found that statements a, b, and c are true. Others are false.
a. True. Certain elementary row operations on a matrix, such as row swaps, row scalings, and row additions, can affect the linear dependence relationships among the columns of the matrix.
b. True. The columns of an invertible matrix form a linearly independent set, which is also a basis for the vector space of the matrix.
c. True. A basis is a spanning set (a set of vectors that can generate any other vector in the space) that is as large as possible, meaning that it has the minimum number of vectors required to generate all other vectors in the space.
d. False. A single vector by itself is linearly independent, meaning that it cannot be expressed as a linear combination of other vectors.
e. False. If W is a subspace of a vector space V, then a basis for W is a set of vectors that can generate any other vector in W, but not necessarily all vectors in V.
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Complete Question:
Show T/F.
a. in some cases, the linear dependence relations amoung the columns of a matrix can be affected by certain elementary row operations on the matrix.
b. the columns of an invertible matrix form a basis for .
c. a basis is a spanning set that is as large as possible.
d. a single vector by itself is linearly dependent.
e. if , then is a basis for .
3.35x + 115 = 3.25x + 125
For the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given expression is:
3.35x + 115 = 3.25x + 125
Regroup all the terms with variable x on one side of the equation:
3.35x - 3.25x = 125 - 115
0.1x = 10
x = 100
Hence, for the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.
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HELP pls will mark you the brainliest
From the given graph solution of lines is (32, 5).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
In the give graph two lines intersect at (32, 6).
Here, 32 represents the number of kites and 6 represents the total cost.
Therefore, from the given graph solution of lines is (32, 5).
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(1 point) a vertical right-circular cylindrical tank measures 7 ft high and 6 ft in diameter. it is full of kerosene weighing 51.2 pounds per cubic feet. how much work does it take to pump the kerosene to the level of the top of the tank?
Work done to pump the kerosene is equal to W = 126106 ft-lbs
"Information available from the question"
Height of the cylinder = 7 ft.
Diameter of cylinder = 8 ft.
Radius of the cylinder = 4 ft
Weight of the kerosene = 51.2 lb/ft³
Calculating the volume of cylinder for dy height
dV = π r² dy
dV = π 4² dy
dV = 16π dy
Force acting on the cylinder
dF = W x dV
dF = 51.2 x 16πdy...….(1)
We know
Work done = Force x displacement
Displacement = 7 - y
dW = 51.2 x 16πdy x (7 - y)
Now, integrating both side
[tex]\int\limits dW = \int\limits^7_0 {819.2\pi(7-y) } \, dy[/tex]
[tex]W = [819.2\pi (7-y)^2]^0_7[/tex]
By solving, we get
W = 126106 ft-lbs
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The function [tex]f(x)=\sqrt[3]{x+4}[/tex] is transformed to [tex]g(x) = \sqrt[3]{x-1} +3[/tex]
What transformations are performed from function f to function g?
Choose the answers that are correct:
1. Function f is translated up 3 units.
2. Function f is translated to the right 5 units.
3. Function f is translated to the right 3 units.
4. Function f is translated down 1 unit.
Answer:
A) Function f is translated up 3 units.
B) Function f is translated to the right 5 units.
Step-by-step explanation:
Given functions:
[tex]f(x)=\sqrt[3]{x+4}[/tex]
[tex]g(x)=\sqrt[3]{x-1}+3[/tex]
To transform function f to function g, first subtract 5 from the x:
[tex]\begin{aligned}f(x-5)&=\sqrt[3]{x-5+4}\\&=\sqrt[3]{x-1}\end{aligned}[/tex]
Now add 3 to the function:
[tex]f(x-5)+3=\sqrt[3]{x-1}+3[/tex]
When a number "n" is subtracted from the x variable of a function, the function is translated "n" units to the right.
When a number "n" is added to a function, the function is translated "n" units up.
Therefore, the transformations performed from function f to function g are:
Function f is translated to the right 5 units.Function f is translated up 3 units.Deion is in the business of manufacturing phones. He pays a cost of $50 per phone produced for materials and labor and also must pay a daily fixed cost of $200 to rent the building and equipment. Make a table of values and then write an equation for � , C, in terms of � , p, representing total cost, in dollars, of producing � p phones in a given day.
C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Deion pays a cost of $50 per phone produced for materials and labor.
Deon also must pay a daily fixed cost of $200 to rent the building and equipment.
C = 200 + 50p
The above equation represents the total cost, in dollars, of producing p phones in a given day.
Number of phones (p) Total cost (C)
0 200
1 250
2 300
3 350
Hence, C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.
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The volume of a gas halved during an adiabatic compression that increases the pressure by a factor of 2.5 What is the specific heat ratio?
A ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.
What is the ratio?In mathematics, a ratio shows how frequently one number appears in another.
For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.
So, e are informed that the volume is halved, and the pressure increases by a factor of 2.5.
We shall therefore have:
PVγ = 2.5P(0.5V)γ
We'll condense this to:
(1/0.5)γ = 2.5
γ = In2.5/In2
γ = 1.32
The volume temperature relation is written as follows if the volume expands in an adiabatic process:
T1V1∧γ-1 = T2V2∧γ-1
T1V1∧1.32-1 = T2(0.5V1)∧1.32-1
Condensing this results in:
T₁ = 1.24T₂
Therefore, a ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease
The rate of change of the exponential function in this problem represents a decay, and the rate of decrease is of 3.7%.
How to model the exponential function?A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which:
a is the initial value.r is the decay rate, as a decimal.The function in this problem is given as follows:
y = 20(0.963)^x.
As 0.963 < 1, this is an exponential decay function, and the decay rate is given as follows:
1 - r = 0.963
r = 1 - 0.963
r = 0.037
r = 3.7%.
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when you solve a system of equations (i.e. two equations with two variables each), what possible form(s) could the solution take
Compare the y-intercepts for the two linear functions represented below.
X Y
-1 -1
0 1
1 3 y = 4x - 1
2 5
3 7
A.
The y-intercept of function A is same as the y-intercept of function B.
B.
The y-intercept of function A is greater than the y-intercept of function B.
C.
The y-intercept of function A is less than the y-intercept of function B.
B. The y-intercept of function A is greater than the y-intercept of function B.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
from the given data, we get,
the 1st line's equation is, y=2x+1
i.e. y-intercept = 1
and,
the 2nd equation is,
1 3 y = 4x - 1
i.e. y-intercept = -1/13
=-0.77
as, 1> -0.77
Hence, B. The y-intercept of function A is greater than the y-intercept of function B.
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Use the bar graph to find the experimental probability of the event.
Spinning a Spinner
12
10
8
642O
0
1 2 3 4 5 6
Number spun
The experimental probability of spinning a number less than 3 is
The experimental probability of spinning a number less than 3 is 0.46 or 46%.
What is probability?This can be defined as the likelihood an event occurs or does not occur. Most of the time, the probability is calculated based on the times a specific outcome is obtained versus the number of total outcomes.
What is the probability in this case?To know the probability, let's use the formula getting less than a 3/ total times:
Times they got less than 3: 23 (8+6+9= 23)
Total times: 50
23/50 = 0.46 or 46% (0.46 x 100)
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Bananas cost $0.48 per pound. Which graph correctly shows the relationship between the pounds of bananas and the cost? O A C 52.50 53.00 $1.50 $1.00 50.50 50.00 $8.00 $7.00 $1.50 $1.00 50.50 50.00 Pounds of Bananas 1 1 2 1 Pounds of Bananas 4 B О в D. 3 25 2 15 1 0.5 O $5.00 $4.00 $3.00 $2.00 $1.00 $0.00 0 Pounds of Bananas 1 2 Pounds of Bananas 2 4 10 points S
Equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that Bananas cost $0.48 per pound.
Since each pound costs $0.85, the cost of one pound is $0.48,
the cost of two pounds is twice that at $0.96
The equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas.
Hence, equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.
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A line has a slope of – 3/5 and a y-intercept of 6. Write its equation in slope-intercept form.
Answer:
y=-3/5x+
Step-by-step explanation:
slope intercept form;
y= mx+c........... mis the gradient while c is the y-intercept
so it will be; y= -3/5x+
a six foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight. when a person is 16 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow. what is the height of the streetlight?
The height of the streetlight is 30 feet.
Let's call the height of the streetlight "h".
When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.
When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.
Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.
Solving for h, we get:
96 / h > 3.2 * h
96 > 3.2h
30 > h
So, the height of the streetlight is less than 30 feet.
To determine the exact height of the streetlight, we can use the equation:
96 / h = 3.2 * h
96 = 3.2h
30 = h
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suppose that a single die with 6 sides (numbered 1, 2, 3, ... , 6) is rolled twice. what is the probability that the sum of the two rolls equals 4 ?
The probability that the sum of the two rolls equals 4 is 1/12.
Given in the question that a single die with 6 sides is rolled twice, we have to calculate the probability that the sum of the two rolls equals 4.
the set of possible outcomes when we roll a die are {1,2,3,4,5,6}
So when we roll two dice there are 6 × 6 = 36 possibilities
The number of possible combinations that will result in a sum of 4 is (1, 3), (2, 2), and (3, 1). Since there are 6 possible outcomes for each die, the probability of rolling a specific combination is 1/36. There are 3 combinations that will result in a sum of 4, so the probability of rolling a sum of 4 is 3/36 or 1/12.
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Find the volume of the cone, height = 11cm radius = 6cm
Therefore , the solution of the given problem of volume comes out to be volume of cone is 132π cm³.
Describe volume.The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.
Here,
Given :
=>height = 11cm
=> radius = 6cm
Volume of cone :
=> 1/3πr²h
=> 1/3*π * 36 * 11
=> 132π cm³
Thus , volume of cone is 132π cm³
Therefore , the solution of the given problem of volume comes out to be volume of cone is 132π cm³.
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Dottie went to the movies with her friends. She bought a soda for $2.35, a pack of bubble gum for $1.15, and a chocolate bar for $1.65. How much did Dottie spend in total?
Answer:
Step-by-step explanation:
The candy bar cost, in dollars, is $1.05
Say the price of a piece of bubble gum is x.
This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.
We can then solve from there.
We have given that,
(x+1)+x=1.10
Simplify above expression
2x+1=1.10
2x=0.10 - Subtract From Both Sides
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.
What is the cost?
Cost is the value of money that a company had to spend to produce its goods or services.
Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
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Answer:
Soda = 2.35
Pack of bubble gum = 1.15
Chocolate bar = 1.64
2.35 + 1.15 + 1.64 = 5.15
Answer: Dottie spent a total of $5.15.
Simplify the expression:
Answer: C!
Step-by-step explanation: Because I'm Him. all jokes aside this is the right answer.
Simplify the expression:
[tex]\frac{1-\frac{1}{y} }{\frac{1}{y} }[/tex]
The simplified form of the expression is y - 1.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is (1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex]
The numerator of the expression can be written as below using the cross multiplication process.
1 - [tex]\frac{1}{y}[/tex] = (y - 1) / y
The whole expression becomes,
(1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex] = [(y - 1) / y] / [tex]\frac{1}{y}[/tex]
= (y - 1) / 1
= y - 1
Hence the simplified form is y - 1.
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Please Help!!! Will mark brainliest!
Answer:
4th
Step-by-step explanation:
first is over y-axis and the linear translation: 6 horizontal and -5 vertical
Solve for x and y in the figure
below. (hint: write a system of
equations)
Check the picture below.
[tex]\begin{cases} ~\hfill 10x+(16y+6)=180\\\\ (4+18y)+(10x-6)=180 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{10x+(16y+6)=180}\implies 10x+16y=174\implies 10x=174-16y \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{substituting on the 2nd equation}}{(4+18y)+(10x-6)=180}\implies 18y+10x-2=180 \\\\\\ 18y+(\underset{10x}{174-16y})-2=180\implies 2y+172=180\implies 2y=8 \\\\\\ y=\cfrac{8}{2}\implies \boxed{y=4} \\\\\\ \stackrel{\textit{since we know that}}{10x=174-16y}\implies 10x=174-16(4)\implies 10x=110 \\\\\\ x=\cfrac{110}{10}\implies \boxed{x=11}[/tex]
PLEASE HELP ANSWERR!!
Solving for a in the triangle gives a = 6
How to solve for the value a in the triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The figure is a triangle. Since the sum of angles in a triangle is 180°. We can write:
106.2° + (3.8a + 29.7)° + (2.4a + 6.9)° = 180°
106.2 + 3.8a + 29.7 + 2.4a + 6.9 = 180
142.8 + 6.2a = 180
6.2a = 180 - 142.8
6.2a = 37.2
a = 37.2/6.2
a = 6
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HELP TIIMED PLEASE HELP
what is the solution of x+4/2x-1 <0
The answer choices are a.) -4 <= x <= 1/2 b.) -4 < x <= 1/2 c.)-4<= x < 1/2 d.) -4 < x < 1/2
The solution to the inequality is x < -4
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
x+4/2x-1 < 0
Multiply both sides of the inequality
So, we have the following representation
x + 4 < 0
Subtract 4 from both sides of the expression
So, we have the following representation
x < -4
Hence, the solution is x < -4
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three consecutive even integers are such that the sum of the smaller two is 52 less than three times the largest. what are the integers?
Three consecutives even integers are 42, 44, and 46.
The three consecutives even integers can be represented as x, x+2, and x+4. We can create an equation to solve for x, using the given information.
3(x+4) = 52 + x + (x+2)
3x + 12 = 54 + 2x
x = 42
Therefore, the three consecutives even integers are 42, 44, and 46. To explain this answer, we can use the equation we created. We know that the sum of the smaller two integers is 52 less than three times the largest. We can represent this as 3(x+4) = 52 + x + (x+2). We can then solve for x by subtracting 2x from both sides and adding 12 to both sides, resulting in x = 42. This means that the three consecutives even integers are 42, 44, and 46.
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suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. a sample of 100 steady smokers revealed that the sample mean is $20. the population standard deviation is $5. what is the probability that a sample of 100 steady smokers spend between $19 and $21? 0.0228 0.4772 1.0000 0.9544
The required probability is 0.9544
A z-score is a quantitative measure obtained when a data point from a normal population with mean μ and standard deviation
σ is transformed. It describes the position of the data point representing its distance from the average value of the normal population measured in number of standard deviations. It is given by:
z =(X − μ)/σ
A standard normal table (z-score table) provides the probability to the left of the z-score so obtained.
Number of randomly selected steady smokers is, n=100.
Sample mean is, M=$20.
The population standard deviation is, σ = $5.
To compute the probability that a sample of 100 steady smokers spend between 19 and 21.
Using the definition of a z-score, computing the z-score for X =$19,
z =(X − μ)/σ /[tex]\sqrt{n}[/tex]
[tex]z = \frac{19-20}{5}/\sqrt{100}[/tex]
z = -2
Again using the definition of a z-score to compute the z-score for X = $21,
z =(X − μ)/σ /[tex]\sqrt{n}[/tex]
[tex]z = \frac{21-20}{5}/\sqrt{100}[/tex]
z = 2
The probability that a sample of 100 steady smokers spend between 19 and 21 is obtained as:
P(19< X < 21) = P(-2 < X < 2)
= P(z< 2) - P(z < -2)
= P(z < 2) − [1 − P (z < 2)]
= 0.9772 - (1 - 0.9772)
= 0.9772 - 0.0288
= 0.9544
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5 cm
3 cm
7 cm
What is the surface area, in cm², of the figure shown above?
In ΔKLM, m = 63 inches, mm∠K=24° and mm∠L=42°. Find the length of l, to the nearest inch.
Check the picture below.
[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(\measuredangle M)}{m}=\cfrac{\sin(\measuredangle L)}{l}\implies \cfrac{\sin(114^o)}{63}=\cfrac{\sin(42^o)}{l} \\\\\\ l\sin(114^o)=63\sin(42^o)\implies l=\cfrac{63\sin(42^o)}{\sin(114^o)}\implies l\approx 46~inches[/tex]
Which length and width are possible dimensions for the garden?
The length and width are possible dimensions for the garden is l = 20 ft; w = 10 ft.
Square & RectangleThe characteristics of a square and a rectangle in a flat shape are very different. Although both are rectangular, the nature and characteristics of these two buildings are different.
The difference between a square and a rectangle can be seen from the properties they have. These properties are also characteristics of squares and rectangles. For this reason, if we want to mention the difference between the two wakes, then we must know their characteristics.
Your question is incomplete but most probably your full question was:
Which length and width are possible dimensions for the garden?
l = 20 ft; w = 5 ft
l = 20 ft; w = 10 ft
l = 60 ft; w = 20 ft
l = 55 ft; w = 30 ft
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Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 74.5 Mbps. The complete list of 50 data speeds has a mean of x= 17.34 Mbps and a standard deviation of s= 20.79 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]?
a. The difference between the highest data speed (74.5 Mbps) and the mean of all 50 data speeds (17.34 Mbps) is:
74.5 - 17.34 = 57.16 Mbps
b. To find the number of standard deviations, divide the difference by the standard deviation:
57.16 / 20.79 = 2.75
So, the difference of 57.16 Mbps is 2.75 standard deviations from the mean.
Mbps known as for “Megabits per second.” This is the standard measure of “speed” or “bandwidth” on home internet connections.
It finds how many bits (units of digital information) can be transferred each second. You’ll normally see speeds ranging from 10-1,000 Mbps advertised for home internet plans.
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jim has received scores of 69 and 82 on his first two 100 point tests. what score must he get on his third 100 point test to keep an average of 85 or greater?
Jim needs a score of 97 on his third test to keep an average of 85 or greater.
Average refers to the sum of a set of numbers divided by the count of numbers in the set. It gives a typical or central value that represents the set of numbers.
Given,
The average of his first two tests is (69 + 82) / 2 = 75.5.
To get an average of 85,
he needs the sum of his three tests to be 3 * 85 = 255.
So, the sum of his first two tests is 255 - x, where x is the score he needs on the third test.
Therefore, x = 255 - (69 + 82) = 255 - 151 = 104.
So, he needs a score of 104 on his third test.
Jim needs a score of 97 on his third test to keep an average of 85 or greater.
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the vertices of triangle wxy are located at w(-14,20). x(10,4) and y (-2,-4). what is the approximate length of the midsegment parallel to xy?
The approximate length of the midsegment parallel to xy is 6.63
The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.
To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.
Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.
First, let's find the midpoint of side xw:
Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)
Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )
The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Length line of midpoint xw and midpoint yw :
√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44
So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63
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