As per the given volume, it take 223 minutes to fill the pool.
The term volume in math is defined as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface and it measured as cubic units.
Here we have given that a 9,000-gallon pool is being filled at a rate of 40 gallon per minute.
Here we need to find the time taken to fill the pool.
While we looking into the given question, we have identified the following values,
Total volume of pool = 9000 gallon.
Amount of water filled in one minute = 40 gallon,
then the time take by the pool to fill is calculated by dividing the total amount by the amount of water per minute then we get,
=> 9000/40
When we simplify this one then we get,
=> 225
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What 3 lengths make a triangle?
The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.
Let's use the triangle inequality theorem to examine the characteristics of a triangle's sides.
The two requirements for a triangle's sides are:
(1) The two sides added together are always larger than the third side.
a+b>c
a+c>b
b+c>a
(2) Less exists between the two sides than there does between the third side.
|a-b|<c
|a-c|<b
|b-c|<a
Therefore, if and only if the total of two sides is always larger than the third side and the difference of the two sides is less than the third side, 3 lengths could be the measures of the edges of a triangle.
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Solve 2(4x+2)= 4x -12(x-1) the solution is x
The Value of x is -1/2 in this Linear equation
As we have the equation 2(4x+2)= 4x -12(x-1)
2(4x+2)= 4x -12(x-1) 8x + 4 = 4x - 12x + 12................. On opening the brackets8x + 4 = -8x + 1216 x + 4 = 12 ----------------- on subtraction 8x from both the sides( As we can perform any operation in both the sides of equation)16x = 8 -------- On subtracting 4 from both the sidesx= 1/2So we can conclude that the Value of x is 1/2
we can verify the answer by putting back the value of x in the equation and both sides will have the same value.
2(4x+2)= 4x -12(x-1)
2(4*1/2+2)= 4*1/2 -12(1/2-1)
2(2+2) = 2-6+12
8=8
Hence Proved that x=1/2 is the correct answer
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Which of the following are Pythagorean triplets 4 cm 6 cm 8 cm 24 cm 10 cm 26 cm 13 cm 27 cm 30 cm 2 cm 17 cm 9 cm?
Pythagorean triplets 4cm,6cm,8cm,24cm,10cm,26cm,13cm,27cm,30cm 2 cm 17 cm 9 cm are 4 , 6 , 8cm and 24 , 10 , 26cm.
What is Pythagorean triplets ?
Pythagorean triplets are a set of three positive integers (a, b, c) such that [tex]a^{2}+b^{2} = c^{2}[/tex]. This relationship is known as the Pythagorean theorem, named after the ancient Greek mathematician Pythagoras. These triplets are often used in geometry, particularly in the study of right triangles.
To find pythagorean triplets ,
The question is asking to identify which sets of 3 positive integers from the given list satisfy the equation [tex]a^{2}+b^{2} = c^{2}[/tex]. The sets of numbers that satisfy this equation are 4 cm, 6 cm, 8 cm and 24 cm, 10 cm, 26 cm, these are pythagorean triplets. The other sets of numbers do not satisfy the equation and hence are not Pythagorean triplets.
Pythagorean triplets 4cm,6cm,8cm,24cm,10cm,26cm,13cm,27cm,30cm 2 cm 17 cm 9 cm are 4 , 6 , 8cm and 24 , 10 , 26cm.
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What ordered pairs are the solutions of the system of equations shown in the graph below?
The ordered pairs which give the solutions of the system of equations are (-4, 1) and (-8, 9)
How to determine what ordered pairs are the solutions of the system of equations?In order to determine the ordered pairs which give the solutions of the system of equations in a linear-quadratic graph, you need to find the points of intersection of the line and curve from the graph.
Then trace to the x and y-axes to find the ordered pairs values (Check the image attached)
Thus, the ordered pairs are (-4, 1) and (-8, 9)
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How is 13 a prime number?
13 is considered as a prime number as there are only two factors of 13 which are equals to 1 and 13 itself.
As given in the question,
Given number is equal to 13,
Prime numbers are those numbers which has only two factors : one and the number itself.
Here is not divisible by any other number.
Factors of 13 are equals to :
1 and 13 itself.
There are only two factors of thirteen which are equals to one and number 13 itself.
Therefore, 13 is considered as a prime number because there are only two factors of 13.
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What is a different common denominator you could use in promblem 2 describe how would you add fractions using this different common denominator is the result equivalent to the sun found In promblem 2 Promblem 2 is: 1/2+3/8
16 is the different common denominator, we can use to solve 1/2+3/8.
The result using 16 as common denominator is equivalent to the sum 1/2+3/8.
What is common denominator?A common denominator is a denominator that you can reach by both denominators.
We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount.
Given expression
1/2 + 3/8
multiplying and dividing 4 with 1/2
4/8 + 3/8
Lowest common denominator = 8
= (4 + 3)/8
= 7/8
Sum = 0.875
Taking expression:
1/2 + 3/8
Multiplying and dividing 8 with 1/2 and 2 with 3/8.
8/16 + 6/16
Different common denominator = 2 × 8 = 16
Now,
= (8 + 6)/16
= 14/16
Result = 0.875
Hence, the result using different common denominator = 16 for solving
1/2 + 3/8 is equivalent to the sum of 1/2 + 3/8.
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ashely bought 6 yds of ribbon for 5.28 . what ratio is proportional to this?
A) $1.36/2 yards C)$2.64/3 yards
B) $1.92/3yards D)$3.25/4 yards
PLEASE HELP AND SHOW WORK!
Graph the following equations.
y=-2x+1
The graph of the given equation will be a straight line.
What is the equation of a line?The equation of a straight line is y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.
Given is an equation, y = -2x+1, we are asked to plot a graph for the same,
To plot the graph, we will firstly find the coordinates,
Therefore, the equation is y = -2x+1,
Put x = 0,
y = 1
The first coordinates = (0, 1)
Put y = 0
x = 1/2
The second coordinates = (1/2, 0)
Now, plot this points on the graph, and connect them, since the equation is linear, we will get a straight line, passing through these points, that will be the line of the equation given, (refer to graph attached)
Hence, the graph of the given equation will be a straight line.
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What is the base in a power of 2?
A power of two is a number of the form 2ⁿ where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
Exponential FunctionThe exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price, etc that are growing or decay exponentially.
Example: Jonathan was reading a news article on the latest research made on bacterial growth. He read that an experiment was conducted with one bacterium. After the first hour, the bacterium doubled itself and was two in number. After the second hour, the number was four. At every hour the number of bacteria was increasing. He was thinking what would be the number of bacteria after 100 hours if this pattern continues. When he asked his teacher about the same the answer he got was the concept of an exponential function.
What is Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
Exponential Function DefinitionIn mathematics, an exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer:
A number line from -5 to 5 in increments of 1. An open circle is at 3 and a bold line starts from 3 and is pointing to the right
A block on the end of a spring is pulled to position x=a and released from rest. In one full cycle of its motion, through what total distance does it travel?.
The total distance it travels during one full cycle of motion is 4A. Hence, the correct answer is D.
When a block on the end of a spring is pulled to position x = A and released from rest, it begins to oscillate. The block will oscillate back and forth along the x-axis between the position x = A and the position x = -A.
In one full cycle of its motion, the block will travel from position x = A to position x = -A and back to position x = A. The total distance traveled by the block in one full cycle of its motion is the sum of the distance traveled in each direction.
The distance traveled by the block in one direction is A, and the distance traveled in the other direction is A. So, the total distance traveled by the block in one full cycle of its motion is:
A + A = 2A.It's important to note that the amplitude of the oscillation is equal to the distance from the equilibrium position to the position x = A. This means that the total distance the block moves in one full cycle is equal to twice the amplitude of the oscillation.
Therefore, the total distance traveled by the block in one full cycle of its motion is:
2.A = 4AHence, the correct answer is D, 4A.
This question should be provided with answer choices, which are:
A. A/2B. AC. 2AD. 4AThe correct answer is D.
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What are the 3 main types of 3D objects?
The three main types of 3D objects are polygonal meshes, NURBS, and implicit surfaces.
There are several types of 3D objects, but the three main categories are:
Polygonal meshes: These objects are made up of a large number of small polygons, such as triangles or quadrilaterals, that are connected to form the surface of the object. These are the most common type of 3D objects used in computer graphics and 3D modeling.NURBS (Non-Uniform Rational B-Splines): These objects are defined by mathematical equations and are used in CAD (computer-aided design) and other applications that require precise, smooth surfaces.Implicit surfaces: These objects are defined by an implicit equation, such as F(x,y,z) = constant, rather than a set of discrete points. They are used in scientific visualization and other applications that require smooth, continuous surfaces.To learn more about 3D objects at
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PLEASE HELP!!
A box holds 12 cans. The dimensions of the box are shown. Calculate the total volume of the twelve
Answer:
49875 cm^3
Step-by-step explanation:
We use the formula, "V = bh" to find the volume of one cylinder (can), where "b" is the area of the circle base of the cylinder, and "h" is the height.
First, we can find the volume of one cylinder.
The base would be calculated by "πr^2", where "r" is the radius. To find the radius, we can use the information given in the diagram: four cans in a row have a length of 84 cm. Thus, if we divide 84 by 4, we get the diameter of one can. If we divide that diameter by 2, we get the radius of one can: 84/4/2 = 10.5 = r
πr^2 --> π10.5^2 = 110.25π
The height is shown in the diagram: one can fits perfectly inside the box, so the height dimension of the box is the same as the can's height dimension.
h = 12
Now, we can calculate the volume of one can: V = 12 * 110.25π = 1323π
As the problem calls for the volume of 12 cans, we can multiply the volume of one can by 12 to find the volume of 12 cans:
12 * 1323π = 15876π = 49875 cm^3
Answer:
Step-by-step explanation:
Firstly we have to find the dimensions of the can.
Height of can - 12 cm
Diameter of can - 21 cm
The radius of can - 21/2 = 10.5 cm
Volume of can - [tex]\pi r^2[/tex] * h ( height )
[tex]3.14 * 10.5^2[/tex] * 12
3.14* 110.25 *12
346.185 *12
4154.22
Volume of 12 cans - 4154.22 *12
Answer - [tex]49850.64cm^3\\[/tex]
How do you label the sides of a 30-60-90 triangle?
We label sides as: the shorter leg is 30-degree angle, the longer leg is 60-degree angle and the hypotenuse is 90 degrees.
Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.
Triangle Properties 30-60-90
A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.
The shorter leg is the one that faces the 30-degree angle.
The longer leg is the one that faces the 60-degree angle.
The hypotenuse is the side that faces the right angle of 90 degrees.
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Given m
||n, find the value of x and y
dy.
(4y-7)°
(2x+3)°
(6x+9)⁰
m
n
The value of x is 21° and y is 13°. The solution is obtained using the properties of parallel lines.
What are Parallel lines?
When two lines in a plane do not cross at any point, they are said to be parallel. In other words, lines that never cross paths with one another and do not have a common junction point are said to be parallel.
The characteristics of parallel lines with respect to transversal are listed below:
Angles that coincide are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that alternate are equal.Exterior angles that alternate are equal.On the same side of the transversal, a pair of interior angles are supplementary.As shown in the figure, angles (2x+3)° and (6x+9)° denote the interior angles on the same side of the transversal.
Therefore, both the angles add upto 180°
So, (2x+3) + (6x+9)=180
8x+12=180
8x= 168
x= 21°
Also, angles (4y-7)° and (6x+9)° form a linear pair.
Therefore, both the angles add upto 180° and we know that x= 21°
So, (4y-7)+((6×21)+9)=180
4y+128=180
4y=52
y=13°
Hence, the value of x is 21° and y is 13°.
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What is class inequality?
Class inequality refers to the unequal distribution of wealth, income, and social status among different groups within a society. This means that some individuals or groups have more resources, such as money, property, and access to education and job opportunities, while others have less.
Economic inequality is one of the main forms of class inequality, where a small group of individuals or families own a disproportionate amount of wealth and control the majority of resources, such as land, businesses, and investments. This can lead to a lack of economic mobility for those in lower classes, making it difficult for them to improve their economic situation.
Another form of class inequality is educational inequality, where individuals from lower socio-economic backgrounds have less access to quality education, which in turn limits their opportunities for higher-paying jobs and career advancement. This can also lead to a lack of social mobility, as education is often seen as a key factor in upward mobility.
Healthcare inequality also plays a role in class inequality, as those from lower socio-economic backgrounds often have less access to quality healthcare, leading to poorer health outcomes and increased health disparities.
These forms of class inequality can perpetuate a cycle of poverty and disadvantage for those in lower classes, while those in higher classes have greater access to resources and opportunities, leading to a widening gap between the rich and the poor.
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Can a triangle be formed with 7 cm 10 cm and 5 cm as its sides?
The sum of 2 sides is greater than the largest side so the triangle can be formed.
How to create triangle ?Triangle Properties
A triangle's (of all varieties) total sum of angles is 180°.The length of a triangle's two longest sides added together is longer than the third side.Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.Any two triangle sides can add up to a length that is longer than the third side. The greatest side of a triangle is the side that faces the largest angle. The sum of the triangle's internal opposing angles is equal to any of its outer angles.
According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
Sum of 2 sides each are :
7 + 10 = 17 cm
7 + 5 = 12 cm
5 + 10 = 15 cm
So the sum of 2 sides is greater than the largest side so the triangle can be formed.
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Drag and drop each angle measure into the correct box to find the measure of each angle.
The measure of angles are,
m ∠K = 50°
m ∠L = 90°
m ∠M = 40°
m ∠LMN = 140°
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let the triangle KLM is given.
We have to find the measure of each angle of triangle.
Since the measure of three angles of triangle is 180 degree.
⇒ m ∠K + m ∠L + m ∠M = 180°
5x + 9x + 4x = 180°
18x = 180°
x = 10°
⇒ m ∠K = 5x = 5(10°) = 50°
m ∠L = 9x = 9(10°) = 90°
m ∠M = 4x = 4(10°) = 40°
m ∠LMN = m ∠L + m ∠K
= 90° + 50°
m ∠LMN = 140°
Hence,
m ∠K = 50°
m ∠L = 90°
m ∠M = 40°
m ∠LMN = 140°
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please help me with this
Answer:
answer is 23&11
Step-by-step explanation:
no explanation
Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not green) when choosing one marble from the bag.
The probability that the selected marble will not be green is 21/25.
What is probability?Probability is a measure of how likely something is to occur.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, we know that:
The bag contains: 2 red, 4 green, 10 yellow, and 9 purple
Probability formula: P(E) = favourable events/total events
Now, calculate as follows:
P(not green) = 21/25
Therefore, the probability that the selected marble will not be green is 21/25.
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Answer:
60%
Step-by-step explanation:
Answer: The answer to your question is 60%
Step-by-step explanation: The total number of marbles in Joseph's bag is:
2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25
The probability of choosing one marble that is not yellow can be found by dividing the total number of marbles that are not yellow by the total number of marbles in the bag:
P(not yellow) = (2 red + 4 green + 9 purple) / 25
P(not yellow) = 15/25
P(not yellow) = 3/5
P(not yellow) = 0.6 or 60%
Therefore, the answer is 60%.
Is 256 an exponential form?
Yes, 256 can be written in exponential form as 2^8 where 2 is the base and 8 is the exponent.
Jason's paycheck was $324.60. He put 12 of his paycheck into a savings acount and used 13 of what was left to pay for a new bike tire. How much money does he have remaining from his paycheck?
Answer:
456 money left and 3 left
Answer:
$246.70
Step-by-step explanation:
Assuming this is a percentages question
12% of $324.60 is $38.95
$324.60-$38.95=$285.65
13% of what was left ($285.65) is $37.13
$285.65-$37.13=$246.70
Parker could pay for 45% of hi college tuition with hi cholarhip. The remaining $10,500 he paid for with a tudent loan. What wa the cot of Parker' tuition? Show your work
The cost of parkers tuition is $19090.9.
The percentage is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
Given that,
The percent he pays with college tuition = 45%
The fee in percent which is not paid by scholarship = 100 - 45 = 55%
Let x be the total amount of parker's tuition, then the value of x:
55/100x = 10,500
55x = 10,50000
x= 19090.9
x = $19090.9
Thus, the cost of parkers tuition is $19090.9 if Parker was able to pay for 45 percent of his college tuition with his scholarship. The remaining $10,500 he paid for with a student loan.
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How do you solve a table of values in a function?
The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table.
what is functions ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.
given
The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table.
Data is recorded in tables of values by scientists and researchers, who then examine the data to look for patterns. As a result, they can use this pattern to anticipate future events.
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What is the solution of the system?
4g + h = -4
12g + 2h = -4
Enter the coordinate pair in the boxes in alphabetical order (_, _)
Which of the following expressions are polynomials ? (i) x^3−5x+2(ii) y^2+√2y–√5(iii) 2√x+7(iv) −6(v) 4t^2+1/6t+2√3(vi) z^2+5/z^2+1(vii) 1/3x(viii) 1−√5x(ix) 1/14x^−2+3x+5(x) 6√x+x^3/2/√x
In the given expression, expression [tex]x^3[/tex]−5x+2 is a polynomial expression. So the option (i) is correct.
In the given question we have to find which of the following expression are polynomials.
As we know that,
The Greek words "polynomial" and "nominal" are the origins of the word polynomial, which is translated as "many phrases" when combined. There is no limit to the number of terms that a polynomial can have.
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents. The expression is categorized as monomial, binomial, or trinomial depending on how many terms are present in it.
So if we see on the given expression then we can see that the option (i) [tex]x^3[/tex]−5x+2 have the degree 3 so [tex]x^3[/tex]−5x+2 is a polynomial expression.
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20 pts!!!! Danielle pays a monthly charge of $69 for her cable bill. She also pays a fee every time she watches a movie on demand.
Answer: y=69x+b
Step-by-step explanation:
x=# of months of her cable bill
b=# movie fees
y=total bill
Write the relation as a set of ordered pairs.
a.
ordered pairs: {(4, –2), (0, 0), (2, 4)}
b.
ordered pairs: {(–2, 4), (0, 0), (4, 2)}
c.
ordered pairs: {(-2, 4), (0, 0), (2, 4)}
d.
ordered pairs: {(4, -2), (0, 0), (4, 2)}
The correct option is C. The ordered pairs: {(–2, 4), (0, 0), (2, 4)}
What is an ordered pair?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.
It's important to remember that, the first the showed in the image represents a domain, and the second set represents a range. That means the values -2, 0, 2, must appear as the first value in the coordinate, and the values 4 and 0, must appear second.
Now, if we associate the given diagram with coordinates, it would be like
Therefore, the right answer is choice c.
Additionally, this relation models a quadratic function actually, because -2 and 2 have the same image 4.
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How do you find the shortest distance between two lines in 3D vectors?
The shortest distance between two lines in 3D represented by vectors can be found by using the dot product of the vector joining the two lines with the cross product of the direction vectors of the lines, divided by the length of the cross product vector.
To find the shortest distance between two lines in 3D space represented by vectors, you can use the following method:
Write the parametric equations of the two lines: Line 1: X = X1 + tv and Line 2: X = X2 + sv, where X1, X2 are the position vectors of the two lines, and v, s are the direction vectors of the two lines, respectively.Find the vector joining the two lines: X2 - X1Find the cross product of the direction vectors of the two lines, this is the vector that is perpendicular to both lines.Take the dot product of the vector joining the two lines and the cross product of the direction vectors, and divide by the length of the cross product vector.The absolute value of the result obtained in step 4 is the shortest distance between the two lines.To learn more about 3D vectors at
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Determine each segment length in right triangle XYZ.
Y
60°
Z 5 W
20
30°
10√/2
X
10√3
5
5√/2
XW
XY
15
5√3
The lengths of segments XY, XW, and YW in right triangle XYZ are given by:
XY = (1/2) * XZ
XW = (√3/2) * XZ
YW = (1 - √3/2) * XZ
Explanation:
To determine the lengths of segments XY, XW, and YW in right triangle XYZ, we can use the trigonometric ratios for the angles Y = 60° and Z = 30°.
Let's start with segment XY. The side opposite the 30° angle is half the length of the hypotenuse. Therefore, XY = (1/2) * XZ.
Next, let's find the length of segment XW. The side opposite the 60° angle is √3 times the length of the side opposite the 30° angle. Therefore, XW = √3 * XY = √3 * (1/2) * XZ = (√3/2) * XZ.
Finally, let's determine the length of segment YW. YW is the difference between XY and XW. Therefore, YW = XY - XW = (1/2) * XZ - (√3/2) * XZ = (1 - √3/2) * XZ.
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