The correct answer is: The lines are skew.
How to determine the relationship between two lines, specifically whether they are distinct parallel lines, skew, or the same line?To determine if the lines are distinct parallel lines, skew, or the same line, we can examine their direction vectors.
Let's denote the first line as L1 and the second line as L2. We'll start by finding the direction vectors of L1 and L2.
For L1, the direction vector is given by ⟨3, 5, -3⟩.
For L2, the direction vector is given by ⟨11, -6, 2⟩.
Now, let's compare the direction vectors to determine the relationship between the lines.
If the direction vectors are scalar multiples of each other, then the lines are parallel.
If the direction vectors are not scalar multiples of each other and not orthogonal (perpendicular), then the lines are skew.
If the direction vectors are orthogonal (perpendicular) to each other, then the lines are the same line.
To check if the direction vectors are scalar multiples, we can calculate their cross-product and check if it equals the zero vector.
The cross product of ⟨3, 5, -3⟩ and ⟨11, -6, 2⟩ is:
=(5 * 2 - (-3) * (-6))i - (3 * 2 - (-3) * 11)j + (3 * (-6) - 5 * 11)k
= (10 - 18)i - (6 - 33)j + (-18 - 55)k
= -8i - 27j - 73k
Since the cross product is not equal to the zero vector, the lines are not parallel.
Since the direction vectors are not scalar multiples and not orthogonal, the lines are skew.
Therefore, the correct answer is: The lines are skew.
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Need help understanding how to solve
For the two figures to be similar, the missing length must be 30.
What is the missing length?For the two figures to be similar, the dimension of each figures must be proportional to each other.
Let the missing length be x.
Hence,
x/25 = 24/20
We cross multiply
x × 20 = 24 × 25
x × 20 = 600
x = 600/20
x = 30
Therefore, for the two figures to be similar, the missing length must be 30.
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Elimination was used to solve a system of equations.
One of the intermediate steps led to the equation 9x = 27.
Which of the following systems could have led to this equation?
O
9x + 2y = 21
-9x - 2y = 21
10x - y = 15
x+y = - 12
7x - 2y = 15
x + y = 6
4x + 3y = 24
-5x - 3y = 3
The system of equation that could have led to the equation 9x = 27 is
7x - 2y = 15
x + y = 6
The correct option is the third option
7x - 2y = 15
x + y = 6
Solving systems of equationsFrom the question, we are to determine the system that could have led to 9x = 27
1.
9x + 2y = 21
-9x - 2y = 21
Subtracting, we get
9x + 2y = 21
-9x - 2y = 21
-------------------
18x + 4y = 0
2.
10x - y = 15
x + y = - 12
Subtracting, we get
10x - y = 15
x + y = - 12
---------------------
9x -2y = 27
3.
7x - 2y = 15
x + y = 6
Here, multiply the second equation by 2
2 × [x + y = 6]
2x + 2y = 12
Now, add to the first equation
7x - 2y = 15
2x + 2y = 12
------------------
9x = 27
4.
4x + 3y = 24
-5x - 3y = 3
Subtracting, we get
4x + 3y = 24
-5x - 3y = 3
---------------------
9x + 6y = 21
Hence, the system of equation that could have led to the equation 9x = 27 is
7x - 2y = 15
x + y = 6
The correct option is the third option
7x - 2y = 15
x + y = 6
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Select all the correct answers.
Which expressions are equivalent to this exponential expression?
Answer:
The answer that you have highlighted is correct.
Step-by-step explanation:
When you are dividing, you divide the exponents
-10 - (-4)
-10 + 4
-6
Joe's company sold insurance policies over the phone. Last month, 2 employees sold three hurricane policies, 6 employees sold two hurricane policies, and 9 employees sold a single hurricane policy. If a single employee is picked at random, what is the probability that the employee sold two hurricane policies or sold one hurricane policy
The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.
According to the statement
Number of employees who sold three hurricane policies is 2
Number of employees who sold two hurricane policies is 6
Number of employees who sold 1 hurricane policies is 9
SO,
The total number of employees is 2+6+9=17.
The number that sold two hurricane policies or sold one hurricane policy is 6+9=15,
so the Probability = Total number of policies sold / total number of employees
Probability = 15/17
So, The probability that the employee sold two hurricane policies or sold one hurricane policy is 15/17.
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Which system is equivalent to startlayout enlarged left-brace 1st row y = 9 x squared 2nd row x y = 5 endlayout
The set of equations that corresponds to the specified function are
y = 5 - x and 5 - x = 9x².
What is linear equation in two variables?
If an equation is expressed as ax + by + c=0, where a, b, and c are all real integers and a and b, the coefficients of x and y, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
The given equation is :
[tex]y=9x^{2}[/tex] equation 1.
[tex]x+y=5[/tex] equation 2.
From equation 2.
[tex]x+y=5\\y=5-x[/tex]
substituting into 1 equation.
[tex]5-x=9x^{2}[/tex]
The system of equations that is equivalent to the provided function is shown by the resulting equation, which is y = 5 - x and [tex]5-x=9x^{2}[/tex]
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A researcher randomly assigns participants to complete a crossword puzzle with or without music. The time it takes to complete the crossword puzzle is compared between groups. The experimental group in this example is:
Answer:
The music group
Step-by-step explanation:
The experiment group is the group where something is being modified, so the music group is the one having their environment modified.
Someone pls pls PLS, help, its urgent!!! ASAP!!
“Complete the proof (geometry)”
1) [tex]\overline{AB} \perp \overline{BD}[/tex], [tex]\overline{AB} \cong \overline{DB}[/tex], [tex]\overline{AC} \cong \overline{DE}[/tex] (given)
2) [tex]\angle ACB[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ABC[/tex] and [tex]\triangle BED[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\therefore \triangle ACB \cong \triangle DEB[/tex] (HL)
5) [tex]\therefore \angle ACB \cong \angle DEB[/tex] (CPCTC)
Which equation describes how the parent function, y = x3, is vertically stretched by a factor of 4?
Oy=x³ +4
O y=(x+4)³
O. y=4x³
O y=x4
Answer: [tex]y=4x^3[/tex]
Step-by-step explanation:
See attached image.
The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The parent function is,
⇒ y = x³
Now, After vertically stretched by a factor of 4 we get;
The value of function is,
⇒ y = 4x³
Hence, The equation of function after vertically stretched by a factor of 4 is,
⇒ y = 4x³
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a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram
The mass of brick is 2478 gram.
What is a rectangular prism?A rectangular prism has a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it has three dimensions- the base width, the height, and the length. The top and base of the rectangular prism are rectangular in shape. The pairs of opposite faces of a rectangular prism are identical or congruent.
A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches.
The volume of rectangular prism = length×width×height
= 8×3.5×2
= 56
Thus volume of brick is 56 cubic inches.
Convert inches to centimeter
1 inch = 2.54 centimeter
Therefore,
56 cubic inches = 56 x 2.54 x 2.54 x 2.54 cubic centimeter
56 cubic inches = 917.676 cubic centimeter
Thus, we get,
volume of a rectangular prism = 917.676 cubic centimeter
The brick has a density of 2.7 grams per cubic centimeter
Density = 2.7 grams
The mass of brick is given by formula = density × volume
[tex]\Rightarrow[/tex] = 2.7 × 917.676
[tex]\Rightarrow[/tex] = 2477.72
[tex]\Rightarrow[/tex] ≅ 2478
Thus mass of brick is 2478 gram.
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Use the drawing tools to form the correct answer on the provided graph.
Graph the line that represents the equation y= -2/3x + 1
The graph of the line is shown in the attached image.
Given that the equation of the line y=-2/3x+1.
The line equation is an algebraic representation of the set of points, which together form a line in an exceedingly frame of reference.
First, we'll take the intercepts of equation y=-2/3x+1 . find
Find the y-intercept
The y-intercept is that the value of y when the worth of x is adequate zero
For x=0
y=-2/3(0)+1
y=1
The y-intercept is that the point (0.1)
Find the x-intercept
The x-intercept is that the value of x when the worth of y is adequate to zero
For y=0
y=-(2/3)x+1
0=(-2/3)x+1
-1=(-2/3)x
x=3/2 or 1.5
The y-intercept is that the point (1.5,0).
To plot the line on a graph, draw the intercepts and connect the dots as shown within the figure.
Therefore, the graph for the line y=-(2/3)x+1 is attached below.
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Helppp please and thank uuu
What transformation is used to create this frieze pattern?
vertical reflection
glide reflection
horizontal reflection
180° rotation
Answer:
Using translation concepts, it is found that the transformation used to create this frieze pattern is a 180º rotation.
Step-by-step explanation:
when x=-1 what is the value of y?
Answer: y=3
Step-by-step explanation:
The x-axis is on the horizontal line, and the y-axis is on the vertical line. On the horizontal line at -1, just go up until you find where y is located.
By doing this, you can find that y=3.
Answer:
Step-by-step explanation:
All we have to do is find the point on the line where x = -1. If we know this, we can see how high the point is (i.e., find it's y-value). Then, we would know the value of y.
If we draw a vertical line from where x equals -1, we see that it crosses the line at point (-1, 3). This means that we can draw a line from the point to the number -1 on the x-axis and another line from the point to the number 3 on the y-axis.
Hence, the y-value when x=-1 would be 3.
A cup holds 2\9 litre of water. How many cups of water can be filled with 3litre bottle
Answer:
the answer might be 13.5
Using a table, find the range of the function for the given domain:
f(x) = 2x² -7 with domain: x = {-4, -2, 0, 3}
OA.y=(-5, 1, 11, 25}
OB. y = {4, 2, 0, -3)
OC. y =(-11,-9, -7,-4}
OD.y = (25, 1, -7, 11)
The range of the function f(x) = 2x² -7 with domain: x = {-4, -2, 0, 3} is y = (25, 1, -7, 11). Option D is the correct answer.
The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we substitute an x value, this set of values is what the function outputs. The y values are those.
In light of the query
x VS F(x) = 2x² -7
-4 F(4) = [tex]2(-4)^2 -7[/tex] = 25
-2 F(-2) = [tex]2(-2)^2 -7[/tex] = 1
0 F(0) = [tex]2(0)^2 -7[/tex] = -7
3 F(3) = [tex]2(3)^2 - 7[/tex] = 11
∴ Option D, y = (25, 1, -7, 11)
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Sandy rakes and bags the leaves on her front lawn in 30 mins. Randy does the same job in 20 mins. How many fewer minutes will it take to complete the same job if sandy and randy work together than if sandy works alone?
The number of minutes it take to complete the same job if sandy and randy work together than if sandy works alone is 18mins.
How to calculate time?According to this question, Sandy rakes and bags the leaves on her front lawn in 30 mins while Randy does the same job in 20 mins.
To calculate the time it will take both of them to work together, we use the following expression;
1/30 + 1/20 = 1/x
x = 12mins
Therefore, it will take 30 - 12 = 18 mins, to complete the same job if sandy and randy work together than if sandy works alone.
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Briana is looking for jobs and is hoping to find one that will allow
her to make at least $2,000 in her first paycheck. She has found
one possible postion at the local shoe store that is offering $200
signing bonues and a wage of $15 per hour. How many hours will
Briana need to work to make $2,000 in her first paycheck?
Answer: 120 hr
Step-by-step explanation: 15$ every hr so for 120 hrs it would be 1,800$ plus the signing bonus of 200$ would total 2,000$ but with out the bonus she would have to work 134 hrs for 2,010$
HURRY PLEASE!!!!!!
Jarrett splits his bag of j jelly beans into two equal piles and gives one pile to his brother. He then gives his brother seven more beans. Write an algebraic expression to represent the number of beans his brother has?
Refreshment we’re set up in one area of the gym . hot pretzels were a dollar lemonade was 50 cents, fruit was 35 cents , and cookies were a quarter . if you purchase two of each . How much money would you needed
Answer:
$4.20
Step-by-step explanation:
1+1+.50+.50+.35+.35+.25+.25=4.20
Nakeisha read 2 and 3/5 pages in 6 minutes at what rate, in pages per hour, did she read?
The rate at which she reads is 26 pages per hour
How to determine the rate?The given parameters are
Pages = 2 and 3/5
Time = 6 minutes
Convert the time from minutes to hour
Time = 6/60 hour
This gives
Time = 0.1 hour
The rate at which she reads is calculated as:
Rate = Page/Time
This gives
Rate = (2 and 3/5)/0.1 hour
Rewrite as:
Rate = 2.6 pages/0.1 hour
Divide
Rate = 26 pages per hour
Hence, the rate at which she reads is 26 pages per hour
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It has taken 3 hours to fill a 5 gallon bucket from leaky hose what is the rate in gallons per hour
Answer: 1.7
Step-by-step explanation:
The rate of gallons per hour is the same as the unit rate. You want to find out how many gallons are filled in one hour, so divide 3 down to one, 3 divided by 3 is one. Then, also divide 5 by 3. 5 divided by 3 is 1.6666... and as an hour is out of 60, round it to 1.7.
I hope this helps!
A university wants to determine the average salary of its graduating computer science majors. the university asks the graduating classes of 50 students to share their starting salaries when hired. the 50 students had an average salary of $100,000 with a standard deviation of $2,000. find a 95% confidence interval for the average starting salary of computer science majors from the university.
Option B. ($99,242.00, $100,758.01)
a) For n - 1 = 49 degrees of freedom, we have form t distribution tables:
P( t < 2.010) = 0.975
Therefore, P(-2.010 < t < 2.010) = 0.95
Therefore the confidence interval here is obtained as:
X +₋ t 8/√ⁿ
100 \pm 2.010*\frac{2}{\sqrt{50}}
100 \pm 0.5685
(99431.61, 100568.39)
Therefore A is the correct interval here.
Q2) From t distribution tables, we have here:
P(-2.680 < t < 2.680) = 0.99
Therefore the confidence interval here is obtained as:
100 \pm 2.010*\frac{2}{\sqrt{50}}
100 \pm 0.7580
(99242, 100785)
1) A university wants to determine the average salary of its graduating computer science majors. The university asks the graduating classes of 50 students to share their starting salaries when hired. The 50 students had an average salary of $100,000 with a standard deviation of $2,000. Find a 95% confidence interval for the average starting salary of computer science majors from the university.
a - ($99,431.61, $100,568.39)
b - ($99,445.64, $100,554.36)
c- ($99,982.26, $100,017.74)
d - The salaries are not normally distributed so we cannot compute a confidence interval
2) Find a 99% confidence interval for the previous problem.
a - ($99,271.44, $100,728.56)
b - ($99,242.00, $100,758.01)
c - ($99,996.46, $100,003.55)
d - The salaries are not normally distributed so we cannot compute a confidence interval
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3 is subtracted from the product of 8 and a number
Answer: (8 * x) -3
Step-by-step explanation:
The term product refers to multiplication, so let the unknown number be x and multiply it by 8. Then you can subtract 3 afterwards.
*= multiplication
The equation shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. If the orbital period of planet y is twice the orbital period of planet x, by what factor is the mean distance increased?.
The mean distance is increased by a factor of [tex]2^{3/2}[/tex] if the orbital period of planet y is twice that of the planet x.
Description of the Kepler's law.
The orbital period T and the mean distance from the sun, A, expressed in astronomical units (AU), are related in accordance with Kepler's third law.
The mathematical formula is,
T² = A³
Here, T denotes the orbital period and A represents the average separation or mean distance from the sun.
Now, if T(y) = 2T(x)
⇒ A'³(y) = 2A³(x)
A'(y) = [tex]2^{3/2}[/tex]A(y)
Thus, if orbital period of planet y is twice the orbital period of planet x, the mean distance is lengthened by a factor of [tex]2^{3/2}[/tex].
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Answer:
2 Superscript three-halves
Step-by-step explanation:
Edge
a data set has 8 numbers and 2 is the highest number what is the lowest?
The lowest number in the data set is -5.
How to illustrate the information?Let the data sets be consecutive numbers that has a highest number of 2.
Consecutive numbers mean that the.numvers follow each other. This will be:
-5, -6, -7, -8, -9, 0, 1, 2
Based on the numbers illustrated above, the lowest number is -5.
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What is the formula for margin of error?
Z•√√5
√r
OME =
OME =
OME =
z. √s
Z•
77
Z•S
√n
Z S
OME= 77
The margin of error is calculated using the formula, C. ME = z × s / √n.
What is the Formula Used to Determine Margin of Error?The formula for finding the margin of error is given as: ME = z × s / √n, where we have the following:
ME = margin of error
z = z-score
s = population standard deviation
n = sample size
The margin of error is used to determine amount of error in a random sampling.
Thus, the formula is: C. ME = z × s / √n.
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A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Find the probability of tossing a head and drawing a red marble. Explain your reasoning.
Using it's concept, there is a 0.1667 = 16.67% probability of tossing a head and drawing a red marble.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the coin, one out of two outcomes are heads.For the marble, two out of six marbles are red.Hence the probability of tossing a head and drawing a red marble is:
[tex]\frac{1}{2} \times \frac{2}{6} = \frac{1}{6} = 0.1667[/tex]
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Find the interval in which the function is negative.
f(x)=x²-3x - 4
1. (-∞0, -1)
II. (-1, 4)
HI. (4, ∞)
Oll only
III only
OLI
LIII
Answer: II only: (-1, 4)
Step-by-step explanation:
x^2 - 3x - 4 is a parabolic function. When you factor the equation, it comes out to f(x) = (x-4)(x+1). Thus, the function as zeros at -1 and 4. Since the a value is positive, the parabola points up. Therefore, if you graph the function, it is negative between -1 and 4, so the answer is II only
My fruit basket contain apples and oranges.The ratio apples to oranges is 3:8.When I remove one apple the ratio changes to 1:3 .How many apples are in the basket
The number of apples in the basket are; 24 apples
How to simplify simultaneous equations?Let there be X number of apples and Y number of oranges.
Thus by the given ratio we can say that;
x/y = 3/8 -----(1)
(x — 1)/y = 1/3
3x — 3 = y ----(2)
Substitute 3x - 3 for y in eq 1 to get;
x/(3x - 3) = 3/8
8x = 9x - 9
9x - 8x = 9
x = 9
Thus;
y = 3(9) - 3
y = 24 apples
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ABCD is a rectangle. What is the value of x
Write the equation of the line that passes through the points (-6,-3) and (-3,1)
Answer:
[tex] y = \frac{4}{3} x + 5[/tex]
Step-by-step explanation:
The slope is
[tex] \frac{ - 3 - 1}{ - 6 - ( - 3)} = \frac{4}{3} [/tex]
Substituting into point-slope form,
[tex]y - 1 = \frac{4}{3} (x + 3) \\ \\ y - 1 = \frac{4}{3} x + 4 \\ \\ y = \frac{4}{3} x + 5[/tex]