Answers
Answer:
1.a. skew
1.b. parallel
1.c. none of the above
1.d. perpendicular
1.e. parallel
1.f. skew
2.a. never
2.b. always
2.c. always
2.d. sometimes, sometimes, sometimes
Step-by-step explanation:
For these questions, it is critical to know the definitions of each of the terms.
DefinitionsPerpendicular: Two intersecting lines that form a right angle.Parallel: Two non-intersecting lines that are coplanar.Skew: Two non-intersecting lines that are not coplanar.Problem Breakdown
1.a. skew [tex]\overset{\longleftrightarrow}{AB} \text{ and } \overset{\longleftrightarrow}{EF}[/tex]
Point E is not on line AB. Any three non-linear points form a unique plane (left face), so A, B, and E are coplanar. Point F is not in plane ABE. Since line EF and line AB do not intersect and are not coplanar, they are skew.
1.b. parallel [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{EH}[/tex]
Line CD is parallel to line AB, and line AB is parallel to line EH. Parallel lines have a sort of "transitive property of parallelism," so any pair of those three lines is coplanar and parallel to each other.
1.c. none of the above [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{GA}[/tex]
Line AC and line GA share point A, necessarily intersecting at A. Therefore, line AC and line GA cannot be parallel or skew.
Any three points form a unique plane, so these two lines are coplanar, however, do they form a right angle? If the figure is cube-shaped, as depicted, then no.
Note that each line segment AC, AG, and CG are all the diagonal of a cube face. A cube has equal edge lengths, so each of those diagonals would be equal. Thus, triangle ACG is an equilateral triangle.
All equilateral triangles are equiangluar, and by the triangle sum theorem, the measures of the angles of a planar triangle must sum to 180°, forcing each angle to have a measure of 60° (not a right angle). So, lines AC and GA are not perpendicular. (If the shape were a rectangular prism, these lines still aren't perpendicular, but the proof isn't as neat, there is a lot to discuss, and a character limit)
"none of the above"
1.d. perpendicular [tex]\overset{\longleftrightarrow}{DG} \text{ and } \overset{\longleftrightarrow}{HG}[/tex]
Line DG and line HG share point G, so they intersect. Both lines are the edges of a face, so they intersect at a right angle. Perpendicular
1.e. parallel [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{FH}[/tex]
Line AC is a diagonal across the top face, and line FH is a diagonal across the bottom face. They are coplanar in a plane that cuts straight through the cube from top to bottom, but diagonally through those faces.
1.f. skew [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{AG}[/tex]
Point A is not on line CD, and any three non-linear points form a unique plane (the top face), so C, D, and A are coplanar. Point G is not in plane ACD. Since line CD does not intersect and is not coplanar with line AG, by definition, the lines are skew.
2.a. Two lines on the top of a cube face are never skew
Two lines are on a top face are necessarily coplanar since they are both in the plane of the top face. By definition, skew lines are not coplanar. Therefore, these can never be skew.
2.b. Two parallel lines are always coplanar.
If two lines are parallel, by definition of parallel lines, they are coplanar.
2.c. Two perpendicular lines are always coplanar
If two lines AB and CD are perpendicular, they form a right angle. To form a right angle, they must intersect at the right angle's vertex (point P).
Note that A and B are unique points, so either A or B (or both) isn't P; similarly, at least one of C or D isn't P. Using P, and one point from each line that isn't P, those three points form a unique plane, necessarily containing both lines. Therefore, they must always be coplanar.
2.d. A line on the top face of a cube and a line on the right side face of the same cube are sometimes parallel, sometimes skew, and sometimes perpendicular
Consider each of the following cases:
Parallel: Consider line CD (top face), and line GF (right face). They are coplanar and don't intersect. By definition, parallel.Skew: Consider line AD (top face), and line GF (right face). They aren't coplanar and don't intersect. By definition, skew.Perpendicular: Consider line AD (top face), and line GD (right face). They do intersect at D, and form a right angle. By definition, perpendicular.None of the above: Consider line AC (top face), and line GC (right face). These lines intersect at C, but as discussed in part 1.c, they form a 60° angle, not a right angle. By definition, "none of the above".These 4 cases prove it is possible for a pair of top face/right face lines to be parallel, perpendicular, skew, or none of the above. So, those two lines are neither "always", nor "never", one of those choices. Therefore, they are each "sometimes" one of them.
Related Questions
Please answer the question down below!
Answers
Answer:
144°Step-by-step explanation:
regular decagon = all side equal and all angles congruent, so your answer is 144°
As part of a weight loss plan, Levi’s average Calories consumed per day, denoted by c, subject to a maximum of 15 calories, is measured to calculate the amount of weight he will lose. If he is losing weight consistently, what is the domain of the function?
a. c < 0
b. c > 0
c. 0 ≤ c ≤ 15
d. 0 < c ≤ 15
Answers
Using it's concept, it is found that the domain of the function is given as follows:
d. 0 < c ≤ 15
What is the domain of a function?The domain is the set that contains all possible input values for the function.
He is losing weight consistently, hence c > 0, and the maximum amount is of 15 calories, hence c ≤ 15 and the domain is given by:
d. 0 < c ≤ 15
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Choose the correct graph of the following condition. {(x, y) : x - y6}
Answers
The correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.
What is a graph?
A graph is a diagram showing the relation between variable quantities each measured along one of a pair of axes at right angles.
In this case, the correct graph of the following condition. {(x, y) : x - y6} is depicted in the graph attached.
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The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minutes). The remaining credit after 22 minutes is $36.70, and the remaining credit after 52 mintues is $32.20. What is the remaining credit after 85 mintues of calls?
Answers
After 85 minutes of calls, there are $27.25 left on the card.
What is the remaining credit after 85 minutes of calls?
A linear equation in slope-intercept form is:
y = a*x + b
Where a is the slope.
If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)
(points of the form (time, dollars)).
So the slope is:
[tex]a = \frac{32.2 - 36.7}{52 -22} = -0.15[/tex]
The linear equation is then:
y = -0.15*x + b
To find the value of b, we use the point (22. 36.7)
36.7 = -0.15*22 + b
36.7 + 0.15*22 = b = 40
Then the linear equation is:
y = -0.15*x +40
The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.
y = -0.15*85 + 40 = 27.25
This means that after 85 minutes of calls, there are $27.25 left on the card.
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Given the first degree function f(x) = 2x +3, what is the value of f(10)?
a) 23
b) 25
c) 30
d) 50
Answers
Answer:
a
Step-by-step explanation:
substitute x = 10 into f(x) , that is
f(10) = 2(10) + 3 = 20 + 3 = 23
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
[tex]\large \bold {ANSWER}[/tex]
[tex]\boxed{\underline{\huge{\tt{\orange{\: \: a)23 \: \: }}}}}[/tex][tex]\large \bold {SOLUTION}[/tex]
Given the first-degree function:
[tex]\Large\begin{array}{c}\rm f(x)=2x+3\end{array}[/tex]
We were asked to determine the value of f(10), so, to find its value, just replace the 10 where there is x in the function, see:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(x)=2x+3\\\\ \rm f(10)=2\cdot 10+3\end{array}\end{gathered}[/tex]
You see, we put that dot there, which indicates multiplication, because when a number is next to a letter it indicates that it is multiplying, thus:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(10)=2\cdot 10+3\\\\ \rm f(10)=20+3\\\\ \red{\boxed{\rm f(10)=23}}\checkmark\end{array}\end{gathered}[/tex]
Hence, the value of f(10) in this function is equal to 23.
Write an equation in point-slope form of the line that passes through the given point and with the given slope m
(-9,2); m=6
Answers
The equation is [tex]\boxed{y-2=6(x+9)}[/tex].
Sarah and her friends split a bag of candy evenly. They each ate 13 pieces of candy and there are 2 pieces leftover. How many pieces of candy were originally in the bag?
Answers
Answer:
54
Step-by-step explanation:
⇒ 1 + 3 = 4
⇒ 4 * 13 = 52
⇒ 52 + 2 = 54 (Basic Operation)
What is the domain of the radical function shown on the graph y = -√x-2-4
Answers
Answer:
all real numbers
Step-by-step explanation:
the answer is all real numbers.
we know this since if you plug in any value for x we will get a real number.
hope this helps
A person buys a used car with a down payment of $1,200 and makes monthly payments of $275 for 3 years.What is the total amount of the person pays for the car?PLEASE EXPLAIN
A.$2,025
B.$9,900
C.11,100
D.13,500
Answers
Answer:
2025 $
Step-by-step explanation:
275 multiply 3 +1200
Answer:
A.$2,025
Step-by-step explanation:
$275 x 3 years + $1,200
= $2,025
which expression is equivalent to...
Answers
Answer:
[tex]\frac{y^{12} }{5}[/tex]Step-by-step explanation:
1) Cancel [tex]x^5[/tex].
[tex]\frac{9y^{16} }{45y^4}[/tex]
2) Take out the constants.
[tex]\frac{9}{45} \times\frac{y^{16} }{y^4}[/tex]
3) Simplify [tex]\frac{9}{45}[/tex] to [tex]\frac{1}{5}[/tex].
[tex]\frac{1}{5} \times\frac{y^{16} }{y^4}[/tex]
4) Simplify.
[tex]\frac{y^{16} }{5y^4}[/tex]
5) Use Quotient Rule: Use Quotient Rule: [tex]\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}[/tex].
[tex]\frac{{y}^{16-4}}{5}[/tex]
6) Simplify [tex]16-4[/tex] to [tex]12[/tex].
[tex]\frac{y^{12} }{5}[/tex]
A radioactive substance decays from 90 mg to 12.6 mg in 29 years according to the exponential decay model y=ae−bx , where a is the initial amount and y is the amount remaining after x years.
Find the b -value.
Use the EXACT b -value to write the exponential decay model for this substance with initial amount 90 mg, then use that model to find the half-life.
Find the half-life.
Answers
The half life of the radioactive substance is 10.22 years.
What is Half Life ?Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).
It is given that
y = ae⁻ᵇˣ
here a is the initial amount , y is the amount remaining after x years
a = 90mg at x =0
Value of y = 12.6 mg at x = 29 years
On substitution of value
12.6 = 90 e⁻²⁹ᵇ
0.14 = e⁻²⁹ᵇ
b = 0.0678
The equation is
[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]
Half life is when the concentration is reduced to half
On 1st half life , the concentration = 90/2 = 45 mg
[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]
x = 10.22 years
Therefore the half life of the radioactive substance is 10.22 years.
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The graphs below have the same shape. What is the equation of the red graph? g(x) = A. g(x)=2^x+3-2 B. 2^x-3-2 C. 2^x-2-3 D. g(x)=^x+2-3
Answers
The equation of the red graph is g(x)=^x+2-3.
Since the upscaling in the y-axis is not the main focus of this equation (being g(x) and not g(y)), the change is not applied to the x-axis.
What is the equation of the graph?
The y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. The slope is the change in y over the change in x.
Hence, we can rule out (-3)^2 and (x+3)^2 since they apply changes to the x-axis.
Finally, since this is an upscaling of the y-value on the y-axis, the answer is x^2 + 3 and not x^2 - 3.
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Help me with this piecewise function!
Answers
Answer:
According to the given function, the value of h(-1) is -1, h(-0.5) is 0 and h(1) is 1.
Step-by-step explanation:
The given function says that:
If the range of the values of x is x∈(-2,-1], then the value of the function is -1.
If the range of the values of x is x∈(-1,0], then the value of the function is 0.
If the range of the values of x is x∈(0,1], then the value of the function is 1.
If the range of the values of x is x∈(1,2], then the value of the function is 2.
In the first case, we have x = -1. This satisfies the first condition. So accordingly, the value that the function will give is -1.
In the second case, we have x = -0.5. This satisfies the second condition. So accordingly, the value that the function will give is 0.
In the third case, we have x = 1. This satisfies the third condition. So accordingly, the value that the function will give is 1.
So, h(-1) = -1, h(-0.5) = 0 and h(1) = 1.
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What is the solution to 3(–3x + 9) = −18?
O x = -5
O x = 5 or x=1
O x = -5 or x = 1
no solution
Answers
Answer:
x = 5 (If solved algebraically)
No Solution (If the parentheses are absolute value lines)
Step-by-step explanation:
Result when solving this way: 3|-3x + 9| = -18
1) Divide both sides by 3
|-3x + 9| = -18/3
2) Simplify 18/3 to 6
|-3x + 9| = -6
3) Break down the problem into these 2 equations.
-3x + 9 = -6
- (-3x + 9) = -6
4) Solve the 1st equation: -3x + 9 = -6
- Subtract 1 from both sides.
-3x = -6 - 9
-Simplify -6 - 9 to -15.
-3x = -15
-Divide both sides by -3.
x = -15/-3
- Two negatives make a positive.
x = 15/3
- Simplify 15/3 to 5.
x = 5
6) Solve the 2nd equation: - (-3x+ 9) = -6
1 - Remove parentheses
3x - 9 = -6
2 - Add 9 to both sides
3x = -6 + 9
3 - Simplify -6 + 9 to 3.
3x = 3
- Divide both sides by 3.
x = 1
6) Collect all solutions.
x = 1,5
7) Check solution.
When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.
We will drop x = 1 from the solution set.
8) Check solution.
When x = 5, the original equation 3|-3x + 9| = -18 does not hold true.
We will drop x = 5 from the solution set.
9) Therefore,
No solution exists.
Result when solving algebraically:
Simplifying
3(-3x + 9) = -18
Reorder the terms:
3(9 + -3x) = -18
(9 * 3 + -3x * 3) = -18
(27 + -9x) = -18
Solving
27 + -9x = -18
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-27' to each side of the equation.
27 + -27 + -9x = -18 + -27
Combine like terms: 27 + -27 = 0
0 + -9x = -18 + -27
-9x = -18 + -27
Combine like terms: -18 + -27 = -45
-9x = -45
Divide each side by '-9'.
x = 5
Simplifying
x = 5
In the diagram below, all the measurements are given correct to the nearest cm.
Not drawn
to scale
28 cm
15 cm
21 cm
42 cm
Calculate the greatest possible area of the shaded region.
+
P
Answers
Answer: 462 square cm
Step-by-step explanation:
The area of the shaded region is the difference between the areas of the two rectangles.
Larger Rectangle: (42)(21)
Smaller Rectangle: (28)(15)
Area of shaded: (42)(21)-(28)(15)=462 square cm
what is the average daily balance for the February 1-28 billing period in the table?
Answers
i added the closing balances and divided by the 4 selected days
either that or 44.54 if you divide by 28 days of February instead…
i might be wrong though
what is the answer to the question?
Answers
Using logic concepts, the correct statement is given by:
[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.
What are the events in this problem?The events are:
Event P: Henry is wearing a red shirt.Event Q: Henry is wearing khaki shirts.The statement is:
Henri is wearing a red or blue shirt today with jeans.
A red or blue shirt can be represent by p or not p, that is:
[tex](p \vee \neg p)[/tex]
Jeans is not khaki, hence the second part is:
[tex]\neg q[/tex]
Combining the statements, we have that the expression is:
[tex](p \vee \neg p) \wedge \neg q[/tex]
Since p and q are true, [tex]\neg q[/tex] is false, and the entire statement is false. Hence the correct option is:
[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.
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The table shows the probabilities of certain prizes in a restaurant’s contest where the first 100 customers are winners.
A 2-column table with 6 rows. The first column is labeled prize with entries 1 dollar drink, 5 dollar meal, 5 dollar gift card, 10 dollar gift card, 20 dollar gift card, 100 dollar gift card. The second column is labeled number of prizes with entries 44, 25, 16, 10, 5, 1.
How does the $100 gift card affect the measure of center of the data?
It increases the mean value of the prizes.
It decreases the mean value of the prizes.
It increases the median value of the prizes.
It decreases the median value of the prizes.
Answers
A mean is an arithmetic average of a set of observations. The correct option is A.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Since the median is the middle value of the given data set, therefore, the median will not be changed for the given data set. But since the mean is the arithmetic average, therefore, the $100 gift will increase the mean value of the prizes.
Hence, the correct option is A.
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Answer:
this is the anwser
this
A vehicle purchased for $20,700 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 15 years after purchase.
Answers
The approximate value of the vehicle 15 years after purchase is $11,221.19.
What is the approximate value of the vehicle 15 years after purchase?Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.
Value of the car = purchase price x (1 - rate of decline)^number of years
20,700 x (1 - 0.04)^15 = $11,221.19
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Calculate this logarithmic expression
Answers
The solution of the logarithmic expression [tex]\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})[/tex] is [tex]\log_2[270][/tex]
How to solve the logarithmic expression?The expression is given as:
[tex]\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})[/tex]
Apply the product law of logarithm
[tex]\log_2[(17 -\sqrt{19}) *(17 +\sqrt{19})]\\[/tex]
Apply the difference of two squares
[tex]\log_2[(17^2 -(\sqrt{19})^2][/tex]
Evaluate the squares
[tex]\log_2[(289 -19][/tex]
Evaluate the difference
[tex]\log_2[270][/tex]
Hence, the solution of the logarithmic expression [tex]\log_2(17 -\sqrt{19}) + \log_2(17 +\sqrt{19})[/tex] is [tex]\log_2[270][/tex]
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A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one- quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number. 16 NO 8 K 3₂ 5 2 4 st 6 8 10 12 14 16 Which equations represent the situation? Hurry
Answers
this is how we do it, jus learn abt it
Algebra 2 help please
Answers
Blank 1: 3
Blank 2: 27
Blank 3: 21
you have to distribute the three to everything inside the parenthesis, and because it's directly in front of the parenthesis it's being multiplied.
3(x - 9) = 3x - 27
Now you need to isolate the y, in this e ample you need to add 6 to both sides
the final equation should be:
y = 3x - 21
This is a lengthy math problem. Help please! Thank you
Answers
Step-by-step explanation:
look at the attached and just plot the data. S on the x-axis and s(x) on the y-axis.
Determine the Theorem or Postulate that proves triangle
congruence. If the triangles cannot be proven congruent,
choose "not congruent."
Answers
Answer:
SSS theorem
Step-by-step explanation:
It is indicated in the image that 2 sides of the triangles are congruent, and the third side is shared, which makes the third side automatically congruent as well. Therefore, we can use the side-side-side theorem to prove that the triangles are congruent.
An elephant went 119 km moving 42 km/h how many hours did the journey take?
2 1/6
2 1/2
2 5/6
Answers
Answer:
1 HR ---> 42 km
? .----> 119 km
119 * 1/42
2.833
Answer:
[tex]\boxed {2 \frac{5}{6}}[/tex]
Step-by-step explanation:
Formula used :
[tex]\boxed {Time = \frac{Distance}{Speed}}[/tex]
Solving :
Time = 119/42
Time = 17/6
Time = 2 5/6 hours
Question 18 25
f(x) = 2x
g(x) = 4x + 1
Find
() (2). Include any restrictions on the domain.
A.
(4) (x) = 477³¹, x ≥ 0
○ B. ( 4 ) (x) = ¹⁄⁄², ¤ / 0
4c-1
x
O c. (1) (₂) -
O D. (5)(x) =
✓/2T
55-1
2,² / 1
2 / -4
Answers
Answer: D
Step-by-step explanation:
[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{4x+1}[/tex].
This eliminates A and B.
Also, the domain excludes when the denominator equals 0, which in this case, makes the answer D
Put the equation y+x^2-10+16 in the form y=(x-h)^2+k
Answers
Answer:
Step-by-step explanation:
hello :
y=x²-10x+16 in the form y=(x-h)²+k
y= x²-2(5)(x)+16
y = x²-2(5)(x)+5²-9
y= (x-5)²-9 when h=5 and k = -9
Covert 3/7into a percent
Answers
Answer:
42.86%
Step-by-step explanation:
Our percent fraction is 42.857142857143/100, which means that 37 as a percentage is 42.86%
Here we are going to show you step by step how to convert the fraction 3/7 to a percentage.
In the fraction 3/7, 3 is the numerator and 7 is the denominator.
First, we are going to divide the numerator by the denominator. Therefore, we are going to divide 3 by 7.
3 ÷ 7 = 0.428571A percentage shows a number as a proportion of one hundred.
Now we are going to multiply 0.72 by 100 to get the percentage.
0.428571 x 100 = 42.86Therefore, the answer to 3/7 percent is
42.86%Note: If necessary, we round to the nearest hundred.
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
help please
what is
Answers
Option A. is correct for the given condition.
Lets solve it through steps of range and functions,
First of all, Solve the equation:
[tex]f(x) = |x|+5[/tex]
[tex]= > x = -5[/tex] (1)
[tex]= > x = 5[/tex] (2)
So these would be the ranges of X in between 5 and -5.
Hence option A. [tex]R{f(x)eR [f(x) < 5}[/tex] is correct.
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This is the full question
Answers
Answer:
< $0 --------------$35------ $50>
Step-by-step explanation:
I see it's still the same, the maximum discount can be put off is still $50
and you can find that out by discount 30% off 50 to get $35 :)
< $0 --------------$35------ $50>
