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
Use Newton’s Method with initial approximation x1=1 to find x4, the third
approximation to the root of the equation x3+3x+sin(x)=5. What is the result?
Answers
Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence
[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]
Differentiating [tex]f(x)[/tex] gives
[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]
Then
[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]
[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]
[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]
which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.
Which expression is to equivalent to....
Answers
Answer:
B.) 2x¹⁰y¹²
Step-by-step explanation:
To begin, because all of the terms in the top and bottom are combined (right next to each other being multiplied), the coefficients can be divided like any normal number. When you divide variables with powers, you need to subtract the denominator powers from the numerator powers.
Therefore,
60 / 30 = 2
x²⁰ / x¹⁰ = x²⁰ ⁻ ¹⁰ = x¹⁰
y²⁴ / y¹² = y²⁴ ⁻ ¹² = y¹²
Combined, the simplified expression is 2x¹⁰y¹².
On Sunday, a local hamburger shop sold a combined total of 512 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?
Answers
Answer:
512? xd
Step-by-step explanation:
Answer:
128
Step-1by-step explanation:
An easy way of solving these sort of problems is to set up an equation
Since we have a total, that being 512 burgers, we can set an equation equal to that number.
We can say that hamburgers is represented by x. Since we sold 3 times more cheeseburgers than the amount of hamburgers, we can represent this as 3x.
Since these totals are combined, we can represent this via an equation:
512 = x + 3x
Solve for x accordingly, and we are given 128, which is equal to the amount of hamburgers.
7/8 yard of material is needed to make a blanket, how many blankets can be made from 21 yards of material?
Answers
Answer:
24
Step-by-step explanation:
the question translates to asking how many times does 7/8 fit in 21, so 21 divided by 7/8.
when we divide by a fraction, we can multiply by it's inverse, so 21 divided by 7/8, is 21 multiplied by 8/7. so:
21×8/7 = (21×8)/7 = (21/7)×8 = 3×8 = 24
2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
Answers
The graph is attached with the answer.
What is an Inequality ?When two algebraic expressions are equated using an inequality operator , The statement formed is called In equality.
The given Inequality is 2x + y ≤ 2
in slope intercept form can be written as
y ≤ -2x +2 , here slope is -2 and intercept is 2
As an equation it will be
y = -2x +2
x y
0 , 2
1 , 0
2 -2
The graph is plotted
The area is shaded and the test for the origin is applied , and it lies in the shaded region.
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Thaddeus models the number of hours of daylight in his town as
D(t) = 3sin(t) + 12, where D is the number of daylight hours and t is the
time in months since January 1.
What are the least and greatest numbers of daylight hours over the course of
a year?
Answers
Answer:
(π2,15)(π2,15) is a local maximal
(3π2,9)(3π2,9) is a local minimal
Step-by-step explanation:
Please help!!! I will give 20 points to the correct answer!! Thanks so much
Answers
Answer:
either it's 7 and 3 but not sure
Step-by-step explanation:
7x3 =21
now for the negative -10 it would basically be -7+-3=-10
For which value(s) of xwill the rational expression below equal zero? Check
all that apply.
(x - 3)(x + 6)/x +7
A. -6
B. -7
C. 7
D. 3
E. 6
F. -3
Answers
Answer:
A. -6
D. 3
Step-by-step explanation:
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard. (the answer is 10 points but can someone please tell me how to do it and pls explain why)
Answers
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Will give brainliest or whatever it’s called
Answers
C is the right answer.
hope it helps...
Answer:
C.
Step-by-step explanation:
Calculating this in Desmos, the closest equation to the points on the graph will have to be c
If each pound of beef costs $3.69, how much does 2 pounds cost? Round to the nearest cent.
Answers
Answer: Two pounds of beef costs $7.38.
Step-by-step explanation:
Multiply the cost for one pound by the amount of pounds you need.
$3.69×2=$7.38
I hope this helps!!
A researcher believes that singing to plants causes them to grow an extra 0.5 inches on average per month. She tests this with 20 of her own plants by bringing 10 to work and leaving 10 at home. The ones at home she sings to each day, and she does not sing to the ones at her work.
Answers
The control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.
How to depict the control variable?According to the information, the researcher wants to seek whether singing to plants causes them to grow taller.
The explanatory variable is singing. Therefore, the researcher can control some of the variables to determine the explanatory variable on the growth of the plant.
Hence, the control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.
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Challenge time! Isn't time to give your brains a break? Its a fun challenge! EARN 20 POINTS NOW
Answers
Answer:
The answer is 64
Step-by-step explanation:
If you find this answer helpful pls mark it the brainliest answer
it's easy 64 the key is in the pic.
144 to the 1/2 power
Answers
Answer:
(144)^1/2
(12^2)^1/2
12 is the answers
Step-by-step explanation:
please mark me as brainlest
Answer:
12
Step-by-step explanation:
Rewrite 144 as 12²
(12²)^1/2
Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
12^2(1/2)
Cancel the common factor of 2.
Cancel the common factor.
Rewrite the expression
12^1
Evaluate the exponent.
12
Determine the next three terms in the following sequence: Negative 1, one-half, negative one-fourth, StartFraction 1 Over 8 EndFraction,____, ____, ____,... a. StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, StartFraction 1 Over 48 EndFraction b. StartFraction 1 Over 16 EndFraction, StartFraction 1 Over 32 EndFraction, StartFraction 1 Over 64 EndFraction c. Negative StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, Negative StartFraction 1 Over 48 EndFraction d. Negative StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, Negative StartFraction 1 Over 48 EndFraction
Answers
The next three terms will be -1/16, 1/32, and -1/64. Then the correct option is B.
What is the geometric sequences?Let a be term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
The sequence is given below.
-1, 1/2, -1/4, 1/8,....
The common ratio will be -1/2.
Then the next three terms will be
a₅ = a₄ x (-1/2)
a₅ = (1/8) x (-1/2)
a₅ = -1/16
a₆ = a₅ x (-1/2)
a₆ = (-1/16) x (-1/2)
a₆ = 1/32
a₇ = a₆ x (-1/2)
a₇ = (1/32) x (-1/2)
a₇ = -1/64
Then the next three terms will be -1/16, 1/32, and -1/64.
Then the correct option is B.
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Answer:
C
Step-by-step explanation:
A line of best fit was drawn for 16 data points. What is the maximum number
of these data points that may not actually be on the line?
OA. 14
OB. 13
O C. 15
OD. 16
Answers
The maximum number of data points that may not actually be on the line is 16. so, the correct option is D.
How to find the line of best fit?We know that a line of best fit is basically a straight line drawn for a given data that may or may not pass through data points.
It is given that the line is drawn for 16 data points.
Hence, the line may or may not pass through all these 16 points.
Therefore, the maximum number of data points that may not actually be on the line is 16.
so, the correct option is D.
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i give brainliest to first person who gets it correct
Answers
Answer:
(-4,-3)
Step-by-step explanation:
The point where those 2 equations intersect is (-4,-3)
Solve x:
3x + 99x= 1224
10 pts
Answers
Reason
Combine like terms
3x + 99 x = 1224
102x = 1224
Now solve for x
Divide both sides by 102
x= 12
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]help me pleaseeeeeeeeeeee i need the answer fast because it is limited
i will mark as brainiest
Answers
Answer:
D
Step-by-step explanation:
Original area = x * x = x^2
New area = x ( x +3.5) = x^2 + 3.5x <====the underlined is the increase in area
For all a and b, what is the sum of (a-b)² and (a+b)²
Answers
Answer:
2a² + 2b²
Step-by-step explanation:
(a - b)² + (a + b)² ← expand both factors using FOIL
= a² - 2ab + b² + a² + 2ab + b² ← collect like terms
= 2a² + 2b²
Step-by-step explanation:
Expand both classic quadratics and combine like terms to find the sum:
(a−b)2+(a+b)2
what is life?bhkbkbkjnmmkjopjlknm nbgvuyihjknm
Answers
Answer:
yessss
Step-by-step explanation:
yessssssss
The condition that distinguishes organism from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to the environment through changes originating internally.
An investor decides to invest some cash in an account paying 13% annual interest, and to put the rest in a stock fund that ends up earning 7% over the course of a year. The investor puts $1300 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1270. How much money was invested at each of the two rates? Round to the nearest integer.
Answers
A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,
x - y =1300
x = 1300 + y
Also, at the end of the year the total interest from the two investments was $1270. Therefore, we can write,
0.13x + 0.07y = 1270
Substitute the value of x from the above,
0.13(1300 + y) + 0.07y = 1270
169 + 0.13y + 0.07y = 1270
0.20y = 1101
y = 5505
substitute the value of y in the first equation,
x - y = 1300
x = 6805
Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
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The figure below is a scatterplot for paired data (x, y), with x values on the horizontal axis and y on the vertical axis. The tick marks are spaced 10 units apart on both axes. (Note that to answer the following questions you don't need the actual values for each tick mark, only differences between them.) 00 00 Oo oo 8 Oo oo (1) What are plausible values for the standard deviations of x and y, respectively? (2) What is a plausible value for the slope of the SD line? (3) Given your answer to part (b), what is a plausible value for the slope of the regression line?
Answers
The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.
What is a scatter plot?Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.
We have a scatter plot shown in the table:
1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:
Standard deviation = SD
6SD(x) = 40
SD(x) = 40/6 = 6.67
6SD(y) = 20
SD(y) = 20/6 = 3.37
2) Slope of the line:
= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5
3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.
Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.
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If the cost, C, for manufacturing x units of a certain product is given by C=x²-10x+65, find the number of units manufactured at a cost of $12,140.
There are_____manufactured at a cost of $12,140.
Answers
Answer:
115
Step-by-step explanation:
You solve this by factoring.
12140 = x^2-10x+65
0 = x^2-10x-12075
0=(x+105)(x-115)
The only positive solution is x=115
Which of the following is a correctly written algebraic equation?
2 + 0.2x
5b - 5x + 2
a - 3x=0
3(x/5)
Answers
For any real number c, √² =
A. ²
B. cl
C. 1
D. C
Answers
Answer:
answer D ( if i interpreted your question correctly )
Step-by-step explanation:
Sqrt (c^2) = √(c^2) = C
can you do this because it is confusion the thing is y=mx+c
Answers
y=[tex]\frac{1}{2}[/tex]x+0.5
Hope it helps!
Urgent!!!
Use the Law of Sines to find all missing sides and angles of the following triangle (side b, side
c, and angle C). Approximate your answers to the nearest tenths. a = 35.0 km, A = 13.0°, B =
65.3°
Answers
Answer:
A = 13 degrees
B = 65.3 degrees
C = 180 - (13 + 65.3) = 101.7 degrees
Side a = 35 km
Side b = 141.4 km
Side c = 152.4 km
height of 24cm with a radius of 7cm. What is the total surface area of the cone?
Answers
Answer:
the answer to this problem is 703.7 in^2
determine weather y varies directly with x. if so find the constant of variation and write the equation
Answers
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The correct option is B.
What is the directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
Since the graph of the equation is a line, therefore, it can be concluded that the relationship is linear as a result y varies directly with x.
Therefore we can write the relationship as,
y ∝ x
y = k x
The line goes through the point (-2,3), thus, substitute the points in the equation formed above,
3 = k × (-2)
k = -3/2
Now, substitute the value of k in the equation,
y = -(3/2)x
Hence, the correct option is B.
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