Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Answers
Answer:
Area = 13.15 square units
Step-by-step explanation:
Let the given vertices be represented as follows:
A(2, -1, 1) = 2i - j + k
B(5, 1, 4) = 5i + j + 4k
C(0, 1, 1) = 0i + j + k
D(3, 3, 4) = 3i + 3j + 4k
(i) Let's calculate the vectors of all the sides:
[tex]\\[/tex]AB = B - A = (5i + j + 4k) - (2i - j + k)
AB = 5i + j + 4k - 2i + j - k [Collect like terms]
AB = 3i + 2j + 3k
BC = C - B = (0i + j + k) - (5i + j + 4k)
BC = 0i + j + k - 5i - j - 4k [Collect like terms]
BC = -5i + 0j - 3k
CD = D - C = (3i + 3j + 4k) - (0i + j + k)
CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]
CD = 3i + 2j + 3k
DA = A - D = (2i - j + k) - (3i + 3j + 4k)
DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]
DA = -i - 4j - 3k
AC = C - A = (0i + j + k) - (2i - j + k)
AC = 0i + j + k - 2i + j - k [Collect like terms]
AC = -2i + 2j
BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)
BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]
BD = -2i + 2j
(ii) From the results in (i) above, we can deduce that;
AB = CD This implies that AB || CD [AB is parallel to CD]
AC = BD This implies that AC || BD [AC is parallel to BD]
(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram
Now let's calculate the area
To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.
In this case, we'll choose AB and AC
Area = |AB X AC|
Where;
[tex]AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right][/tex]
AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)
AB X AC = - 6i - 6j + 10k
|AB X AC| = [tex]\sqrt{(-6)^2 + (-6)^2 + (10)^2}[/tex]
|AB X AC| = [tex]\sqrt{172}[/tex]
|AB X AC| = 13.15
Area = 13.15 square units.
PS: ACBD is also a parallelogram. The diagram has also been attached to this response.
Related Questions
Give the standard form for 7,000+300+40+2.
Answers
Answer:
7,342
Step-by-step explanation:
In the thousands place, we have 7,000
In the hundreds place, we have 300
In the tens place, we have 40
In the ones place, we have 2
Put them each in their place, you will get 7,342. It's also the same as adding all of them together.
Answer:
7342 is the standard form
Step-by-step explanation:
simple!
7000
300
40
+ 2
_______
7432
_______
Hope it helped you! :)
If a menu has a choice of 4 appetizers, 5 main courses, and 5 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert?
Answers
What is the mean for the set of data
shown below?
27, 32, 14, 19, 24, 26, 22, 32, 29
A 18
C 26
B 25
D 32
Answers
Answer:
B) 25
Step-by-step explanation:
First, you add up all the numbers. Then, you divide it by 9 which is the total amount of numbers there are.
Name all the sets of -15 The real Numbers
Answers
The real numbers is one set, and so is the the set of integers since this set is { ..., -3, -2, -1, 0, 1, 2, 3, ...} composed of positive and negative whole numbers, along with 0.
The value -15 is also in the rational set because we can write it as a fraction of two integers: -15 = -15/1
The 3 answers are: real numbers, integers, rational numbersf(x) = -×-3
find f(-4)
Answers
Answer:
Hey there!
Original function: f(x)=-x-3
Substituting -4: f(-4)=4-3
Simplify: f(-4)=1
Let me know if this helps :)
F(x) = -x - 3
F(-4)
Replace x with -4 and solve:
F(-4) = -(-4) -3
-(-4) = positive 4
So you have 4-3
4-3 = 1
F(-4) = 1
h(x)=x2+1 k(x)=x-2
(h-k)(3)
Answers
Answer:
(h-k)(3) = 9Step-by-step explanation:
h(x) = x² + 1
k(x) = x - 2
To find (h-k)(3) we must first find (h - k)(x)
To find (h - k)(x) subtract k(x) from h(x)
That's
(h - k)(x) = x² + 1 - ( x - 2)
(h - k)(x) = x² + 1 - x + 2
(h - k)(x) = x² - x + 1 + 2
We have
(h - k)(x) = x² - x + 3
To find (h-k)(3) substitute the value of x that's 3 into (h - k)(x) that's replace every x in (h - k)(x) by 3
We have
(h-k)(3) = (3)² - 3 + 3
= 9 - 3 + 3
= 9 - 0
We have the final answer as
(h-k)(3) = 9Hope this helps you
Which numbers are prime numbers? Check all that apply.
3
1
27
9
11
13
Answers
Answer:
3,11,13 are the prime numbers.
Answer:
1, 3, 11, 13
Step-by-step explanation:
you can't multiply two numbers to equal them
A ........... divides a two dimentional shape into two congruent shapes.
Answers
Answer:
A rectangle is a two - dimensional shape, so let me explain using it as an example.
The diagonal of a rectangle divides the rectangle into two triangles that are congruent (the same size and shape.)
Another example is parallelogram; the diagonal of a parallelogram also divides the figure into two separate shapes that are congruent.
Hope this helps!
-10r-20=-20 i need help with this question
Answers
Answer:
r = 0
Step-by-step explanation:
To solve this for r, add 20 to both sides. The result will be -10r = 0, and so
the solution is r = 0.
Answer:
0
Step-by-step explanation:
-10r - 20 = -20
-10r = -20 + 20
-10r = 0
r = 0
The face of a cat is symmetrical, with the bridge of the nose falling on the line of symmetry
directly between the eyes. If a cat’s right eye is 3 inches from the bridge of its nose, how far is
the cat’s left eye from its right eye?
Answers
Answer:
6 inches
Step-by-step explanation:
just make
3 - (-3) = 6
So you will be calculating that distance.
Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Recording the number of televisions in 150 households
Choose the correct answer below.
A. No, because the probability of success does not remain the same in all trials.
B. Yes, because all 4 requirements are satisfied.
C. No, because there are more than two possible outcomes and the trials are not independent.
D. No, because there are more than two possible outcomes.
Answers
Answer:
A. No, because the probability of success does not remain the same in all trials.
Step-by-step explanation:
In this procedure the number of televisions could vary in each house. Some people have one , two, even three or some may not have any. So the number of successes in each trial varies as the number of televisions varies.
Therefore, it is not a binomial distribution. It is necessary that for a binomial distribution the probability of success for each trial remains fixed.
1945 pounds to ounces
Answers
Answer:
31120 ounce
Step-by-step explanation:
Answer:31120
Step-by-step explanation:Use google
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 60 cm, find ts area.
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{125 \: {cm}^{2} }}}}}[/tex]
Step-by-step explanation:
Let the width be 'w'
Length of a rectangle = 5w
Perimeter of a rectangle = 60 cm
Area of a rectangle = ?
First, finding the value of width ' w '
[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(l + w)}}[/tex]
plug the values
⇒[tex] \sf{60 = 2(5w + w)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{60 = 10w + 2w}[/tex]
Collect like terms
⇒[tex] \sf{60 = 12w}[/tex]
Swap the sides of the equation
⇒[tex] \sf{12w = 60}[/tex]
Divide both sides of the equation by 12
⇒[tex] \sf{ \frac{12w}{12} = \frac{60}{12} }[/tex]
Calculate
⇒[tex] \sf{w = 5}[/tex] cm
Finding the value of length ( l )
[tex] \sf{length = 5w}[/tex]
Substitute the value of w
⇒[tex] \sf{length = 5 \times 5}[/tex]
⇒[tex] \sf{length = 25 \: cm}[/tex]
Finally, Finding the area of rectangle having length of 25 cm and width of 5 cm
[tex] \boxed{ \sf{area \: of \: a \: rectangle = l \times b}}[/tex]
plug the values
⇒[tex] \sf{area \: = \: 25 \times 5}[/tex]
Multiply the numbers
⇒[tex] \sf{area \: = \: 125 \: {cm}^{2} }[/tex]
Hope I helped!
Best regards!!
To the nearest whole number,
which is the best estimate?
45.29+63.92+4.02 (29.92
A.198
B.229
C.254
D.3390
Answers
Answer:
B. 229
Step-by-step explanation:
I solved it by multiplying the 4.02 and 29.92. Then, added the numbers together and rounding the solution to the nearest whole number.
Lisa is framing a rectangular painting the length is three more than twice the width she uses 30 inches of framing material what is the length of the painting right and solve the equation
Answers
Answer:
The width is 4 inches
The length is 11 inches
Step-by-step explanation:
Let the width be x inches
Let the length be (2x+3 )inches
Perimeter= 30 inches
therefore, 2(length +breadth)= perimeter
=>2(2x+3+x)=30
=>2(3x+3)=30
=>6x+6=30
=>6x=30-6
=>6x=24
=>x=24/6
=>x=4
The width is 4 inches
The length is 11 inches
To solve this question:
First, we have to understand the concept of perimeter, and how it is calculated for a rectangle.Relating the length and the width of the triangle, and using this to solve the perimeter equation for the length.Doing this, we get that the length of the painting is: 11 inches.
Perimeter of a rectangle:
The perimeter of a polygon is the sum of it's sides.
For a rectangle, as the one given in the picture at the end of this answer, which is of the format of the painting, the perimeter is given by:
[tex]P = 2l + 2w[/tex]
Lisa is framing a rectangular painting the length is three more than twice the width.
This means that:
[tex]l = 3 + 2w[/tex]
Since we want to solve for the length, we write the width as a function of the length, thus:
[tex]2w = l - 3[/tex]
She uses 30 inches of framing material
This means that the perimeter is of 30 inches, that is:
[tex]2l + 2w = 30[/tex]
Since [tex]2w = l - 3[/tex]
[tex]2l + l - 3 = 30[/tex]
[tex]3l = 33[/tex]
[tex]l = \frac{33}{3}[/tex]
[tex]l = 11[/tex]
Thus, the length of the painting is of 11 inches.
A similar question is found at https://brainly.com/question/21894434
−
4
v
−
25
>
2
v
+
17
Answers
Answer:
v < -7
Step-by-step explanation:
Step 1: Write out equation
-4v - 25 > 2v + 17
Step 2: Add 4v to both sides
-25 > 6v + 17
Step 3: Subtract 17 on both sides
-42 > 6v
Step 3: Divide both sides by 6
-7 > v
Step 4: Rewrite
v < -7
Find the rate of change and describe it in context. # of tickets 5, 6, 7, 8 Total cost 75, 90, 105, 120
Answers
Answer:
The cost of 1 ticket is 15 dollars
Step-by-step explanation:
The rate of change is another word for slope
m = (y2-y1)/(x2-x1)
= (90-75)/(6-5)
= 15/1
The cost of 1 ticket is 15 dollars
The rate of change is a ratio that compares the change in y/change in x.
We can see that the y-values increase by 15 each time and
we can see that the x-values increase by 1 each time.
So the change in y/change in x is 15/1.
This means that for every ticket bought, you pay $15.
Find the slope of the line passing through the points (-5,1) and (2,4).
Enter your answer in as a fraction.
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{3}{7} }}}}}[/tex]Step-by-step explanation:
Let the points be A and B
A ( -5 , 1 ) ⇒( x₁ , y₁ )
B ( 2 , 4 )⇒( x₂ , y₂ )
Finding the slope of the line passing through these Points
Slope = [tex] \sf{ \frac{y2 - y1}{x2 - x1} }[/tex]
plug the values
⇒[tex] \sf{ \frac{4 - 1}{2 - ( - 5)} }[/tex]
We know that [tex] \sf{( - ) \times ( - ) = ( + )}[/tex]
⇒[tex] \sf{ \frac{4 - 1}{2 + 5} }[/tex]
Subtract 1 from 4
⇒[tex] \sf{ \frac{3}{2 + 5} }[/tex]
Add the numbers
⇒[tex] \sf{ \frac{3}{7} }[/tex]
Hope I helped!
Best regards!!
At the movie theatre, child admission is $5.50 and adult admission is $8.60. On Wednesday, 131 tickets were sold for a total sales of $946.80 . How many adult tickets were sold that day?
Answers
Answer:
73
Step-by-step explanation:
Let a represent the number of adult tickets sold. Then the total revenue was ...
8.60a +5.50(131 -a) = 946.80
8.60a -5.50a +720.50 = 946.80 . . . . eliminate parentheses
3.10a = 226.30 . . . . . . subtract 720.50, collect terms
a = 73 . . . . . . . . . . . . . . divide by 3.10
73 adult tickets were sold that day.
6. Do planes GFE and HBC intersect? Explain.
Answers
Answer:
yes at line HE.
Step-by-step explanation:
Plane GFE is the plane that contains face EFGH of the prism.
Plane HBC is the plane that contains face BCEH of the prism.
The two planes do intersect, and their intersection is line HE.
x + 2 – z; use x = 6, and z = 2
Answers
Answer:
6
Step-by-step explanation:
x + 2 - zIf x = 6 and z = 2 then : 6 + 2 -26 +2 is 8 - 2 is sixanswer is 6If x2 = 20, what is the value of x?
±square root of 10
±square root of 20
±10
±40
Answers
Answer:
+ square root of 20 -------> +[tex]\sqrt{20}[/tex]
Step-by-step explanation:
[tex]x^{2}=20[/tex]
[tex]x=\sqrt{20}[/tex]
Answer:
b
Step-by-step explanation:
The $x$-intercept of a positively-sloped line is -5, and the area of the triangle formed by the line, the $x$-axis, and the $y$-axis is 10. What is the slope of the line?
Answers
Answer:
4/5 OR -4/5
Step-by-step explanation:
So, area of triangle = 1/2 * base * height
base = 5 (because x-axis is base, x-intercept is -5, so x-length = 5)
height is unknown
area = 10
We can form the equation: 1/2 * 5 * height = 10
Rearrange terms to get: height (y-height) = 10 / (0.5 * 5) = 4
Following the formula for gradient, dif in y / dif in x, we get 4/5
Therefore our gradient is (4/5), or 0.8.
But because we are only told the x-intercept, it can cross the y axis at y = 4 or y = -4. So there are actually 2 possible gradients, 4/5 and -4/5
Compund Inequalities. Solve for x. 11x+4 −25 A. -3/2 -3/2 C. x<1 D. There are no solutions. E. All values of x are solutions.
Answers
Answer:
A
Step-by-step explanation:
11x + 4 < 15 OR 12x - 7 > -25
11x < 11 OR 12x > -18
x < 1 or x > -1.5
The answer is -3/2 < x < 1.
What are the two types of hypotheses used in a hypothesis test? type I and type II null and alternative Your answer is correct. left-tailed and right-tailed population and sample How are they related? They sum to zero. One is a subset of the other. They are equal. They are complements.
Answers
Answer:
There are two types of hypotheses tests. null and alternative
They are complements.
Step-by-step explanation:
There are two types of hypotheses tests. null and alternative
the table shows the summary of both tests.
True Situation DECISION
Accept H0 Reject H0
(or accept Ha)
H0 is true Correct decision Wrong Decision
(no error) type I error
H0 is false Wrong Decision Correct decision
type II error ( no error)
The probability of making a type I error is conventionally denoted by alpha and that of committing a type II error is indicated by beta.
∝ = P ( type I error) = P (reject H0 / H0 is true)
β = P (type II error) = P (accept H0 / H0 is false)
When ∝ becomes larger, β tends to become smaller . There is inverse relationship between ∝ and β.
When H0 is true Ha is false when Ha is false H0 is true. So they are compliments of each other.
What is the domain of the function
{(−5,6),(2,−8),(7,12),(−2,−8)}
A.{−5,6,2,−8,7,12,−2}
B.{6,−8,12}
B.{−5,2,7,−2}
B.{6,2,7,12}
Answers
Answer:
Domain { -5,2,7,-2}
Step-by-step explanation:
The domain is the input values, in this case the x values
Domain { -5,2,7,-2}
Answer:
{ - 5 , 2 , 7 , - 2 }Option C is the correct option.
Step-by-step explanation:
Domain is the set of all values of x
{( -5 , 6 ) , ( 2 , -8 ) , ( 7 , 12 ) , ( -2 , -8 )
⇒ { - 5 , 2 , 7 , - 2 }
Hope I helped!
Best regards!
Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric receive (Disregard the $ sign when gridding your answer.)
Answers
Answer:
Cedric's share=$120
Abel's share=$60
Step-by-step explanation:
Abel will receive half as much as Cedric
Let
Cedric's share=x
Abel's share = 1/2 of x
Total money=$180
x + 1/2x = 180
2x+x/2 =180
3/2x=180
Divide both sides by 3/2
x= 180÷3/2
=180 × 2/3
=360/3
=120
Therefore,
Cedric's share = x = 120
Abel's share=1/2x
=1/2 × 120
=120/2
=60
Cedric's share=$120
Abel's share=$60
Find the academic calendar, and then answer: How many days after the end of the course are the final grades published?
Answers
Find the academic calendar, and then answer: How many days after the end of the course are the final grades published? Select one:
a. 12 days
b. 7 days
c. 14 days
d. 3 days
Answer:
7 days
Step-by-step explanation:
Take note that under standard practice and based on the information available that it would take up to 7 days after the end of a course for the final grades to be published.
Thus, the correct option is 7 days.
A city council consists of six Democrats and seven republicans. If a committee of four people is selected, find the probability of selecting two Democrats and two Republicans.
Answers
Answer:
[tex]\bold{\dfrac{63}{143}}[/tex]
Step-by-step explanation:
Number of Democrats = 6
Number of Republicans = 7
Total number of members = 6+7 = 13
To find:
Probability of selecting two Democrats and two Republicans if 4 members are selected in the committee = ?
Solution:
This is a selection problem.
Total number of ways to select 4 members in the committee out of total 13 = [tex]_{13}C_4 = \dfrac{13\times 12\times 11\times 10}{4\times 3\times 2} = 715[/tex]
Number of ways to select 2 Democrats = [tex]_{6}C_2 = \dfrac{6\times 5}{2} = 15[/tex]
Number of ways to select 2 Republicans = [tex]_{7}C_2 = \dfrac{7\times 6}{2} = 21[/tex]
Number of ways to select 2 Democrats and 2 Republicans = 15 [tex]\times[/tex] 21 = 315
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, required probability:
[tex]\dfrac{315}{715} = \bold{\dfrac{63}{143}}[/tex]
Consider the following information:
Observations 1 2 3 4 5 6
Num. of defects 10 18 13 15 9 12
The number of runs above and below the sample median is:__________
a) 3.
b) 4.
c) none of these.
d) 5.
e) 6.
Answers
Answer:
A. 3Step-by-step explanation:
Formula for locating the Median of a grouped data = (N+1)/2 th where
N is the total number of defects.
Total defects = 10+18+13+15+9+12
Total defects = 77
Median value = (77+1)/2 th value
Median value = 78/2 = 39th value.
We will cummulate the frequency (number of defects up to the 38th value) and locate the corresponding observation value.
On cummulating:
10+18+13 = 41
We can see that the value of 38 falls on the third column(13), hence the median will be the equivalent number of observations i.e 3.
Therefore the sample median is 3