Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (2, â1, â1), (2, 4, â2), and (2, â6, 1).

Answers

Answer 1

Answer:

23

Step-by-step explanation:

Here is the complete question

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -3), (1, 2, 4), and (5, 1, 0).

Solution

We find the volume of the parallelepiped by making a 3 × 3 column matrix whose columns are the corresponding coordinates of the vertices of the parallelepiped.

So, (1, 0, -3), (1, 2, 4)  and (5, 1, 0)

[tex]A = \left[\begin{array}{ccc}1&1&5\\0&2&1\\-3&4&0\end{array}\right][/tex]

The determinant of A is the volume of the parallelepiped. So,

detA = 1(2 × 0 - 4 × 1) - 1(0 × 0 - (-3) × 1) + 5(0 × 4 - (-3) × 2)

= 1(0 - 4) - 1(0 + 3) + 5(0 + 6)

= 1(-4) - 1(3) + 5(6)

= -4 - 3 + 30

= 23

So the volume of the parallelepiped is 23


Related Questions

Sarah’s was given 12 cups of bird seed for 3 bird feeders. She filled the bird feeders for a whole week. How many cups of seeds did sarah put in each bird feeder each day?

Answers

Answer:

1.7 everyday

Step-by-step explanation:

What is 0.612 repeating (meaning the repeating line is over 612) as a fraction

Answers

Answer:

[tex]\frac{612}{999}[/tex]

Step-by-step explanation:

To convert repeating decimals to fractions, you take the numbers that are repeating, in this case 612, and you see how many numbers are repeating. Here we have 3 numbers repeating and so you would divide 612 by 3 9's meaning 999. So 0.612 repeating is equal to [tex]\frac{612}{999}[/tex]. To make sure the answer is right, you can divide the numbers in a calculator to make sure you get the correct decimal.

Please give me the correct answer ​

Answers

Your answer would be: 3 x 10^-5

Hope this helps and happy holidays!!

Joey wants to paint this side of his cottage. What is the area of this side?

A. 56 square feet
B. 238 square feet
C. 294 square feet
D. 462 square feet

Answers

Answer:

238 B

Step-by-step explanation:

8.5*28    

HELP ME PLEASE!!!
On a scale drawing of a house, the dimensions of the living room are 4 inches by 3 inches. If the scale drawing is 1 in: 6 ft , find the actual length and width of the living room.

Answers

Answer:

The width is 18

Step-by-step explanation:

6x3 and get 18 as the width

A wooden board that is 108 inches long is cut into two equal parts. What is the length of each part in feet? (feet : inches = 1 : 12) A. 0.45 feet B. 4.5 feet C. 9 feet D. 54 feet

Answers

Answer:

the answer is c. 9 feet

Step-by-step explanation:

i just did the math and i got 9 so i hope this helps!

Herbert has 30 total movies. 18 of them are adventure. What percent of his movies are adventure movies

Answers

Answer:

60%

Step-by-step explanation:

18 out of 30 movies are adventure so we can vizualize this as

18/30 this giving us the decimal 0.60

Now to convert from a decimal to a percent just multiply by 100 or move the decimal to the right 2 decimal point.

0.60 x 100 = 60%

Answer:

hi

Step-by-step explanation:

because

Select all ratios equivalent to 4:2.

Answers

Answer:

Step-by-step explanation:

4 : 2

8 : 4

12 : 6

16:8

The ratio in the form of n: 1 will be 2: 1.

What are ratio and proportion?

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The ratio is given below.

⇒ 4: 2

Simplify the ratio in the form of n: 1, then we have

⇒ 4: 2

⇒ 2: 1

The ratio in the form of n: 1 will be 2: 1.

More about the ratio and the proportion link is given below.

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SENDING CASHAPP TO WHOEVER GETS THIS RIGHT GL HURRY ONLY 1 PERSON!!!

Answers

Answer:

i think its b i dont have a cash app discord nitro will do jk its free idc

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

an isosceles triangle has 2 sides the same and 1 side a different length no need to pay me :)

Which points are separated by a distance of 4 units? a. (7,7) (1,7) b. (3,3) (1,3) c. (4,2) (8,2) d. (2,4) (5,4)

Answers

Answer:

c

Step-by-step explanation:

with the knowledge that we are comparing the x position we can get the equation |x_1-x_2|=4, then just do the maths

(4,2) (8,2) points are separated by a distance of 4 units.

What is distance formula?

The 2D distance formula gives the shortest distance between two points in a two-dimensional plane.

Distance Formula =  [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2}-y_{1} )^{2} }[/tex]

Given

Distance of 4 units

Option A:

[tex](x_{1} ,y_{1})=(7,7)[/tex]

[tex](x_{2} ,y_{2})=(1,7)[/tex]

Distance = [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2}-y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-7)^{2}+(7-7)^{2} } =6[/tex]

Option B:

[tex](x_{1} ,y_{1})=(3,3)[/tex]

[tex](x_{2} ,y_{2})=(1,3)[/tex]

Distance = [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2}-y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-3)^{2}+(3-3)^{2} } =2[/tex]

Option C:

[tex](x_{1} ,y_{1})=(4,2)[/tex]

[tex](x_{2} ,y_{2})=(8,2)[/tex]

Distance = [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2}-y_{1} )^{2} }[/tex]

= [tex]\sqrt{(8-4)^{2}+(2-2)^{2} } =4[/tex]

Option C is correct.

Option D:

[tex](x_{1} ,y_{1})=(2,4)[/tex]

[tex](x_{2} ,y_{2})=(5,4)[/tex]

Distance = [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2}-y_{1} )^{2} }[/tex]

= [tex]\sqrt{(5-2)^{2}+(4-4)^{2} } =3[/tex]

Hence, (4,2) (8,2) points are separated by a distance of 4 units.

Find out more information about distance formula here

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Select two ratios that are equivalent to 2:9

Choose 2 correct answers 40 points

Answers

Answer:

4:18 6:27 8:36

Step-by-step explanation:

Which polynomial represents the product of 2x - 4 and x2 + 6x - 2 ?
ОА
2x3 + 8
thing
B
2x3 + 8x2 - 4x + 8
с
2x3 + 8x2 - 28x + 8
D
2x3 - 24x - 2

Answers

Answer:

C. [tex] 2x^3 + 8x^2 - 28x + 8 [/tex]

Step-by-step explanation:

Product of [tex] 2x - 4 [/tex] and [tex] x^2 + 6x - 2 [/tex]

[tex] (2x - 4)(x^2 + 6x - 2) [/tex]

[tex] 2x(x^2 + 6x - 2) -4(x^2 + 6x - 2) [/tex] (distributive property)

[tex] 2x^3 + 12x^2 - 4x -4x^2 - 24x + 8 [/tex]

Collect like terms

[tex] 2x^3 + 12x^2 - 4x^2 - 4x - 24x + 8 [/tex]

[tex] 2x^3 + 8x^2 - 28x + 8 [/tex]

PLEASE HELPPPP
Find the equation of the linear function represented by the table below in slope-
intercept form.
X
O
1
2
3
4
y
6
14
22
30
38
Answer: y =
Submit Answer

Answers

Answer:

yo done so easy

Step-by-step explanation:

the answer is y=8x + 6

3) For the graph below, the graphical representation between the speed of an object and its
mass could best be described as
2
Sood
0
Mass
A. The speed of the object is directly proportional to its mass.
B. The speed of the object is proportional to the square root of its mass.
C. The speed of the object is inversely proportional to its mass.
D. The speed of the object is proportional to the square of its mass,
E. There is no relationship between the speed of the object and its mass.

Answers

Answer:

it Eeeeeeeeeeeeeeeeeeeee

identify the independent variable in this situation:


the amount you sleep at night determines the amount of energy you have during the day.

Answers

The amount you sleep at night

This is independent because the energy you have during the day relies on how much you have slept

A rentail truck company charges $25 per day plus $0.35 for every mile (m) driven. Which equation can be used to find the number of miles driven for a truck that costs a total of $42.50 to rent for one day?

Answers

Answer:

0.35m + 25 = 42.50

Step-by-step explanation:

If you were to rent a truck for one day you will first have to pay a $25 fee for one day. This is represented by + 25 in the equation above.

Then for every mile you go you must pay $0.35, represented as 0.35m.

As an example to make it easier if you had to pay 1 dollar per mile and you went 10 miles it would cost $10. This can be proved by 1m (m being the variable for number of miles) Plug in 10 for m and you can asee 1(10)=10, because obviously 1 times 10 is 10.

Same premise with $0.35

Then both of those fees added up are equal to a total of $42.50.

To prove it can find the exact number of miles that need to be driven to cost a total of $42.50 just follow steps bellow.

1. 0.35m + 25 - 25 = 42.50 - 25

Subtracting the inital fee since it is part of the total, and if you add/subtract/multiply/divide on one side you must do to the other.

2. 0.35m/0.35 = 17.50/0.35

You divide because m is being multiplied with 0.35 and to undo the multiplication you divide. Doing the same to both sides.

3. m = 50

Plug in 50 to "m" in the equation above and if both sides are equal the answer is valid.

Write an equation of a line that is parallel to y = x - 7 and passes through the point (-6, -11).

Answers

Answer:

y = x - 5

Step-by-step explanation:

Comparing the given y = x - 7 to y = mx + b, we see that the slope is +1.

In y = x + b we replace y with -11 and x with -6 to determine the y-intercept, b:

-11 = -6  + b

Then b must be -5, and so the desired new equation is

y = x - 5

in a packet or Skittles there are, 40 Skittles,30 are red how many Skittles are not red

Answers

Answer:

10

Step-by-step explanation:

hope this helps ")

I need help on a math problem on my homework

Answers

What’s the question

Answer: Where is the question?

Step-by-step explanation:

Write the quadratic function in vertex form, then identify the vertex

h(x)=x^2+20x+90

h(x)=

Vertex:

I need this answered ASAP please !

Answers

Answer:

vertex = (- 10, - 10 )

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

h(x) = x² + 20x + 90

add/subtract ( half the coefficient of the x- term )²

h(x) = x² + 2(10)x + 100 - 100 + 90

      = (x + 10)² - 10 ← in vertex form

with (h, k ) = (- 10, - 10 )

please help me out!!​

Answers

Step-by-step explanation:

Given

f(x) = 2x - 4

Then

f(2) = 2 * 2 - 4

= 4 - 4

= 0

Therefore f(2) = 0 .

Hope this helps :)

Find the location of A' given that A is (7, 1).
Translate 1 unit left.
The location of A' is ____

Answers

Answer:

We conclude that the location of A' is: A'(6, 1)

Step-by-step explanation:

Given

A(7, 1)

To determine:

The location of A'

Translation Rule:

As we have to translate 1 unit left, meaning we need to subtract 1 unit from the x-coordinate of point A(7, 1) to determine the location of A'.

In other words, the translation rule is:

A(x, y) → A'(x-1, y)

as

A(7, 1)

so

A(7, 1) → A'(7-1, 1) = A'(6, 1)

Therefore, we conclude that the location of A' is: A'(6, 1)

What is the volume in cubic centimeters of the prism

Answers

Answer: 36 cm^3

Step-by-step explanation:

To solve this you multiply the length by the width by height (so 6x2x3) this is the same formula you use to solve volume for similar equations. 6x2x3 is 36 but you need to remember to add the unit of measurement and to cube it (^3). I hope this helps!!!!

Solve for x
4x + 188
6x+216

Answers

X=-14
Explanation is :

Which equations represents the model

Answers

the answer for this is A

ANSWER ASAP PLEASE
If Jose drove 330 miles in 5.5 hours, how many miles did he drive per hour?

Answers

Answer:

60mph

Step-by-step explanation:

330 divided by 5.5 is 60

What value of n makes the equation true?



n =

Answers

-1/5n+7=2
-7 -7
-1/5n= -5
Multiplied by 5/-1

Answer is 25
n=25

N=25
Explanation:
Times the whole expression by 5
-1n+35=10
Minus 35 on both sides
-1n=-25
Divide by -1
N=25

Lana correctly answered 48 of 60 questions on a math exam. What percent of questions did she answer correctly?

Answers

Answer:

I think it roughly 66.67%

Step-by-step explanation:

sorry if I'm no help

The percent of questions she answered correctly is 80%.

How to find the percentage from the total value?

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Given;

Lana correctly answered 48 of 60 questions on a math exam

Now,

=48*100/60

=480/60

=80

Therefore, the percentage will be 80%.

Learn more about percent here:

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Hello! :)
Please help me answer this question ! And explain how you answers it. I will give brainslt :)

Answers

Answer:

1. False

2. False

3. True

Step-by-step explanation:

1. It fails the 'Vertical Line Test.' Draw a line through the center of the relation and see if the line passes through the graph more than once. It does, therefore it fails the test. Meaning it is not a function.

2. Domain (x) is all the x-values in the equation, the relation only contains the x-values x>0 and x<7 (0 - 7). Meaning it does not contain all real numbers.

3. The range (y) contains negative numbers because the relation is partially in the 4th quadrant, meaning it MUST contain a negative y-value.

What is the quotient of Three-fifths and StartFraction 1 Over 10 EndFraction?

A number line going from 0 to 1 in increments of 0.2.
One-sixth
One-third
3
6

Answers

Answer:

D:6

Step-by-step explanation:

3/5 = 6/10

6/10 divided by 1/10 equals 6

so 6 is your answer.

Answer:

d

Step-by-step explanation:

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