1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natali [406]
2 years ago
5

1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a

plane.b) a line.c) a circle.d) a point.2) What does the equation y + 3x = 2 represent in R^3? a) a plane.b) a circle.c) a line.d) a point.What does z - 4y = 8 represent? a) a line.b) a circle.c) a point.d) a plane.What does the pair of equations y = 2, z = 8 represent? In other words, describe the set or points (x, y, z) such that y = 2 and z = 8. a) a line.b) a circle.c) a plane.d) a point.
Mathematics
1 answer:
Sunny_sXe [5.5K]2 years ago
5 0

Answer:

The equation x=4 represents in R^2 c) a line

The equation x=4 represents in R^3 a) a plane

The equation y+3x=2 represents in R^3 a) a plane

The equation z-4y=8 represents d) a plane

The pair of equations y=2,z=8 represents a) a line

Step-by-step explanation:

Let's start by studying each question :

1)

In R^2 , x=a with a ∈ IR is the equation of all vertical lines

In this case, the only free variable is the variable ''y''

R^2 has two dimensions (x and y) so if we set x=4 we will have only one free variable in R^2 (which is a line in R^2). Therefore, x=4 represents a line in R^2

Now, in R^3 we have three dimensions (x, y and z) so if we set x=4 we will have only two free variables (y and z) and x=4 will represent a plane (which have two dimensions) in R^3.

2) The equation y+3x=2 in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.

The equation y+3x=2 in R^3 (given that we have two free variables) represents a plane.

Using the same reasoning, the equation z-4y=8 represents a plane (given that it has two free variables : ''y'' and ''x'')

Finally, the pair of equations y=2,z=8 set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.

The final answer is a) a line.

You might be interested in
The surface area for a rectangular prism with a square base is SA=2s2+4sh.
torisob [31]
We know that
[surface area for a rectangular prism with a square base ]=2*s²+4*s*h

2*s²----> Is the surface area of the bases
4*s*h---> is the lateral area
s=2 units
h=4 units

[surface area for a rectangular prism with a square base ]=2*2²+4*2*4
surface area=8+32----> 40 units²

the answer is
40 units²
3 0
3 years ago
Read 2 more answers
How do you Round 96,286 to the nearest thousand.
Varvara68 [4.7K]

Answer:

The correct answer is 96,000

Step-by-step explanation:

To round you look at the thousands place and there is a 9 then you look at the number to the right of it which is 2 and it is lower than 5 since it is lower than five it rounds down so the correct answer is 96,000.

HAVE A GOOD DAY!

8 0
2 years ago
Read 2 more answers
How do you find the product of -9over5 times 5over 3? please help.
Inessa [10]
Here look at this for my answer...

3 0
3 years ago
Complete the equation of the line through ( − 9 , 7 ) and ( − 6 , − 3 ) Use exact numbers. y =
sesenic [268]

Answer:

Step-by-step explanation:

first we need to find the slope using the slope formula :

slope = (y2 - y1) / (x2 - x1)

(-9,7)...x1 = -9 and y1 = 7

(-6,-3)....x2 = -6 and y2 = -3

now we sub

slope = (-3 - 7) / (-6 - (-9) = -10 / (-6 + 9) = -10 / 3

so our slope is -10/3

now we use y = mx + b....with m representing the slope

slope(m) = -10/3

use either of ur points....I will use (-9,7)...x = -9 and y = 7

we are solving for b, the y intercept

now we sub

7 = -10/3(-9) + b

7 = 30 + b

7 - 30 = b

- 23 = b

so ur equation is : y = -10/3x - 23

4 0
3 years ago
If a translation of (x,y) → (X + 6, 7-10) is applied to figure
horrorfan [7]
The correct answers would be a b and 2 because I don’t know this is a test to be honestly
4 0
3 years ago
Other questions:
  • How do you do monomial
    6·1 answer
  • I need help with my work<br>​
    11·1 answer
  • Necesito ayudaaaaa pls
    9·1 answer
  • Which cat are you today?
    13·2 answers
  • 2x + 2x + 2 = 4x + 2​
    11·1 answer
  • What is the formula of a soccer ball
    7·1 answer
  • HELP PLS HURRY! The graph shows the proportional
    8·2 answers
  • 3x + 2y = 12<br> y = x - 9
    10·1 answer
  • F '(x) = sin(x) - 65<br> What is f(x)?
    15·1 answer
  • Solve this pls<br> -5x - 10 = 10
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!