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]
3 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]3 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
Please help.<br> Is algebra.<br> PLEASE HELP NO LINKS OR FILES.<br> I don't want links.
BartSMP [9]

Answer:

Question 3: B

Question 4: A, D, E

Step-by-step explanation:

Polynomials can not have a variable appear in the denominator.

4b^4-9b+2, 2x+7, and x-3 are in standard form.

6 0
3 years ago
Write the equation of the circle whose center is (-5, -8) with diameter 12
lora16 [44]

Answer:

(x + 5)^2 + (y + 8)^2 = 6^2

Step-by-step explanation:

A circle formula: (x - h)^2 + (y - k)^2 = r^2

We are given diameter. To find the radius divide diameter by 2.

d = 12

12/2 = r = 6

H and K are given to be (-5 , -8)

(x - (-5))^2 + (y - (-8))^2 = 6^2

(x + 5)^2 + (y + 8)^2 = 6^2

I have plot this equation to confirm my answer is correct where the origin is (-5 , -8) and has a radius of 6.

3 0
2 years ago
Deepak is using blocks to represent the four operation on 8 and 2 witch operation will require the greatest number of blocks
Vadim26 [7]

Answer:

18

Step-by-step explanation:

8 0
3 years ago
Choose the expression that represents a linear expression.
tresset_1 [31]

Answer:

Step-by-step explanation:

A linear expression has the highest power of the variable to 1, i.e ax+b

Then only the first option is in a linear expression format

9x-2

6 0
3 years ago
Read 2 more answers
Write an equation in slope-intercept form of the line through (1,3) and (-3,7)
kupik [55]
Y=-X+4 finding the y intercept, b and slope, mx thus y=mx+b
8 0
3 years ago
Read 2 more answers
Other questions:
  • What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3?
    13·1 answer
  • Multiply the rational expression
    6·2 answers
  • What does it mean for a function to have a root?
    14·2 answers
  • Escriba un polinomio de grado 6 que contenga 4 términos, que su coeficiente principal sea un número par y el término independien
    10·1 answer
  • You mix 1/ 3cup of blue paint for every 2/ 3cup of yellow paint to make green paint. You use 4 cups of yellow paint. How much bl
    15·1 answer
  • The profit for a new website can be represented by 5", in thousands of dollars, where x is the time, in
    12·2 answers
  • Jill was solving a system using the elimination method.After she added the equations together,she got 5=7.What does this mean fo
    14·1 answer
  • List the numbers from greatest to least .<br>-3.25, 5.6, 9, 5 5/10, -2​
    10·2 answers
  • Find the length of the segment with the endpoints (3,-8) and (5,-2).
    15·1 answer
  • Brian scored 92, 87 and 88 on three science tests. Write and solve an equation to find the score Brian will need on the fourth s
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!