Mathematics, 26.07.2019 06:30 cgkiepe5759

How would you describe the graph of a system of equations if the solution to the system were all real numbers

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Let's solve this problem by using System of Linear Equations in two variables. We know that a Linear Function is given by:

f(x)=ax+b

that is a line with slope m=a

and

Both the domain and the range of this function are All Real Numbers. When the number of equations. in a system of linear equations, is the same as the number of variables there is likely to be a solution. It is not guaranteed, but likely there will be a solution or solutions.

In fact, there are three possible cases:

1. No solutions (Inconsistent System).
2. One solution (Consistent and Independent System)
3. Infinitely many solutions (Consistent and Dependent System)

We need our solution to be all real numbers, therefore our system must be Consistent and Dependent, that is, a system that has Infinitely many solutions because the two equations are really the same line. For instance:

$(1) \ x+y=3 \\ (2) \ 4x+4y=12$

Those equations are Dependent, because, in fact, the are the same equation, just multiply (1) by 4 and you will get (2). Therefore, the graph of this system is shown in the figure below. You can see that the solution is All Real Numbers, because both the domain and the range are All Real Numbers.

How would you describe the graph of a system of equations if the solution to the system were all rea

How would you describe the graph of a system of equations if the solution to the system were all rea

Answer from: Quest

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

Lots of points! show all of your work! i need #9-#14 and 12 + 16!

Answer from: Quest

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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