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maw [93]
3 years ago
9

How do you know or what indicates to you that the solution set of an equation is all real numbers?

Mathematics
1 answer:
Harrizon [31]3 years ago
3 0

Answer:

  the equation is a tautology, or the system of equations is under-specified

Step-by-step explanation:

By definition, an equation that is a tautology is true for all values of the variable(s). Hence, its solution set is "all real numbers."

One such equation is ...

  x = x

__

An under-specified system of equations* may also have "all real numbers" as a solution set. For example, two equations in 3 unknowns:

  x + y = 3

  x + z = 5

The solution set is ...

  (x, y, z) = (x, 3-x, 5-x)

Every value of x will give a solution.

__

Similarly, a dependent system of equations may have "all real numbers" as a solution. A system is dependent when one or more of the equations can be derived from the others.

For example, adding the equation 2x+y+z=8 to the above set will give 3 equations in 3 unknowns. However, this added equation can be obtained by adding together the two above. It adds nothing that would restrict the solution set.

A system of two equations in two unknowns will be <em>dependent</em> if one of the equations is a constant multiple of the other. For example, x+y=1, 2x+2y=2 has a second equation that is 2 times the first. This set of equations has "all real numbers" as its solution set. (Of course, y = 1-x.)

_____

* Non-linear equations may impose limits on the variables, so that "all real numbers" cannot be a solution.

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Liula [17]

Answer:

he got 24 right

Step-by-step explanation:

30 time 80% is 24

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3 years ago
6b.) Hence, or otherwise, evaluate g(f(3))
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Answer:

-25

Step-by-step explanation:

g(f(3))= g(-5)

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= -20-5

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Answer:

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Step-by-step explanation:

8 0
3 years ago
At the soup to nuts cafeteria, larry orders two pieces of toast and a bagel, which comes out to $\$1.30$. Curly orders a bagel a
kotegsom [21]

Let us take costs of a piece of toast = $t, , one bagel cost=$b and a muffin cost=$m.

Larry

Two pieces of toast and a bagel cost  = $1.30

2t+b=1.30   -------------equation(1)

Let us solve the equation(1) for t in terms of b, because we need to find one bagel cost.

Subtracting b from both sides we get

2t+b-b=1.30-b

2t= 1.30-b

Dividing by 2 on both sides.

2t/2= (1.30-b)/2

t= (1.30-b)/2

Curly

A bagel and a muffin cost = $2.50.

b + m = 2.50 -------------equation(2)

Solving equation for m in terms of b, we get

m= 2.50-b.

Moe

A piece of toast, two bagels, and three muffins cost = $6.95

t + 2b + 3m = 6.95    ......................equation(3).

Substituting t= (1.30-b)/2 and m= 2.50-b in equation (3)

(1.30-b)/2 + 2b + 3(2.50-b) = 6.95 .

Multiplying each term by 2 to get rid 2 from denominator of (1.30-b).

2*(1.30-b)/2 + 2*2b + 2*3(2.50-b) = 2*6.95

1.30-b + 4b + 6(2.50-b) = 13.90.

1.30 - b + 4b  +15 - 6b = 13.90

Combining like terms

-3b +16.30 = 13.90

Subtracting 16.30 from both sides.

-3b +16.30-16.30 = 13.90-16.30.

-3b= -2.4

Dividing both sides by -3.

-3b/-3 = -2.4/-3

b = 0.8

Therefore, cost of one bagel = $0.80.

7 0
3 years ago
Is -5 a solution to the equation 6x+5=5x+8+2x? explain
boyakko [2]

Answer:

no

Step-by-step explanation:

6x-5x-2x=8-5

-1x=3

-1x/-1=3/-1

x=-3

3 0
3 years ago
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