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3 years ago

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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3 years ago

X- (5-3x)<=2x-1 solve

kkurt [141]

Answer:

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Step-by-step explanation:

7 0

3 years ago

Last Saved: 2:10 PM

WARRIOR [948]

Step-by-step explanation:

The number of students in each bus is s.

There are 6 buses.

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Total number is 221.

<u>The equation to reflect it is:</u>

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3 years ago

Read 2 more answers

If the compound ratio of 7:5 and 8:x is 83:60 then find X

baherus [9]

Note: Consider 84 instead of 83 because the value of x is a decimal value of 83 which is not possible.

Given:

Compound ratio of 7:5 and 8:x is 84:60.

To find:

The value of x.

Solution:

Compound ratio of 7:5 and 8:x is 84:60.

$\dfrac{7}{5}\times \dfrac{8}{x}=\dfrac{84}{60}$

$\dfrac{7\tims 8}{5\times x}=\dfrac{84}{60}$

$\dfrac{56}{5x}=\dfrac{84}{60}$

By cross multiplication, we get

$56\times 60=84\times 5x$

$3360=420x$

Divide both sides by 1420.

$\dfrac{3360}{420}=x$

$8=x$

Therefore, the value of x is 8.

5 0

3 years ago

All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of

Darina [25.2K]

Answer:

Here's what I get

Step-by-step explanation:

a. Net of a cube

Fig. 1 is the net of a cube

b. Does the formula work?

Tony's formula works if you ignore dimensions.

There are six squares in the net of a cube.

If each side has a unit length s, the total area of the cube is 6s.

c. Will the formula work for any rectangular prism?

No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.

d. Area of a rectangular prism

A rectangular prism has six faces.

A top (T) and a bottom (b) — A = 2×l×w

A left (L) and a right (R) — A = 2×l×h

A front (F) and a back (B) — A = 2×w×h

Total area = 2lw + 2lh + 2wh

If l = 5 m, w = 6 m and h = 8 m,

$\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}$

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3 years ago