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Nikolay [14]
2 years ago
13

Solve each given equation and show your work the whether each equation has one solution, an infinite number of solutions, or no

solution. Explain your answer.
2x+4(x-1)=2+4x
25-x=15-(3x+10)
4x=2x+2x+5(x-x)
Mathematics
1 answer:
Triss [41]2 years ago
8 0
2x+4x-4=2+4x
2x+4x-4x=2+4
2x=6
x=3

25-x=15-3x-10
3x-x= 15-10-25
2x= -20
x= -10

4x=2x+2x+5x-5x
2x+2x+5x-5x-4x
0 . no solution
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There are 4 books on a shelf. books are added to the shelf at a rate of 2 books per minute. the total number of books on the she
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The algebraic equation to represent the given situation is as follows,

y = 4 + 2x

What is an algebraic equation?

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Forming the Algebraic Equation

Number of book present on the shelf initially = 4

It is given that 2 books are added per minute to the shelf.

If x is the number of minutes, then the books added will be 2x.

If y is the total number of books present on the shelf, then the algebraic equation is given as,

y = Number of books initially present on the shelf  + 2x

⇒ y = 4 + 2x

Thus, y = 4 + 2x is the required algebraic equation.

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9) In the standard co-ordinate system, which of the following points in the greatest distance from origin? A. (-4, -1) B. (-3, 3
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The point with the greatest distance to the origin is given by:

B. (-3, 3).

<h3>What is the distance between two points?</h3>

Suppose that we have two points, (x_1,y_1) and (x_2,y_2). The distance between them is given by:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:

D = sqrt(x² + y²).

Hence the distances for each point given in the problem are:

  • A. Distance = sqrt((-4)² + (-1)²) = sqrt(17).
  • B. Distance = sqrt((-3)² + (3)²) = sqrt(18).
  • C. Distance = sqrt((4)² + 0²) = sqrt(16).
  • D. Distance = sqrt((2)² + 3²) = sqrt(13).

Hence option B has the greatest distance.

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