Solve the system with elimination. 2x+2y=4 x+3y=6
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John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.
<h3>What is a slope?</h3>In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent the slope; reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
He priced all items at a dime or a quarter. His sales totaled less than $5
Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25
Let x=x= the number of the items sold for a dime
Let y=y= the number of the items sold for a quarter
0.10x+0.25y<5
0.10x+0.25y<5
Inequality in the slope-intercept form
0.10x+0.25y Subtract 0.10x from both sides
0.25y<-0.10x+5 Divide both sides by 0.25
Subtract 0.10x from both sides
The slope is, and the y- intercept is 20
Since inequality sign is << so, draw a dashed line
Test point (0,0)(0,0)
Substituting the values 0 for x and 0 for y,
Since inequality is true
So, (0,0)(0,0) is solution of the inequality
Shade region containing (0,0)(0,0).
The graph below shows all possible solutions
Since boundary line is dashed and the number of items is always positive
The solution is shaded region in quadrant I
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Like terms have the same variable and power. The simplification of the expression (6x²-3-5x³)-(4x³+2x²-8) is -9x³+4x²+5.
<h3>What are Like terms?</h3>Like terms are those terms that are having the same variables, also the variables are of the same order as well.
for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.
We know that to simplify an expression we need to add or subtract like terms, therefore,
Hence, the simplification of the expression (6x²-3-5x³)-(4x³+2x²-8) is -9x³+4x²+5.
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