A consistent system of equations has at least one solution.
A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.
A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.
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Answer:
Step-by-step explanation:
Part A: 5/26
Part B: 5/26+ 1/2 which is 18/26 or 9/13
Part C: 5/26 +21/25. 'without replacing' means there is one less option in the bag. So denominator becomes 26-1=25. Numerator is 21 because there are a total of 21 consonants in the alphabet. Since we removed a vowel and not a consonant, it will remain 21.
The price p based on the equation given is p = 3000 - 0.1x.
<h3>How to express the price?</h3>
The equation given in the question is x = 3000 - 10p. The price(p) will be:
x = 3000 - 10p.
Make p the subject of the formula
x + 10p = 3000
10p = 3000 - x
p = (3000 - x)/10
p = 3000 - 0.1x
The revenue will be price multiplied by quantity. This will be:
= (3000 - 0.1x) × x
= 3000x - 0.1x²
The marginal revenue will be calculated after differentiating. This will be:
= 3000x - 0.1x²
= 3000 - 0.2x
The demand which is the quantity based on the information will be:
3000 - 0.2x = 0
0.2x = 3000
x = 1500
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Given:
Last year Lira earned $12,000 less than her husband Todd.
Together they earned $75,000.
To find:
The amount earned by Lira in last year.
Solution:
Let x be the amount earned by Lira's husband inn last year.
Last year Lira earned $12,000 less than her husband Todd.
Amount earned by Lira = 
Total amount earned by Lira and her husband = 
= 
Together they earned $75,000.
Now,
Amount earned by Lira =
= 
= 
Therefore, the amount earned by Lira in last year is $31500.
Answer:
See below
Step-by-step explanation:
Assuming a number line:
rs + st = rt
3x-16 + 4x-8 = 60
7x -24 = 60
7x = 84
x = 12
