1. 4x + 8y = 12....divide by 4
x + 2y = 3
2y = -x + 3
y = -1/2x + 3/2...slope is -1/2, y int is 3/2
x + 2y = -3
2y = -x - 3
y = -1/2x - 3/2...slope is -1/2 and y int is -3/2
when the slopes are the same, and the y int are different, then the lines are parallel and never intersect...so they have no solution and are inconsistent
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2. y = 2x - 1...slope is 2 and y int is -1
y = -2x + 5 ...slope is -2 and y int is 5
when the slopes are different and the y int are different, then there is 1 solution making it independent
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3. 4x - 12y = 8...divide by 4
x - 3y = 2
same as other equation meaning the equations are the same line...meaning they have infinite solutions making them dependent
factorising the first denominator
x²-2x-3 = x² -3x+x-3 = (x+1)(x-3)
(a) 
finding LCD
(b) LCD of (x-3)(x+1) and (x-3) is (x-3)(x+1)
(c)
(d)
Answer:
The minimum number of fish each must have caught is 90 fishes
Step-by-step explanation:
The number of fishes Tisha's net can hold = 15
The number of fishes Dana's net can hold = 18
Let the total number of fishes both Tisha and Dana caught = X
15 × A = 18 × B = X
Therefore, X is the lowest common multiple (LCM) of 15 and 18 given as follows;
15 = 3 × 5
18 = 3 × 6
Therefore, the LCM of 18 and 5 = 3 × 5 × 6 = 90
Which gives, the minimum number of fish each must have caught = 90 fishes.
Answer:
Rate = 4.5
Step-by-step explanation:
It is given that,
A cookie recipe calls for 1/3 of a cup of sugar and 1 1/2 cups of flour.
We need to find the unit rate of flour to sugar for the cookie recipe. It can be calculated as follows :
So, the unit rate of flour to sugar for the cookie recipe is 4.5
Answer:23
Step-by-step explanation:
