Answer:
Step-by-step explanation:
Just solve for , then substitute back into either expression and calculate either BC or AD. The other one is then the same amount.
The one about the square is the same thing except you don't care how the figure is named because all 4 sides are equal anyway. Just set the two expressions equal to one another and then solve for
Answer:
p = -5
Step-by-step explanation:
11p-3p = 8p
-47+ 7 = -40
8p = -40
-40/8 = -5
400 pages in 5 days
but 120 on the first day
so 400-120=280
280 is what he read in the 4 days following
so divide 280 equally among the 4 days
You get 70 per day after the first
<h3>
Answer: The two factors are 5x+3 and x+1</h3>
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Explanation:
We could use the AC factoring method here. Multiply the first coefficient (10) with the last term (3) to get 10*3 = 30.
We need to find factors of 30 that add to 11
1+30 = 31
2+15 = 17
3+10 = 13
5+6 = 11
we have found the pair of factors that add to 11. So we'll break the 11x into 5x+6x and then use factor by grouping method
10x^2 + 11x + 3
10x^2 + 5x + 6x + 3
(10x^2 + 5x) + (6x + 3)
5x(2x + 1) + 3(2x + 1)
(5x+3)(2x+1)
We see the two factors are 5x+3 and 2x+1.
To check the answer, use either the box method, distribution, or FOIL rule to expand out (5x+3)(2x+1) and you should get 10x^2+11x+3 again.
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As an alternative, you can solve 10x^2+11x+3 = 0 through any method you prefer (graphing, completing the square, quadratic formula). The quadratic formula is the best option as it works for any quadratic. The two solutions you should get are x = -3/5 and x = -1/2
Using x = -3/5 and x = -1/2, we can do the following
- x = -3/5 becomes 5x = -3 after multiplying both sides by 5, then you add 3 to both sides to get 5x+3 = 0
- x = -1/2 becomes 2x = -1 after multiplying both sides by 2, and then turns into 2x+1 = 0 after adding 1 to both sides
Note how we have the 5x+3 and 2x+1 as found in the section above. At this point we can stop as we found the factors needed. I'm using the zero product property which says that if A*B = 0, then either A = 0 or B = 0.
