1. Given that the width of the rectangle is x, and the area of the rectangle may be represented by the equation x^2 + 5x = 300, we can solve this equation for the width (x) as such:
x^2 + 5x = 300
x^2 + 5x - 300 = 0 (Subtract 300 from both sides)
(x - 15)(x + 20) = 0 (Factorise x^2 + 5x - 300)
From this, we get: x = 15 or x = -20
Since the width must be a positive length (ie. more than 0), -20 would be an invalid answer in the given context and thus the width is given by x = 15.
2. If we know that the length is 5 inches more than the width, we simply need to add 5 to the width we found above to obtain the length:
Length = x + 5
Length = 15 + 5 = 20
Thus, the width of the rectangle is 15 inches and the length of the rectangle is 20 inches.
Answer:
2.5 seconds since the first ball was hit.
Step-by-step explanation:
The equations that model the heights are:
When the balls meet, both heights are equal, therefore:
-16t² + 56t = -16t² + 156t - 248
-16t² + 56t + 16t² - 156t + 248 = 0
- 100t + 248 = 0
248 = 100t
248/100 = t
t = 2.48 ≈ 2.5
Answer:
C) 1/4
Step-by-step explanation:
P(Y,Y) = 3/6 x 3/6 = 1/2 x 1/2 = 1/4
9514 1404 393
Answer:
KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP
Step-by-step explanation:
Instead of starting with adjacent letters in the list, we start with the same letter. There are 15 possible pairs.
KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP
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<em>Additional comment</em>
We leave out pairs with letters previous, because you've said KL is the same as LK, and KL has already been listed. The problem with this list is that it misstates the probabilities of randomly obtaining a given pair. It is not 1/15, but is 2/25 for all but letter duplicates. For duplicates (KK), the probability is 1/25, not 1/15.