G>-1 is your solution and it would look like this on a graph..( see below)
2. Tim bought 12 books. 2/3 of the books are science fiction. How many of
2 answers:
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Answer:
Step-by-step explanation:
Perform the multiplication and addition:
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<em>Comment on the squaring</em>
There are several ways you can find the square (x+4)².
- Use your knowledge that (x+a)² = x²+2ax+a².
- Use FOIL* to compute (x+4)(x+4) = x² +4x +4x +4² = x²+8x+16
- Use the distributive property: (x+4)(x+4) = x(x+4) +4(x+4) = x² +4x +4x +4² (same as FOIL for two binomials)
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* FOIL is mnemonic for {First, Outer, Inner, Last} referring to pairs of terms in the factors (x +a)(x +b). The x terms are the First terms. The Outer terms are the first x and b. The Inner terms are "a" and the second x. The Last terms are "a" and "b". You are to form the sum of those pairs of terms to find the product of the binomials.
Answer:
148 meters
Step-by-step explanation:
Answer: approximately 5148 feet directly north of point A
This is equivalent to 0.975 miles
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Explanation:
Check out figure 1 (attached image below) to see how the drawing is set up.
Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.
Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.
The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.
Note that triangle ABC is a right triangle. The 90 degree angle is at point A.
We can use the pythagorean theorem to solve for x
See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.
This means the sound wave takes about 4.68 seconds to go from point C to point A.
With this x value, we can compute the expression 1100x to get
1100*x = 1100*4.68 = 5,148 feet
To convert this to miles, divide by 5280
(5148)/(5280) = 0.975
Therefore,
5148 feet = 0.975 miles
