What conclusions can you draw about the two track teams from the data shown?
2 answers:
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Answer:
2. w = -3
4. c = -2
6. r = 7
8. n = 4
Step-by-step explanation:
It's hard to read the photo, but I'll try.
2.
On the left side, you have a product of 2 powers with the same base.
Give the same base and add the exponents, as in the rule
You get on the left side 2 to the sum of the exponents.
Simplify the long exponent on the left side.
Now we have another rule we can use. If two powers are equal, and their bases are equal, then the exponents must be equal.
Here, 2 to the power 5w + 10 equals 2 to the power 2w + 1. Since both bases are 2 and are equal, then the exponents must be equal.
5w + 10 = 2w + 1
Subtract 2w from both sides. Subtract 10 from both sides.
3w = -9
Divide both sides by 3.
w = -3
4.
We need to write the left side as a power of 5. Then we equate the exponents like we did in problem 2.
Recall the rule:
Apply this rule to the left side in reverse.
Now we have two powers that are equal, both having the same base, 5, so the exponents must be equal.
2c + 3 = -1
2c = -4
c = -2
6.
This is the same idea as problem 4. Write the left side as a power of 6.
r = 7
8.
This problem is similar to problem 2.
3n - 9 = 3
3n = 12
n = 4