If her second test was x and her third was x+1 (since it was 1 more than the second), we get 75+x+x+1=76+2x as our total test scores. Next, to get the average you add up the numbers and divide it by the amount of numbers you have. Since we have 3 tests and our sum is 76+2x, we divide it by 3 to get (76+2x)/3=average=82. Multiplying both sides by 3, we get 246=76+2x. Next, we subtract both sides by 76 to get 170=2x. Lastly, we divide both sides by 2 to get 85=x= the second test score. Her third test score is x+1=85+1=86
Distance = speed x time
Let the time to the appointment = x
The time home would be x + 1/4 hour
set up an equation you have 90x = 80(x + 1/4)
Simplify:
90x = 80x + 20
Subtract 80x from both sides:
10x = 20
Divide both sides by 10:
x = 2 hours
Distance = 90 x 2 = 180 miles
Answer:
- (b +4)(b +9)
- (c -5)(c +9)
- (k +2)(k +3)
Step-by-step explanation:
Consider the product ...
(x +a)(x +b) = x^2 +(a+b)x +ab
You will notice that the linear term (a+b)x has a coefficient (a+b) that is the sum of the factors of the constant term (ab).
For problems like this, it is useful to be able to factor the constant term, so you can choose the factors with the appropriate sum.
Signs are important. If the constant is positive, its factors will have the same sign, both positive or both negative. If the constant is negative, its factors will have opposite signs.
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1. b^2 +13b +36
Factors of 36 are ...
36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6
The sums of these are 37, 20, 15, 13, and 12. So, the factor pair we're looking for is 4 and 9. The factorization is ...
= (b +4)(b +9)
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2. c^2 +4c -45
The middle term is positive, so the larger magnitude factor will be positive. Factors of -45 are ...
-45 = -1·45 = -3·15 = -5·9
Sums of these factors are 44, 12, 4. So, the factor pair we're looking for is -5 and 9. The factorization is ...
= (c -5)(c +9)
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3. k^2 +5k +6
6 = 1·6 = 2·3 . . . . sums are 7 and 5 ⇒ factors of interest are 2 and 3
= (k +2)(k +3)