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)
x = longer section
y = shorter section
x + y = 109
x = 2y + 10
so we sub in eq 2 into eq 1
2y + 10 + y = 109
3y + 10 = 109
3y = 109 - 10
3y = 99
y = 99/3
y = 33 <=== shorter section is 33 cm
x = 2y + 10
x = 2(33) + 10
x = 66 + 10
x = 76 <=== longer section is 76 cm
The answer to ur questions is $39.96
To solve for y get it by it’s self
y=-2x-4
to solve for x get it by it’s self
2x=-y-4
divide by 2
x=-1/2y-2
The answer is D
Hope this helps :)