<span>So we want to know how many individual heels did the shoemaker bought if he bought 30 pairs of heels. So to get to the answer we must know that one pair of heels is equal to two individual heels. So now we can calculate the individual number of heels: 30 pairs * 2 = 60 individual heels. </span>
Answer:
syd is 23 and dev is 69
Step-by-step explanation:
Let Dev's age be x and Syd's age be y
Since Dev is 3 times older than Syd, we may write
x
=
3
y
Since the sum of their ages is 92, we may write
x
+
y
=
92
Now replacing x with 3y, we get :
3
y
+
y
=
92
Hence
y
=
92
4
=
23
and so Syd is 23 year old.
Back substituting we get Dev is 69 years old.
L=R*angle, but the angle *must* be in radians. So, just translate 43 degrees into radians: 43 * pi / 180, and you'll get:
L = 42 * ( 43 * pi / 180 ) ~ 31.504666, which rounded to the nearest hundredth is 31.50 cm.
Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
_____
<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.