Answer:
2c + 3l ≤ 60
No
Step-by-step explanation:
Let's say you buy c yards of cotton lace and l yards of linen lace. The cotton lace will cost $2 per yard, and for c yards, you have to pay $2 c times, coming to a total of 2*c for the cotton lace. For the linen lace, you'd have to pay 3*l for l yards. The total amount of lace is thus equal to cotton lace cost + linen lace cost = 2c + 3l.
Total amount needs to be less than or equal to 60 (at most 60), so total amount = 2c + 3l ≤ 60
We can then plug our values of cotton and linen lace into our equation
12 yards of cotton lace, 15 yards of linen lace
2c + 3l ≤ 60
2(12) + 3(15) ≤ 60
24 + 45 ≤ 60
69 ≤ 60
This is false, so you cannot buy these amounts of lace.
The correct answer is 9.45×10^15
Answer:
(x +
+
)(x +
-
)
Step-by-step explanation:
solve the polynomial for x then express in product of factor form
Solve
x² + x - 10 = 0 ( add 10 to both sides )
x² + x = 10
Using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(
)x +
= 10 + ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
(x +
)² =
( take the square root of both sides )
x +
= ±
= ±
( subtract
from both sides )
x = -
± ![\frac{\sqrt{41} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B41%7D%20%7D%7B2%7D)
Thus corresponding factors are
(x - (-
-
) ) and (x - (-
+
), that is
(x +
+
) and ( x +
-
)
Thus
x² + x - 10 = ( x +
+
)(x +
-
) ← in factored form