9514 1404 393
Answer:
x = 16
Step-by-step explanation:
Corresponding sides are proportional.
BE/CD = AE/AD
20/(3x+8) = (x-1)/(x-1+27)
20(x+26) = (3x+8)(x -1)
In standard form, this is ...
3x^2 -15x -528 = 0
x^2 -5x -176 = 0 . . . . . . divide by 3
(x -16)(x +11) = 0 . . . . . . . factor
x = 16
__
This is the positive value that makes the product zero. x=-11 will also make the product 0, but gives negative segment lengths in the geometry. It is an extraneous solution.
Answer:
A. x is less than or equal to 1 OR x is greater than or more than 2
Answer:
9, 11, 13
Step-by-step explanation:
We can rephrase an odd number into an algebraic equation of (2n+1)
Therefore, 3 consecutive odd numbers would be written as:
(2n+1), (2n+3), (2n+5)
We can then rewrite the question as:
3 x (2n+1) = 2 x (2n+5) + 1
Work out the equation to find n:
6n + 3 = 4n + 10 + 1
(minus 4n from both sides)
2n + 3 = 11
(minus 3 from both sides)
2n = 8
(divide both sides by 2 to get)
n = 4
To find the original 3 consecutive numbers, we just input (4) into (2n+1), (2n+3), (2n+5) to get:
(8+1), (8+3), (8+5)
= 9, 11 and 13
Answer:
Step-by-step explanation:
We have 8 dozen bagels, or 8*12=96 bagels. Each plate can hold 14 bagels, so we have enough bagels to fill 96/14=about 6.86 plates. However, we cannot have a fraction of a plate, so we round up to have a total of seven plates. To fill all seven plates fully, 7*14=98 bagels would be needed, which is two more than we have.
To summarize, Mr. Corsetti has seven plates of bagels, and would need two more bagels to fill the last one up.
