As stated in the question
Bethany - x
Amanda - y
the relationships are
Lauren is 13 years older than Bethany
Laurens age = x + 13
David is 11 years older than Amanda
Davids age = y + 11
product of Bethany's and Laurens ages equal to twice Amandas age
x * (x+13) = 2y
x² + 13x = 2y
divide all by 2
x²/2 + 13/2x = y
if they subtract 20 from Bethany and Laurens, then product is equal to Davids age
(x-20)(x+13-20) = y +11
(x-20)(x-7) = y+11
x² -7x -20x+140 = y+11
x² -27x +129 = y
the 2 equations to determine the relationships are
y = x²/2 + 13/2x
y = x² -27x +129
the first option is correct
Answer:
CD=20 cm and DE=15 cm. CD=20 cm and DE=15 cm.
Step-by-step explanation:
A rhombus DMFN is inscribed in such a way that it is inscribed in triangle CDE with the vertices M, F, and N l on the sides CD , CE , and DE respectively.
Now, in rhombus, the parallel sides are always parallel, therefore
MF║DE, thus,
by the basic proportionality condition.
It is given that CF=8 cm and EF=12 cm, therefore,
.
That is CM=8 cm and MD=12 cm. Therefore, CD=CM+MD=8+12=20.
According to question, Perimeter of △CDE =55 cm
⇒CD+DE+CE=55
⇒20+DE+20=55
⇒DE=15 cm
Hence, CD=20 cm and DE=15 cm.
Total possibilities would be:
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
You want 5 on at-least one, so mark 5th column & 5th raw.
There are 6 in both lines with 1 common = (5,5)
In short, Your Answer would be 11
Hope this helps!