The third choice, 4x²+18x+0.25=0, is correct.
The frame will have the same thickness on both sides of the mirror. Therefore we add 5+x+x to get the total length, and we have 4+x+x to get the total width.
The area is found by multiplying the total width and total length:
A=(5+x+x)(4+x+x)
A=(5+2x)(4+2x)
Multiplying the binomials, we have:
A=5*4+5*2x+2x*4+2x*2x
A=20+10x+8x+4x²
A=20+18x+4x²
We know that the area is 19.75:
19.75=20+18x+4x²
We need quadratics set equal to 0, so subtract 19.75 from each side:
19.75-19.75 = 20+18x+4x²-19.75
0=0.25+18x+4x²
In standard form, it will be:
4x²+18x+0.25=0
Assuming the question marks are minus signs
to find max, take derivitive and test 0's and endpoints
take derivitive
f'(x)=18x²-18x-108
it equal 0 at x=-2 and 3
if we make a sign chart to find the change of signs
the sign changes from (+) to (-) at x=-2 and from (-) to (+) at x=3
so a reletive max at x=-2 and a reletive min at x=3
test entpoints
f(-3)=83
f(-2)=134
f(3)=-241
f(4)=-190
the min is at x=3 and max is at x=-2
each die has 6 numbers so there are 6*6= 36 different combinations possible
there are 6 ways the die could be the same ( both 1's. both 2's, 3's, 4's 5's 6's)
so there is a 6/36 reduced to 1/6 probability of them matching
Answer:
70 / 3
Step-by-step explanation:
x / 7 = 10 / 3
x = ( 10 / 3 ) x 7
= ( 10 x 7 ) / 3
x = 70 / 3
30:60:90 is 3:6:9 in ratio form
