Answer:A
Step-by-step explanation:
-- The probability of HEADS on a fair coin is 1/2 .
-- The probability of an even number (2, 4, or 6) on a die is 3/6 = also 1/2 .
-- The probability of both outcomes in the same toss is
(1/2 x 1/2) = 1/4 = 25% .
-- There are 3 possible successful outcomes.
They are:
H - 2
H - 4
H - 6
-- There are 9 other outcomes that are not successful:
H - 1
H - 3
H - 5
T - 1
T - 2
T - 3
T - 4
T - 5
T - 6
9.) <span>1/2(4x-6)=11
</span>Multiply 4 and -6 by 1/2
2x-3=11
Add 3 to both sides
2x=14
Divide 14 by 2
Final Answer: x=7
10.) 2/3(6x-9)=-34
Multiply 6 and -9 by 2/3
4x-6=-34
Add 6 to both sides
4x=-34
Divide -34 by 4
Final Answer: x=-8.5
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
