Answer: Choice C
x/w and z/(y+v)
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Explanation:
All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.
Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).
So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w
x/w is one of the answers
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Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z
Therefore,
sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)
z/(y+v) is the other answer
Side note: triangle ACD is not used at all.
Your answer should be c ....................
Answer: x=24
Step-by-step explanation:
x+5x/12=x/6+2x/3+14
Multiply both sides of the equation by 12, the least common multiple of 12,6,3.
12x+5x=2x+4×2x+168
Combine 12x and 5x to get 17x.
17x=2x+4×2x+168
Multiply 4 and 2 to get 8.
17x=2x+8x+168
Combine 2x and 8x to get 10x.
17x=10x+168
Subtract 10x from both sides.
17x−10x=168
Combine 17x and −10x to get 7x.
7x=168
Divide both sides by 7.
x= 168/7
Divide 168 by 7 to get 24.
x=24
First, calculate for the volume of the cube before each edges are cut.
V = e³
where e is the length of each sides. Substituting the known value,
V = (4/5 cm)³ = 0.512 cm³
Then, calculate for the volume of each of the small cubes cut out from the corners.
V = (1/5 cm)³ = 0.008 cm³
Since there are 8 of these small cube, we multiply the volume by 8.
8V = 8(0.008 cm³) = 0.064 cm³
Then, subtracting the volumes will give us an answer of <em>0.448 cm³</em>