This seems like a lot more work than it is, but here we go
Simplifying<span>8 + -2y = 3y + -2
Reorder the terms: 8 + -2y = -2 + 3y
Solving 8 + -2y = -2 + 3y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right.
Add '-3y' to each side of the equation. 8 + -2y + -3y = -2 + 3y + -3y Combine like terms: -2y + -3y = -5y 8 + -5y = -2 + 3y + -3y
Combine like terms: 3y + -3y = 0 8 + -5y = -2 + 0 8 + -5y = -2 Add '-8' to each side of the equation. 8 + -8 + -5y = -2 + -8
Combine like terms: 8 + -8 = 0 0 + -5y = -2 + -8 -5y = -2 + -8 Combine like terms: -2 + -8 = -10 -5y = -10
Divide each side by '-5'. y = 2
Simplifying y = 2</span><span>
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Answer:
Height above the bottom gorge is 113 feet
Step-by-step explanation:
The width of the gorge = 40 feet
The height of the higher cliff = 158 feet
The height of the lower cliff = 98 feet
The length of the bridge = √((158-98)² + 40²) = 72.11 feet
The slope of the bridge = (158-98)/40 = 1.5
The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet
The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°
The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet
Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;
Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.
Just draw the graphs, and you should find y = 10x² is the only graph narrower than the given one.
Answer:
111 / 190
Step-by-step explanation:
Let us first compute the probability of picking 2 of each sweet. Take liquorice as the first example. There are 12 / 20 liquorice now, but after picking 1 there will be 11 / 19 left. Thus the probability of getting two liquorice is demonstrated below;
Apply this same concept to each of the other sweets;
Now add these probabilities together to work out the probability of drawing 2 of the same sweets, and subtract this from 1 to get the probability of not drawing 2 of the same sweets;
The probability that the two sweets will not be the same type of sweet =
111 / 190
