About 10 hrs because he got at least 11 hours of sleep
Answer:
329/9, the answer seems wrong but I triple checked because I thought so too. The answer is 100% correct
Step-by-step explanation:
Angle EFG + Angle FGH + Angle GEF = 180 degrees
(2x+1) + (6x+2) + (x + 19) = 180 degrees
9x + 22 = 180 degrees
9x = 158 degrees
x= 158/9
x+19 = Angle GEF
158/9 + 19 = Angle GEF
329/9 =Angle GEF
Double check:
(2x+1) + (6x+2) + (x + 19), x=158/9
2(158/9) + 1 = 325/9
6(158/9) +2 = 322/3
(158/9) +19 = 329/9
325/9 + 322/3 + 329/9 = 180
Answer:
12(3+1)
Step-by-step explanation:
use distributive property to solve
13 times 3 is 36
12 times 1 is 12
so 12(3+1) is equal to 36+12
have a good day :)
The equation of the perpendicular line to the given line is: y = -5/4x - 30.
<h3>What is the Equation of Perpendicular Lines?</h3>
The slope values of two perpendicular lines are negative reciprocal of each other.
Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.
Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.
Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:
20 = -5/4(-40) + b
20 = 50 + b
20 - 50 = b
b = -30
Substitute m = -5/4 and b = -30 into y = mx + b:
y = -5/4x - 30
The equation of the perpendicular line is: y = -5/4x - 30.
Learn more about about equation of perpendicular lines on:
brainly.com/question/7098341
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Answer:
Therefore the population will be maximum when x=30 inches.
Step-by-step explanation:
Given that, the mosquito population is a function of rainfall and can be approximated by the formula
where x is the number of inches of rainfall.
Differentiating with respect to x
Again differentiating with respect to x
Now we set N'(x)=0
Since at x=30, N''(x)<0, So at x=30, N(x) has maximum value.
Therefore the population will be maximum when x=30 inches.
