Answer:
y = 4/3x-7/3
Step-by-step explanation:
Slope intercept form is y=Mx+b; m=slope & b= y intercept
y=-4/3x+b
Now substitute x & y with the point given
(-9)=-4/3(5)+b
-9= -20/3+b
+20/3 +20/3
-7/3=b
Now substitute this into the original equation
y = 4/3x-7/3
Answer:
32 feet
Step-by-step explanation:
area of square is given by side^2
Perimeter of square is given by 4*side
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Given
area of square = 64 sq feet
side^2 = 64
side^2 = 8^2
side = 8
thus side = 8 feet
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The dog pen is fenced with chain, hence chain will be fence at the edge of square and at the perimeter.
Thus, length of chain required will be same as the Perimeter of square.
Perimeter of given dog pen with side length 8 feet = 4*8 = 32 feet.
Thus, 32 feet of chain fence is required.
Add 3 to both sides so that the equation becomes -2x^2 + 5x + 5 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -5 ± √(5^2 - 4(-2)(5)) ] / ( 2(-2) )
x = [-5 ± √(25 - (-40) ) ] / ( -4 )
x = [-5 ± √(65) ] / ( -4)
x = [-5 ± sqrt(65) ] / ( -4 )
x = 5/4 ± -sqrt(65)/4
The answers are 5/4 + sqrt(65)/4 and 5/4 - sqrt(65)/4..
Answer:
- hemisphere volume: 262 m³
- cylinder volume: 942 m³
- composite figure volume: 1204 m³
Step-by-step explanation:
A. The formula for the volume of a hemisphere is ...
V = (2/3)πr³
For a radius of 5 m, the volume is ...
V = (2/3)π(5 m)³ = 250π/3 m³ ≈ 261.799 m³
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B. The formula for the volume of a cylinder is ...
V = πr²h
For a radius of 5 m and a height of 12 m, the volume is ...
V = π(5 m)²(12 m) = 300π m³ ≈ 942.478 m³
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C. Then the total volume is ...
V = hemisphere volume + cylinder volume
V = 261.799 m³ +942.478 m³ = 1204.277 m³
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Rounded to the nearest integer, the volumes are ...
- hemisphere volume: 262 m³
- cylinder volume: 942 m³
- composite figure volume: 1204 m³
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As a rule, you only want to round the final answers. Here, the numbers are such that rounding the intermediate values still gives the correct final answer. That is not always the case.
