Answer:
A) y = 1/3x + 4
B) y = 1/2x - 9
Step-by-step explanation:
A) In order to find this, we must first solve the initial equation for y to get the slope.
-x + 3y = 6
3y = x + 6
y = 1/3x + 2
Now we know the slope to be 1/3 since parallel lines have the same slope. So we take this slope and the point and use point-slope form to find the equation.
y - y1 = m(x - x1)
y - 5 = 1/3(x - 3)
y - 5 = 1/3x - 1
y = 1/3x + 4
B) To find this line, we again have to find the slope of the initial equation by solving for y.
2x + y = -4
y = -2x - 4
Now we know our new slope to be 1/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use this and the point to solve in the same way.
y - y1 = m(x - x1)
y - - 8 = 1/2(x - 2)
y + 8 = 1/2x - 1
y = 1/2x - 9
<h3>Answer:
122 degrees</h3>
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Explanation:
Angle BAC can be shortened to "angle A" since the letter A is in the middle.
Angle BCA can be shortened to "angle C" for similar reasoning.
We're told that angles A and C are base angles. For any isosceles triangle, the base angles are congruent
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Let's use this fact to solve for x.
angle A = angle C
7x+1 = 5x+9
7x-5x = 9-1
2x = 8
x = 8/2
x = 4
Once we know what x is, we can find each base angle
- angle A = 7x+1 = 7*4+1 = 28+1 = 29
- angle C = 5x+9 = 5*4+9 = 20+9 = 29
Both angles A and C are 29 degrees each, so this confirms we have the correct x value.
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The last step is to use the fact that all three angles of a triangle add to 180 degrees. This will help us find angle B, which is the vertex angle.
A+B+C = 180
29+B+29 = 180
B+58 = 180
B = 180-58
B = 122
The vertex angle is 122 degrees.
So we can say either angle B = 122, or we could say angle ABC = 122
"angle ABC" is the same as "angle CBA".
Answer: B) 4 BTUs/ft^3
Step-by-step:
For a cuboid of length L, width W and height H, the volume is:
V = L*W*H
In this case, we have:
L = 20ft
W = 15ft
H = 10ft
Then the volume of the room is:
V = 20ft*15ft*10ft = 3000 ft^3
Now we have 6 people, and each generate 400 BTUs per hour.
Then in total, they generate:
6*400 BTUs per hour
2400 BTUs per hour.
Now we want to find the BTUs per ft^3 produced in 5 hours.
Then if they generate 2400 BTUs per hour, in 5 hours they generate a total of:
5*2400 BTUs = 12000 BTUs
Now we take the quotient between the total BTUs and the volume of the room:
Q = (12000 BTUs)/(3000 ft^3) = 4 BTUs/ft^3
The correct option is B.
Answer:
-8 • (6 + 3) + 390 + 6=324
Step-by-step explanation:
To fint the length first one must find circumference to do that we use the formula D*Pi (diameter times Pi. Diameter = 8 Pi is the constant of 3.1415
so. 8*3.1415 = appox 25.1327. cow that we have circumference we should multiply by the amount of times the wheel rotates (15)
so. 15*251327 = appox 376.9911in now convert to feet. 12 in = 1 foot so divide by 12
so 376.9911 / 12 = about 31.4
round down to 31 feet
