Answer:
Equation of a line is y = mx + c
where
m = slope
c = y intercept
y = 1/6x - 3
Comparing with the above formula
m = 1/6
Since the lines are parallel their slope are also the same
So the equation of the line using point (-4,2) is
y - 2 = 1/6( x + 4)
y - 2 = 1/6x + 2/3
y = 1/6x + 2/3 + 2
y = 1/6x + 8/3
Hope this helps
<h3>
Answer: B) Only the first equation is an identity</h3>
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I'm using x in place of theta. For each equation, I'm only altering the left hand side.
Part 1
cos(270+x) = sin(x)
cos(270)cos(x) - sin(270)sin(x) = sin(x)
0*cos(x) - (-1)*sin(x) = sin(x)
0 + sin(x) = sin(x)
sin(x) = sin(x) ... equation is true
Identity is confirmed
---------------------------------
Part 2
sin(270+x) = -sin(x)
sin(270)cos(x) + cos(270)sin(x) = -sin(x)
-1*cos(x) + 0*sin(x) = -sin(x)
-cos(x) = -sin(x)
We don't have an identity. If the right hand side was -cos(x), instead of -sin(x), then we would have an identity.
Answer:
15 days
Step-by-step explanation:
Well, as you would be able to tell, you just have to find the LCM of 3 and 5. These do not have one before 3 x 5, so it is 15.
Answer:
500 pounds
Step-by-step explanation:
Let the pressure applied to the leverage bar be represented by p
Let the distance from the object be represented by d.
The pressure applied to a leverage bar varies inversely as the distance from the object.
Written mathematically, we have:

Introducing the constant of proportionality

If 150 pounds is required for a distance of 10 inches from the object

Therefore, the relationship between p and d is:

When d=3 Inches

The pressure applied when the distance is 3 inches is 500 pounds.
<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>
<em><u>Solution:</u></em>
The given pyramid has 3 lateral triangular side
The figure is attached below
Base of triangle = 12 unit
<em><u>Find the perpendicular</u></em>
By Pythagoras theorem

Therefore,

<em><u>Find the lateral surface area of 1 triangle</u></em>


<em><u>Thus, lateral surface area of 3 triangle is:</u></em>
3 x 48 = 144
Thus lateral area for the pyramid with the equilateral base is 144 square units