<span>y=−3x+2</span> is a linear equation in slope-intercept form with
slope <span>m=<span>(−3)</span></span>
(and y-intercept <span>=2</span>)
We want the equation of a line with slope <span>m=<span>(−3)</span></span> through the point <span>(<span>−2</span>,<span>−8</span>)</span>
Using the point-slope linear equation form:
<span><span>(y−<span>(−8)</span>)</span>=<span>(−3)</span><span>(x−<span>(−2)</span>)</span></span>
Simplifying
<span>y+8=−3x−6</span>
or, in standard form
<span>3x+y=−<span>14</span></span>
226.19 / 2/3 =
226.19 x 3/2 =
226.19 x 1.5 =
339.285
339.285 is your answer.
Answer: 55
Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.
Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.
Thus, we could label the points A, B, and C, and set up an algebraic expression.
Let A = 27, B = 98, and C = x.
A + B + C = 180°.
Substituting A, B, and C we get:
27 + 98 + x = 180°.
Adding, we get:
125 + x = 180°
Subtracting 125 by 180, we get:
x = 55°
Thus, the angle X is 55°.
We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.
Answer:
L = w+2
L+w = 60
W+2+w = 60
2w+2 = 60
W+1 = 30
W = 29
L = 31
The volume of a triangular prism is V = 1/2 x a x c x h where a is height of the triangle, c is the base of the triangle and h is the height of the prism.
120 = 1/2 x a x c x h; we write a from the previous equation in terms of c and h thus,
a = 240 / ( c x h)
If the dimensions where halved then a = a/2 ; c = c/2 ; h=h/2
We use the volume formula again and substitute the given values to find the new volume,
V = 1/2 x a/2 x c/2 x h/2
Substitute the previously determined a term,
V = 1/2 x (240/2ch) x c/2 x h/2
We cancel and evaluate the constants therefore the new volume is,
V= 15 cm^3
