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
9) Separate the polygon into 2 shapes (a rectangle and triangle). Then plug in the formula for those 2 shapes separately and add the 2 areas.
First, the triangle's area = bh x 1/2 or bh/2.
b=5 and h=5, so 5x5/2 or 25/2 = 12.5.
Next, solve the area for the rectangle(lw=A). l=5 and 2=8, so 5x8=40.
Add 40 +12.5 = 52.5cm^2 (always include units).
10) It is similar to the last problem. You will separate the polygon into 2 shapes (a circle and a square), but this time you will subtract the area of the sector formed from the circle (draw a dotted line where the circle would be formed in the square).
So, the area of the square is 2x2=4ft^2.
area of a circle is (pi)r2 or (pi)2^2= 4pi or about 12.5ft^2.
4+12.5 = 16.5 ft^2.
Now, the area of the sector must be subtracted from the combination of the 2 areas found above.
The area of a sector is 2(pi)r x (C/360).
The angle is given as 90°, the radius is 2 ft. Now plug these into the equation.
2(pi)(2)x(90/360) = 3.14ft^2.
16.5-3.14= 13.4 ft^2.
Answers:
Positive slopes:
Y = 8x - 6 with a slope of 8.
30x - 5y = 25 with a slope of 6.
Negative slopes:
-3x + 3y = 18 with a slope of -1.
Y = -3x + 7 with a slope of -3.
20x + 10y = 90 with a slope of -2.
Step-by-step explanation: Have a great day! :)
Answer: -2 2/3
Step-by-step explanation: ok so use the slope formula
y2-y1 divided by x2-x1
so then we plug in the numbers
(1/10, -1) and (-1/5,-1/5)
the y corrdinates are (-1/5-(-1) and the x corrdinates are (-1/5-1/10)
were goning get y= 4/3 and x=-3/10 and final answer is -2 2/3
I hope this is right and helps xD
