Answer:
78 sqr units
Step-by-step explanation:
Use the Pythagorean Theorem to help find the base opposite the two.
The base of the second parallel line is sqrt( (15^2) - (12^2) ) = sqrt(81) = 9
The second base = 9 + 2 = 11
Area = (b1 + b2)*h/2
h = 12
b1 = 2
b2 = 11
h = 12
Area = (11 + 2)*12/2
Area = 13 * 12/2
Area = 78 square units
Angles 6 and 8 add up to equal 180, so 2x - 5 + x + 5 = 180. 3x = 180 so x = 60. Angle 3 is alternate interior to angle 6 which is 2(60) - 5 = 115, so angle 3 is also 115
Answer: y - 5 = 0(x - 1)
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Explanation:
Recall that point slope form in general is written as such
y - y1 = m(x - x1)
where,
m is the slope
(x1,y1) is the point the line goes through
The given equation y = 7 can be written as y = 0x+7. So we see that this line has a slope of m = 0
Plug m = 0 along with the given point (x1,y1) = (1,5) into the point slope equation and we get
y - y1 = m(x - x1)
y - 5 = 0(x - 1)
which is the final answer
note: the equation in bold can be rearranged and simplified to get y = 5; however your teacher seems to want the answer in point-slope form, so we leave it as such.
Volume of the cone:
V = 3.14 x 3^2 x 9/3 = 84.78
Volume of half sphere on top of cone:
V = (4/3 x 3.14 x 3^3 )/2 = 56.52
Total volume = 56.52 + 84.78 = 141.3 cm^3
Let x represent the larger number.
Let y represent the smaller number.
x-y=4 Given
3x=5y-2 Given
Now we can just substitute; let x=4+y
Substitute 4+y for x in the second equation:
3(4+y)=5y-2
12+3y=5y-2
-2y=-14
y=7
Substitute back (into BOTH equations to double check work).
x, the larger number, is 11
