The answer is true the product of two rational numbers is never equal to 1
Equation of the perpendicular
y= 2x+6
slope of the perpendicular = 2
slope of the req. line = -1/2
equation of the req. line
y - y1 = m(x - x1)
y - 2 = -1/2(x + 4)
2(y - 2) = -1(x + 4)
2y - 4 = -x - 4
2y = -x
y = (-1/2)x
this is your req. equation of line.
Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)
Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;
Volume = L³
The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;
VB = 8³
VB = 512 cm³
The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;
VM = L³
VM = 6³
VM = 216 cm³
The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;
VT = L³
VT = 4³
VT = 64
From the calculations shown, the total volume of the cubes in the tower is given as;
Total volume = VB + VM + VT
Total volume = 512 + 216 + 64
Total volume = 792 cm³
Total volume is 792 cubic centimetres.
<h3>
Answer: 79 full rotations</h3>
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Explanation:
150 cm = 150/100 = 1.5 m
The wheel has a diameter of 1.5 meters
The circumference of the wheel is
C = pi*d
C = pi*1.5
C = 1.5pi
C = 4.71238898038469
I'm using my calculator's stored version of pi to get the most accuracy.
Then we divide the 376.8 over the circumference found
(376.8)/(4.71238898038469) = 79.9594434093682
Despite being very close to 80, we must round down to 79 because we don't have enough to get that full 80th rotation. In other words, we have 79 full rotations and then some change leftover.
Though for the sake of simplicity, I can see how it's useful to say "about 80 rotations" if 79 seems a bit clunky. I'll stick with 79 however. Let me know if your teacher instructs otherwise.
1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation
MO= (1/2) LP
If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be:
2x+6= (1/2)( 8x-20)
2x+6= 4x-10
2x-4x= -10 - 6
-2x= -16
x=8
2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2
Then, the answer would be:
A.F= 1/(1+2) * AC
A.F= 1/3 * 12= 4
FC= 2/(1+2) * AC
FC= 2/3 * 12= 8
3. Since
∠BAD=∠DAC
∠ABD=∠ACD
AD=AD
The triangle ABD and ACD are similar. You can get this equation
BD=DC
x+8= 3x+12
x-3x= 12-8
-2x=4
x=-2
DC=3x+12= 3(-2) +12= 6
4. Orthocenter made by intersection of triangle altitude
A
BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be:
y=-x +a
0= 1+a
a=-1
y=-x-1
B
AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be:
y=1/3x+a
-1=1/3(4)+a
a=-7/3
y=1/3x - 7/3
C
BC lines slope would be (-1)-(-1)/4 = 0/4.
The line would be
0=x+a
a=-1
0=x-1
x=1
y=-x-1 = 1/3x-7/3
-x-(1/3x)=-7/3 +1
-4/3x= -4/3
x=1
y=-x-1
y=-1-1= -2
The orthocenter would be (1,-2)
5.
a. Circumcenter: the intersection of perpendicular bisector lines<span>
b. Incenter: the intersection of bisector lines
c. Centroid: </span>the intersection of median lines<span>
d. Orthocenter: </span>the intersection of altitude lines
