4 unknowns needs 4 equations. I'll call the unknown numbers a,b,c,d in that order left to right.
4 + a = b
a + b = c
b + c = d
c + d = 67
let's use substitution to get rid to combine equations and get rid of variables.
If a + b = c then a = c - b
4 + (c - b) = b
4 + c = 2b
If b + c = d then b = d - c
4 + c = 2(d - c)
4 + c = 2d - 2c
4 + 3c = 2d
then we have c + d = 67 so c = 67 - d
4 + 3(67 - d) = 2d
4 + 201 - 3d = 2d
205 = 5d
d = 41
Should be easy now, subtract backwards.
67 - 41 = 26
41 - 26 = 15
26 - 15 = 11
15 - 11 = 4
4, 11, 15, 26, 41, 67
Answer:
1120 in³
Step-by-step explanation:
The volume (V) of a cuboid is calculated as
V = area of base × height , then
V = 80 × 14 = 1120 in³
Answer:
it equals to 1032000
Step-by-step explanation:
because 3000 x 344 = 1032000
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
Step-by-step explanation:
Solving
2x + 6 = 4x - 4
Bringing like terms on one side
6 + 4 = 4x - 2x
10 = 2x
10 / 2 = x
5 = x
