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
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
Answer:
Only table C shows proportional relationship
Step by Step Explanation:
Given
Tables A, B an C
Required
Which table shows proportional relationship?
In table A .
x = 2 and y = 20
k = 20/2
k = 10
Also, x = 12, y = 132
k =. 132/12.
k = 11
Both values of k are not equal.
Hence, the table is not proportional
In table B
x = 5 and y = 20
k = 20/5
k = 4
Also, x = 7, y = 30
k =. 30/7
k = 4.29
Both values of k are not equal.
Hence, the table is not proportional
In table C
x = 9 and y = 90
k = 90/9
k = 10
Also, x = 14, y = 140
k =. 140/14
k = 10
Also, x = 24, y = 240
k =. 240/24
k = 10
All values of k are equal.
Hence, the table is proportional
Answer: 12 acres could be planted (at most)
Step-by-step explanation: Since there will be twice as many acres of wheat in comparison to the corn, out of the total 36 acres at least 24 of those will need to be wheat. That leaves 12 acres left for the corn.
A and D that’s the answer
