Answer:
Step-by-step explanation:
Given the vertices 
, 
and
. The area of triangle JKL is given by:
We substitute the values to get:
This simplifies to
Answer:
Step-by-step explanation:
Let the number be x
5 times a number = 5x
24 - 5x = 15
-5x = 15-24
-5x = -9
x= -9/-5
x = 9/5
or x = 1.8
Answer:
360 × 30
= (360 × 3) × 10
= 1080 × 10
= 10800
Step-by-step explanation:
For the first two blanks, we will have to find a pair of factors of 30 that will make this the easiest to solve. Lets pair up all of the factors of 30.
1, 30
2, 15
3, 10
5, 6
So now we have found all of the factors of 30. We can eliminate 1 and 30, since we will just end up with 360 × 30 in the second line. We could use 2 and 15, but we will end up with _____ × 15 in the second line, which would be more difficult to solve for than the other two options. Now, you should use any one of the final two pairs of factors. I would use 3 and 10, since I find it much easier to multiply something by 3 and 10 than 5 and 6.
Lets put 3 in the first blank and 10 in the second blank. We will end up with:
(360 × 3) × 10
Now 360 × 3 would be 1080. So the second line would be:
1080 × 10
1080 × 10 would equal 10800. So the final line and the final blank would be:
10800
So in order, the lines would be:
= (360 × 3) × 10
= 1080 × 10
= 10800
I hope you find my answer and explanation to be helpful. Happy studying.
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
