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Dmitry_Shevchenko [17]
3 years ago
15

1. Use Substitution Method, Show Steps. 3x=2y=11 y=5x-1

Mathematics
1 answer:
ladessa [460]3 years ago
4 0
3x=2(5x-1)=11
3x=10x-2=11
-10x -10x
-------------------
-7x=-2=11
       +2   +2
------------------
-7x=13
-----  ------
-7      -7

x= -1.9

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1. M is the midpoint of LN and O is the midpoint of NP.
Reptile [31]
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
5 0
3 years ago
Chandani purchased some parrots. 20% flew away and 5% died. Of the remaining, 45% were sold. Now 33 parrots remain. How many par
Paha777 [63]

Answer:

80 parrots were purchased.

Step-by-step explanation:

Let the total number of parrots be k.

If 20% (or 20/100 = 1/5) flew away and 5% (5/100 = 1/20) died, the remaining parrots will be k – (¹/₅k + ¹/₂₀k) = k – ¼k = ¾k.

Of the remaining, 45% (or 45/100 = 9/20) were sold, which means the total number of sold parrots will be ¾k × ⁹/₂₀ = ²⁷/₈₀k.

The remaining parrots = ¾k – ²⁷/₈₀k = ³³/₈₀k = 33

k = 33 × ⁸⁰/₃₃ = 80 parrots were purchased.

8 0
3 years ago
Work out the value of x.
Alona [7]
2x+3x=180
5x=180
x=180/5
x=36
3 0
3 years ago
Which of the following is the same as 8.4 x 10 2<br>A.840 B. .84 C.84 D.8,400
kaheart [24]
8.4 x 10^2 (10 to the 2nd power) = 8.4 x 100 = 840

The answer is A. 840
5 0
3 years ago
HELP ASAP!! Can you explain how to decompose a rectangle into congruent triangles? How does the area of the decomposed pieces re
Aleksandr-060686 [28]

Answer: You would divide the rectangle into half, to form two congruent triangles. When you multiply the area of 1 of the triangles, it gives you the area of both triangles, and so the area of the triangle as a whole

7 0
3 years ago
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