Answer:
The lead statue is 87 inches tall
Step-by-step explanation:
Let
x ----> the height of the lead statue
using proportion
we know that
The height of the lead statue divided by the length of his shadow must be equal to the height of the tourist divided by the length of his shadow.
so
Problem 1
x = measure of angle N
2x = measure of angle M, twice as large as N
3(2x) = 6x = measure of angle O, three times as large as M
The three angles add to 180 which is true of any triangle.
M+N+O = 180
x+2x+6x = 180
9x = 180
x = 180/9
x = 20 is the measure of angle N
Use this x value to find that 2x = 2*20 = 40 and 6x = 6*20 = 120 to represent the measures of angles M and O in that order.
<h3>Answers:</h3>
- Angle M = 40 degrees
- Angle N = 20 degrees
- Angle O = 120 degrees
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Problem 2
n = number of sides
S = sum of the interior angles of a polygon with n sides
S = 180(n-2)
2700 = 180(n-2)
n-2 = 2700/180
n-2 = 15
n = 15+2
n = 17
<h3>Answer: 17 sides</h3>
====================================================
Problem 3
x = smaller acute angle
3x = larger acute angle, three times as large
For any right triangle, the two acute angles always add to 90.
x+3x = 90
4x = 90
x = 90/4
x = 22.5
This leads to 3x = 3*22.5 = 67.5
<h3>Answers:</h3>
- Smaller acute angle = 22.5 degrees
- Larger acute angle = 67.5 degrees
Answer:
Step-by-step explanation:
Given that,
y=x+2 equation 1
2x-y=-4 equation 2
This is a simultaneous equation.
Substitute equation 1 into equation 2
2x-y=-4. Since y=x+2
2x-(x+2) = -4
2x-x-2 = -4
x-2 = -4
x = -4+2
x = -2
Also from equation 1
y=x+2
Since x=-2
y=-2+2
y=0
Then, solution (x, y) = (-2,0)
Right change flip it's simple
Answer:
104
155
180
Step-by-step explanation:
an easy way is to solve what is in the parenthesis then multiply by the outside number
but if you need to use the distributive property:
1. 4 x (20 - -6)
(4 x 20) - (4 x -6) = 80 - -24 = 80 + 24 = 104
2. -5 x (24 - -7)
(-5 x 24) - (-5 x -7) = -120 - 35 = 155
3. 12 x (-30 + 45)
(12 x -30) + (12 x 45) = -360 + 540 = 180
