The external angle is suplementary to the internal angle close to it. We also know that the sum of all the internal angles of the triangle are equal to 180 degrees, this means that the angle "a" is suplementary to the sum of the angles "b" and "c". Through this logic, we can conclude that since:
Then we can conclude that:
Therefore the statement is true, the exterior angle is equal to the sum of its remote interior angles.
Let's use an example:
On this example, the external angle is 120 degrees, therefore the sum of the remote interior angles must also be equal to that. Let's try:
The sum of the remote interior angles is equal to the external angle.
-12 + 9 - (-3) - 11
Remember PEMDAS: This is the order of operation.
P-Paragrahp
E-Exponent
M-Multiply
D-Divide
A-Add
S-Subtract
1st step: PEM
-(-3) is actually -1 * -3 = + 3
-12 + 9 + 3 - 11
2nd step: D is not possible, so we do A.
9 + 3 = 12
3rd Step: Subtract
12 - 12 - 11 = 0 - 11 = -11 CHOICE B.
Answer: See Annex
z (max) = 190
x = 10
y = 20
Step-by-step explanation:
z = 5*x + 7*y to maximize
Subject to:
x + y ≤ 30
2*x + y ≤50
2*x - y ≥ 0
x≥= y ≥0
Answer:
A. y + 6= -2(x - 4)
Step-by-step explanation:
Let A(a , b) be a point of the line
and m be the slope.
The equation of the line in Point-slope form :
y - b = m (x - a).
…………………………
Given :
Slope = -2
A(4 , -6)
Then
Point-slope equation : y + 6= -2(x - 4)
Let assume that the the two numbers are X and Y and that X is the large number.
According to the question,
X + Y = 53 .................. Equation 1
then, X = 11 + Y........... Equation 2
Substitute equation 2 into equation 1.
[11 + Y] + Y = 53
11 + 2Y = 53
2Y = 53 - 11 = 42
2Y = 42
Y = 42 / 2 = 21,
Therefore, Y = 21 [Small number].
According to equation 1,
X +Y = 53
X + 21 = 53
X = 53 - 21 = 32.
Therefore, X = 32 [Big number].
