Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)
The third side of the triangle is 26.
Explanation:
Given:
Two sides of the isosceles triangle are 26 and 10.
To Find:
The possible value of the third side
Solution:
Definition of Isosceles triangle:
An isosceles triangle is a triangle with (at least) two equal sides. Isosceles triangle has both two equal sides and two equal angles.
We also know the property of the triangle that
Sum of two sides of triangle > third side of the triangle
Case1. When third side is 10
Thee third side can’t be equal to 10 because it does not follow the rule of triangle
10+10>26………which is not possible
So the third side of the isosceles triangle is 26.
Answer:
2 minutes, 40 seconds
Step-by-step explanation:
set up a proportion and cross-multiply:
4/3 = x/2
3x = 8
x = 2 2/3 which is 2 minutes, 40 seconds
First, we'll find the slope of the new line. The first line has a slope of 
. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by 
) to get 
for the new slope.
Then, we'll use the point-slope form to make the new equation, where 
is the slope and 
is a point on the line:
