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)
Answer:
the answer would be d
Step-by-step explanation:
(8+12) is the sum
(8+12)10 would give you the answer of the sum of 8 and 12 times 10
Step-by-step explanation: In geometry, a vertex is where two rays share a common endpoint or where they interest each other.
The rays are called the sides of the angle and
common endpoint is called the vertex.
The vertex is very important when naming angles because
the vertex is always at the center when naming the angle.
Below is an example of two rays that share a
common endpoint which is called the vertex.
Answer:
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- <u>She should aim 6 feet down the wall</u>
Explanation:
The diagram attached sketches the situtation.
Since the angle with which the ball hits the wall is the same with which it bounces, angle β is the same for the two shown triangles.
Then, since both are right triangles, then all the angles are congruent and the triangles are similar. Hence, you can equal the ratios of the sides, to make an equation:
You have other equation:
Substitute
- 2y + y = 18
- 3y = 18
- y = 18/3
- y = 6 ← this is the distance down the wall where the ball should hit
Then, she should aim 6 feet down the wall.
Answer: 2/15
Explanation: 2/9 x 3/5 then simplify it