Answer:
Option A is correct
The expression which is equivalent to is
Step-by-step explanation:
Using the formula:
.....[1]
Given the expression:
Substitute the value of x = 5 in [1]
we get;
Therefore, the expression which is equivalent to is
I've drawn a graph in order to a better understanding of this problem. We know that:
BC is perpendicular to AC
∠DBE = 2x - 1
∠CBE = 5x - 42
Let's call the intersection of line BC and AC the point P, so:
∠P=90°
And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:
∠PCB = ∠CBE = 5x - 42
Moreover:
∠PBC = 2x - 1 - (5x - 42)
∠PBC = 2x - 1 - 5x + 42
∠PBC = -3x + 41
The internal angles of any triangle add up to 180°. Hence for ΔBPC:
90° + ∠PBC + ∠PCB = 180°
90° - 3x + 41 + 5x - 42 = 180°
2x + 89 = 180
2x = 91
x = 45.5°
<em>Question:</em>
<em>Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. </em>
<em>The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is . </em>
<em>The solution to the inequality is . </em>
<em>Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.</em>
Answer:
a.
b.
c. At least 13 months
Step-by-step explanation:
Given
First Phone;
<em>(monthly)</em>
Second Phone;
<em /><em> (monthly)</em>
<em></em>
Solving (a): The inequality
<em></em>
Represent the number of months with x
The first phone is expressed as:
The second phone is expressed as:
For the second to be less expensive that the first, the inequality is:
Solving (b): Inequality Solution
Collect Like Terms
Solve for x
Solving (c): Interpret the solution in (b)
implies 13, 14, 15....
Hence, She'll keep the second phone for a period of at least 13 months
