A ladder leans against a building, making a 70° angle of elevation with the ground. The top of the ladder reaches a point on the
1 answer:
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Answer:
$75
Step-by-step explanation:
Joni currently earns $300 per week (given)
To find how much more she will earn each week, write an expression adding the original pay and the raise amount.
$300 + 25%
Find 25 as a decimal for multiplication
25% = 25/100 = 0.25
Write an expression to represent the scenario
Expression example 1:
$300 + 0.25(300)
This expression adds the original pay and the new raise together.
Expression example 2:
$300 (1.25)
This expression already takes the new pay into account by finding 125% of the original pay.
Simplify both expressions
Expression 1:
$300 + 0.25(300)
$300 + $75
$375
Expression 2:
$300 (1.25)
$375
Both expressions represent the same scenario and therefore come out to the same result. Now that we know how much Joni made after the raise, we need to find how much more money she will earn in a week with the following equation.
New amount - original amount = amount increase
Substitute known values into the equation
$375 - $300
Simplify
$75
Joni will earn $75 more each week.
Let me know if you have any questions!
Answer:
C. is your answer
Step-by-step explanation:
In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is
,
where x = h is the equation of the line of symmetry.
To get this into vertex form we will complete the square. The first couple of steps I will combine into 1. We will set the quadratic equal to zero, then move the constant over to the other side:
The next rule is that the leading coefficient HAS to be a positive 1. Ours is a positive 88, so we have to factor it out:
Now we can perform the process of completing the square. The rule is to take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2, and 3/2 squared is 9/2. We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored. It serves as a multiplier into the parenthesis. What we actually added in, then, was 88(9/2) which is 198:
The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex. We will state that binomial and at the same time do the addition on the right:
Now we can move the constant back over and set it back equal to y:
From that form you can see that the equation of the line of symmetry is x = 1.5. The coordinates of the vertex are (1.5, 102). If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.
C then is your answer.