Answer:

Step-by-step explanation:
Given:

Required
Rewrite in vertex form
The vertex form of an equation is in form of: 
Solving: 
Subtract 2 from both sides


Factorize expression on the right hand side by dividing through by the coefficient of x²


Get a perfect square of coefficient of x; then add to both sides
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<em>Rough work</em>
The coefficient of x is 
It's square is 
Adding inside the bracket of
to give: 
To balance the equation, the same expression must be added to the other side of the equation;
Equivalent expression is: 
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The expression becomes



Factorize the expression on the right hand side





Make y the subject of formula

<em>Solved</em>
950 * .05 = $47.5
550 * .04 = $22
$47.5 + $22 = $69.50 interest earned
answer: amount in 4% account = $550
Answer:
segment EF over segment LM equals segment FG over segment MN
Step-by-step explanation:
The triangles are similar, not congruent, so any answer choice with the word "congruent" can be ignored.
The sequence of letters in the triangle name tells you the corresponding segments:
- EF corresponds to LM
- EG corresponds to LN
- FG corresponds to MN
Corresponding segments have the same ratio, so ...
EF/LM = FG/MN . . . . . . matches the first answer choice
EF/LM = EG/LN . . . . does not match the 3rd answer choice
Answer:
b ≤ 50
Step-by-step explanation:
Since no more than 400 pounds of b number of 8 pound boxes can be taken off to ensure that the plane is in balance, this can be represented by the inequality:
8b ≤ 400
b ≤ 400/8
b ≤ 50
This means that a maximum number of 50 8 pounds boxes can be taken off the plane for a 600 pound crate to be put on ensuring that the plane is in balance.
Complete Question
A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthorn wand has a price of 45.20. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places
Answer:
0.1151
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score = $45.20
μ is the population mean = $50
σ is the population standard deviation = $4
We are solving for x < 45.20
Hence:
z = 45.20 - 50/4
z = -1.2
Probability value from Z-Table:
P(x<45.20) = 0.11507
Approximately to 4 decimal places = 0.1151
Therefore, the proportion of wand prices that are lower than the price of the blackthorn wand is 0.1151