Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Coordinates (x, y)
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
Point (3, -10)
Point (4, -21)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>
- Substitute in points [Slope Formula]:
- [Fraction] Add/Subtract:
- [Fraction] Divide:
The length of the AC is x^2 + 4x - 12.
<h3>What is a parallelogram?</h3>
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given :
In Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
AE = x^2 - 12,
CE = 4x
We know that the diagonal of a parallelogram bisect each other.
x^2 - 12 = 4x
x^2 - 4x - 12= 0
(x-6)(x-2) = 0
Hence, the value of x = 6, 2.
AC = AE + CE = x^2 + 4x - 12.
The length of the AC is x^2 + 4x - 12.
Learn more about Parallelogram ;
brainly.com/question/12871564
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Answer:
it is an absolute function
or more precisely
y = - I x - 1 I + 8 (shown in the screenshot)
Answer:
a) 19.6%
b) 9.93%
c) 55.515 hours
Step-by-step explanation:
The average American last year worked 44 hours per week and a population standard deviation of 7 hours.
We solve using z score formula
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
a) What percentage of people work at least 50 hours per week?
At least means greater than or equal to
z = 50 - 44/7
z = 0.85714
P-value from Z-Table:
P(x<50) = 0.80432
P(x>50) = 1 - P(x<50) = 0.19568
Converting to Percentage
= 0.19568 × 100
= 19.568
= 19.6%
b) What percentage of people work less than 35 hours per week?
z = 35 - 44/7
z = -1.28571
P-value from Z-Table:
P(x<35) = 0.099271
Converting to percentage
= 0.099271 × 100
= 9.9271 %
= 9.93%
c) How many hours does someone need to work to be in the upper 5% of hours worked per week?
Upper 5% = 95%
z-score for 95th percentile = 1.645
Hence:
1.645 = x - 44/7
Cross Multiply
1.645 × 7 = x - 44
x = 44 + (1.645 × 7)
x = 44 + 11.515
x = 55.515 hours
Answer:
Olivia sold 16 chocolate bars and Emily sold 32.
Step-by-step explanation:
Let's set the amount of chocolate bars Olivia sold as x.
Since Emily sold twice as many, she would have sold 2x chocolate bars as a result.
Therefore, since the total is 48 bars, the equation would be 
.
Hence, Olivia sold 16 chocolate bars.
Substituting the new value into the equation, we would find that Emily had sold 2x = 2(16) = 32 chocolate bars.
Checking the answer, we would find that (16 + 32) chocolate bars is indeed 48 chocolate bars, which fits the question.
Finally, we can arrive at the conclusion that Olivia sold 16 chocolate bars and Emily sold 32.
Hope this helped!
