Answer:
x ≈ 58.9
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Geometry</u>
- [Right Triangles Only] tan∅ = opposite over adjacent
Step-by-step explanation:
<u>Step 1: Define</u>
We are given a right triangle. We can use trig to find the missing side length.
<u>Step 2: Identify Variables</u>
<em>POV from the angle measure</em>
Angle = 23°
Opposite Leg = 25
Adjacent Leg = <em>x</em>
<em />
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitution [tangent]: tan23° = 25/x
- Multiply <em>x</em> on both sides: xtan23° = 25
- Isolate <em>x</em>: x = 25/tan23°
- Evaluate: x = 58.8963
- Round: x ≈ 58.9
Answer: y = -5x/3 - 7/4
Step-by-step explanation:
The equation of a line in slope and point form is given as
y - 
= m(x - 
)
where m is the slope
= 2
= -3
m = -5/8
Substituting into the formula , we have
y - ( -3 ) = -5/8 ( x - 2 )
y + 3 = -5x/8 + 5/4
This could also be written in slope - intercept form , that means we will make y the subject of the formula
y = -5x/8 + 5/4 - 3
y = -5x/3 - 7/4
Answer:
53 hours
Step-by-step explanation:
If A is the time it takes Company A, and B is the time it takes Company B, then:
1/27 = 1/A + 1/B
A = B + 2
Substitute and solve:
1/27 = 1/(B + 2) + 1/B
1/27 = (B + B + 2) / (B (B + 2))
1/27 = (2B + 2) / (B² + 2B)
27 (2B + 2) = B² + 2B
54B + 54 = B² + 2B
0 = B² − 52B − 54
B = [ -(-52) ± √((-52)² − 4(1)(-54)) ] / 2(1)
B = (52 ± √2920) / 2
B ≈ 53.0
It would take Company B approximately 53 hours.
The blue dot is at -11.3 on the number line.
