Answer:
8934 (8933.58542585)
Step-by-step explanation:
8,500 (population currently) * 1.01 (1 percent) ^ 5 (years) = 8933.58542585 ≅ 8934 people.
Note that when two lines have slopes of m₁ and m₂, then
(i) If m₁ = m₂, then the lines are parallel.
(ii) If m₁*m₂ = -1, then the lines are perpendicular.
Let us evaluate the given lines.
a. y = 4x - 1 and 12x = 3y + 7
y = 4x - 1 => m₁ = 4
Write the second equation in standard form.
3y = 12x - 7
y = 4x - 7/3 => m₂ = 4.
m₁ = m₂.
Answer: PARALLEL
b. x - 7y = 10 and 2x + 14y = 21
In standard form,
7y = x - 10 or y = (1/7)x - 10/7 => m₁ = 1/7
14y = - 2x + 21 or y = -1/7 + 3/2 => m₂ = -1/7
m₁ ≠ m₂ and m₁*m₂ ≠ -1.
Answer: NEITHER
c. 5x + 6y = 18 and 18x - 15y = 36
In standard form,
6y = -5x + 18 or y = -(5/6)x + 3 => m₁ = -5/6
15y = 18x - 36 or y = (6/5)x - 12/5 => m₂ = 6/5
m₁*m₂ = -1
Answer: PERPENDICULAR
d. x =1 and y = 1
x = 1 => m₁ is undefined
y = 1 => m₂ = 0
m₁ ≠ m₂ and m₁*m₂ ≠ -1
Answer: NEITHER
Answer:
62.5
Step-by-step explanation:
P = (6.50f) - 100
All you have to do is plug in 25 for f in the equation and solve for P.
P = (6.50*25) - 100
P = 162.5 - 100
P = 62.5
Answer:
Esmerelda did not use the reciprocal of the divisor.
Step-by-step explanation:
A complex fraction is another way to show division of two fractions. In this case, we are dividing -5 1/4 by 3/2.
We first convert -5 1/4 to an improper fraction. To do this, multiply the whole number by the denominator; this gives us -5(4) = -20. Then add the -1 (negative since the fraction is negative); this gives us -21/4.
This means we are dividing -21/4 by 3/2.
To divide fractions, we multiply by the reciprocal; this means we flip the second fraction and multiply. We would then multiply -21/4 by 2/3. This is the step Esmerelda did not do.