Answer:
slope = 
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = (- 4, 1) and (x₂, y₂ ) = (0, 2) ← 2 points on the line
m = 
= 
=
Given:
The product of a particular number is 65.
Second value is given by the sum of 8 and the original number.
To find:
The unknown number.
Solution:
Let x be the unknown number.
Then, second number = x+8
The product of a particular number is 65.
Splitting the middle term, we get
Using zero product property, we get
and 
and 
So, the unknown number is either 5 or -13.
Therefore, the correct option is B.
Multiply both sides of the equation by (x+1), on the right hand side the denominator then goes away and on the left hand side you get (x+1)(x+1), foil that out then just solve for x
Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
Answer:
16,080 km.
Step-by-step explanation:
We want the total number of kilometers in one year.
so
4 weeks /month.
for Work: 9 months in the year 60 km/day 5 days/week
Family Visit : 720 km for 4 times a year
Personal: 200 km / month
Work total = 60 km/day * 5 days/week * 4week/month * 9 months
WorkTotal= 60*5*4*9 = 10,800 km
FamilyTotal= 4*720 = 2880 km
Personal = 200*12 = 2400 km
Total = 10,800 + 2880 + 2400 = 16,080 km
