Answer: B. 1975
Step-by-step explanation:
Given: The model of population of a certain city between the years 1965 and 1995 by the radical function
![P(x)=75000\sqrt[3]{x-1940}](https://tex.z-dn.net/?f=P%28x%29%3D75000%5Csqrt%5B3%5D%7Bx-1940%7D)
To find the x year at which population is 245,000, put this in equation we get
![245000=75000\sqrt[3]{x-1940}\\\\\Rightarrow\frac{245000}{17000}=\sqrt[3]{x-1940}\\\\\Rightarrow3.266=\sqrt[3]{x-1940}\\\\\Rightarrow\ x-1940=(3.266)^3..........\text{[by taking cube on both sides]}\\\\\Rightarrow\ x-1940=34.8587\\\\\Rightarrow\ x=1940+34.8587\\\\\Rightarrow\ x=1974.8587\approx1975](https://tex.z-dn.net/?f=245000%3D75000%5Csqrt%5B3%5D%7Bx-1940%7D%5C%5C%5C%5C%5CRightarrow%5Cfrac%7B245000%7D%7B17000%7D%3D%5Csqrt%5B3%5D%7Bx-1940%7D%5C%5C%5C%5C%5CRightarrow3.266%3D%5Csqrt%5B3%5D%7Bx-1940%7D%5C%5C%5C%5C%5CRightarrow%5C%20x-1940%3D%283.266%29%5E3..........%5Ctext%7B%5Bby%20taking%20cube%20on%20both%20sides%5D%7D%5C%5C%5C%5C%5CRightarrow%5C%20x-1940%3D34.8587%5C%5C%5C%5C%5CRightarrow%5C%20x%3D1940%2B34.8587%5C%5C%5C%5C%5CRightarrow%5C%20x%3D1974.8587%5Capprox1975)
Hence, at year 1975 the population of the city is 245,000.
Answer:
1728 inches
Explanation:
There are 3 feet in 1 yard and 12 inches in 1 foot, so we have:
48 yards * 3 = 144 feet
144 ft * 12 = 1728 inches
Emily bought 1728 inches.
Answer:
x = 2±sqrt(11)
Step-by-step explanation:
x^2 -4x - 7 =0
Add 7 to each side
x^2 -4x -7+7 =0+7
x^2 -4x =7
To complete the square take the coefficient of the x term and divide by 2 and then square it. Add it to both sides
-4 /2 = -2 then square
(-2)^2 = 4
Add 4 to both sides
x^2 -4x+4 =7+4
x^2 -4x+4 = 11
Factor the left side into (x-b/2)^2
(x-2)^2 =11
Take the square root of each side
sqrt((x-2)^2) =±sqrt(11)
x-2 = ±sqrt(11)
Add to to each side
x-2+2 = 2±sqrt(11)
x = 2±sqrt(11)
Answer: the father is 44 years old now
Step-by-step explanation:
Let Bob's present age be represented by x
Let his father's present age be represented by y
Bob's age is 15 years less than half his father's age. This means that
x = y/2 - 15
x + 15 = y/2
y = 2x + 30
y - 2x = 30 - - - - - - - - - -1
In six years his father's age will be eleven years more than triple Bob's age. This means that
y + 6 = 3(x + 6) + 11
y + 6 = 3x + 18 + 11
y - 3x = 18 + 11 - 6
y - 3x = 18 + 11 - 6
y - 3x = 23 - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
x = 7
y = 2x + 30
y = 2×7 + 30
y = 14 + 30
y = 44
Answer:
Step-by-step explanation:
Write the quotient as a mixed number
we divide 77 by 6
1 2
-----------------------
6 7 7
6
-----------------------(subtract)
1 7
1 2
--------------------------(subtract)
5
Quotient is 12 and remainder is 5
we write mixed fraction as 
