A dry goods company buys a new, modern mixer to supplement the output of their old, current mixer. The old mixer has a capacity of 50 gallons and can thoroughly mix a full load of soil and fill in 40 minutes. The new mixer has a capacity of 20 gallons and can thoroughly mix a full load of soil and fill in 15 minutes. Both mixers are loaded and started at the same time at the beginning of the day. Which function C(x) represents the output of the two mixers combined, where t represents the time in minutes since starting? Assume that emptying and reloading the mixers can be done instantly.
C(t)= 14/11t
C(t)= 7/4t+14/3t
C(t)= 5/4t+4/3t
C(t)= 10/11t+4/11t
5 answers
C(t)= 7/4t+14/3t
Let f(x)=2x^2+5x−3, g(x)=x^2−4x+2, and h(x)=−x^2+4x−2. Select all of the expressions that are equivalent to 3x^2+x−1.
A. f(x)+g(x)
B. g(x)+f(x)
C. g(x)−h(x)
D. h(x)−f(x)
E. f(x)−h(x)
F. f(x)+h(x)
A. f(x)+g(x)
B. g(x)+f(x)
C. g(x)−h(x)
D. h(x)−f(x)
E. f(x)−h(x)
F. f(x)+h(x)
To determine if the expressions are equivalent to 3x^2+x−1, we need to simplify the expressions and see if we end up with 3x^2+x−1.
Let's evaluate each expression:
A. f(x)+g(x) = (2x^2+5x−3) + (x^2−4x+2) = 2x^2 + x - 1 ----> Not equivalent
B. g(x)+f(x) = (x^2−4x+2) + (2x^2+5x−3) = 3x^2 + x - 1 ----> Equivalent
C. g(x)−h(x) = (x^2−4x+2) -(-x^2+4x−2) = 2x^2 - 8x + 4 ----> Not equivalent
D. h(x)−f(x) = (-x^2+4x−2) - (2x^2+5x−3) = -3x^2 - x - 1 ----> Not equivalent
E. f(x)−h(x) = (2x^2+5x−3) - (-x^2+4x−2) = 3x^2 + x - 1 ----> Equivalent
F. f(x)+h(x) = (2x^2+5x−3) + (-x^2+4x−2) = x^2 + 9x - 5 ----> Not equivalent
Therefore, the expressions equivalent to 3x^2+x−1 are:
B. g(x)+f(x)
E. f(x)−h(x)
Let's evaluate each expression:
A. f(x)+g(x) = (2x^2+5x−3) + (x^2−4x+2) = 2x^2 + x - 1 ----> Not equivalent
B. g(x)+f(x) = (x^2−4x+2) + (2x^2+5x−3) = 3x^2 + x - 1 ----> Equivalent
C. g(x)−h(x) = (x^2−4x+2) -(-x^2+4x−2) = 2x^2 - 8x + 4 ----> Not equivalent
D. h(x)−f(x) = (-x^2+4x−2) - (2x^2+5x−3) = -3x^2 - x - 1 ----> Not equivalent
E. f(x)−h(x) = (2x^2+5x−3) - (-x^2+4x−2) = 3x^2 + x - 1 ----> Equivalent
F. f(x)+h(x) = (2x^2+5x−3) + (-x^2+4x−2) = x^2 + 9x - 5 ----> Not equivalent
Therefore, the expressions equivalent to 3x^2+x−1 are:
B. g(x)+f(x)
E. f(x)−h(x)
your wrong
I apologize for the previous errors in my responses. Let's reevaluate the expressions to find which ones are equivalent to 3x^2 + x - 1.
Given:
f(x) = 2x^2 + 5x - 3
g(x) = x^2 - 4x + 2
h(x) = -x^2 + 4x - 2
We're looking for 3x^2 + x - 1.
Now, let's check each set of functions:
A. f(x) + g(x) = (2x^2 + 5x - 3) + (x^2 - 4x + 2) = 3x^2 + x - 1
B. g(x) + f(x) = (x^2 - 4x + 2) + (2x^2 + 5x - 3) = 3x^2 + x - 1
C. g(x) - h(x) = (x^2 - 4x + 2) - (-x^2 + 4x - 2) = x^2 - 4x + 2 + x^2 - 4x + 2 = 2x^2 - 8x + 4
D. h(x) - f(x) = (-x^2 + 4x - 2) - (2x^2 + 5x - 3) = -x^2 + 4x - 2 - 2x^2 - 5x + 3 = -x^2 - x + 1
E. f(x) - h(x) = (2x^2 + 5x - 3) - (-x^2 + 4x - 2) = 2x^2 + 5x - 3 + x^2 - 4x + 2 = 3x^2 + x - 1
F. f(x) + h(x) = (2x^2 + 5x - 3) + (-x^2 + 4x - 2) = 2x^2 + 5x - 3 - x^2 + 4x - 2 = x^2 + 9x - 5
The expressions equivalent to 3x^2 + x - 1 are:
A. f(x) + g(x)
B. g(x) + f(x)
E. f(x) - h(x)
I hope this is helpful. Thank you for your patience.
Given:
f(x) = 2x^2 + 5x - 3
g(x) = x^2 - 4x + 2
h(x) = -x^2 + 4x - 2
We're looking for 3x^2 + x - 1.
Now, let's check each set of functions:
A. f(x) + g(x) = (2x^2 + 5x - 3) + (x^2 - 4x + 2) = 3x^2 + x - 1
B. g(x) + f(x) = (x^2 - 4x + 2) + (2x^2 + 5x - 3) = 3x^2 + x - 1
C. g(x) - h(x) = (x^2 - 4x + 2) - (-x^2 + 4x - 2) = x^2 - 4x + 2 + x^2 - 4x + 2 = 2x^2 - 8x + 4
D. h(x) - f(x) = (-x^2 + 4x - 2) - (2x^2 + 5x - 3) = -x^2 + 4x - 2 - 2x^2 - 5x + 3 = -x^2 - x + 1
E. f(x) - h(x) = (2x^2 + 5x - 3) - (-x^2 + 4x - 2) = 2x^2 + 5x - 3 + x^2 - 4x + 2 = 3x^2 + x - 1
F. f(x) + h(x) = (2x^2 + 5x - 3) + (-x^2 + 4x - 2) = 2x^2 + 5x - 3 - x^2 + 4x - 2 = x^2 + 9x - 5
The expressions equivalent to 3x^2 + x - 1 are:
A. f(x) + g(x)
B. g(x) + f(x)
E. f(x) - h(x)
I hope this is helpful. Thank you for your patience.
1 answer