The "bases" are the two sides of the trapezoid that are parallel.
Answer:
The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.60
Step-by-step explanation:
Let $x be the cost of 1 pound of salmon.
The swordfish costs $0.20 per pound less than the salmon, then $(x-0.20) is the cost of 1 pound of swordfish.
Melissa buys 2.5 pounds of salmon and pays $2.5x for salmon.
Melissa buys 1.25 pounds of swordfish and pays $1.25(x-0.20) for swordfish.
She pays a total of $31.25, then
![2.5x+1.25(x-0.20)=31.25](https://tex.z-dn.net/?f=2.5x%2B1.25%28x-0.20%29%3D31.25)
Solve this equation.
![2.5x+1.25x-0.25=31.25\\ \\2.5x+1.25x=31.25+0.25\\ \\3.75x=31.50\\ \\375x=3,150\\ \\x=\dfrac{3,150}{375}\\ \\x=8.4](https://tex.z-dn.net/?f=2.5x%2B1.25x-0.25%3D31.25%5C%5C%20%5C%5C2.5x%2B1.25x%3D31.25%2B0.25%5C%5C%20%5C%5C3.75x%3D31.50%5C%5C%20%5C%5C375x%3D3%2C150%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B3%2C150%7D%7B375%7D%5C%5C%20%5C%5Cx%3D8.4)
Costs:
1 pound of salmon - $8.40
1 pound of swordfish - $8.20
Combined - $16.60
Answer:
![z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%280.9808%29%5Et)
![z(t) = (1.0196)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0196%29%5Et)
![z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%280.9808%29%5Et)
![z(t) = (1.03)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.03%29%5Et)
![z(t) = (1.0404)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0404%29%5Et)
![z(t) = (1.0001)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0001%29%5Et)
Step-by-step explanation:
We are given the following in the question:
![x(t)=(1.04)^t\\y(t)t=(1.02)^t](https://tex.z-dn.net/?f=x%28t%29%3D%281.04%29%5Et%5C%5Cy%28t%29t%3D%281.02%29%5Et)
We have to find the growth rate z(t) in each of the following cases:
(a) z = xy
![z(t) = x(t)y(t)\\z(t) = (1.04)^t.(1.02)^t\\z(t) = (1.04\times 1.02)^t\\z(t) = (1.0608)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20x%28t%29y%28t%29%5C%5Cz%28t%29%20%3D%20%281.04%29%5Et.%281.02%29%5Et%5C%5Cz%28t%29%20%3D%20%281.04%5Ctimes%201.02%29%5Et%5C%5Cz%28t%29%20%3D%20%281.0608%29%5Et)
(b) z=x/y
![z(t) =\displaystyle\frac{x(t)}{y(t)}\\\\z(t) = \frac{(1.04)^t}{(1.02)^t} = \bigg(\frac{1.04}{1.02}\bigg)^t\\\\z(t) = (1.0196)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cdisplaystyle%5Cfrac%7Bx%28t%29%7D%7By%28t%29%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%5Cfrac%7B%281.04%29%5Et%7D%7B%281.02%29%5Et%7D%20%3D%20%5Cbigg%28%5Cfrac%7B1.04%7D%7B1.02%7D%5Cbigg%29%5Et%5C%5C%5C%5Cz%28t%29%20%3D%20%281.0196%29%5Et)
(c) z=y/x
![z(t) =\displaystyle\frac{y(t)}{x(t)}\\\\z(t) = \frac{(1.02)^t}{(1.04)^t} = \bigg(\frac{1.02}{1.04}\bigg)^t\\\\z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cdisplaystyle%5Cfrac%7By%28t%29%7D%7Bx%28t%29%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%5Cfrac%7B%281.02%29%5Et%7D%7B%281.04%29%5Et%7D%20%3D%20%5Cbigg%28%5Cfrac%7B1.02%7D%7B1.04%7D%5Cbigg%29%5Et%5C%5C%5C%5Cz%28t%29%20%3D%20%280.9808%29%5Et)
(d) z=x^(1/2) y^(1/2)
![z(t) = (x(t))^{\frac{1}{2}}(y(t))^{\frac{1}{2}}\\z(t) = ((1.04)^t)^\frac{1}{2} ((1.02)^t)^\frac{1}{2}\\z(t) = (1.0608)^{\frac{t}{2}}\\z(t) = (1.03)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%28x%28t%29%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%28y%28t%29%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5Et%29%5E%5Cfrac%7B1%7D%7B2%7D%20%28%281.02%29%5Et%29%5E%5Cfrac%7B1%7D%7B2%7D%5C%5Cz%28t%29%20%3D%20%281.0608%29%5E%7B%5Cfrac%7Bt%7D%7B2%7D%7D%5C%5Cz%28t%29%20%3D%20%281.03%29%5Et)
(e) z=(x/y)^2
![z(t) =\bigg(\displaystyle\frac{x(t)}{y(t)}\bigg)^2\\\\z(t) =\bigg( \frac{(1.04)^t}{(1.02)^t}\bigg)^2 = \bigg(\frac{1.04}{1.02}\bigg)^{2t}\\\\z(t) = (1.0404)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cbigg%28%5Cdisplaystyle%5Cfrac%7Bx%28t%29%7D%7By%28t%29%7D%5Cbigg%29%5E2%5C%5C%5C%5Cz%28t%29%20%3D%5Cbigg%28%20%5Cfrac%7B%281.04%29%5Et%7D%7B%281.02%29%5Et%7D%5Cbigg%29%5E2%20%3D%20%5Cbigg%28%5Cfrac%7B1.04%7D%7B1.02%7D%5Cbigg%29%5E%7B2t%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%281.0404%29%5Et)
(f) z=x^(-1/3)y^(2/3)
![z(t) = (x(t))^{\frac{-1}{3}}(y(t))^{\frac{2}{3}}\\z(t) = ((1.04)^t)^{\frac{-1}{3}}((1.02)^t)^{\frac{2}{3}}\\z(t) = ((1.04)^{\frac{-1}{3}})^t((1.02)^{\frac{2}{3}})^t\\z(t) = (1.04^{\frac{-1}{3}}\times 1.02^{\frac{2}{3}})^t\\z(t) = (1.0001)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%28x%28t%29%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%28y%28t%29%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5Et%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%28%281.02%29%5Et%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%29%5Et%28%281.02%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5Et%5C%5Cz%28t%29%20%3D%20%281.04%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%5Ctimes%201.02%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5Et%5C%5Cz%28t%29%20%3D%20%281.0001%29%5Et)
Answer:
A
Step-by-step explanation:
logb √(41/97)
Square root can be written in exponent form:
logb (41/97)^½
Using log exponent rule:
½ logb (41/97)
Using log quotient rule:
½ (logb 41 - logb 97)
Answer:
197
Step-by-step explanation:
![5 \times 5 \times 2 + 5 \times (5 + 9) \times \frac{1}{2} \times 2 + 5 \times 9 + 5 \times 6.4 = 197](https://tex.z-dn.net/?f=5%20%5Ctimes%205%20%5Ctimes%202%20%2B%205%20%5Ctimes%20%285%20%2B%209%29%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%202%20%2B%205%20%5Ctimes%209%20%2B%205%20%5Ctimes%206.4%20%3D%20197)