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nignag [31]
3 years ago
8

According to the Census Bureau, in 2014 California had an estimated population of 3.88 x 10^7 and Wyoming had an population of 5

.84 x 10^5. The population of California is ______ more than the population of Wyoming. Alternatively the population of California is _____ times the population of Wyoming.
Mathematics
1 answer:
Verdich [7]3 years ago
8 0
The population of California is 3.88 x 10^7 - 5.84 x 10^5 = 3.82 x 10^7 more than the population of Wyoming. Alternatively the population of California is 3.88 x 10^7 / 5.84 x 10^5 = 66 times the population of Wyoming. 

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Find all solutions of the given system of equations (If the system is infinite many solution, express your answer in terms of x)
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Answer:

(a) The system of the equations \left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right. has no solution.

(b) The system of the equations \left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right. has many solutions y=\frac{2x}{3}-\frac{5}{3}

Step-by-step explanation:

(a) To find the solutions of the following system of equations \left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right. you must:

Multiply 2x-3y=3 by 2:

\begin{bmatrix}4x-6y=6\\ 4x-6y=3\end{bmatrix}

Subtract the equations

4x-6y=3\\-\\4x-6y=6\\------\\0=-3

0 = -3 is false, therefore the system of the equations has no solution.

(b) To find the solutions of the system \left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right. you must:

Isolate x for 4x-6y=10

x=\frac{5+3y}{2}

Substitute x=\frac{5+3y}{2} into the second equation

16\cdot \frac{5+3y}{2}-24y=40\\8\left(3y+5\right)-24y=40\\24y+40-24y=40\\40=40

The system has many solutions.

Isolate y for 4x-6y=10

y=\frac{2x}{3}-\frac{5}{3}

3 0
3 years ago
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