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marishachu [46]
3 years ago
9

Examine the following system of inequalities.

Mathematics
1 answer:
lubasha [3.4K]3 years ago
7 0

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

y > -x+4 ----> inequality A

The solution of the inequality A is the shaded area above the dotted line y=-x+4

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

y \leq -(1/2)^{x} +6 -----> inequality B

The solution of the inequality B is the shaded area above the solid line y=-(1/2)^{x} +6

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

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Step-by-step explanation:

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For them to have the same value, we should equal them:

(x+2)+(x+3)+(x+3)=(x+2)+(x+2)+x+x

Working with this:

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The two problems are almost identical: you have to set up a system, and then solve it.

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So, we have the system

\begin{cases}g=2b+4\\g+b=61\end{cases}

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g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19

And then solve for g:

g=2b+4=2\cdot 19+4=38+4=42

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Answer:

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Givens

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