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dusya [7]
3 years ago
7

Solve the exponential equation 1/2^x-5=8^x

Mathematics
1 answer:
dexar [7]3 years ago
7 0

( \frac{1}{2} ) {}^{x - 5}  = 8 {}^{x}  \\  2 {}^{ - x + 5}  = 2 {}^{3x}  \\  - x + 5 = 3x \\  - 4x =  - 5 \\ x =  \frac{ - 5}{ - 4}  =  \frac{5}{4}
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Answer:

x=-1

Step-by-step explanation:

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Which systems of equations intersect at point A in this graph?
abruzzese [7]

Answer:

The point of intersection of the system of equations is:

(x, y) =  (-2, 1)

The correct system of equations intersect at point A in this graph will be:

\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}

Thus, the second option is correct.

Step-by-step explanation:

Given the point

  • A (-2, 1)

Let us check the system of equations to determine whether it intersect at point A in this graph.

Given the system of equations

\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}

Arrange equation variable for elimination

\begin{bmatrix}y-4x=9\\ y+3x=-5\end{bmatrix}

so

y+3x=-5

-

\underline{y-4x=9}

7x=-14

so the system of equations becomes

\begin{bmatrix}y-4x=9\\ 7x=-14\end{bmatrix}

Solve 7x = -14 for x

7x=-14

Divide both sides by 7

\frac{7x}{7}=\frac{-14}{7}

Simplify

x = -2

For y - 4x = 9 plug in x = 2

y-4\left(-2\right)=9

y+4\cdot \:2=9

y+8=9

Subtract 8 from both sides

y+8-8=9-8

Simplify

y = 1

Thus, the solution to the system of equations is:

(x, y) = (-2, 1)

From the attached graph, it is also clear that the system of equations intersects at point x = -2, and y = 1.

In other words, the point of intersection of the system of equations is:

(x, y) =  (-2, 1)

Therefore, the correct system of equations intersect at point A in this graph will be:

\begin{bmatrix}y=4x+9\\ y=-3x-5\end{bmatrix}

Thus, the second option is correct.

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Reductio ad absurdum is a Latin phrase that means "reduction to the absurd". The phrase describes a kind of indirect proof. It's proof by contradiction and is a common form of argument. It shows that a statement is true because its denial leads to a contradiction or a false or absurd result.

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