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3 years ago

Which of the following shows the extraneous solution to the logarithmic equation below???

Mathematics

2 answers:

avanturin [10]3 years ago

7 0

Short Answer x = - 6
Remark
You gave the second best answer.

The trick here is not to divide both sides by 2. Solve the problem this way.

log_5(x + 1)^2 = 2 Take the antilog of both sides
(x + 1)^2 = 5^2 Expand the equation
x^2 + 2x + 1 = 25 Subtract 25 from both sides.
x^2 + 2x - 24 = 0 Factor
(x + 6)(x - 4) = 0 Find the zeros.

x + 6 = 0
x = - 6 <<<<<<<< Answer. This is the extraneous root.
The reason this is an extraneous root is that x<=0 do not have a logarithem

x - 4 = 0
x = 4 This is a legitimate result to the original equation.

Romashka-Z-Leto [24]3 years ago

5 0

Answer:

Step-by-step explanation:

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Evaluate 82.5÷0.25 express the answer in standard form

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3 years ago

He coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .

Nitella [24]

Answer: The perimeter is 17.52

Step-by-step explanation:

1. You can plot the points, as you can see in the graph attached.

2. As you can see in the graph, the points are:

$A(-2,-2)\\B(-2,3)\\C(2,4)\\D(3,1)\\E(0,-2)$

And the lenghts <em>AB</em> and <em>EA</em> are:

$AB=5$

$EA=2$

3. To find the other lenghts, you can apply the formula for calculate the distance between two points:

$distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

4. Thefore, you have:

$BC=\sqrt{(2-(-2))^{2}+(4-3)^{2}}=4.12\\CD=\sqrt{(2-3)^{2}+(4-1)^{2}}=3.16\\DE=\sqrt{(3-0)^{2}+(1-(-2))^{2}}=4.24$

5. The perimeter is:

$P=AB+CD+DE+EA\\P=5+4.12+3.16+4.24+2\\P=17.52$

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3 years ago

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3 years ago

Jessica and Raphael are saving money for concert tickets. Jessica has $20 and saves 10 per week.

Burka [1]

They have the same amount on week 5 ($70)
The Answer would be: $70
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The easiest way to do this is to not pay attention to the y=x equation, because the solution is already in the information, this may confuse you and youre wasting time to solve it. Jess has $20 BEFORE saving and gets $10 WEEKLY, Raph has $40 BEFORE saving and gets $6 WEEKLY. In the chart/information, add the amount it takes to get Jess up to $40 then add $10 for every week on going until both their balances are equal. They match on the 5th week with $70 // If the information is different substitute the names/numbers/etc. Hope this helped you and anyone else looking for the answer!

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4 years ago

The graph of y = f (x) is given in the figure. Sketch = 1/2 ( + 2) − 2.

jolli1 [7]

Answer:

y=1/2+2

Step-by-step explanation:

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3 years ago