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2 years ago

What is the true solution to 3 In 2+In 8 = 2 In(4x)? 60f Š O OOO TNT 00

Mathematics

1 answer:

alina1380 [7]2 years ago

4 0

Answer:

x = 2

Step-by-step explanation:

Taking antilogs, you have ...

2³ × 8 = (4x)²

64 = 16x²

x = √(64/16) = √4

x = 2 . . . . . . . . (the negative square root is not a solution)

___

You can also work more directly with the logs, if you like.

3·ln(2) +ln(2³) = 2ln(2²x) . . . . . . . . . . . write 4 and 8 as powers of 2

3·ln(2) +3·ln(2) = 2(2·ln(2) +ln(x)) . . . . use rules of logs to move exponents

6·ln(2) = 4·ln(2) +2·ln(x) . . . . . . . . . . . . simplify

2·ln(2) = 2·ln(x) . . . . . . . . . . . subtract 4ln(2)

ln(2) = ln(x) . . . . . . . . . . . . . . divide by 2

2 = x . . . . . . . . . . . . . . . . . . . take the antilogs

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What is the product of (-1/4) times (-3/7)

weqwewe [10]

Answer:

3/28

Step-by-step explanation:

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3 years ago

Which triangle would be most helpful in finding the distance between the points (-4, 3) and (1,-2) on the coordinate

earnstyle [38]

Answer:

On a coordinate plane, a triangle has points (negative 4, 3), (negative 4, negative 2), (1, negative 2).

Step-by-step explanation:

The points (-4,3), (1,2) and (-4, -2) would form a right triangle when graphed and connected by lines.

(-4,3), (1,2) and (1,3) would also work as well

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1 year ago

Is (2, 2) a solution of y < 4x - 6? Choose 1 answer yes or no

zalisa [80]

No, (2,2) is not solution of y < 4x - 6

Step-by-step explanation:

To solve above linear problem, we use standard method of Back- Substitution.

First of all, A point (2,2) only becomes solution of equation, if it satisfies equation $y < 4x - 6$ .

Here, the $y < 4x - 6$ seems to be like a linear equation.

In this Equation, using Back- Substitution method,

Point (2,2) : first digit 2 corresponds to x- coordinate and second digit 2 corresponds to y-coordinate.

$y < 4x - 6.....(1) \\\ x= 2 .....(2) \\\ y= 2 .....(3)$

By putting value of x and y in equation (1),

Equation becomes,

$2 < 4 \times 2 - 6$

$2 < 8 - 6$

$2 < 2$ .... not true mathematically.

Finally, the result came is not true. Therefore, (2,2) is not solution for equation

$y < 4x - 6$

4 0

3 years ago

What is the slope of this graph? −1/3 3 1/3 −3

FromTheMoon [43]

I'm assuming there is probably a graph that goes with this problem so here is all the info I can give you with the four choices: If it is -1/3, the line will go DOWN 1, over 3 (just count on the graph) If it is 3, the line will go UP 3, over 1 If it is 1/3, the line will go UP 1, over 3 And if it it -3, it will go DOWN 3, over 1 (If the slope is 3 or -3, it would be quite steep compared to a slope of 1/3 or -1/3) Hope that helps!

4 0

3 years ago

1500 soldiers arrive at a training camp. A few soldiers desert the camp. The drill sergeants divide the remaining soldiers into

iren [92.7K]

Answer:

The number of deserters is 34.

Step-by-step explanation:

We have to calculate the number of desertors in a group of 1500 soldiers.

The sergeant divides in groups of different numbers and count the lefts over.

If he divide in groups of 5, he has on left over. The amount of soldiers grouped has to end in 5 or 0, so the total amount of soldiers has to end in 1 or 6.

If he divide in groups of 7, there are three left over. If we take 3, the number of soldiers gruoped in 7 has to end in 8 or 3. The only numbers bigger than 1400 that end in 8 or 3 and have 7 as common divider are 1428 and 1463.

If we add the 3 soldiers left over, we have 1431 and 1466 as the only possible amount of soldiers applying to the two conditions stated until now.

If he divide in groups of 11, there are three left over. We can test with the 2 numbers we stay:

$(1431-3)/11=1428/11=129.82\\\\(1466-3)/11=1463/11=133$

As only 1466 gives a possible result (no decimals), this is the amount of soldiers left.

The deserters are 34:

$D=1500-1466=34$

6 0

3 years ago