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)
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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
9514 1404 393
Answer:
(b) 40°
Step-by-step explanation:
Angle x and the one marked 70° are alternate interior angles, so are congruent. The sum of the two base angles of the isosceles triangle is ...
x° +x° = 70° +70° = 140°
So, the remaining angle 1 in the triangle is ...
180° -140° = 40°
∠1 = 40°
Answer: 
is parallel to 
Step-by-step explanation:
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The complete exercise is: "Is parallel, perpendicular or neither to ?
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The equation of the line in Slope-Intercept form is:
Where "m" is the slope of the line and "b" is the y-intercept.
First, in order to solve this exercise it is important to remember that, by definition:
1. The slopes of parallel lines are equal.
2. The slopes of perpendicular lines are negative reciprocal.
In this case, you have the following line given in the exercise:
You can identify that "m" and "b" are:
And the other line provided in the exercise is this one:
So, you can identify that:
As you can notice, the slopes of both lines are equal; therefore, you can conclude that those lines are parallel.
Assuming that the figures given are square such that the scale factor between them is equal to 28/8 which can be further simplified into 7/2. The ratio of the perimeter is also equal to this value, 7/2. However, the ratio of the areas is equal to the square of this value giving us an answer of 49/4.
Answer:
21, 144, 12
Step-by-step explanation:
Given that a sample of 30 distance scores measured in yards has a mean of 7, a variance of 16, and a standard deviation of 4.
Let X be the distance in yard.
i.e. each entry of x is multiplied by 3.
New mean variance std devition would be
E(3x) = 
Var (3x) = 
Std dev (3x) = 
Thus we find mean and std devition get multiplied by 3, variance is multiplied by 9
