Which expressions are equivalent to the one below? Check all that apply.

Mathematics

1 answer:

Paha777 [63]3 years ago

8 0

Answer:

The answer is C.

Step-by-step explanation:

You have to apply Logarithm Law,

$log( {a}^{n} ) \: ⇒ \: n log(a)$

So for this question :

$log( {10}^{3} ) = 3 log(10)$

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The line segment joining the points ( 3,-4) and (1,2) is trisected at the points P and Q . If the coordinates of P and Q are (p

sdas [7]

Answer:

P = 7/3 and q = 0

Step-by-step explanation:

The given parameters are;

The endpoints of the segment are, (3, -4) and (1, 2)

The points that trisect the given points are P and Q with coordinates (p, -2) and (5/3, q) respectively

Therefore, we have;

The first point of the trisection cuts 1/3 of the length from one point and the second point of the trisection cuts 2/3 of the length from the same point

The coordinates of P or Q = (3 - (3 - 1)/3, -4 - (-4 - 2)/3) = (7/3 , -2)

Therefore, given that the y-coordinate value of the derived point coincides with the y-coordinate value of the point P, (p, -2) and there is only one point with x = -2 on the line, we have that the coordinate of the point P is (p, -2) = (7/3 , -2)

∴ P = 7/3

Similarly we have the second point of the trisection, Q, given as follows;

We are already given the x-coordinate value of the point Q as the 5/3 in (5/3, q)

Point Q = (5/3, q) = (3 - 2×(3 - 1)/3, -4 - 2×(-4 - 2)/3) = (5/3 , 0)

Point Q = (5/3, q) = (5/3 , 0)

∴ q = 0.

3 0

3 years ago

Which of the following represents the set of possible rational roots for the

yawa3891 [41]

<h3>Answer: Choice D</h3>

The plus/minus of the following: 1/2, 1, 2, 5/2, 4, 5, 10, 20

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Explanation:

Refer to the rational root theorem. To find the possible rational roots, we divide the factors of the last term 20 over the factors of the first coefficient 2.

Factors of 20 are: 1,2,4,5,10,20
Factors of 2 are: 1,2

Dividing those said factors leads us to the list in choice D. We include the positive and negative versions of each result. For example, divide 10 over 2 to get 10/2 = 5 as one possible root (which leads to -5 as well).

A table like the one shown below might be handy to keep track of all the terms.