The simplified expression are as follows;
6mn³ - mn² + 3mn³ + 15mn² = 9mn³ + 14mn²
a⁴b³ + 8a⁴b³ = 9a⁴b³
<h3>How to simplify an expression?</h3>
A simplified expression is express to its lowest term.
Therefore,
6mn³ - mn² + 3mn³ + 15mn²
combine like terms
6mn³ + 3mn³ - mn² + 15mn²
9mn³ + 14mn²
a⁴b³ + 8a⁴b³ = 9a⁴b³
learn more on simplification here: brainly.com/question/403991
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You can convert (1/625) to an exponent, and it would be ideal to have 5 as the base of it because you want your log base to cancel it out. what i usually do in this case is just test out 5^1, 5^2, etc until i find one that matches the number i need. in this case because the number you're trying to work with is a small fraction, you'll want to use NEGATIVE exponents so it'll create a fraction instead of a large whole number:
5^-1 = 1/5
. . . keep trying those. . .
5^-4 = 1/625
so, because they're equal to one another, it'll be waaay easier after you substitute 5^-4 in place of 1/625
x = log₅ 5⁻⁴
log base 5 of 5 simplifies to 1. subbing in the 5^-4 gets rid of the log for you altogether, and your -4 exponent drops down:
x = -4 is your answer
if the exponent dropping down doesn't make sense to you, you can think of it in another way:
x = log₅ 5⁻⁴
expand the expression so that the exponent moves in front of the log function:
x = (-4) log₅ 5
then, still, log base 5 of 5 simplifies to 1, so you're left with:
x = (-4)1 or x = -4
Answer:
= 3√3 + 3i
Step-by-step explanation:
Cos 30° = √3/2
Sin 30° = 1/2
Therefore;
z = 6 (cos 30° + i6 sin 30°)
= 6 (√3/2) + i 6 (1/2)
= 3√3 + 3i
Answer:
x = 15
Step-by-step explanation:
the 2 angles are a linear pair and sum to 180° that is
8x - 3 + 4x + 3 = 180
12x = 180 ( divide both sides by 12 )
x = 15
Answer:
- Dilation
- Reflection
- Translation
- Rotation
- Reflection
- Translation
Step-by-step explanation:
<em>Dilation</em>
Dilation multiplies the distance from a point to the center of dilation by the dilation factor. It does this for every point.
The center of dilation itself has zero distance from the center of dilation. Multiplying that by the dilation factor still gives zero, so the point that is the center of dilation remains unchanged.
<em>Reflection</em>
Reflection mirrors a point across some line. Each point ends up the same distance on the other side of the line that it was originally from the line.
The segment joining a point with its reflection is perpendicular to the line, so the line of reflection is the perpendicular bisector of the segment joining any point with its image.
<em>Rotation</em>
The angle defined by a point, the center of rotation, and the point's image is the angle of rotation. It is the same for every point.
The center of rotation doesn't go anywhere; it is "invariant".
<em>Translation</em>
Moving an image without changing its size or orientation is translation. Every point moves the same distance in the same direction, so any lines in the original figure have the same length and orientation in the translated figure: they are parallel.
