It is reflection in x axis and then vertical shift up by 4 units and horizontal shift to the left by 2 units
Explanation:
It is reflection in x axis and then vertical shift up by 4 units and horizontal shift to the left by 2 units
Look at the three graphs y=|x| in pink. y=-|x| in white and y=4-|x+2| in red
Answer:
Step-by-step explanation:
The two given angles form a linear pair and therefore supplementary.
<u>Supplementary angles sum to 180°:</u>
- 2.4x + 9.6x = 180
- 12x = 180
- x = 180/12
- x = 15
<u>The larger angle measure:</u>
Answer:
The value of y is 3.
Step-by-step explanation:
Given points: P(12,-2), Q(5,-10), R(-4,10) and S(4,y).
We need to find the value of y so that line PQ is perpendicular to line RS.
Slope formula:
Slope of PQ is
Slope of RS is
The product of slopes of two perpendicular lines is -1.
Add 10 on both sides.
Therefore, the value of y is 3.
Log₄8 + 3 · log₄x
so the easiest way to do this is to note that these logs are separated by an addition symbol--it isn't "log₄8 + 3" times "log₄x"
log₄8
plus
3 · log₄x
for the second log, you can condense it with log properties/rules: the coefficient out front, when you condense it, becomes the exponent for the argument of your log:
3 · log₄x = log₄(x³)
so, having condensed that, your equation reads:
log₄8 + log₄(x³)
you could technically evaluate the first log, but the question wants both of these to become a single logarithm, which means you want to combine them. log properties state that if logs are being added, you can multiply their arguments (for example: logₓab = logₓa + logₓb)
you just want to apply that property to this, so you'll be multiplying your arguments 8 and x³:
log₄(8x³) is the answer, expressed as one logarithm.
angle A = angle B corresponding angles
8x - 8 = 5x + 25
3x = 33
x = 11
angle B
5x + 25
55 + 25
80°