Answer:
10 divided by 12 equals 0.833333333
Answer:
For this answer, I will label the points. Starting at the top left, then top right, then bottom left and bottom right let the points be A, B, C, D.
The new coordinates will be
A(-4,10)
B(4,10)
C(-4,4)
D(4,4)
Step-by-step explanation:
The question is asking for a dilation which is a transformation that makes an image proportionately smaller or larger by a scale factor. The scale factor is how much smaller or larger the shape will be, if the scale factor is between 0 and 1 then it will shrink, if it is greater than one then the image will stretch (be larger). In this case, the scale factor is 2, therefore the image will stretch. Since the center of dilation is the origin, to find the new coordinates simply multiply each x and y value by the scale factor. So A's original coordinates (-2,5) become (-4,10) and so forth. Therefore the equation for this dilation is (x, y) → (2x,2y).
Answer:
- 7 - i
Step-by-step explanation:
Given
(- 10 - 2i) + (3 + i) ← remove parenthesis
= - 10 - 2i + 3 + i ← collect like terms
= - 7 - i
Answer:
Step-by-step explanation:
if we consider x as the number we can write this inequality:
4x ≤ 36
If we divide the two members by 4 we have:
x ≤ 9
Answer:
a) cos(α+β) ≈ 0.8784
b) sin(β -α) ≈ -0.2724
Step-by-step explanation:
There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.
Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.
For the first problem, we'll do it the first way:
sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524
cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820
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a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)
= 0.926×0.993820 -0.377524×0.111
cos(α+β) ≈ 0.8784
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b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)
= sin(-15.8074°)
sin(β -α) ≈ -0.2724