Throw a dice randomly. Out of 10 times throwing, the 1 dot side shows up everytime. What are the chances of having the 1 dot sid
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Answer:
a) x = 30°
b) mRS = x = 30°
mST = 4x = 4(30°) = 120°
mTU = 4x = 4(30°) = 120°
mUR = 3x = 3(30°) = 90°
Question:
The complete question as found on Chegg website:
In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs
intercepted have the following ratio of measurements:
mRS : mST :MTU : mUR=1:4:4:3
(a) If mRS = x, then write an equation that could be used to solve for x
and find the value of x.
(b) State the measure of each of the four arcs.
mRS =
mST =
MTU
MUR =
Step-by-step explanation:
Find attached the diagram related to the question
mRS : mST : mTU : mUR = 1:4:4:3
Since mRS = x
Writing the ratios of the measure of angle in terms of mRS:
mST = 4× mRS = 4×x = 4x
mTU = 4× mRS = 4×x = 4x
mUR= 3× mRS = 3×x = 3x
The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)
mRS + mST + mTU + mUR = 360°
x + 4x + 4x + 3x = 360
12x = 360
x = 360/12
x = 30°
b) The measure of angle
mRS = x = 30°
mST = 4x = 4(30°) = 120°
mTU = 4x = 4(30°) = 120°
mUR = 3x = 3(30°) = 90°
General Idea:
When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)
Applying the concept:
In the diagram given, the coordinate of C is (6, 3). Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6).
If C (x, y) centered at origin with a scale factor of k, then the dilated point will be given by C' (kx, ky)
We know &
Substituting 6 for x in the equation , we get
.
Dividing 6 on both sides
Simplifying fractions on both sides
Point A from the diagram is (-3, 3)
x-coordinate of A' =
y-coordinate of A' =
Point A' is given by (-3.6, 3.6)
Conclusion:
<u>Scale factor of dilation is 1.2</u>
<u>The coordinates of point A' is (-3.6, 3.6)</u>