10) because of the alternative exterior angle theorem angle 2 is the same as angle 8 and because of the vertical angles congruence theorem angles 2 and 4 are also the same so if angle 2 is the same as both 4 and 8,
then x=5 because 4x+57 =77
subtract 57 from both sides and 4x=20
divide both sides by 4 and x equals 5
Answer:
Given
Step-by-step explanation:
Given that: △RST ~ △VWX, TU is the altitude of △RST, and XY is the altitude of △VWX.
Comparing △RST and △VWX;
TU ~ XY (given altitudes of the triangles)
<TUS = <XYW (all right angles are congruent)
<UTS ≅ <YXW (angle property of similar triangles)
Thus;
ΔTUS ≅ ΔXYW (congruent property of similar triangles)
<UTS + <TUS + < UST = <YXW + <XTW + <XWY = 
(sum of angles in a triangle)
Therefore by Angle-Angle-Side (AAS), △RST ~ △VWX
So that:
= 
(corresponding side length proportion)
Answer:
Step-by-step explanation:
Use the <u>Slope Formula</u> to determine the slope of two given points:
First Point: 
Second Point: 
-Substitute both points:
First Point: 
Second Point: 
-Solve for the slope:
Therefore, the slope is 
We know that: <span>3(x-1)^2-162=0
or (x-1)</span>²= 162:3
and (x-1)²= 54
we <span>take the square root of both sides
* x-1=</span>√54= 3√6 or x=1+3√6
* x-1= -<span>√54= -3√6 or x=1-3√6
This equation has 2 solutions</span>
195 students voted for eagle in the election
What is ratio?
Ratio means expressing the a figure as a fraction of total figure, in the case of falcon, the number of students that voted for falcon is seen as 5 whereas the total number of students that voted is 8 whereas for eagle, the total number of students that voted for eagle is 1 compared to 3 which represents the total number of votes cast.
In a bid to determine the number of students that voted eagle in the election, we would simply multiply total votes of 536 by 1/3
votes for eagle=1/3*586
votes for eagle=195 votes
We have rounded to the nearest whole number since number of votes cannot be fractional
Find out more on fractions:brainly.com/question/11562149
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