Question 1:
Find the last angle to make things easier.
The sum of all angles in a triangle is 180
180 - 58 - 61 = 61
Angle F = 61
We have an isosceles triangle where FD = ED
That's one of your answer choices.
The third answer choice is your answer.
Question 2:
It doesn't matter if these two triangles aren't congruent.
Imagine that the dividing line suddenly disappeared.
You would have an isosceles triangle.
That means 5x = 3x + 28
Solve that equation
5x = 3x + 28
Subtract both sides by 3x
2x = 28
Divide both sides by 2
x = 14
The answer is the first choice.
Have an awesome day! :)
Answer:
Mean of the numbers is 41
Step-by-step explanation:
1) You add 28 + 40 + 53 +39 +45
2) Divide whatever number by 5 because that is how many numbers there are given
In this case it would 205 divided by 5 which is how I get 41
The value of that <span>(√5 + 1)/8 and We can prove it like this:
</span>cos 2A= 2cos^2 A-1=1-2sin^2 A
<span>so cos^2 48 – sin^2 12 </span>
<span>=(1/2)(1+cos 96) - (1/2)(1-cos24) </span>
<span>=(1/2)(cos 96 +cos 24) and using cos(A)+cosB)=2cos((A+B)/2)cos((A-B)/2) </span>
<span>=cos60cos36 </span>
<span>=(1/2)cos36 </span>
<span>and you have to find cos36. </span>
<span>Suppose 5x=180, then </span>
<span>cos(5x)=cos(180) then x=-180,-108, -36, 36, 108 </span>
<span>Also 3x=180-2x </span>
<span>so cos(3x)=cos(180-2x)=-cos2x </span>
<span>so 4cos^3(x) -3cos(x)=1 - 2cos^2(x) </span>
<span>giving 4c^3+2c^2 - 3c-1=0 where c=cosx </span>
<span>c=-1 is a root and factorizing gives </span>
<span>(c+1)(4c^2-2c-1)=0 </span>
<span>so 4c^-2c-1=0 giving </span>
<span>c=(2±√20)/8=(1±√5)/4 and these have values cos(36) and cos(108) </span>
<span>the positive root is therefore cos(36)=(1+√5)/4 </span>
<span>and the required value (1/2)cos(36)=(1+√5)/8
</span>I think this can be very useful
this is me when people take 20 hours to answer my questions
Answer:
468.75 cubic inches
Step-by-step explanation:
The volume of a rectangular prism is the area of its base times its height.
The volume formula is 
. Substitute B = 37.5 and h=12.5.
