Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
Total Score = 10*85=850
Final total after throwing out top and bottom scores = 850-60-92
=698
Therefore Final Average
= 698/8
=87.25
Remember: We have to work from either the LHS or the RHS.
(Left hand side or the Right hand side)
You should already know this:
1.
2.
3.
<span>So, our question is:
</span>
Plug in the first two identities I gave you.
Apply the first identity I said you needed to know on 1/(tan θ). We should get:
Multiply the first fraction by sinθ, on both the numerator and denominator.
Multiply the second fraction by cos<span>θ, on both the numerator and denominator.
</span>
Now, use the third identity I said that you needed to know to simplify the numerator.
LHS = RHS
<span>
Therefore, identity is verified.</span>
Answer:
69
Step-by-step explanationits 69
Answer:
25%
Step-by-step explanation:
First we calculate the probability of rolling a number greater than 3, that is, it can be 4, 5 or 6.
The probability of each number is 1/6, so:
P1 = (1/6) + (1/6) + (1/6) = 3/6 = 1/2
Then, we calculate the probability of rolling a prime number, that is, 2, 3 or 5.
As we have again 3 numbers, the probability P2 will also be 1/2
Then, the final probability is the product of both P1 and P2:
P = P1 * P2 = (1/2) * (1/2) = 1/4 = 25%