Answer:
A) 6
Step-by-step explanation:
The angle 12x is the same angle as the one below 108 degrees. They are supplementary angles so they add up to 180 degrees. 180-108 = 72, 12x = 72 divide each side by 12, x = 6 :)
Step-by-step explanation:
S + L = 6 => L= 6-S
8S + 10L = 56
8S + 10(6-S) = 56
8S +60 -10S = 56
-2S = 56-60
-2S = -4
S = -4/-2
S = 2
=> S = small notebook = 2
L = large notebook = 6-2 = 4
To do this problem, break the pic up into its individual shapes.
For the top box:
You're given that the length of the bottom shape is 3 2/5, and that the top box is bordered by 1/2 inch of open space on each side. This means the length of the top box is 3 2/5 -(2x1/2), which equals 2 2/5.
The area occupied by the top box is the result of multiplying 2 2/5 (the base) by 1 1/3 ( the height.) therefore, the area of that part is 48/15, or 16/5 in reduced form.
Now for the bottom shape:
Break it up into a rectangle and two triangles, one of which is already drawn in for you. For the other triangle, draw a vertical line connecting the bottom corner of the bottom shape to the edge of the top shape. The line should be parallel to the line that's already drawn in.
Because you're given the 1/2 inch space to either side of the top box, you can conclude that the base of each triangle will be 1/2 inch. You're also given a height. The area of a triangle is b times h divided by two, so the area of each triangle is (1/2)(2)/2, which equals 1/2.
Put together, the area of the two triangular components is 1.
Now, you have one more component to calculate, which is the rectangular component of the bottom shape. Since you already accounted for the bases of the triangular components, subtract those from the base, giving you 3 2/5 -(1/2 x 2), which means the base of the rectangle is 2 2/5. Now just multiply that by the height, which is 2. The area of the rectangle is therefore 24/5.
Final answer: You now have all the component areas, you just need to add them all together to get the total area. 16/5 + 1 + 24/5 = 45/5, which reduces to 9.
Your final answer is B, 9 in^2.
Answer:
So the blank is cos.
Step-by-step explanation:
There is an identity for this:
Let's see if this is fit by your left hand and right hand side:
So 
while 
.
Let's plug these in to the identity above:
Ok, we definitely have the left hand sides are the same.
Let's see if the right hand sides are the same.
Before we move on let's see if we can find the sum and difference of 
and 
.
We will need a common denominator. How about 12? 12 works because 4 and 6 go into 12. That is 4(3)=12 and 6(2)=12.
.
.
Let's go back to our identity now:
We can rearrange the right hand side inside the ( ) using commutative property of addition:
So comparing my left hand side to their left hand side we see that the blank should be cos.
Quadratic formula is x=(-b+-sqrt(b^2-4ac))/(2a)
a= 1, b=-4, and c=3
Therefore, x=(-(-4)+-sqrt((-4)^2-4(1)(3))/(2(1))
Solve for both the plus and minus equations; the answers will be the roots to the quadratic equation.
