Answer:
Step-by-step explanation:
Construction: To copy angle CAB.
i. On angle CAB, with center A and any radius; draw an arc to intersect CA at E and AB at F.
ii. Place a divider at EF to copy the angle.
iii. Draw a separate straight line MN of approximate length to AB.
iv. Mark point P on MN. Place the divider with radius EF at P to mark Q.
v. Draw a line LM from M through Q.
vi. Therefore, angle CAB would be equal to angle LMN.
For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.
So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)
The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches
Answer:
x = 5/8 for 5x - 3 = (1/5)x
Step-by-step explanation:
To find x, we want to isolate our 3 from our x-values. You can add three to both sides of the equation and get it to the other side and then subtract 1/5x from 5x.
(5x - 3) + 3 = ((1/5)x) + 3
5x = (1/5)x + 3
5x = (25/5)x
((25/5)x) - (1/5)x = ((1/5)x + 3) - (1/5)x
(24/5)x = 3
From here, you would want to solve for x. This would mean multiplying 3 by 5 and dividing your product by 24.
5*3 = 15
15/24 = 5/8 = x
Hope this helps!
Supplementary angles are angles that are adjacent to each other and when summed to get a total of 180 degrees. In this case, DEF and FEG are supplementary. Thus the equation is <span>9x +1 + 8x + 9 = 180 = 17 x + 10; x then is equal to 10 so
<</span>DEF = <span>9*10 +1 =91 degrees
</span><FEG = <span>8*10 + 9 = 89 degrees</span>
Let's set up two equations:
x+y=20 We know she brought total of 20, some of each so x=small y=big
20x+ 30y=450
x+y= 20
-y -y
------------
x= 20 -y
substitute into the other equation:
20 (20-y) + 30y = 450
400 - 20y + 30y = 450
400+ 10 y = 450
10 y = 50
y= 5
So she brought 5 big cases. Then substitute the value of y into one of the equations.
5+ x = 20
x= 15
So we bought 15 small cases and 5 big cases.
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