Answer:
Angle ABF is 120°.
Step-by-step explanation:
Vertical angles are used to get the measure of angle ABG (3x) and FBE (2x) and all of those added together are 180. Then you use PEMDAS to get x. Then you find ABF by multiplying 3 by 30 (what you get when you use PEMDAS to find x) then you add 30 to that and you get 120.
Answer:
She invested $30,000 at 9%
Step-by-step explanation:
Let the amount invested per percentage be $x and $y respectively
Total investment is 40,000
This means that;
x + y = 40,000 ••••••••••(i)
Now for her income;
9/100 * x = 9x/100
for the 12% = 12/100 * y = 12y/100
Now;
9x/100 + 12y/100 = 3,900
9x + 12y = 390000 •••••••••(ii)
we solve both simultaneously
From i, y = 40,000-x
Substitute this into ii
9x + 12(40,000-x) = 390,000
9x + 480,000-12x = 390,000
3x = 480,000-390,0000
3x = 90,000
x = 90,000/3
x = $30,000
Answer:
Prime factorization of 50 is 2 x 5 x 5 or 2 x 5^2
Step-by-step explanation:
<span>It is required to find the highest altitude (in meters) .
</span>
For the given <span>quadratic function ⇒⇒ A(t) = −(t − 11)² + 115</span>
From the attached figure which represents the graph of the given function
the maximum will be at point (11,115)
So, <span>
the highest altitude (in meters) = 115 meter</span>
<span>
and it will reach it at t = 11 </span><span>
seconds</span>