Answer:
38 degrees
Step-by-step explanation:
Angle ABE is 90 degrees, and angle FBE is 52 degrees. 90-52 is 38.
Answer:
Ok so the area of the frame is 18*12 = 216cm^2
Let’s suppose the width of the frame is x
The total area (painting and frame) is (2x+18)(2x+12) and this is equal to 432
4x^2 + 60x + 216 = 432
4x^2 + 60x - 216 = 0
x^2 + 15x - 54 = 0
(x+18)(x-3) = 0
Therefore x = {-18,3}
Since width of the frame has to be positive, the width has to be 3cm Step-
i hope i helped!
Answer:
1. 401.92 2.6782.4 3. 113,040
Step-by-step explanation:
for all 
in [-3, 0], so 
is non-decreasing over this interval, and in particular we know right away that its minimum value must occur at 
.
From the plot, it's clear that on [-3, 0] we have 
. So
for some constant 
. Given that 
, we find that
so that on [-3, 0] we have
and
Answer:
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Step-by-step explanation:
- <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>
==================
Let the parts be x, y and z
<u>As per given we get below system of equations:</u>
- x + y + z = 25000
- 0.1x + 0.12y + 0.16z = 3200
- 0.1x + 0.2y = 0.16z
<u>Substitute 0.1x + 0.2y in the second equation:</u>
- 0.16z + 0.16z = 3200
- 0.32z = 3200
- z = 3200/0.32
- z = 10000
<u>Now we have:</u>
- x + y + 10000 = 25000 ⇒ x + y = 15000
and
- 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600
<u>Multiply the second equation and then subtract the first one:</u>
- 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
- x + 1.2y - (x + y) = 16000 - 15000
- 0.2y = 1000
- y = 10000
Then
<u>So the parts are:</u>
- $5000 at 10%, $10000 at 12% and 10000 at 16%
