Answer:
x = 26.5
Step-by-step explanation:
Step 1: Write equation
(t + 10.5) + 2t + 90 = 180
Step 2: Solve for <em>t</em>
<u>Combine like terms:</u> 3t + 100.5 = 180
<u>Subtract 100.5 on both sides:</u> 3t = 79.5
<u>Divide both sides by 3:</u> t = 26.5
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
<u>Substitute:</u> (26.5 + 10.5) + 2(26.5) + 90 = 180
<u>Parenthesis:</u> 37 + 56 + 90 = 180
<u>Add:</u> 180 = 180
∴ x = 26.5
1 bag=2cups. so, he uses 1 and 0.25 bags. there are 3.75 bags left. hope that helps)
Choice C for problem 6 is correct. The two angles (65 and 25) add to 90 degrees, proving they are complementary angles.
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The answer to problem 7 is also choice C and here's why
To find the midpoint, we add up the x coordinates and divide by 2. The two points A(-5,3) and B(3,3) have x coordinates of -5 and 3 respectively. They add to -5+3 = -2 which cuts in half to get -1. This means C has to be the answer as it's the only choice with x = -1 as an x coordinate.
Let's keep going to find the y coordinate of the midpoint. The points A(-5,3) and B(3,3) have y coordinates of y = 3 and y = 3, they add to 3+3 = 6 which cuts in half to get 3. The midpoint has the same y coordinate as the other two points
So that is why the midpoint is (-1,3)
Answer:
the Largest shed dimension is 13.5 ft by 13.5 ft
Largest Area is 182.25 ft²
Step-by-step explanation:
Given that;
Perimeter = 54 ft
P = 2( L + B ) = 54ft
L + B = 54/2
L + B = 27 ft
B = 27 - L ------------Let this be equation 1
Area A = L × B
from equ 1, B = 27 - L
Area A = L × ( 27 - L)
A = 27L - L²
for Maxima or Minima
dA/dL = 0
27 - 2L = 0
27 = 2L
L = 13.5 ft
Now, d²A/dL² = -2 < 0
That is, area is maximum at L = 13.5 using second derivative test
B = 27 - L
we substitute vale of L
B = 27 - 13.5 = 13.5 ft
Therefore the Largest shed dimension = 13.5 ft by 13.5 ft
Largest Area = 13.5 × 13.5 = 182.25 ft²
Here you go hope this helps
