Answer: The height of the building is 6.49 meters.
Step-by-step explanation:
This can be translated to:
"A building projects a 7.5 m shadow, while a tree with a height of 1.6 m projects a shadow of 1.85 m.
Which is the height of the building?"
We can conclude that the ratio between the projected shadow is and the actual height is constant for both objects, this means that if H is the height of the building, we need to have:
(height of the building)/(shadow of the building) = (height of the tree)/(shadow of the tree)
H/7.5m = 1.6m/1.85m
H = (1.6m/1.85m)*7.5m = 6.49m
The height of the building is 6.49 meters.
Answer:
x = -9
Step-by-step explanation:
6 - 2/9x = 8
Subtract 6 from each side
6-6 - 2/9x = 8-6
-2/9 x = 2
Multiply each side by -9/2 to isolate x
-9/2 * -2/9x = 2*-9/2
x = -9
Vacation is nice January is nice
Call the notebooks x, and the pencils y.
<span>3x + 4y = $8.50 and 5x + 8y = $14.50 </span>
<span>Then just solve as simultaneous equations: </span>
<span>3x + 4y = $8.50 </span>
<span>5x + 8y = $14.50 </span>
<span>5(3x + 4y = 8.5) </span>
<span>3(5x + 8y = 14.5) </span>
<span>15x + 20y = 42.5 </span>
<span>15x + 24y = 43.5 </span>
<span>Think: DASS (Different Add, Similar Subtract). 15x appears in both equations so subtract one equation from the other. Eassier to subtract (15x + 20y = 42.5) from (15x + 24y = 43.5) </span>
<span>(15x + 24y = 43.5) - (15x + 20y = 42.5) = (4y = 1) which means y = 0.25. </span>
<span>Then substitue into equation : </span>
<span>15x + 20y = 42.5 </span>
<span>15x + 5 + 42.5 </span>
<span>15x = 42.5 - 5 = 37.5 </span>
<span>15x = 37.5 </span>
<span>x = 2.5 </span>
<span>15x + 24y = 43.5 </span>
<span>15(2.5) + 24(0.25) </span>
<span>37.5 + 6 = 43.5 </span>
<span>So x (notebooks) are 2.5 ($2.50) each and y (pencils) are 0.25 ($0.25) each.</span>
