In exercises 11-15, find the value of x:
1 answer:
Refer to attached annotated figure below.
Step 1: prove triangle ABD is similar to triangle BCD
1. ∠ ADB = ∠ BDC (given)
2. ∠ BAD = 90-y; ∠ DBC= 90-y, => ∠ BAD is congruent to ∠ CBD.
=> triangle ABD is similar to triangle BCD [AA]
Step 2: find length of AD
Using Pythagoras theorem, AD^2=AB^2-BD^2 = 5^2-4^2=9
=> AD=3
Step 3: use the property that corresponding sides of similar triangles are proportional: BC/BD = AB/AD
substitute values
AB=5, AD=3, BD=4, BC=x
x/4=5/3
solve for x
x=5*4/3=20/3
or x=6.67 (to 2 decimal places)
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The inequality representing their combined hours working would be
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.