Answer:
x = ± 
Step-by-step explanation:
3x² + 7 = 28 ( subtract 7 from both sides )
3x² = 21 ( divide both sides by 3 )
x² = 7 ( take square root of both sides )
x = ±
that is x = - , x =
You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
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Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
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As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
Answer:
Lillian worked 7h and Jacob worked 6h
Step-by-step explanation:
the number of hours Lillian worked are x (h)
the number of hours Jacob worked are y (h)
(0 < x,y < 13)
=> Lilian ironed: 25x (shirts)
Jacob ỉroned: 20y (shirts)
because Lillian and Jacob worked a combined 13 hours and ironed 295 shirts, we have:
so Lillian worked 7h and Jacob worked 6h
