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2 answers:
Answer:
a = 15, b = - 14
Step-by-step explanation:
Given the 2 equations
-
= 10 ( multiply through by 10 to clear the fractions )
2a - 5b = 100 → (1)
a - b = 29 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate the a- term
- 2a + 2b = - 58 → (3)
Add (1) and (3) term by term to eliminate a
0 - 3b = 42
- 3b = 42 ( divide both sides by - 3 )
b = - 14
Substitute b = - 14 into (2) and evaluate for a
a - (- 14) = 29
a + 14 = 29 ( subtract 14 from both sides )
a = 15
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Answer:
C
Step-by-step explanation:
Calculate AC using Pythagoras' identity in ΔABC
AC² = 20² - 12² = 400 - 144 = 256, hence
AC = = 16
Now find AD² from ΔACD and ΔABD
ΔACD → AD² = 16² - (20 - x)² = 256 - 400 + 40x - x²
ΔABD → AD² = 12² - x² = 144 - x²
Equate both equations for AD², hence
256 - 400 + 40x - x² = 144 - x²
-144 + 40x - x² = 144 - x² ( add x² to both sides )
- 144 + 40x = 144 ( add 144 to both sides )
40x = 288 ( divide both sides by 40 )
x = 7.2 → C