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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Given:
Total number of cubes = 40
Red cubes = 18
Blue cubes = 13
Yellow cubes = 9
Aysha adds some more red cubes into the bag.
The probability now that she will take a red cube is 0.5.
To find:
The probability that she will take a yellow cube.
Solution:
Let Aysha adds x red cubes into the bag. Then,
Number of total cubes = 40+x
Number of red cubes = 18+x
Probability of getting a red cube is:
The probability now that she will take a red cube is 0.5. So,
Divide both sides by 0.5.
It means Aysha adds 4 more red cubes into the bag.
Now, the total number of cubes int he bag is:
Probability of getting a yellow cube is:
Therefore, the required probability is .