Which system of equations has infinitely many solutions? On a coordinate plane, 2 lines are parallel to each other. On a coordin
2 answers:
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Definitions:
1. A real number can be represented on a number line.
2. A rational number can be represented as a fraction, with both the numerator and denominator as integers. The denominator cannot be zero.
3. An irrational number has decimals that go on indefinitely.
4. An integer is a real number that is countable.
5. A repeating decimal has a group of numbers that repeat indefinitely as decimals.
6. A complex number involves the use of the quantity i, defined as i² = -1.
Answers:
a. 7/8
Real, Rational.
b. √36
Real, Rational because its value is +6 or -6.
c. √24
Real, Irrational.
d. 0.75
Real, rational because 0.75 = 3/4.
e. 0
Real, rational
f. √(-100)
Complex, because √(-1) * √100 = +/- i√100
g.
Irrational, Repeating decimal because
h -18/6
Real, Integer, Rational because -18/6 = -3.
1. A real number can be represented on a number line.
2. A rational number can be represented as a fraction, with both the numerator and denominator as integers. The denominator cannot be zero.
3. An irrational number has decimals that go on indefinitely.
4. An integer is a real number that is countable.
5. A repeating decimal has a group of numbers that repeat indefinitely as decimals.
6. A complex number involves the use of the quantity i, defined as i² = -1.
Answers:
a. 7/8
Real, Rational.
b. √36
Real, Rational because its value is +6 or -6.
c. √24
Real, Irrational.
d. 0.75
Real, rational because 0.75 = 3/4.
e. 0
Real, rational
f. √(-100)
Complex, because √(-1) * √100 = +/- i√100
g.
Irrational, Repeating decimal because
h -18/6
Real, Integer, Rational because -18/6 = -3.
Answer:
12 hours
Step-by-step explanation:
Time taken by pipe A = 24 hours
Time taken by pipe B = 36 hours
Time taken by pipe C = 32 hours
To find:
How long would it take the three pipes to fill the pool if pipe B is turned on 3 hours after pipe A and pipe C is turned on 1 hour after pipe B?
Solution:
First of all, let us assume the total capacity of the pool.
Let us take LCM of 24, 36 and 32.
LCM of 24, 36 and 32 = 288
Let the total capacity of the pool = 288 units
Total units filled by pipe A in one hour =
Total units filled by pipe B in one hour =
Total units filled by pipe C in one hour =
Now, for the first 3 hours, only pipe A operates, so units filled in first three hours =
For the next one hour, A and B both operate together, so units filled in the next 1 hour = 12 + 8 = 20 units
Total number of units filled in 4 hours = 36 + 20 = 56 units
Units to be filled to completely fill the pool = 288 - 56 = 232 units
Now, after the 4th hours, all the pipes operate together.
So, number of units filled in each hour = 12 + 8 + 9 = 29 units
Time taken to fill 232 units =
Total time taken = 4 + 8 = <em>12 hours</em>