Answer:
Step-by-step explanation:
36 = 6* 6 = 2* 3 * 2* 3 = 2*2*3*3
180 = 2 * 2 * 3 * 3 * 5 = 2 * 2 * 3*3*5
Factors that are common will be cancelled
Answer:
1.) The correct answer is A.
2.) The correct answer is C.
3.) The correct answer is B.
4.) The correct answer is A.
5.) The correct answer is B.
Step-by-step explanation:
<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>
Given that,
A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream
Therefore,
Upstream distance = 165 km
Upstream time = 3 hours
<h3><u>Find upstream speed:</u></h3>
Thus upstream speed is 55 km per hour
Downstream distance = 510 km
Downstream time = 6 hours
<h3><u>Find downstream speed:</u></h3>
Thus downstream speed is 85 km per hour
<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>
Speed downstream = u + v km/hr
Speed upstream = u - v km/hr
Therefore,
u + v = 85 ----- eqn 1
u - v = 55 ----- eqn 2
Solve both
Add them
u + v + u - v = 85 + 55
2u = 140
u = 70
<em><u>Substitute u = 70 in eqn 1</u></em>
70 + v = 85
v = 85 - 70
v = 15
Thus rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr
Answer:
42 minutes
Explanation:
The total amount of anything expressed in percentage is 100%.
The reason for this is that per cent means per hundred.
So, 100% is
100
×
1
100
=
100
×
1
100
=
1
, which is a whole.
Moving to the question, a total of 25% + 5% = 30% of the time is used up by commercials and credits.
The time left for the program is 100% - 30% = 70%.
This is 70% of 60 minutes or
70
100
×
60
=
7
0
1
00
×
6
0
=
Step-by-step explanation:
Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"
A polynomial can have:
constants (like 3, −20, or ½)
variables (like x and y)
exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed
that can be combined using addition, subtraction, multiplication and division ...
... except ...
... not division by a variable (so something like 2/x is right out)
So:
A polynomial can have constants, variables and exponents,
but never division by a variable.
Also they can have one or more terms, but not an infinite number of terms.
These are polynomials:
3x
x − 2
−6y2 − ( 79 )x
3xyz + 3xy2z − 0.1xz − 200y + 0.5
512v5 + 99w5
5
(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)
These are not polynomials
3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
2/(x+2) is not, because dividing by a variable is not allowed
1/x is not either
√x is not, because the exponent is "½" (see fractional exponents)
But these are allowed:
x/2 is allowed, because you can divide by a constant
also 3x/8 for the same reason
√2 is allowed, because it is a constant (= 1.4142...etc)
