How many solutions are there to the system of equations? StartLayout enlarged left-brace 1st row 4 x minus 5 y = 5 2nd row negat
2 answers:
You might be interested in
we have 630 one-inch unit cubes and we want to completely fill the rectangular box (unknown dimensions).
If all the cubes are fitted tightly inside rectangular box without living any space, then box volume would be equal to cubes volume.
There are 630 one-inch unit cubes, so volume of cubes = 630 cubic inches.
Now the volume of rectangular box would also be 630 cubic inches.
We know the formula for volume of rectangular box = length × width × height.
So we need to find any three positive integers whose product is 630.
Out of all given choices, only option A satisfies the condition of factors of 630.
Hence, option A i.e. (7 in x 9 in x 10 in) is the final answer.
Answer:
Speed of Current = 5 miles per hour
Step-by-step explanation:
We know distance formula,
D = RT
Where
D is distance
R is rate
T is time
If we let speed of boat (assume) to be "x" and speed of current to be "c"
Then downstream rate is (with current) = x + c
Upstream rate is (against current) = x - c
40 mins to go 20 miles downstream, that means:
D = RT
20 = (x + c)(40)
and
60 minutes to go upstream, 20 miles, that means:
D = RT
20 = (x - c)(60)
Simplifying first equation:
40x + 40c = 20
Simplifying second equation:
60x - 60c = 20
Multiplying first equation by 60, we get:
60 * [40x + 40c = 20] = 2400x + 2400c = 1200
Multiplying second equation by 40, we get:
40 * [60x - 60c = 20] = 2400x - 2400c = 800
Now we add up both these equations:
2400x + 2400c = 1200
2400x - 2400c = 800
----------------------------------
4800x = 2000
x = 2000/4800 = 5/12
We need speed of current, that is "c", so we plug in the value of x into first equation and solve for c:
Speed of Current = 1/12 miles per minute
Since there is 60 minutes in an hours, that would be:
(1/12) * 60 = 5 miles per hour
Speed of Current = 5 miles per hour