Answer: it will take them 28 minutes to fill the tank.
Step-by-step explanation:
The first pipe alone can fill the tank in 84 minutes. This means that the rate at which the first pipe fills the tank per minute is 1/84
The second pipe can fill the tank in 42 minutes by itself. This means that the rate at which the second pipe fills the tank per minute is 1/42
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined rate of filling the tank would be
1/84 + 1/42
Assuming it takes t hours for both pipes to fill the tank working together, the working rate per minute would be 1/t. Therefore,
1/84 + 1/42 = 1/t
3/84 = 1/t
t = 84/3
t = 28 minutes
Number 5 should be no solution becuase the n's cancel out.
For 6:
Part A is -2 because slope represents the change in weigh/change in time (-2/1 or -2)
Part B is y=-2x+231 (-2 is the slope and 231 is the y-intercept)
For part C, based on the slope, we can find that her weight will go below 200 at week 16 when it is 199
Hope this helps!
The ordered pair is a solution of x - y = 2 and 3y - x = 8 is (x, y) = (7, 5)
<h3><u>Solution:</u></h3>
Given two equations are:
x - y = 2 and 3y - x = 8
<em><u>To find: orderes pair i.e (x, y)</u></em>
Let us consider:
x - y = 2 ------- eqn 1
3y - x = 8 --------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "x" and "y"</u></em>
On rearranging eqn 2, we get
-x + 3y = 8 ------ eqn 3
Add eqn 1 and eqn 3
x - y = 2
-x + 3y = 8
(+) ---------------
0 + 2y = 10
2y = 10
<h3>y = 5</h3>
Therefore from eqn 1,
x - y = 2
x - 5 = 2
x = 5 + 2 = 7
<h3>x = 7</h3>
Thus the ordered pair to the given equations are (x, y) = (7, 5)
The answer is n+7 and 7+n
<h2>
Explanation:</h2>
In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.
So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.
So let's name the vertices as:
First pair of opposite sides:
<u>Slope:</u>
Second pair of opposite sides:
<u>Slope:</u>
So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:
So the diagonals measure the same, therefore this is a rectangle.
