Answer:
12 units
Step-by-step explanation:
The quickest way to go about this is;
From the figure, when you count the number of full square boxes inside the rectangle, they add up to 7 full square boxes of 1 unit by 1 unit. And the number of half square boxes inside the rectangle add up to 10 which is equal to 5 full square boxes.
So the total number of full square boxes of 1 unit by 1 unit inside the rectangle add up to 12 full square boxes. The area of each full square box is 1 * 1 = 1 units, therefore the area of the rectangle is equal to 1 * 12 = 12 units.
Answer:
Step-by-step explanation:
Answer:
Tap A 3hrs
Tap B 6hrs
Step-by-step explanation:
Let the volume of the swimming pool be Xm^3.
Now, to get the appropriate volume, we know we need to multiply the rate by the time. Let the rate of the taps be R1 and R2 respectively, while the time taken to fill the swimming pool be Ta and Tb respectively.
x/Ta= Ra
x/Tb= Rb
X/(Ra + Rb)= 2
Ta = Tb - 3
From equation 2:
X = 2( Ra + Rb)
Substituting the values of Ra and Rb Using the first set of equations
X = 2( x/Ta + x/Tb)
But Ta = Tb - 3
1/2 = 1/(Tb - 3)+ 1/Tb
0.5 = (Tb + Tb-3)/Tb(Tb - 3)
At this juncture let’s say Tb = y
0.5 = (2y - 3)/y(y - 3)
y(y-3 ) = 4y - 6
y^2 -3y - 4y + 6 = 0
y^2 -7y + 6= 0
Solving the quadratic equation, we get y =
y = Tb = 6hrs or 1hr
We remove one hour as we know that Tap A takes 3hrs left than tap B and there is nothing like negative hours
Now, we get Ta by Tb -3 = 6 - 3 = 3hrs
Step-by-step explanation:
The last step is a little wrong. Lemme show you:
x(x + 2) + (x + 2)
Imagine there is an invisible '1' infront of (x + 2) like this:
= x(x + 2) + 1(x + 2)
Now we can combine the like terms together:
= (x + 1)(x + 2)
This is the correct factorization.
