Answer:
The sum of all the sides to this quadrilateral will equal a total of 20 inches, so you set up the equation:
2 + 2x + 7 + x + 2 = 20
Solve for x by combining like terms;
(2 + 7 + 2) + (2x + x) = 20
Which simplifies to;
11 + 3x = 20
Get rid of constants;
-11 -11
3x = 9
Isolate x by getting rid of it's coefficient;
/3 /3
<u>x = 3</u>
Now, to find the length of PQ, we plug in the value of x(3) into the equation that contains the line PQ.
x + 2
<u>3</u> + 2
= <u>5 inches.</u>
Now, to find the length of RS, we plug in the value of x(3) into the equation that contains the line RS.
2x
2(3)
= <u>6 inches.</u>
Answer:
G
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
Answer:
n=64
Step-by-step explanation:
3/4(n)*7=1/2(672)
21
/4
n=336
n=64
Angle measures are ∠M = 90° and ∠L = 24°
Step-by-step explanation:
- Step 1: In the figure, LM is a tangent to the circle N at point M.
Tangents create right angles at the point of contact with a circle.
So ∠M = 90°
- Step 2: Sum of angles in a triangle is equal to 180°
⇒ ∠L = 180° - (∠M + ∠N) = 180° - (90° + 66°)
= 180° - 156° = 24°
