2 (a) The diagram shows two adjacent rectangular plots, one with area 60 m², length p metres and width (x + 5) metres, and the other with area 25 m², length q metres and width x metres. x+5 Area = 60m² Express the following in terms of x: P (i) p. (ii) q. (iii) p + q as a single fraction in its simplest form. (b) Make a the subject of the formula √y-ax=t. Area = 25 m² 9 X [1] [1] [3] [3]
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Answer:
(a) We are given the following information:
Plot 1:
Area = 60 m²
Length = p meters
Width = (x + 5) meters
Plot 2:
Area = 25 m²
Length = q meters
Width = x meters
We can set up the following equations:
Plot 1: Area = Length × Width
60 = p(x + 5) -- Equation 1
Plot 2: Area = Length × Width
25 = qx -- Equation 2
(i) To express p in terms of x, we can rearrange Equation 1:
60 = px + 5p
px = 60 - 5p
p = (60 - 5p)/x
(ii) To express q in terms of x, we can rearrange Equation 2:
qx = 25
q = 25/x
(iii) To express p + q as a single fraction in its simplest form, we substitute the expressions for p and q from parts (i) and (ii) into the equation:
p + q = (60 - 5p)/x + 25/x
p + q = (60 - 5p + 25)/x
p + q = (85 - 5p)/x
(b) We are given the equation √y - ax = t, and we need to make "a" the subject of the formula.
Step 1: Move the term with "a" to one side:
√y - ax = t
-ax = t - √y
Step 2: Divide both sides by "-x" to isolate "a":
a = (t - √y)/(-x)
Therefore, the subject of the formula √y - ax = t is "a" and it can be expressed as:
a = (t - √y)/(-x)
Step-by-step explanation:
Answer:
(a) We are given the following information:
Plot 1:
Area = 60 m²
Length = p meters
Width = (x + 5) meters
Plot 2:
Area = 25 m²
Length = q meters
Width = x meters
We can set up the following equations:
Plot 1: Area = Length × Width
60 = p(x + 5) -- Equation 1
Plot 2: Area = Length × Width
25 = qx -- Equation 2
(i) To express p in terms of x, we can rearrange Equation 1:
60 = px + 5p
px = 60 - 5p
p = (60 - 5p)/x
(ii) To express q in terms of x, we can rearrange Equation 2:
qx = 25
q = 25/x
(iii) To express p + q as a single fraction in its simplest form, we substitute the expressions for p and q from parts (i) and (ii) into the equation:
p + q = (60 - 5p)/x + 25/x
p + q = (60 - 5p + 25)/x
p + q = (85 - 5p)/x
(b) We are given the equation √y - ax = t, and we need to make "a" the subject of the formula.
Step 1: Move the term with "a" to one side:
√y - ax = t
-ax = t - √y
Step 2: Divide both sides by "-x" to isolate "a":
a = (t - √y)/(-x)
Therefore, the subject of the formula √y - ax = t is "a" and it can be expressed as:
a = (t - √y)/(-x)
Step-by-step explanation: