Substituting Values into Formulae

In algebra, substitution involves replacing letters with numbers to calculate the value of an expression. A formula is a mathematical relationship connecting two or more quantities, such as F = ma, expressing F in terms of m and a.

Let’s look at some examples that involve substituting values into formulae and expressions.

Examples

Example 1:

Given that e=3 and f=4, find the value of the expression 40ef.

We substitute the values to find the expression’s value:

40ef = 40 \times 3 \times 440ef = 40 \times 3 \times 4

= 480= 480

Example 2:

Given that m = 3 and a = 14, find the value of F using F = ma

F = ma = 3 \times 14F = ma = 3 \times 14

= 42= 42

Example 3:

Given that a = 2, b = 5, and c = -12, find the value of x using the quadratic formula.

X = \frac{-b + \sqrt{b^2 - 4ac}}{2a} = \frac{-5 + \sqrt{5^2 - 4(2)(-12)}}{2(2)}X = \frac{-b + \sqrt{b^2 - 4ac}}{2a} = \frac{-5 + \sqrt{5^2 - 4(2)(-12)}}{2(2)}

= \frac{3}{2}= \frac{3}{2}

Example 4:

Find the value of T in the formula T = mg + mw(g^2 - 81) when m = 5, g = 10, and w = -3

T = 5(10) + 5(-3)(10^2 - 81) = 50 - 15(100 - 81) = 50 - 15(19)T = 5(10) + 5(-3)(10^2 - 81) = 50 - 15(100 - 81) = 50 - 15(19)

= 50 - 285= 50 - 285

= -235= -235

Example 5:

Find the value of S in the formula S = ut + \dfrac {1}{2}at^2 when u = 3, t = 5, and a = 4

S = ut + \dfrac {1}{2}at^2 = (3)(5) + \dfrac{1}{2}(4)(5^2)S = ut + \dfrac {1}{2}at^2 = (3)(5) + \dfrac{1}{2}(4)(5^2)

= 15 + 50= 15 + 50

= 65= 65

Example 6:

Given that u = 4, a = 5, and S = 4.8, find the possible values of V using {V}^2 = u^2 + 2aS

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V^2 = 4^2 + 2(5)(4.8) = 16 + 10 \times 4.8</span>
<span style="color: #000000;">
*** Error message:
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V^2 = 16 + 48
*** QuickLaTeX cannot compile formula:
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*** Error message:
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V^2 = 64
*** QuickLaTeX cannot compile formula:
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V = \sqrt{64} = \pm8
*** QuickLaTeX cannot compile formula:
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<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 7:</mark></strong>
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<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given
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Missing $ inserted.
a = 5andandb = 12, find the possible values of x using, find the possible values of x usingx = \sqrt{a^2 + b^2}
*** QuickLaTeX cannot compile formula:
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Missing $ inserted.
x = \sqrt{5^2 + 12^2} = \sqrt{25 + 144}
*** QuickLaTeX cannot compile formula:
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= \sqrt{169} = 13
*** QuickLaTeX cannot compile formula:
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<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 8:</mark></strong>
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<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given
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u = 1,,v = 2,,z = 3,,a = 0, and, andb = 4, find the value of w in the formula, find the value of w in the formulaw = u^2 + v^2 + z^2 + a^3 + b^3
*** QuickLaTeX cannot compile formula:
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*** Error message:
Missing $ inserted.
w = 1^2 + 2^2 + 3^2 + 0^3 + 4^3
*** QuickLaTeX cannot compile formula:
</span>
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*** Error message:
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w = 1 + 4 + 9 + 0 + 64
*** QuickLaTeX cannot compile formula:
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*** Error message:
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w = 78
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<strong><mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Example 9:</mark></strong>
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<mark style="background-color:rgba(0, 0, 0, 0)" class="has-inline-color has-black-color">Given
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m = 100,000,000andandc = 300,000,000, find the value of E in standard form, in the formula, find the value of E in standard form, in the formulaE = mc^2
*** QuickLaTeX cannot compile formula:
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*** Error message:
Missing $ inserted.
E = mc^2 = 10^8 \times (3 \times 10^8)^2
*** QuickLaTeX cannot compile formula:
</span>
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*** Error message:
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E = 10^8 \times 3^2 \times 10^{16}
*** QuickLaTeX cannot compile formula:
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*** Error message:
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E = 9 \times 10^{24}$

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