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[tex]\[
k = \frac{a^2 + t}{2 - a}
\][/tex]

Work out the value of [tex]\( t \)[/tex] when [tex]\( a = 4 \)[/tex] and [tex]\( k = -11 \)[/tex]. Give your answer as an integer or as a decimal.


Sagot :

To find the value of [tex]\( t \)[/tex] given the equation

[tex]\[ k = \frac{a^2 + t}{2 - a} \][/tex]

where [tex]\( a = 4 \)[/tex] and [tex]\( k = -11 \)[/tex], we will follow these steps:

1. Substitute the given values into the equation:

[tex]\[ -11 = \frac{4^2 + t}{2 - 4} \][/tex]

2. Evaluate the expressions inside the fraction:

[tex]\[ -11 = \frac{16 + t}{-2} \][/tex]

3. Simplify the right-hand side of the equation:

[tex]\[ -11 = \frac{16 + t}{-2} \][/tex]

To eliminate the fraction, multiply both sides of the equation by -2:

[tex]\[ (-11) \times (-2) = 16 + t \][/tex]

[tex]\[ 22 = 16 + t \][/tex]

4. Solve for [tex]\( t \)[/tex]:

Subtract 16 from both sides of the equation:

[tex]\[ t = 22 - 16 \][/tex]

[tex]\[ t = 6 \][/tex]

Therefore, the value of [tex]\( t \)[/tex] is:

[tex]\[ \boxed{6} \][/tex]