Given the following information,
find the value of 𝑧. 𝑧 is equal to 𝑥 squared minus
nine 𝑦. 𝑥 is equal to four. 𝑦 is equal to negative five.
So looking at the information we’ve
been given, we’ve been given an expression for 𝑧 in terms of 𝑥 and 𝑦. 𝑧 is equal to 𝑥 squared minus
nine 𝑦. We’ve also been given the values of
𝑥 and 𝑦. To work out the value of 𝑧, we
just need to substitute the numeric or number values of 𝑥 and 𝑦 into the algebraic
expression for 𝑧.
So substituting four for 𝑥 and
negative five for 𝑦, we have that 𝑧 is equal to four squared minus nine multiplied
by negative five. Now, we do have a calculator to
help with this. So we can type the calculation into
our calculator exactly as it’s written on screen. And the value that the calculator
will return is 61.
However, we could also work this
out ourselves. Firstly, we have four squared,
which remember means four multiplied by four. And four multiplied by four is
16. Then, we have nine multiplied by
negative five. Now, nine multiplied by five is
45. And as we have a positive number
multiplied by a negative number, this will give a negative answer overall. So nine multiplied by negative five
is negative 45.
Our calculation for 𝑧 then has
become 16 minus negative 45. Next, we just need to remember that
these two minus signs next to each other will make a positive. So our expression becomes 16 plus
45. 16 plus 45 is indeed equal to
61. So we found the value of 𝑧.