Given that and , what can we conclude about the value of ?

We will put the given value of into the equation for . Step 1 — Calculate y We are given the equation for . We are also given the value of . Let's substitute into the equation. > Answer > (i)

Appendix 1: Proofs in Mathematics | A1.2

Question 4

Given that $y = x^2 + 6$ and $x = -1$ , what can we conclude about the value of $y$ ?

Solution

We will put the given value of $x$ into the equation for $y$ .

Step 1 — Calculate y

We are given the equation for $y$ .

We are also given the value of $x$ .

Let's substitute $x = \mathbf{-1}$ into the equation.

$y = x^2 + 6$

$y = (-1)^2 + 6$

$y = 1 + 6$

$\boxed{y = 7}$

Answer

(i) $y = 7$

More questions in A1.2

Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?

Given that the product of two rational numbers is rational, and suppose $a$ and $b$ are rationals, what can you conclude about $ab$ ?

Given that the decimal expansion of irrational numbers is non-terminating, non-recurring, and $\sqrt{17}$ is irrational, what can we conclude about the decimal expansion of $\sqrt{17}$ ?

Given that $y = x^2 + 6$ and $x = -1$ , what can we conclude about the value of $y$ ?

Given that ABCD is a parallelogram and $\angle B = 80^\circ$ . What can you conclude about the other angles of the parallelogram?

Given that PQRS is a cyclic quadrilateral and also its diagonals bisect each other. What can you conclude about the quadrilateral?

Given that $\sqrt{p}$ is irrational for all primes $p$ and also suppose that 3721 is a prime. Can you conclude that $\sqrt{3721}$ is an irrational number? Is your conclusion correct? Why or why not?