Live practice

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

From \((0,-1)\), \(b=-1\). From \((1,1)\), \(a+b=1\), hence \(a=2\). The rule \(f(x)=2x-1\) also gives \(f(2)=3\) and \(f(-1)=-3\), confirming all pairs.

Find the masses of C and H in the sample. Convert all carbon to CO₂ by the \(\frac{44}{12}\) mass ratio and all hydrogen to H₂O by the \(\frac{18}{2}\) ratio.

The magnitude of K indicates equilibrium position: extremely small K gives almost only reactants, extremely large K almost only products, and K near unity appreciable amounts of both.

Sigma bonds arise from head-on overlap with electron density on the internuclear axis and permit rotation. Pi bonds arise from sidewise overlap with density above/below the axis and restrict rotation; π overlap is generally weaker.

Balance the common ionic charges or usual covalencies. Element 71 is Lu and commonly forms Lu³⁺.

Combine Bohr's angular-momentum condition with de Broglie's relation.

Calculate the abundance-weighted mean. Convert each percentage to a fraction before multiplying.

From \((0,-1)\), \(b=-1\). From \((1,1)\), \(a+b=1\), hence \(a=2\). The rule \(f(x)=2x-1\) also gives \(f(2)=3\) and \(f(-1)=-3\), confirming all pairs.

1. False: the intersection is \(\{3\}\).
2. False: the intersection is \(\{a\}\).
3. True: the intersection is \(\varnothing\).
4. True: the intersection is \(\varnothing\).