How do you solve these algebra questions?
1. Solve for [tex]m[/tex]:
\[ 2m^2 - 7m - 3 = 0 \]
2. Solve for [tex]b[/tex]:
\[ 4b^2 + 8b + 7 = 4 \]
3. Simplify:
\[ 5\sqrt{80a^2} \]
4. Simplify:
\[ -6\sqrt{150r} \]
5. Rationalize the denominator:
\[ \frac{2}{\sqrt{3}} \]
6. Simplify:
\[ \frac{\sqrt{6}}{5\sqrt{3}} \]
Answer (2)
2 m 2 − 7 m − 3 = 0 a = 2 ; b = − 7 ; c = − 3 Δ = b 2 − 4 a c → Δ = ( − 7 ) 2 − 4 ⋅ 2 ⋅ ( − 3 ) = 49 + 24 = 73 x = 2 a − b ± Δ → x = 2 ⋅ 2 7 ± 73 = 4 7 ± 73
4 b 2 + 8 b + 7 = 4 4 b 2 + 8 b + 7 − 4 = 0 4 b 2 + 8 b + 3 = 0 4 b 2 + 2 b + 6 b + 3 = 0 2 b ( 2 b + 1 ) + 3 ( 2 b + 1 ) = 0 ( 2 b + 1 ) ( 2 b + 3 ) = 0 ⟺ 2 b + 1 = 0 or 2 b + 3 = 0 2 b = − 1 or 2 b = − 3 b = − 2 1 or b = − 2 3
5 80 a 2 = 5 80 ⋅ a 2 = 5 16 ⋅ 5 ⋅ ∣ a ∣ = 5 ⋅ 16 ⋅ 5 ⋅ ∣ a ∣ = 5 ⋅ 4 ⋅ 5 ⋅ ∣ a ∣ = 20∣ a ∣ 5
− 6 150 r = − 6 25 ⋅ 6 r = − 6 25 ⋅ 6 r = − 6 ⋅ 5 6 r = − 30 6 r
3 2 = 3 2 ⋅ 3 3 = 3 2 3
5 3 6 = 5 1 ⋅ 3 6 = 5 1 3 6 = 5 1 2 = 5 2
To solve the first two equations, use the quadratic formula and factorization. The simplifications involve extracting square roots and rationalizing denominators. Each step follows algebraic rules to arrive at simplified forms or solutions.
;
