🧮 algebra

1. **Stating the problem:** Find the graphs of the functions:

1. Problem (35): Solve the quadratic equation $$-x^2 - 8x + 3 = 0$$. 2. Rewrite the equation as $$-x^2 - 8x + 3 = 0$$ or equivalently $$x^2 + 8x - 3 = 0$$ by multiplying both sides

1. Problem (25): Simplify $\frac{\sqrt{6} \sqrt{24}}{2\sqrt{6}}$ and verify if it equals 12. Step 1: Simplify numerator $\sqrt{6} \sqrt{24} = \sqrt{6 \times 24} = \sqrt{144} = 12$.

1. **Solve the equation** $x^2 - 18 = 0$. 2. Add 18 to both sides: $$x^2 = 18$$

1. **Solve the quadratic equation** $x^2 - 10x + 16 = 0$. Step 1: Factor the quadratic.

1. **State the problem:** We have a box with 40 marbles. The ratio of red marbles to total marbles is $2:5$, and the ratio of green stones to total stones is $3:10$. We want to fin

1. **State the problem:** Calculate the total cost for Yaa who buys 2 skirts, 1 dress, and 4 pairs of pantyhose during a 20% off sale on skirts.

1. The problem states that a mountain path is 12.1 miles long and a hiker walks at a rate of 1.96 miles per hour. 2. We need to find the time it takes for the hiker to walk the ent

1. Stating the problem: Solve the logarithmic equation $$\log_5 (x+3) - \log_5 (x-1) = 2$$. 2. Use the logarithmic property: $$\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)

1. The problem states that Kofi earned 50 Cedis yesterday mowing lawns. 2. Today, Kofi earned 60% of what he earned yesterday.

1. We are given multiple logarithmic expressions and an equation to simplify or solve. 2. Simplify each logarithmic expression:

1. The function given is $f(x) = -x^2 - x + 6$. 2. To find the equation of $h$, we first reflect $f$ about the x-axis. Reflection about the x-axis changes $f(x)$ to $-f(x)$.

1. **State the problem:** An engineer drives to his brother's house at 50 mph and it takes 3 hours. We need to find the time it takes to drive back at 60 mph. 2. **Calculate the di

1. **State the problem:** We have a stamping machine that can stamp 40 envelopes in 8 minutes. We want to find how many such machines working simultaneously are needed to stamp 120

1. Muammo: $X$ ning qiymati 9 chiqadi, lekin 12 noto'g'ri natija sifatida berilgan. 2. Bu yerda $X$ ning qiymatini topish uchun tenglama yoki ifoda kerak.

1. **State the problem:** An engineer drives to his brother's house at 50 mph taking 3 hours. We need to find the time it takes to drive back at 60 mph. 2. **Calculate the distance

1. **State the problem:** We have the matrix equation \( \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 23 \\ 37 \end{bmatrix}

1. The problem states that \( \frac{AC}{36} = \frac{60}{48} \). 2. To find \( AC \), we can cross-multiply: \( AC \times 48 = 60 \times 36 \).

1. **State the problem:** We need to solve for the principal amount $P$ in the equation $$27660 = P(1 + 6.7\%)^5.$$ 2. **Convert the percentage to decimal:**

1. **State the problem:** Mary has a parcel weighing 10.5 kg and needs to split it into two parcels, each weighing at most 6 kg, to ship to China. The shipping cost depends on the

1. Problem a) Simplify $\sqrt{25a^{2}b^{2}} \times \sqrt[3]{27a^{3}}$. - $\sqrt{25a^{2}b^{2}} = 5ab$ because $\sqrt{25} = 5$, $\sqrt{a^{2}} = a$, and $\sqrt{b^{2}} = b$.