🧮 algebra

1. **Problem 1: Calculate the discount and sale price for a knapsack originally priced at 2500 with a 20% discount.** Step 1: Calculate the discount amount.

1. State the problem: Prove that $-(-a) = a$ for any number $a$. 2. Understand the sign notation: The negative sign $-$ before a number means the additive inverse of that number.

1. The problem asks for the percent of change when the alcohol volume changes from 78 ml to 96.72 ml. 2. Percent change formula is $$\text{Percent Change} = \frac{\text{New Value}

1. Problem: Calculate the 5% discount on a cellular phone worth 12,690. Step 1: Calculate discount = $5\% \times 12,690 = 0.05 \times 12,690$

1. The problem is to find the percent of change in enrolment from the previous year to this year. 2. Let the previous year's enrolment be $P$ and this year's enrolment be $T$.

1. **Problem 1:** Write the equation for the joint variation "x varies jointly as y and z". Since x varies jointly as y and z, the formula is:

1. We are given three squares with numbers at their corners and a value inside each square. The first two squares have known values inside them, and we need to find the missing val

1. The user mentions "Image of 6," which is ambiguous as it could relate to multiple math topics involving the number 6. 2. Assuming the request is about the image of a number unde

1. The problem states that the total change in temperature over 4 hours is \(-28^\circ\text{F}\), and the change is the same each hour. 2. To find the hourly change, we need to div

1. The problem shows a 3x3 grid with numbers and a missing number represented by a question mark in the bottom left cell. 2. The grid rows are:

1. Diberikan sistem persamaan linear tiga variabel: $$\begin{cases} 4i_1 + 5i_2 + 6i_3 = 3 \\ 8i_1 - 7i_2 - 3i_3 = 9 \\ 7i_1 - 8i_2 + 9i_3 = 6 \end{cases}$$

1. The problem asks us to compare the fractions $\frac{9}{11}$ and $\frac{10}{11}$.\n2. Both fractions have the same denominator, which is 11.\n3. When two fractions have the same

1. Stating the problem: We have three triangles, each with three numbers at the vertices and one number inside. We need to find the missing number inside the third triangle. 2. Obs

1. **State the problem:** We need to compare the fractions $\frac{5}{6}$ and $\frac{3}{4}$.\n\n2. **Find a common denominator:** The denominators are 6 and 4. The least common deno

1. Problem 1: We want to find the water level in Macopo Dam on May 5. 2. The water level decreases to 5% of the previous day’s level each day, so the decay factor is $0.05$.

1. The problem is to find the missing number represented by ? in the matrix: $$\begin{matrix}7 & ? & 108 \\ 8 & 12 & 96 \\ 9 & 132 & 84\end{matrix}$$

1. We are asked to compare the fractions $\frac{2}{3}$ and $\frac{3}{4}$. 2. To compare fractions, we find a common denominator or convert them to decimals.

1. **Problem (a)**: Find the amount of discount. Given discount is Rs. 6,000. 2. **Problem (b)**: Find the selling price after giving discount.

1. Show whether each function is one-to-one (injective). 1.i) Consider $f(x) = 10x + 7$.

1. Problem 1 (Finding Rate): Given a principal of $1000$, a simple interest of $150$, and a time period of $3$ years, find the rate of interest.

1. We are asked to solve the equation involving the absolute value: $|2x - 3| = 4 - x$. 2. Recall that $|A| = B$ means $A = B$ or $A = -B$ if $B \geq 0$. We must also ensure that t