🧮 algebra

1. We are asked to express the quadratic expression $19 - 4x + x^2$ in the form $(x + a)^2 + b$, where $a$ and $b$ are integers. 2. The general approach is to complete the square.

1. **State the problem:** We want to express the quadratic expression $d^2 - 8d + 9$ in completed square form. 2. **Recall the formula:** The completed square form of a quadratic e

1. The problem asks us to determine whether the function $f(x) = x^2 + 1$ is even, odd, or neither. 2. Recall the definitions:

1. **Problem:** Solve the equation $$\lfloor x \rfloor^2 - 5\lfloor x \rfloor + 6 = 0$$ where $$\lfloor x \rfloor$$ is the greatest integer function (floor function). Find the inte

1. **State the problem:** Find the center and radius of the circle given by the equation $$x^2 + y^2 + 2x - 6y + 5 = 0$$. 2. **Rewrite the equation:** Group $x$ and $y$ terms:

1. **State the problem:** Given functions $f(x) = 2x + 3$, $g(x) = x^2 + 1$, and $h(x) = x^3$, find the following: (i) $f \circ g$, $g \circ f$, $f^2$, $g^2$ and prove that $(f \ci

1. **Problem 1:** Nayeon won 40 lollipops and gave 2 to every student in her math class. She has at least 7 left. 2. **Write the inequality:** Let $x$ be the number of students. Th

1. Mari kita hitung hasil pembagian polinomial pertama: Diberikan: $$\frac{4x^3 + 7x^2 - 7x + 2}{2x + 3}$$

1. **Problem 1:** The larger of two numbers is 5 less than twice the smaller, and their sum is 28. 2. Let $x$ be the smaller number and $y$ be the larger number.

1. The problem is to find the value of a variable or expression that equals 30. 2. Since the answer is given as 30, we assume the problem was to solve for a variable or evaluate an

1. **Problem 1: Draw the graph of the piecewise function and find its range** Given:

1. **State the problem:** A shirt has a marked price (m.p) of 800. A discount of 13% is given to the customer, and the trader makes a profit of 20%. We need to find the cost price

1. **State the problem:** We have the quadratic expression $$4x^2 + bx - 45$$ where $$b$$ is a constant. It can be factored as $$(hx + k)(x + j)$$ where $$h, k, j$$ are integers. W

1. **State the problem:** We are given the equation $$2(kx - n) = - \frac{28}{15} x - \frac{36}{19}$$ where $k$ and $n$ are constants and $n > 1$. The equation has no solution. We

1. **State the problem:** Convert the decimals 3.125 and 0.48 to fractions, then simplify the product of 14.56 and 7.3. 2. **Convert 3.125 to a fraction:**

1. **State the problem:** We start with the inequality:

1. **Problem statement:** We have a rectangular grazing area measuring 36 m by 60 m. One side of length 60 m is along a rock wall, so it does not need fencing. The other three side

1. **State the problem:** Simplify the expression $8x^4 + 12x^2 + 18$ and verify the given steps. 2. **Analyze the original expression:** The expression is $8x^4 + 12x^2 + 18$.

1. **State the problem:** Solve the equation $-2(x+6)=24$ for $x$. 2. **Use the distributive property:** Multiply $-2$ by each term inside the parentheses.

1. The problem asks if number 3 is also solved using the quadratic formula. 2. The quadratic formula is used to solve quadratic equations of the form $$ax^2 + bx + c = 0$$.

1. **Problem:** A football player punts a ball. The path of the ball is modeled by the equation $$h = -0.004d^2 + d + 25$$ where $d$ is the horizontal distance in feet and $h$ is t