🧮 algebra

Problem: You asked whether the answer to Q5 is 70 but you did not provide the text of Q5. 1. State the question as I understand it.

1. **State the problem:** We are given two functions $f(x) = \frac{1}{4}x - 9$ and $g(x) = \frac{3}{4}x + 21$. The function $h$ is defined as $h(x) = f(x) + g(x)$. We need to find

1. **State the problem:** We have two polynomial functions: $$y_1 = (x + a)^2 + b$$

1. **Problem 9:** Given the polynomial division $$4x^3 - 10x^2 - 7x + 8 = d(x) \times (x^2 - 3) + (2x - 1)$$

1. **Problem (a):** Prove without a calculator that $$\log_{10}\left(\frac{170}{7}\right) - \log_{10}\left(\frac{18}{35}\right) + \log_{10}\left(\frac{36}{17}\right) = 2.$$ 2. **Fo

1. **Problem 9:** Given the polynomial division $$4x^3 - 10x^2 - 7x + 8$$ divided by $$d(x)$$, the quotient is $$x - 3$$ and the remainder is $$2x - 1$$. Find $$d(x)$$. 2. **Proble

1. **Problem 4:** Given $f(x) = x^3 - px^2 + 2px - 3p$ where $p \neq 0$, and the remainder when $f(x)$ is divided by $x - p$ is $5p$, find the remainder when $f(x)$ is divided by $

1. Convert $\frac{1}{4}$ to a percent. To convert a fraction to a percent, multiply by 100 and add the percent symbol.

1. **Stating the problem:** We have a quadratic equation with roots $\alpha$ and $\beta$ given by

1. Convert $\frac{54}{13}$ into a mixed fraction. Step 1: Divide the numerator by the denominator.

1. The problem is to understand the properties of the natural logarithm function $\ln$ and the exponential function $e^x$. 2. The key formulas are:

1. **Problem Statement:** Find the domain of the function $g(x) = |x|$ and describe its graph. 2. **Understanding the function:** The function $g(x) = |x|$ represents the absolute

1. The problem is to calculate $184,756 \times (0.5)^{20}$ and understand how to type this expression in a calculator. 2. The expression involves multiplying 184,756 by $0.5$ raise

1. نبدأ بحساب محدد المصفوفة 3x3 المعطاة: $$\begin{vmatrix} 1 & 2 & 0 \\ 0 & 1 & 1 \\ 2 & 0 & 4 \end{vmatrix}$$

1. The problem is to calculate the binomial coefficient $\binom{20}{10}$, which is defined as the number of ways to choose 10 items from 20 without regard to order. 2. The formula

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 5$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. The problem is to solve the equation $\ln 4 = 5x$ for $x$. 2. Recall that $\ln$ is the natural logarithm, which is the logarithm base $e$. The equation $\ln a = b$ can be rewrit

1. The problem asks to find the sum of the squares of each number in a given set or sequence. 2. The formula to find the sum of squares of numbers $x_1, x_2, \ldots, x_n$ is:

1. **Problem Statement:** We are given the hyperbolic function $$f(x)=\frac{1}{x-2}+3$$ and need to find its domain, range, intercepts, asymptotes, axes of symmetry, and sketch the

1. The problem states that we have a variable $a$ with the value $509857.39$. 2. Since this is a straightforward assignment of a numerical value to a variable, no further calculati

1. **Problem Statement:** Simplify the expression $$\frac{\sqrt{a+b}}{a+b}$$ and solve the given algebraic equations: 2. **Simplify the expression:**