| Topic | Problem | Solution |
|---|---|---|
| None | A blue candle and red candle are lit at the same … | Let's denote the remaining length of the blue candle as \(l_b\) and the remaining length of the red… |
| None | Candle A and Candle B are lit at the same time an… | The question is asking for the number of solutions to the system of equations representing the leng… |
| None | Particle A and Particle B begin moving away from … | Substitute \(t=24\) into the function \(a(t)=7t+14\) to find the distance of Particle A from the wa… |
| None | An investor deposited some money at $1.7 \%$ annu… | Let's denote the amount of money invested at 1.7% as x, and the amount of money invested at 2.3% an… |
| None | For each pair of functions $f$ and $g$ below, fin… | Given the first pair of functions, $f(x) = \frac{x}{3}$ and $g(x) = 3x$, we substitute $g(x)$ into … |
| None | VAriable Description TVhours Total number of TV h… | Given the number of TV hours watched per day by each child: [2, 3, 1, 4, 2, 3, 1, 2, 3, 4, 2, 3, 1,… |
| None | For each pair of functions $f$ and $g$ below, fin… | Given the functions \(f(x) = \frac{3}{x}\) and \(g(x) = \frac{3}{x}\), we need to find \(f(g(x))\) … |
| None | Suppose that the functions $u$ and $w$ are define… | Let's first find the value of the function \(u(x)\) at \(x=-4\). So, \(u(-4) = -(-4) + 2 = 6\). |
| None | Re compute the mean without the outliers? variabl… | Given the total number of TV hours watched per day, we are asked to compute the mean excluding the … |
| None | Solve the following logarithmic equation. \[ \log… | The given equation is a logarithmic equation with base 2. The properties of logarithms state that t… |
| None | Suppose a metal block is cooling so that its temp… | Given the temperature formula \(T=200 \cdot 4^{-0.1t}+20\), where \(t\) is the time in hours. |
| None | Solve the following logarithmic equation. \[ \log… | Combine the two logarithms on the left side of the equation into one using the property of logarith… |
| None | Solve the logarithmic equation. \[ 1+\log (3 x-10… | Given the logarithmic equation \(1+\log (3 x-10)=0\) |
| None | Solve the exponential equation. Write the exact a… | Given the exponential equation \(e^{x+4}=7\) |
| None | Exercise $A$ Copy the problems. Find the products… | Calculate the products by multiplying the factors in parentheses first for each equation. |
| None | Solve the logarithmic equation. \[ \log _{3} x=-2… | The logarithmic equation is in the form \(\log_b a = n\), which can be rewritten in exponential for… |
| None | Use the specified row transformation to change th… | The problem is asking to perform a row operation on a matrix. The operation is to multiply the firs… |
| None | \[ \begin{array}{l} p(x)=2 x+2 \\ q(x)=-x^{2}-2 \… | Define the functions \(p(x)=2x+2\) and \(q(x)=-x^2-2\). |
| None | Write the given expression in condensed form. \[ … | Given the expression \(\frac{1}{2} \ln x+9 \ln y\) |
| None | Use properties of logarithms to expand the logari… | The given expression is a logarithm with base 4. The argument of the logarithm is a seventh root of… |
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