The process of solving by graphing entails the depiction of equations on a graph with a goal to identify their solutions or the points where they intersect. This strategy is extremely beneficial in visualizing the correlations between variables and comprehending the overall pattern of an equation. It is frequently applied in finding solutions for linear, quadratic, or systems of equations.
| Topic | Problem | Solution |
|---|---|---|
| None | Solve the system of equations by graphing: \(y = … | Step 1: Draw the graph of each equation on the same set of axes. For \(y = 2x + 3\), the y-intercep… |
| None | $\frac{5 u-7}{4}-\frac{3 u-8}{2}=2$ | The given equation is \(\frac{5 u-7}{4}-\frac{3 u-8}{2}=2\). |
| None | Question 10 Find all zeros of $f(x)=x^{3}+4 x^{2}… | The question is asking to find the zeros of the cubic function \(f(x)=x^{3}+4 x^{2}+3 x-2\). The ze… |
| None | What value of $v$ makes this multiplication sente… | The multiplication property of equality states that if you multiply both sides of an equation by th… |
| None | A cylinder has a height of 20 inches. Its volume … | The volume of a cylinder is given by the formula \(V = \pi r^2 h\), where \(V\) is the volume, \(r\… |
| None | $5 x+7+3 y+4=2 x+8 y$ | Understand the problem: The problem is a linear equation with two variables, x and y. We are asked … |
| None | While on a tour in Greece, Tatyana saw that the t… | Given the temperature in Celsius, \(C=35^{\circ}\), and the formula used to convert from Celsius to… |
| None | McDonald's sells 5 times as many coffees as Burge… | Let's denote the number of coffees sold by Burger King as \(x\). Then, the number of coffees sold b… |
| None | 3. Sharon went bowling with her friends. She paid… | Let's denote the number of games Sharon bowled as x. The total cost of bowling is made up of a fixe… |
| None | 3. Peyton is three years younger than Justin. Mat… | Let's represent the ages of Justin, Peyton, and Matt with the variables J, P, and M respectively. |
| None | how many zeros and multiplicities does $f(x)=2 x^… | The zeros of a polynomial are the values of x that make the polynomial equal to zero. The multiplic… |
| None | If 5 is added to a number and the sum is tripled,… | Let's denote the number as x. According to the problem, we have the following equation: \(3*(x+5) =… |
| None | $S$ is the midpoint of $\overline{R T}$. If $S T=… | Given that S is the midpoint of RT, it means that ST = SR. |
| None | $0.9=0.4+B+0.4 \times B$ | Combine like terms on the right side of the equation to get \(1.4B + 0.4 = 0.9\). |
| None | A 20 -foot piece of string is cut into two pieces… | Let's denote the length of the shorter piece as \(x\). According to the problem, the longer piece i… |
| None | A 20 -foot piece of string is cut into two pieces… | Let's denote the length of the shorter piece as \(x\). According to the problem, the longer piece i… |
| None | Write an equation for the following situation, an… | Translate the problem into an equation: \(5n + 8 = 63\). |
| None | The length of a rectangular pool is 3 meters less… | The problem gives us two pieces of information that we can use to form two equations. The first is … |
| None | ution. 2. $\frac{x}{4}=2+8$ | The question is asking to solve for x in the equation \(\frac{x}{4}=2+8\). To solve for x, we need … |
| None | Question 11 Find all zeros of $f(x)=x^{3}-4 x^{2}… | We are given the function \(f(x)=x^{3}-4 x^{2}+2 x+4\) and we are asked to find all its zeros. |
| None | M.9 Solve two-step equations: complete the soluti… | Subtract 3 from each side of the equation to get \(12r = 15 - 3\). |
| None | Solve the equation. Check your proposed solution.… | Combine like terms on the left side of the equation: \(4x - 3x + \frac{1}{8} = \frac{1}{2}\) simpli… |
| None | Solve the equation. \[ -9 y-3 y=\frac{6}{7} \] | Combine like terms on the left side of the equation to get \(-12y = \frac{6}{7}\). |
| None | 17. $\frac{1}{2} r+2\left(\frac{3}{4} r-1\right)=… | The given equation is \(\frac{1}{2} r+2\left(\frac{3}{4} r-1\right)=\frac{1}{4} r+6\). |
| None | Question 5 Find all zeros of $f(x)=x^{3}+x^{2}-8 … | Set the function \(f(x)=x^{3}+x^{2}-8 x-6\) equal to zero and solve for x to find the real zeros of… |
| None | In a particular year, a total of 57,918 students … | Let's denote the number of students who studied in the most popular host country as \(x\) and the n… |
| None | The new dolphin tank at the city aquarium is in t… | Given that the tank is in the shape of a rectangular prism, with a length of \(25 yd\), a width of … |
| None | Solve the equation. \[ \frac{x}{5}-x=8 \] \[ \mat… | Multiply every term by 5 to get rid of the fraction: \(x - 5x = 40\) |
| None | Two trucks leave a warehouse at the same time. On… | Two trucks leave a warehouse at the same time. One travels due north at an average speed of 48 mile… |
| None | Solve the following formula for $x$ \[ y=(7-4 k) … | The question is asking to solve for x in the equation \(y = (7-4k)x\). To do this, we need to isola… |
| None | 3. A, B, and $\mathrm{C}$ are collinear points wi… | Given that B is the midpoint of AC, it means that AB = BC. |
| None | Find a polynomial function of least degree having… | The zeros of a polynomial are the values of x for which the polynomial equals zero. If a polynomial… |