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To determine if a value is a solution to the quadratic equation x² + 3x + 2 = 0, substitute the value into the equation. If the result equals zero, the value is a solution; if not, it isn't.
To solve the equation $5x^2 + 75x = 0$, factor out $x$ to get $x(5x + 75) = 0$. This gives solutions $x = 0$ and $x = -15$.
To factor the quadratic equation $x^2 + 4x - 32 = 0$, find two numbers that multiply to -32 and add to 4. The numbers -4 and 8 work, leading to the factored form $(x - 4)(x + 8) = 0$.
To maintain a 90% average with a current grade of 98%, you need to score at least 60.6 on the midterm. However, since grades can't exceed 100%, achieving this average is impossible without adjusting your expectations.
To complete the square for the equation x² + 6x = 2, take half of the coefficient of x, square it, and add to both sides. This transforms the equation into a perfect square trinomial, simplifying the solution process.
Completing the square is a method used to solve quadratic equations by rewriting them in the form (x - a)² = b. This technique helps find the roots of the equation and is useful in various mathematical applications.
'AND' refers to counting common elements between sets, while 'OR' includes all elements from both sets, avoiding double counting. Using Venn diagrams can help visualize these concepts effectively.
To find the unknown number when 9 is 0.03 of it, convert 0.03 to a fraction (3/100). Then, set up the equation 9 = (3/100) * x and solve for x to find that it equals 300.
To find the zeros of a quadratic function like y = -3x² + 12x + 15, set y equal to zero and solve for x. The zeros are the x-values where the graph crosses the x-axis, which are (5, 0) and (-1, 0) in this case.
The greatest common factor (GCF) is the largest number and variable factor shared by two or more terms. To find the GCF, identify the highest common number and the smallest powers of shared variables in each term.
To find the maximum profit from a quadratic profit function, use the vertex formula. For a function like P(l) = -4l² + 32l - 52, the vertex gives you the maximum profit value, which you can calculate even if L isn't provided directly.
Converting between percents, decimals, and fractions is straightforward! To convert a decimal to a percent, multiply by 100. To convert a percent to a decimal, divide by 100. To convert a decimal to a fraction, write it over the appropriate place value and simplify.
To factor the expression 2s^3 - 6s^2, identify the greatest common factor (GCF), which is 2s^2. This leads to the factored form: 2s^2(s - 3). Use Desmos to visualize the expressions.
To find the original price after a discount, divide the sale price by the percentage remaining. In this case, if the sale price is $150 after a 25% discount, the original price is $200.
'No three' can refer to various contexts, such as rules in games or a concept in math. Clarifying the context helps provide a better understanding. Feel free to share more details for tailored assistance!
Yes, the graph shows a parabola that crosses the x-axis at x = 3 and x = 7, indicating these points are the zeros of the function. The equation -(x - 3)(x - 7) correctly represents this parabola, opening downward due to the negative sign.
To simplify T + T + T divided by 4, first combine the terms to get 3T. Then, divide by 4 to get the equivalent expression as 3T/4 or 3/4 T.
Significant digits are the digits in a number that carry meaning contributing to its precision. Understanding how to identify them is crucial in scientific calculations and measurements.
Two-variable equations can help model real-world scenarios, such as costs based on group size. For example, to find the total cost for 25 students when there's a flat fee and a per-ticket charge, you can use the equation y = 50 + 15x.
To find the distance between two points J (−3, 2) and K (1, −6), use the distance formula: Distance = √((x2 - x1)² + (y2 - y1)²). Plugging in the coordinates gives a distance of 4√5.
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