How do you solve the equation 3x – 7 = 11 and check your answer?To solve the equation 3x – 7 = 11, first add 7 to both sides to get 3x = 18. Then, divide both sides by 3 to find x = 6. To check the answer, substitute x back into the original equation: 3(6) – 7 = 11, which is true. Therefore, x = 6 is correct.
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What is the area of a triangle that has a base of 9 cm and a height of 6 cm?
What is the area of a triangle that has a base of 9 cm and a height of 6 cm?To find the area of a triangle, use the formula: Area = 1/2 * base * height. Here, the base is 9 cm and the height is 6 cm. So, Area = 1/2 * 9 cm * 6 cm = 27 square centimeters.
How can you solve a quadratic equation using the quadratic formula?
How can you solve a quadratic equation using the quadratic formula?To solve a quadratic equation ax^2 + bx + c = 0 using the quadratic formula, use x = (-b ± √(b²-4ac)) / (2a). First, identify coefficients a, b, and c. Then, substitute these values into the formula and calculate the discriminant (b²-4ac). Finally, solve for x using the plus and minus variations.
How do you determine the area of a trapezoid when given the lengths of its bases and height?
How do you determine the area of a trapezoid when given the lengths of its bases and height?To determine the area of a trapezoid, use the formula: Area = 0.5 * (Base1 + Base2) * Height. Here, Base1 and Base2 are the lengths of the two parallel sides (bases), and Height is the perpendicular distance between the bases. This formula calculates the average of the two bases, multiplied by the height.
What is the sine of a 30-degree angle?
What is the sine of a 30-degree angle?The sine of a 30-degree angle is 0.5. This is derived from the properties of a 30-60-90 right triangle, where the ratio of the length of the side opposite the 30-degree angle to the hypotenuse is 1:2, resulting in a sine value of 1/2 or 0.5.
What is the difference between a derivative and an integral?
What is the difference between a derivative and an integral?A derivative represents the rate of change of a function with respect to a variable, essentially measuring how a function changes as its input changes. An integral, on the other hand, represents the accumulation of quantities, such as areas under curves. Derivatives focus on instantaneous rates of change, while integrals focus on total accumulation.
How do you find the global maximum and minimum values of a function on a closed interval using derivatives and critical points?
How do you find the global maximum and minimum values of a function on a closed interval using derivatives and critical points?To find the global maximum and minimum values of a function on a closed interval [a, b], follow these steps: 1. Compute the derivative of the function. 2. Find the critical points by setting the derivative equal to zero and solving for x. 3. Evaluate the function at the critical points and at the endpoints a and b. 4. Compare these values to determine the global maximum and minimum.
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