May 27, 2025 · Final Answer Therefore, the solutions to the absolute value equation 5∣x − 7∣ = 40 are x = 15 and x = −1. Examples Absolute value equations are useful in many real-world …

Aug 17, 2025 · Final Answer Therefore, the graph of f (x) = (x+ 4)6(x+ 7)5 crosses the x-axis at the root x = −7. Examples Understanding roots and their multiplicities is crucial in analyzing …

Aug 13, 2025 · Add 7 to both sides of the equation: 5x2 + 20x = 7. Factor out 5: 5(x2 + 4x) = 7. Complete the square: 5(x2 + 4x + 4) = 7 + 20. Take the square root: x + 2 = ± 527 . …

Aug 16, 2025 · The value of x in the equation 5(x − 7) = 30 is 13. To find this, we divide by 5 and then add 7 to isolate x. Hence, the correct answer is option C: 13.

Nov 6, 2023 · The polynomial with a leading coefficient of 1 and roots (7+ i) and (5-) forms by including factors for the complex root and its conjugate. The correct polynomial is f (x) = (x - …

Jul 21, 2020 · To simplify the expression x5 ⋅ x7, you can use the property of exponents that states: when multiplying two expressions with the same base, you add the exponents. This …

Jul 31, 2025 · For example, if a store charges a base fee of $7 plus $5 for each product, and your total is $22, solving the given equation helps determine how many products you purchased, …

Mar 31, 2025 · For example, using the expression (5 x)7, we see that taking the square root first and then raising to the power of 7 returns us to the original exponent of 1.4.

Apr 27, 2025 · Expand the right side: 7(x +1) = 7x + 7. The equation now is: 8x −5 = 7x + 7. Step 2: Isolate the variable. Subtract 7x from both sides to eliminate x on the right side: 8x −7x − 5 …

May 17, 2016 · The solution to the inequality 5 > x + 7 is x < -2. Therefore, the correct answer is B: {x | x ∈ ℝ, x < -2}. This indicates that x can be any value less than -2.