This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Formulate the total number of goals. Team A scores n goals. Team B scores (n+5) goals. The total number of goals scored by both teams is the sum of their individual scores: Total goals = n + (n+5) Step 2: Formulate the inequality. The total number of goals is less than 15. n + (n+5) < 15 Step 3: Solve the inequality for n. Combine like terms: 2n + 5 < 15 Subtract 5 from both sides: 2n < 15 - 5 2n < 10 Divide by 2: n < (10)/(2) n < 5 The inequality is n < 5. Step 1: Identify the properties of a parallelogram. In a parallelogram RSTU, opposite angles are equal, and consecutive angles are supplementary (add up to 180^). Given: RUT = (2x+30)^ RST = (7x-25)^ Step 2: Use the property of opposite angles to find x. Angles RUT (at vertex U) and RST (at vertex S) are opposite angles in the parallelogram RSTU. Therefore, they are equal. RUT = RST 2x+30 = 7x-25 Step 3: Solve for x. Subtract 2x from both sides: 30 = 7x - 2x - 25 30 = 5x - 25 Add 25 to both sides: 30 + 25 = 5x 55 = 5x Divide by 5: x = (55)/(5) x = 11 Step 4: Calculate the measure of RST. Substitute x=11 into the expression for RST: RST = (7x-25)^ = (7(11)-25)^ RST = (77-25)^ RST = 52^ Step 5: Calculate the value of STU. Angles STU (at vertex T) and RST (at vertex S) are consecutive angles in the parallelogram RSTU. Therefore, they are supplementary. STU + RST = 180^ Substitute the value of RST: STU + 52^ = 180^ Subtract 52^ from both sides: STU = 180^ - 52^ STU = 128^ The value of angle STU is 128^. Send me the next one 📸