2 times a number added to another number is 25. 3 times the first number minus the other number is 20. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]2x + y = 25 [*]3x - y = 20 [/LIST] Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable. (2 + 3)x + (1 - 1)y = 25 + 20 Simplifying, we get: 5x = 45 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D45&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]x = 9[/B] To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1): 2(9) + y = 25 y + 18 = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=y%2B18%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 7[/B] So we have (x, y) = (9, 7) Let's check our work for equation (2) to make sure this system works: 3(9) - 7 ? 20 27 - 7 ? 20 20 = 20 <-- Good, we match!

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers. [U]The phrase [I]a number[/I] means an arbitrary variable[/U] A first number is written as x A second number is written as y [U]Twice a second number means we multiply y by 2:[/U] 2y [U]A first number plus twice a second number:[/U] x + 2y [U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U] x + 2y = 10 [U]Twice the first number means we multiply x by 2:[/U] 2x [U]Twice the first number plus the second:[/U] 2x + y [U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U] 2x + y = 35 Therefore, we have a system of two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 35 [/LIST] Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -20 [*]2x + y = 35 [/LIST] Because the x variables are opposites, we can add both equations together: (-2 + 2)x + (-4 + 1)y = -20 + 35 The x terms cancel, so we have: -3y = 15 To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-5 [/B] Now we substitute this y = -5 into equation 2: 2x - 5 = 35 To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get: x = [B]20[/B]

Andrea has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph, how long should she plan to spend walking back? Let the distance be d. Running full speed one way, 7d Walking back the opposite way, 3d And we know 7d + 3d = 6 hours 10d = 6 hours d =3/5 hour

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E. We find the range of this interval: Range = Upper Bound - Lower Bound Range = 0.479 - 0.039 Range = 0.44 Each piece on opposite sides of p gets: 0.44/2 = 0.22 So our expression becomes [B]p ± 0.22 [MEDIA=youtube]FGZcvcuWCpE[/MEDIA][/B]

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level. Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following: 1,684 - (-216) Since subtracting a negative is a positive, we have: 1,684 + 216 [B]1,900 feet[/B]

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina? [U]Assumptions and givens:[/U] [LIST] [*]Let Justin's age be j [*]Let Martina's age be m [*]j > m ([I]since Justin is older than Martina[/I]) [/LIST] We're given the following equations : [LIST=1] [*]j - m = 22 [*]j + m = 54 [/LIST] Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2) (j + j) + (m - m) = 22 + 54 2j = 76 To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%3D76&pl=Solve']type this equation into our math engine[/URL] and we get: j = 38 The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1): 38 - m = 22 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=38-m%3D22&pl=Solve']type it in our math engine[/URL] and we get: m = [B]16[/B]

Free Opposite Direction Distance Calculator - Word Problem calculator to measure distance between 2 people moving in opposite directions with rate and time solved for as well

Free Opposite Numbers Calculator - Given a positive or negative integer (n), this calculates the opposite number of n

opposite of twice the quotient of a and a the quotient of a and a: a/a 1 Twice the quotient of a and a 2(1) 2 Opposite means multiply 2 by -1: -1 * 2 [B]-2[/B]

Opuesto de 15 [URL='https://www.mathcelebrity.com/opposite.php?num=15&pl=Calculate']Escribimos lo contrario de 15 en nuestro motor de búsqueda y obtenemos[/URL]: [B]-15[/B]

I don't understand this word problem: If each of these shapes in Figure 1 were separated and filled with water, could the sphere that contains the cube hold all of the water? [I]Assume in the second image the corners of the cube touch the sphere so the diagonal from one corner of the cube to the opposite diagonal corner is the diameter of the sphere. [IMG]https://classroom.ucscout.org/courses/1170/files/191225/preview?verifier=mT7v59BhdVHalyprWq0KmBEItbf4CPWFqOgwoEa8[/IMG][IMG]https://classroom.ucscout.org/courses/1170/files/191494/preview?verifier=nsLscsxToebAVXTSYsoMr7rwIl536LrCJSDGPaHp[/IMG][/I] Could you guys help me please?

rectangle abcd prove: triangle adc is congruent to triangle bcd 1. Given: ABCD is a rectangle 2. AB = CD since opposite sides of rectangle are congruent 3. BC = AD since opposite sides of rectangle are congruent 4. AC = AC by the Reflexive Property of Equality 5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property

Scott and Dylan both leave the park at the same time, but in opposite directions. If Scott travels 12 mph and Dylan travels 19 mph, how long until they are 186 miles apart? Hour 1, they are 19 + 12 = 31 miles apart. So each hour, they get 31 miles more apart. When they are [URL='https://www.mathcelebrity.com/fraction.php?frac1=186%2F31&frac2=3%2F8&pl=Simplify']186 miles apart[/URL], we divide this by 31 miles apart per hour: 186/31 = [B]6 hours[/B]

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. (a) Which of the following is the hypothesis to be conducted? A. H0: p = 0.122, H1 p > 0.122 B. H0: p = 0.122, H1 p <> 0.122 C. H0: p = 0.122, H1 p < 0.122 (b) Which of the following is a Type I error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. c) Which of the following is a Type II error? A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% (a) [B]C H0: p = 0.122, H1: p < 0.122[/B] because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased. (b) [B]C.[/B] The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true c) [B]C.[/B] The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.

The difference between the opposite of a number and 6. The phrase [I]a number means[/I] an arbitrary variable, let's call it x. x The opposite of a number means we multiply by x by -1 -x The phrase [I]the difference between[/I] means we subtract 6 from -x: [B]-x - 6[/B]

The opposite of the difference of h and 5 The difference of h and 5 h - 5 The opposite of the difference of h and 5 means we multiply the difference of h and 5 by -1: -(h - 5) Distribute the negative sign: [B]5 - h[/B]

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages? [U]Givens[/U] [LIST] [*]Let Mr. Adam's age be a [*]Let Mrs. Benson's age be b [*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract: [/LIST] [LIST=1] [*]a + b = 55 [*]a - b = 3 [/LIST] Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2: (a + a) + (b - b) = 55 + 3 Combining like terms and simplifying, we get: 2a = 58 To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get: a = [B]29 [/B] If a = 29, then we plug this into equation (1) to get: 29 + b = 55 b = 55 - 29 b = [B]26 [MEDIA=youtube]WwkpNqPvHs8[/MEDIA][/B]

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is its angle of depression? The sin of the angle A is the length of the opposite side / hypotenuse. sin(A) = Opposite / Hypotenuse sin(A) = 193.4 / 1090/3 sin(A) = 0.1774 [URL='https://www.mathcelebrity.com/anglebasic.php?entry=0.1774&pl=arcsin']We want the arcsin(0.1774)[/URL]. [B]A = 10.1284[/B]