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question:Michelle uses 40 beads in making a necklace. She uses x blue beads and 2 times as many red beads as blue beads. Then she uses the same number of white beads as the blue and red beads combined. If the rest of the beads she uses are silver, She uses 10 silver beads. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of blue beads Michelle uses. Let's break down the information given: Number of blue beads: x Number of red beads: 2x (twice as many as blue beads) Number of white beads: x + 2x (same as blue and red beads combined) Number of silver beads: 10 Total number of beads used: 40 We can set up the equation as follows: Number of blue beads + Number of red beads + Number of white beads + Number of silver beads = Total number of beads used x + 2x + (x + 2x) + 10 = 40 Let's simplify and solve for x: 6x + 10 = 40 To isolate x, we subtract 10 from both sides of the equation: 6x + 10 - 10 = 40 - 10 6x = 30 To solve for x, we divide both sides of the equation by 6: x = 30 / 6 x = 5 The value of x is 5. 5 The answer is: 5
question:For what positive value of n does |3+ni|=3sqrt{10}?
answer:Recall that the absolute value of a complex number a+bi is sqrt{a^2+b^2}. So, |3+ni|=sqrt{3^2+n^2}. Setting this equal to 3sqrt{10}, we get sqrt{3^2+n^2}=3sqrt{10}. Squaring both sides, we get 3^2+n^2=(3sqrt{10})^2=90. Simplifying, we have n^2=81, so n=boxed{9}. The answer is: 9
question:w many toy blocks did Pablo use in total if he made 4 stacks of blocks, with each stack having a specific height? The first stack was 5 blocks tall, the second stack was 2 blocks taller than the first, the third stack was 5 blocks shorter than the second, and the last stack was 5 blocks taller than the third.
answer:The first stack was 5 blocks tall. The second stack was 2 blocks taller than the first, so it was 5 + 2 = 7 blocks tall. The third stack was 5 blocks shorter than the second, so it was 7 - 5 = 2 blocks tall. The last stack was 5 blocks taller than the third, so it was 2 + 5 = 7 blocks tall. To find the total number of blocks used, we add up the number of blocks in each stack: 5 + 7 + 2 + 7 = 21 blocks. 21 The answer is: 21
question:When the base-12 integer 1531_{12} is divided by 8, what is the remainder?
answer:We can convert the base-12 integer to base-10 to make the division easier. 1531_{12} = 1 cdot 12^3 + 5 cdot 12^2 + 3 cdot 12^1 + 1 cdot 12^0 = 1 cdot 1728 + 5 cdot 144 + 3 cdot 12 + 1 cdot 1 = 1728 + 720 + 36 + 1 = 2485. Now we divide 2485 by 8 using long division. begin{array}{c|cccc} 8 & 2485 & cline{2-2} & 3 & cline{2-2} & 24 & cline{2-3} & 8 & 5 cline{2-3} & 8 & 0 cline{2-3} & 0 & end{array} The remainder is boxed{5}.The answer is: 5