5841 Shares

Super hard algebra, prove your math skills!?

Super hard algebra, prove your math skills!? Topic: Super hard algebra, prove your math skills!?
June 16, 2019 / By Chrystal
Question: Solve the verbal problem with a quadratic equation 1. The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. Find the dimensions. length = 2w+3, width = w. 2. The width of a rectangle is two-thirds of its length, and its area is 216 square meters. Find the dimensions. length = L, width = 2/3L
Best Answer

Best Answers: Super hard algebra, prove your math skills!?

Avis Avis | 7 days ago
1) Because area = lw, this gives the equation 'w(2w + 3) = 65'. Distributing gives 2w^2 + 3w - 65 = 0 The Quadratic Formula is {-b ± sqrt(b^2 - 4ac)}/2a. a = coefficient of w^2, 2 b = coefficient of w, 3 c = the constant, -65 Now you have everything you need to do this on your own. 2) L(2/3L) = 216. 2/3L^2 - 216 = 0. Now repeat the steps shown in problem 1, knowing that b will be 0 because there is no x.
👍 182 | 👎 7
Did you like the answer? Super hard algebra, prove your math skills!? Share with your friends
Avis Originally Answered: Super hard!math problem need help!?
Hi, The first boy takes 1/3 of the coins and leaves 2/3 of the coins. The second boy takes 1/3 of the remaining 2/3, which is 1/3 x 2/3 =2/9 of the original amount. The 1/3 the first boy took plus the 2/9 the second boy took adds up to 5/9 of the original number of coins, meaning only 4/9 of the original coins are there when the third boy gets up. The third boy takes 1/3 of 4/9 which is 4/27 of the original coins. Adding this 4/27 onto the 5/9 the original 2 boys took means they have taken 19/27 of all of the coins. That means the remaining 216 coins the leprechaun fins are only 8/27 of his original amount. You can find that original amount by setting up a proportion and cross-multiplying it to solve. 8_____216 === = ===== 27_____x underlines are for spacing purposes 8x = 27(216) 8x = 5,832 x = 729 This is the amount the leprechaun had originally. Boy 1 had 1/3 of 729 or 243 coins Boy 2 had 2/9 of 729 or 162 coins Boy 3 had 4/27 of 729 or 108 coins 216 + 243 + 162 + 108 = 729, the original amount I hope that helps!

Abigayle Abigayle
1) area=65=(2w+3)*w=2w2+3w implies 2w2+3w-65=0 (2w + 13)(w - 5)=0 implies 2w+13=0 implies w= - 13/2 impossible or w-5 =0 implies w=5 inches and L = 13 inches 2) 216 = L*2/3L=2/3L2 implies L2 = 3*216/2=324 IMPLIES L= 18 and w =12
👍 70 | 👎 0

Stu Stu
1) w*(2w+3)=65 ------ 2w^2 +3w-65=0 you will need to do the Pythagorean theorem for this one. I don't really feel like doing it but it is just plugging in numbers. 2) 2/3L*L=216 ------- 2/3L^2=216 ----- L^2=324-------- L=18 meters^2
👍 64 | 👎 -7

Pancras Pancras
area = width*length area = 65 in^2 = (2w + 3)*w 2w^2 + 3w = 65 w + (3/2)w = 65/2 (w + 3/4)^2 = 529/16 w = 5.75 - 0.75 = 5 in therefore length = 2(5) + 3 = 13 area = 65 = width*length = 5*13 The second one is done the same way
👍 58 | 👎 -14

Livy Livy
1. 65=(2w+3)w 65=2w^2+3w 0=2w^2+3w-65 0=(w-5)(2w+13) w=5 2w=-13, w= -13/2 (width can't be negative so this value is not the answer. Therefore, w=5 in l=2w+3 l=2(5)+3 l=13 in 2. w=2/3L, A=lw 216=L(2/3L) 216=2/3L^2 2/3L^2-216=0 3/2(2/3L^2-216)=3/2(0) L^2-324=0 L^2=324 L=√324 L=18 m w=2/3L w=2/3(18) w=12m
👍 52 | 👎 -21

Jashub Jashub
1. 2w^2 + 3w -65 = 0 (w-5)(2w+13) = 0 w = 5 l = 13 2. 2L^2/3 = 216 L^2 = 3*216/2 = 144 L = 18 W = 12
👍 46 | 👎 -28

Jashub Originally Answered: super hard math problem. I can't solve it, need help?
AC : y = x + a, so A(-a,0) y = x^2 = x + a x^2 - x - a = 0 (x - 1/2)^2 = a + 0.25 x = 0.5 +- √(a+0.25) B with the -ve x, so B(0.5 - √[a+0.25],Yb) and C(0.5 + √[a+0.25],Yc) B is the middle /center point of AC, so 2(0.5 - √[a+0.25]) = -a + [0.5 + √(a+0.25)] 0.5 + a = 3√[a+0.25] (a^2 + a + 1/4) = 9(a + 1/4) a^2 - 8a - 2 = 0 (a - 4)^2 = 2 + 16 a = 4 +- 3√2 since a > 0, a = 4 + 3√2 y-intercept = a = 3√2 + 4 = 8.24264

If you have your own answer to the question Super hard algebra, prove your math skills!?, then you can write your own version, using the form below for an extended answer.