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# If the ratio of grapes to walnuts to oranges is 9:3:11, how many grapes are there if the total number of fruits is 161? (answer)

add the numbers together: 9+3+11 = 23 you want the ratio of total number of grapes to total number of fruits this should be consistent no matter how many fruits you have, so: 9/23 = x/161 cross-multiply and solve for x (number of grapes in a total of 161 fruits) 23x = 9*161 --->...

okay, that's an upside-down U and the maximum value is at the top  if you put the function in vertex form you can easily find the vertex: group the first two terms and factor out the negative (essentially factoring out -1): p = - (x²-14x) + 54 complete the square by taking the middle...

bring all terms to one side and set equal to 0 4n²+12n+6=0 factor out 2 2(2n²+6n+3)=0 ===> 2n²+6n+3=0   complete the square 2(n²+3n+9/4) + 3 = 0 + 9/2 ===> 2(n+3/2)² = 3/2 ===> (n+3/2)² = 3/4 take square root of both sides (n+3/2)=±√3/2 solve for n n = (-3+√3)/2 =...

# 80 lettertiles 10 of the tiles are e's 2 are g's ratio of e's to g;s (answer)

10 e's ---------  = 10/2 = 5/1 = 5 2 g's

# 5m^2+12m+6=0 complete the square (answer)

separate the first two terms on the left and factor out 5 5(m² + (12/5)m ) + 6 = 0 take half the middle coefficient (12/5), square it, and add it to the terms in parentheses 5(m² + (12/5)m + 36/25) + 6 = 0 + 36/5 (this has the effect of adding 36/5 to both sides) simplify and rearrange: 5(m...

assuming those are 3 terms and not 2 you should start by noting all restrictions for x. In this case, x cannot be 0 because we can't divide by 0. multiply both sides by the lcm (2x) 9 + 2x = 8 ===> 2x = -1 ===> x = -1/2

# (-9x² + 6x + 2) + ( 4x² - x -1)= (answer)

you need to simplify the expression by collecting like terms: (-9 + 4)x² + (6 + -1)x + (2 + -1) = -5x² + 5x + 1

# f(x) =2x-1 a) Determine the range value when the domain value is 0. b) Determine the domain value when the range value is 5. (answer)

range value is the y value domain value is the x value (a) find y when x = 0     y = 2x-1 = 2(0)-1 = -1 y = -1 (b) find x when y = 5 5 = 2x-1 6 = 2x x = 3

# Which equation has roots of -3 and 5 (answer)

if the roots are r1 and r2, then the simplest equation is the quadratic: (x-r1)(x-r2) = 0 since yours are -3 and 5, the simplest (quadratic) equation is: (x - -3)(x - 5) = 0 (x+3)(x-5) = 0 which expands to x²-2x-15 = 0

# Angie borrowed \$400 from her parents at 6.5% simple interest for 3 years. What is the total amount Angie must repay? (answer)

simple interest equations: A = P(1+rt) = P + Prt             I = Prt                       A = accumulated amount P = principal r = interest rate t = time (in years)     angie borrowed \$400 (P), so she has to pay it back with interest (I) I = Prt = \$400*0...

# Dave purchased a \$24000 life insurance policy at the price of \$31 per \$1000 of coverage. If he pays the premium quarterly, how much is each installment? (answer)

Cost = \$31/\$1000  *  \$24000 = \$744 Quarterly payment = \$744 / 4 = \$186

# what's the ordered pair of y=2X-5 and 4X-Y=7 ? (answer)

4x  - y = 7 -2x + y = -5             (rearranging the first equation) --------------------------------------------- 2x        = 2             (adding the two equations) x = 1 y = 2(1)-5 = -3      (substituting the value for x in the first equation)   x=1, y=-3...

check the number of digits in the number you have 3 possibilities: 1-digit numbers 2-digit numbers 3-digit numbers the only 3-digit candidate you have is 100 and that results in a 1, so this is an easy case for a 1-digit number the only way for the digits to add to 1 is for that number to be =...

# what are four consecutive integers whose sum is 86? (answer)

suiye is right, and that way is probably even quicker, but another way to arrive at the answer is to set up an equation four consecutive integers: x, (x+1), (x+2), and (x+3) sum them up and get 86 x + x+1 + x+2 + x+3 = 86 now solve for x, the smallest one 4x + 6 = 86 4x =...

they ask for parametric equations and they give you the speed this is really projectile motion (the ball is moving both in the x and y dir. due to downward acceleration) but to answer the question you only need the quantities for the x-dimension: v(t) = 140           x(t) = 140t   from...

# 2 dimensional motion problem (answer)

(a) from  a = v²/r  we get  0.86 = v²/3.6 which leads to v = 1.76 m/s period is the time it takes to complete a full cirle (your distance) from v = d/t we get 1.76 = 2π(3.6) / T which leads to T = 12.9s     (b) again from v = d/t we get v = 2π(1.9)/12.9 which...

# 1\4 x + 1\2 y= -8 using y+mxtb (answer)

multiply both sides by 2 1/2 x + y = -16 rearrange, leaving y alone on one side y = -1/2 x - 16