Henry2,

Vp = L*W*h = 1/2 * 1/2 * 3/4 = 3/16 m^3 = Vol. of prism. Vc = L*W*h = 1/12 * 1/12 * 1/12 = 1/1728 m^3 = Vol. of cube. Vp/Vc = (3/16)/(1/1728) = 3/16 * 1728/1 = 324 Cubes.

6 years ago

h = 0.5g*t^2 = 0.8 m. 4.9t^2 = 0.8, t = 0.404 s. d = Xo * t = 3.37 * 0.404 =

6 years ago

1. (140 - 8 ) - 12x => 0. -12x => -132, X =< 11 Chicken pizzas. Note: When dividing or multiplying by a negative number, the inequality sign is reversed.

6 years ago

2. 240 + 0.06*x => 600. X => ?

6 years ago

KE = 0.5*M*V^2.

6 years ago

The ratios should be equal if linear: 35/1 = ? 50/2 = ? 70 /3 = ? 90/4 = ?.

6 years ago

2x/3 = 1 1/2. 2x/3 = 3/2, Multiply both sides by 6: 4x = 9, X = 9/4 = 2 1/4.

6 years ago

10 Pumps: Rate = 40,000L/3h = 13,333.3 L/h. 9 Pumps: Rate = 9/10 * 13,333.3 = 12,000 L/h. T = 60,000/12000 = 5 Hours.

6 years ago

1. V = Vo + g*Tr = 0. 18 + (-9.8)Tr = 0, Tr = 1.84 s. = Rise time. Tf = Tr = 1.84 s. = Fall time. Tr + Tf = 1.84 + 1.84 = 3.68 s. = Total time in air or hang time. 2. V^2 = Vo^2 + 2g*h = o. 18^2 + (-19.6)h = 0, h = 16.53 m.

6 years ago

V = I * R = 10*10^3 * 0.2*10^-3 = 2.0 Volts.

6 years ago

(-1, 5), (x, y), (4, -3). x - (-1) = 4 - x. X = 3/2 = 1.5. y - 5 = -3 - y. Y = 1.

6 years ago

Log6 1296 = x. 6^x = 1296, x*Log 6 = Log1296, X = Log1296/Log6 = 4.

6 years ago

Eq1: x * y = 21.In Eq1, replace X with y = 21/x. Eq2: x + y = 10. In Eq2, replace Y with 21/x and solve for X: x + 21/x = 10. Multiply both sides by X: x^2 + 21 = 10x, x^2 - 10x + 21 = 0, (x-3)(x- 7) = 0, X = 3, or X = 7. In Eq1, replace X with 3 and solv...

6 years ago

Note: The first line of my response should be Eq1: x * y = 21.

6 years ago

99 = 1/2(2h+4)h. 99 = (h+2)h, 99 = h^2 + 2h, h^2 + 2h - 99 = 0. Solve for h: h = (-B +- Sqrt(B^2-4AC))/2A. h = (-2 +- Sqrt(4 + 396))/2, h = (-2 +- 20)/2 = -1 +- 10 = 9, and -11 Ft. Use the positive number: h = 9 Ft.

6 years ago

90/6 * T = 300. 90T = 1800, T = Time in days.

6 years ago

Length = L. Width = 2L-3. A = L * W = 170. L * (2L-3) = 170. 2L^2 - 3L - 170 = 0, L = (-B +- Sqrt(B^2-4AC))/2A. L = (3 +- Sqrt(9 + 1360))/4, L = (3 +- 37)/4 = 0.75 +- 9.25 = 10, and -8.5. In. Use positive value: L = 10 In.

6 years ago

Answer: B.

6 years ago

756ft. * 1in/280ft. =

6 years ago

6ft.-1in = 6 1/12 Ft. = 6.0833 Ft. = Actual width. Scale = 6.0833ft/4in = 1.52 Ft./in.

6 years ago

Paycheck = $X. Cost of coat = $X/4. x - x/4 = 96. 4x - x = 384, X = 128. x/4 = 128/4 = $32.

6 years ago

Tax = 98 * 7.65%/100% = $7.50. Tax = 240 * 7.65%/100% = Tax = 150 * 7.65%/100% =

6 years ago

m1 = -A/B = 3/6 = 1/2. m2 = -A/B = 3/6 = 1/2. So the lines are parallel, because they have equal slopes. Parallel lines do not intersect. Therefore, there are no solutions.

6 years ago

Given: M1 = 5000kg, Vi = 3m/s. M2 = 2500kg, V2 = 0 before taut. V3 = Velocity of M1 after taut(tight). Momentum before taut = Momentum after taut. M1*V1 = (M1+M2)V3. 5000 * 3 = 7500*V3, V3 = 2 m/s. Note: The car is not a part of the system until the rope...

6 years ago

(-4, 6), (x, y), m = 3/4. m = (y-6)/(x-(-4)) = 3/4. cross multiply: 4(y-6) = 3(x+4), y-6 = 3/4(x+4).

6 years ago

305*10^-5/250.75 = 1.21635*10^-5 = 0.0000121635.

6 years ago

94.00 + 15 + 182.113 = 291.113.

6 years ago

8.000/532 = 0.015

6 years ago

Wavelength = V * 1/F = V/F = 331/15 = 22.07 m. Note: 15 Hz means 15 cycles/second. The wall sockets in our homes are 60 cycles/second(cps). 9 cps).

6 years ago

As = 45/360 * pi*r^2 = 45/360 * pi*144 = 18pi in.^2.= Sector area.

6 years ago

a. 75 = (73+82+73+77+77+G)/6 < 80. 75 = (382 + G)/6 < 80, Multiply by 6: 450 = (382+G) <480, 450-382 = G < 480 - 382, 68 = G < 98, So he will need a grade(G) of at least 68 but less than 98. b. (73+82+73+77+77+G)/6 = 80. (382+G)/6 = 80. G = ?

6 years ago

I'm assuming 1/4x means (1/4)x or x/4. Y = -x + 5. Y = x/4 + 10. In Eq2, replace Y with -x + 5: -x + 5 = x/4 + 10 Multiply both sides by 4 and solve for x: -4x + 20 = x + 40. -5x = 20, X = -4. In Eq1, replace x with -4 and solve for Y: Y = -(-4) + 5 = 9....

6 years ago

8ft. * 12in/ft * 2.54cm/in. = 243.64 cm. 12ft * 12in/ft * 2.54cm/in = 365.76 cm. Ab = 243.84 * 365.76 = 89,187 cm^2. = Area of bathroom. 4cm * 4cm Tiles. Ab/At = 89,187/16 = 5575 Tiles. Cost = 5575 * 0.19 = $1059.10. 8cm * 8 cm Tiles: Ab/At = 89,187/64 =...

6 years ago

Temp. = 6 - 4*9 =

6 years ago

Assumption: F1 = 60N. @ 0o. = F2 = 80N @ 90o. Fr = Sqrt(60^2 + 80^2) = 100N. = Resultant force. TanA = F2/F1 = 80/60. A = 53.1o = Direction.

6 years ago

116Copies/4min. * 60min/h * 1.25h = 2175 Copies.

6 years ago

Salary = $X. Gave $X/6 to her mother. Bal. = X - X/6 = 5x/6. Amt.saved = 2/5 * 5x/6 = 10x/30 = $X/3. Fraction saved = (x/3)/x = x/3 * 1/x = 1/3.

6 years ago

1 cup = 8 oz. 7 3/8cups - 3 4/8cups = 59/8 - 28/8 = 31/8 = 3 7/8 cups.

6 years ago

Divide Eq2 by 2 and you will get 7x - 3y = 3. So the Eqs are identical. Therefore, we have an infinite number of solutions.

6 years ago

Eq1: 4x + 6y = 21. Eq2: 7x - 3y = 3. Multiply both sides of Eq2 by 2 and add the Eqs: 4x + 6y = 21 14x - 6y = 6 Sum: 18x = 27. X = 1 1/2 = 3/2. In Eq1, replace x with 3/2 and solve for y.

6 years ago

Please disregard my first response; I misunderstood the problem.

6 years ago

Ap/As = (6000cm * 120cm)/(12*7.5) = 8000 stones.

6 years ago

36mi/4gal = 9mi/1gal. 1. 9/1 = 9/g. g = gal. used. 3. 9/1 = d/7. d = miles traveled. 4. 9/1 = 81/g. 5. 9/1 = d/10.

6 years ago

V^2 = Vo + 2a*d. 2^2 = 0 + 2a*1, a = 2m/s^2.

6 years ago

V = Vo + a*t = 0. 20 + a*0.002 = 0, a = -10,000 m/s^2. V^2 = Vo^2 + za*d = 0. 20^2 + (-20,000)d = 0, d = 0.02 m.

6 years ago

8000 + 300n = 700n.

6 years ago

He charged $X per sandwich. $Y per drink Eq1: 2x + y = 10. Eq2: x + y = 6.5. Subtract Eq2 from Eq1 and get X = 3.50. In Eq2, replace x with 3.50 and solve for Y.

6 years ago

Monthly fee = $X. 100 + 12x = 700.

6 years ago

20in/46in = 10/23.

6 years ago

I = P*r*t = 5000*0.045*2 =

6 years ago

Deposit = $X per mo. x/mo. * 12mo. = $12x/yr. 12mo./10mo * x/mo. = $1.2x/mo. (1.2x/x) * 100% = 1.2 * 100% = 120%. % increase = 120% - 100% = 20%.

6 years ago

5/7 = B/G. 5/7 = B/56, 7B = 280, B = ?

6 years ago

12tacos * (1/8) Lb/taco = 12/8 = 1.5 Lbs.

6 years ago

1. V^2 = Vo^2 + 2g*h = 0 + 19.6*50 = V = ? 2. 0.5g*t^2 = 50. 4.9t^2 = 50, 3. F = M*g = 2 * 9.8 =

6 years ago

T = 6 - (2/5+1/2)6 = 6 - (4/10+5/10)6 = 6 - (0.9)6 = 0.6 h.

6 years ago

F1 = M*g = 300*9.8 = 2940 N. F2 = ? F1*d1 = F2*d2. 2940 * 0.5 = F2 * 1.5, F2 = ?

6 years ago

X meters = Total distance. X - x/4 = 3x/4 meters remaining. 3x/4 - (3/5*3x/4) = 3x/4 - 9x/20 = 15x/20 - 9x/20 = 6x/20 = 3x/10 m. left. 3x/10 = 3600. 3x = 36,000, X =

6 years ago

Given: E = 120 volts. R1 = 27 Ohms. R2 = 47 Ohms. X1 = j50 Ohms. X2 = j40 Ohms. , Z = (R1+R2) + j(X1+X2) = Total impedance. Z = 74 + j90 = 116.5 Ohms[50.6o]. Z = Sqrt(74^2+90^2. Tan A = 90/74. I = E/Z = 120[0o]/116.5[50.6o] = 1.03Amps[-50.6o]. The negativ...

6 years ago

V = Vo + g*t = 0. 40 + (-10) t = 0,

6 years ago

a*t = 40. 5t = 40, t = 8 s. V = a*t = 5(8+1) = 45 m/s.

6 years ago

1.4 * 1.8*10^-4/oC * (51-20)oC = 0.0078 L. = 7.8mL increase in volume. 7.8 - 7,6 = 0.2 mL saved. 1.4 * K * (51-20) = 0.2mL. K = 4.61^10^-3 /oC,

6 years ago

Please save a slice for me! LOL

6 years ago

Compliment: 6.3 + X = 90o. Supplement: 6.3 + X = 180o.

6 years ago

20 - 14 = 6 People do not like chocolate. 6/20 * 100% =

6 years ago

cot A = -0.5. cot A = 1/Tan A, 1/Tan A = -0.5, Tan A = -2.0. A = -63.4o(CW). = 296.6o CCW. Yes, the cot can = -0.5.

6 years ago

r = d/t = 226/2 = 113 mi./h. d = r * t = 113 * 8 =

6 years ago

(1/2x-3)(4x-1/3). 2x^2 - 1/6x - 12x + 1, 2x^2 - 73/6x + 1.

6 years ago

0.5g*t^2 = 10. 4.9t^2 = 10, t = 1.43 s.

6 years ago

Y = mx + b. Y = mx + 18.

6 years ago

In Eq2, replace Y with -x + 5: -x + 5 = x/4 + 10. Multiply both sides by 4: -4x + 20 = x + 40, X = -4. In Eq1, replace X with -4 and solve for Y: Y = -(-4) + 5 = 9. Solution:(-4, 9). .

6 years ago

m<1 = 53. m < 4 = 4 * 53 , m < 4 = 212.

6 years ago

F(x) = x^2 + x - 20. x^2 + x - 20 = 0, (x-4)(x+5) = 0, x-4 = 0. X = x + 5 = 0. X =

6 years ago

(1, -3), (3, 1). m = (1-(-3)/(3-1) = 4/2 = 2. Y = mx + b. -3 = 2*1 + b, b = -5. Y = 2x - 5.

6 years ago

P = F*d/t = (M*g)*d/t = (500)*5/5 = 500 J./s = 500 Watts.

6 years ago

X = 180 - (90+45) =

6 years ago

TE = Total energy. TE = PE + KE. TE = M*g*h + 0 = 8*9.8*100 = 7840 Joules @ 100m. V^2 = Vo^2 + 2g*d = 0 + 19.6*40 = 784, V = 28 m/s. TE = Mgh + KE = 8*9.8*60 + 0.5*8*28^2 = 7840 J. @ 60m. Yes, there is no change in TE.

6 years ago

4d = 1/2 * 1/4. 4d = 1/8, d = (1/8)/4 = 1/8 * 1/4 = 1/32.

6 years ago

1. Given: M1 = 80kg, V1 = 6.0m/s. M2 = 100kg, V2 = -3.0m/s. V3 = Velocity of M1 and M2 after colliding. Momentum before = Momentum after. M1*V1 + M2*V2 = M1*V3 + M2*V3. 80*6 + 100*(-3) = 80V3 + 100V3, 480 - 300 = 180V3, V3 = 1m/s in the direction of M1 be...

6 years ago

1a. PE change = PE2 - PE1 = Mgh2 - Mgh1 = (10*9.8*1.8) - (10*9.8*1.0) = 1b. W = F*d =(M*g) * d = (98) * 0.8 Joules. 3. What is the direction of the plane? 4. Vo = 15m/s[60o]. a. Xo = 15*Cos60 = 7.5 m/s = Hor. component of initial velocity. Yo = 15*sin60 =...

6 years ago

a. Mrs. Walters: 360mi./25gal. = b. Mr. Walters: 480mi./32gal. =

6 years ago

Another approach. 1/4^3*4^n = 1/256, Invert both sides: 4^3*4^n = 256, 64*4^n = 256, 4^n = 4, n*Log4 = Log4, n = Log4/Log4 = 1. 84 6n =

6 years ago

(12,000/4,000) * 100% = 300%, %Change = 300% - 100% = 200%.

6 years ago

V^2 = Vo^2 + 2a*d = 0. 500^2 + 2a*0.1 = 0, a = -1,25*10^6 m/s^2. F = M*a = 1*10^-2 * 1.25*10^6 = -1.25*10^4 = -12,500 N. Work = F*d = 12,500 * 0.1 = -1250 Joules. Note: The negative sign means that the force opposes the bullet motion.

6 years ago

A(2, 5), B(3, 1). m = (1-5)/(3-2) = -4. Y = mx + b. 5 = -4*2 + b, b = 13 = Y-intercept. Eq: Y = -4x + 13. Slope-intercept form. 4x + y = 13. Standard form.

6 years ago

Speed of slowest cyclist = X mi/h. Speed of Fastest cyclist = 2x mi/h. d = 4*x + 4*2x = 84. 4x + 8x = 84, 12x = 84, X = 7 mi/h. 2x = 14 mi/h.

6 years ago

Vo = 108km/h = 108,000m/3600s. = 30 m/s. V = Vo + a*t = 0. 30 + a*15 = 0, a = -2 m/s^2.

6 years ago

42/6 = Y/1. Y = 7.

6 years ago

If two sides of a triangle are equal, the angles opposite the sides are equal.

6 years ago

72 + A = 90o.

6 years ago

Friend collected X cans. You collected 4x/5 cans. x + 4x/5 = 180. 5x + 4x = 900,

6 years ago

1/2x + 1/3y = 5, and 1/4x + y = 0. Multiply the 1st Eq. by 6 and the 2nd Eq. by 12 and subtract: Eq1: 3x + 2y = 30. Eq2: 3x + 12y = 0. Diff,: -10y = 30, Y = -3. In Eq1, replace Y with --3 and solve for X: 3x + 2(-3) = 30. X = 12.

6 years ago

a. Vb - 5i = 9. Vb = 9 + 5i = 10.3km/h[29.1o] N. of E. = Velocity of boat. b. d = V*t = 1.5. 9 * t = 1.5, t = 0.166h = 10 min.

6 years ago

Vb + 3 = 10i. Vb = -3 + 10i = 10.44km/h[-73.3o] = 10.44km/h [106.7o] CCW. = 16.7o W. of N. d = V * t = 5 km. 10t = 5, t = 0.5h.

6 years ago

L = 284cm * 15ft/cm =

6 years ago

Do you mean the Sum = 15? If so: X = The larger #. x-1 = Smaller #. x + (x-1) = 15. X = 8. X-1 = 8 - 1 = 7.

6 years ago

n * 100% = 4%. n = 4%/100% = 4/100 = 1/25.

6 years ago

1. Ratio = 12/(18+12) = 2. 6/9 = 18/27. This is correct, because the numerator and denominator has been multiplied by the same #(3). 3. Cost = 29.85/3 = 4. 35words/min * 7min = 5.

6 years ago

Complement: 53 + A = 90o. Supplement: 53 + A = 180.

6 years ago

2/4 = 12/24. 2/3 = 16/24. 2/8 = 6/24. 2/6 = 8/24. Put them order.

6 years ago

135berries/15min = 9 berries/min. 9 * T = 486.

6 years ago