Let's say Als frog jumped x inches Fred's frog jumped 7x inches   7x + x = 56 8x = 56 x = 7   Fred's frog = 7x = 7* 7 = 49 inches

Number of students creating a dessert = d Number of students creating an appetizer  = d + 7 Number of students creating two dishes = total number of students - total number creating single dish = 50 - (d+d+7) = 50 -(2d+7) According to the problem the above is...

Moving -3/2 to the other side of the equals sign changes the -ve sign to a +ve 3/2 (5/3)d = -1/2+3/2 (5/3)d = 1 d = 1/(5/3) = 3/5

Number of seagulls in the flock now = 1/3 * 12 = 4 seagulls Number of ducks -= 12 - 4 = 8 ducks Let x be the new seagulls that should join the flock to make the ratio change to 19:8 Total number of birds = x+12 Total number of seagulls = x+4 , since all the birds that...

Add 3/8 on both sides n - 3/8 + 3/8 = 1/8 +3/8 Therefore, n  = 1/8 + 3/8 = (3+1)/8  = 4/8  = 1/2

X2- 8x + 3x - 24 =0 x(x-8) +3(x-8) = 0 (x+3) (x-8)   = 0 x  = -3, 8 answer c.

x = sqrt (4) x = +2 , - 2 answer a.

= -2^4 x^3 y^6/(-2^2 x^-2 y^-3) = -2(4-2)   x(3+2)    y(6+3) = -22 x5  y9 = 4x5  y9  Answer d.

X2-10X+3X-30 = X(X-10)+3(X-10) = (X-10) (X+3)

y = -3x-6 comparing the above line in the form: y  = mx +c m = -3 The equation of the line perpendicular to the above line  will have the slope m = 1/3 ( opposite reciprocal) so the equation of the line passing through ( -1, 5) using the slope intercept form...

a) l (brightness) = 19/  (4 * 22) watt per sq. meter The brightness/intensity of the light varies inversely to the distance you are from the source of light, if d is increased to 3 meters for example, the brightness decreases even further.   b) The sum of the intensities of...

(2.5x 103) (4.2 x 102) = (2.5 x 4.2) x ( 103+2 ) = 10.50 x 105 Answer is c.

(3x2/5y3)-2 = 1/(3x2/5y3)2 = (5y3)2/(3x2)2 = 25y6/9x4 Answer is d.

(4x2y3  ) (5x-3 y-2 z0) Rearranging, = (4*5) x(2-3) y(3-2) (1) Note: z0 = 1 = 20 x-1y = 20y/x Could you please check d., Appears to be a typo.

Find the homogeneous solution first by writing the characteristic equation: r^4 - 1 = 0 (r^2 + 1) ( r^2-1) = 0 r = 1, -1, i, -i The homogeneous solution is of the form: yh = c1et + c2 e-t + c3 cos(t) + c4 sin (t) Particular solution can be solved in 2 steps...

if you have a bunch of points represented as (x,y) and if you are able to plot the points on a graph and connect all the lines using a straight line using a scale, you can say the relationship is linear. for ex: speed of travel  (x-axis)            ...