(5/12 - 1/4) ÷ (1/3 + 1/16)​

8/9 = 0.421052632

Step-by-step explanation:

(5/12 - 1/4) / (1/3+1/16)

Least common multiple of 12 and 4 is 12. Convert 5/12 and 1/4 o fractions with denominator 12.

5/12 - 3/12 / 1/3+1/16

Since 5/12 and 3/12 have the same denominator, subtract them by subtracting their numerators.

5-3/12 / 1/3+1/16

Subtract 3 from 5 to get 2.

2/12 / 1/3+1/16

Reduce the fraction 2/12 to lowest terms by extracting and canceling out 2.

1/6 / 1/3 + 1/16

Least common multiple of 3 and 16 is 48. Convert 1/3 and 1/16 to fractions with denominator 48.

1/6 / 16/48 = 3/48

Since 16/48 and 3/48 have the same denominator, add them by adding their numerators.

1/6 / 16+3/48

Add 16 and 3 to get 19.

1/6 / 19/48

Divide 1/6 by 19/48 by multiplying 1/6 by the reciprocal of 19/48

1/6 x (48/19)

Multiply 1/6 times 48/19 by multiplying numerator times numerator and denominator times denominator.

1 x 48/6 x 19

Do the multiplications in the fraction 1 x 48/6 x 19

48/114

Reduce the fraction 48/114  to lowest terms by extracting and canceling out 6.

8/19

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.