Triangles ABC and DEF are similar and shown below. Which of the following is the length of DE

#1) 4; #2) 12 inches; #3) (-0.8, 2.4); #4) (3.5, 8.75); #5) 32 inches by 64 inches

Explanation:

#1) To get the image points, each pre-image point was multiplied by 4.  This means that the scale factor is 4.

#2) The perimeter of GAME is 177.  We know that three of the sides are 35, 56 and 56.  This means the fourth side, GA, would be

177-(35+56+56) = 177-147 = 30 inches

This means that GA to G'A' would have the same ratio as ME to M'E'; this gives us the proportion

Cross multiplying, we have

35(x) = 14(30)

35x = 420

Divide both sides by 35:

35x/35 = 420/35

x = 12

#3) To find the coordinates of I', we multiply the coordinates of I by the scale factor:

I' = (-2(2/5), 6(2/5)) = (-4/5, 12/5) = (-0.8, 2.4)

#4) To find the coordinates of S', multiply the coordinates of S by the scale factor:

S' = (2(7/4), 5(7/4)) = (14/4, 35/4) = (3.5, 8.75)

#5) The generic version is 3/8 the size of the brand name version.  This means that the brand name version is 8/3 of the generic version.  To find the dimensions of the brand name version, we multiply the dimensions of the generic version by 8/3:

12(8/3) = 96/3 = 32

24(8/3) = 192/3 = 64

The dimensions of the generic version are 32 by 64.

#1) 4; #2) 12 inches; #3) (-0.8, 2.4); #4) (3.5, 8.75); #5) 32 inches by 64 inches

Explanation:

#1) To get the image points, each pre-image point was multiplied by 4.  This means that the scale factor is 4.

#2) The perimeter of GAME is 177.  We know that three of the sides are 35, 56 and 56.  This means the fourth side, GA, would be

177-(35+56+56) = 177-147 = 30 inches

This means that GA to G'A' would have the same ratio as ME to M'E'; this gives us the proportion

Cross multiplying, we have

35(x) = 14(30)

35x = 420

Divide both sides by 35:

35x/35 = 420/35

x = 12

#3) To find the coordinates of I', we multiply the coordinates of I by the scale factor:

I' = (-2(2/5), 6(2/5)) = (-4/5, 12/5) = (-0.8, 2.4)

#4) To find the coordinates of S', multiply the coordinates of S by the scale factor:

S' = (2(7/4), 5(7/4)) = (14/4, 35/4) = (3.5, 8.75)

#5) The generic version is 3/8 the size of the brand name version.  This means that the brand name version is 8/3 of the generic version.  To find the dimensions of the brand name version, we multiply the dimensions of the generic version by 8/3:

12(8/3) = 96/3 = 32

24(8/3) = 192/3 = 64

The dimensions of the generic version are 32 by 64.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The total nom of  code that can be used is equal to 5+3 = 8

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The answer is in the image 

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students  

Let the father's age be x and son's be y

10 years before-

Father age=x-10

sons age=y-10

Given,

x-10=10(y-10)

x-10=10y-100

Given present age of father=40

therefore,

x=40

40-10=10y-100

10y-100=30

10y=130

y=130/10

y=13

Therefore present age of son=13years