Mohan is standing at a distance of 4 units from the origin in the negative direction of the x- axis. His friend Sohan is standing at a distance of 7 units from the origin in the negative direction of the y- axis. Find the distance between them

8.06 units

Step-by-step explanation:

To obtain the distance, find the hypotenus using Pythagoras rule :

Hypotenus² = opposite² + adjacent²

Hypotenus² = 4² + 7²

Hypotenus² = 16 + 49

Hypotenus² = 65

Hypotenus = √65

Hypotenus = 8.06

Hypotenus = distance between the two points = 8.06 units

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.