2. A drawing of a sailboat was made using a rectangle and two right triangles, as shown. What
is the area of the drawing of the sailboat in square centimeters?

  45 square centimeters

Step-by-step explanation:

The area of the triangle is given by ...

  A = (1/2)bh

where b is the base, 2 cm + 3 cm = 5 cm, and h is the height, 6 cm.

  A = (1/2)(5 cm)(6 cm) = 15 cm^2

__

The area of the rectangle is given by ...

  A = bh

where b is the base, 12 cm, and h is the height, 2.5 cm.

  A = (12 cm)(2.5 cm) = 30 cm^2

__

The area of the whole figure is the area of the triangle added to the area of the rectangle:

  drawing area = 15 cm^2 + 30 cm^2 = 45 cm^2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form