Before painting a picture on canvas, an artist must stretch the canvas on a rectangular wooden frame. To be sure the angles are true right angles, the artist can measure the diagonals of the stretched canvas. What should be the diagonal measure of a canvas whose sides are 55 inches and 1212 inches in length?

9514 1404 393

  13 inches

Step-by-step explanation:

The Pythagorean theorem can help. The square of the diagonal is the sum of the squares of the sides:

  d^2 = 5^2 +12^2 = 25 +144 = 169

  d = √169 = 13

The diagonal measure is 13 inches.

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Additional comment

The integer triple (5, 12, 13) is called a "Pythagorean triple." One of the more famous ones is (3, 4, 5). Another one commonly seen in Algebra problems is (7, 24, 25). It is worth noting these, as they show up often.

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

(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