2. the sum of three consecutive even
integers is 72. what are the three
numbers?
3. latanya buys 5 yards of blue fabric
and 8 yards of green fabric. the
blue fabric costs $2 more per yard
than the green fabric. she pays a
total of $62. what would be the
combined cost of 1 yard of blue
fabric and 1 yard of green fabric?
@ $6
ⓡ $10
© $9
0 $14
4. how many solutions are there to
this equation?
5x+ 2-2(x - 1) = 3x + 4
@ no solution
exactly one solution
© at least two solutions
stions

hypotenuse (h) = 17 cm

using area of a triangle formula to solve for x

A = bh ( b is the base and h the height )

× 5x(3x - 1 ) =60 ( multiply through by 2 )

5x(3x - 1)=120

15x² - 5x - 120 = 0 ← in standard form ( divide all terms by 5 )

3x² - x - 24 = 0

consider the factors of the product 3 × - 24 = - 72 which sum to - 1

The factors are - 9 and + 8 ( split the middle term using these factors )

3x² - 9x + 8x - 24 = 0 ( factor by grouping )

3x(x - 3) + 8(x - 3) = 0 ( take out common factor (x - 3) )

(x - 3 )(3x + 8) = 0 ( equate each factor to zero and solve for x )

x - 3 = 0 ⇒ x = 3

3x + 8 = 0 ⇒ x = -

x > 0 ⇒ x = 3

the sides are 5x = 15 and 3x - 1 = 8

h = √(15² + 8² ) = √(225 + 64 ) = 17 ← ( hypotenuse )