Completing the square
alrighty
minus 31 both sides
x²+12x=-31
take 1/2 of the linear coefient and square it
12 is the linear coefient
12/2=6, (6)²=36
add that to both sides
x²+12x+36=36-31
factor perfect square trinomial
(x+6)²=5
square root both sides, remember to take positive and negative root
x+6=+/-√5
so what you want to write is
x+6=√5 and
x+6=-√5
the solutions
minus 6 both sides
x=-6+√5 and -6-√5
Answer:
8.16 Kg
Step-by-step explanation:
average is calculated as
average = 
here average = 0.17 and count = 48 , then
0.17 =
( multiply both sides by 48 )
8.16 = sum
that is total mass = 8.16 Kg
Answer:
Surface Area = 150
Step-by-step explanation:
The surface area of this triangular prism is the sum of area of all the sides.
Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)
- Triangle 1 area:

- Triangle 2 area:

- Lateral surface 1 (rectangle):

- Lateral surface 2 (rectangle):

- Bottom surface (rectangle):

Summing all these gives us the total surface area.
Total surface area = 
**** <em>The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).</em>
<em>Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use </em><em>Pythagorean Theorem</em><em>. Which is:</em>
<em>
</em>
<em>Hence, the side length of the hypotenuse is 5 [used above in the calculation]</em>
Answer:
X= -1/2
Step-by-step explanation:
8x-4(-5x-2)=12x
8x+20x+8=12x
28x+8=12x
8=-16x
-1/2=x