Answer:
15 feet.
Step-by-step explanation:
A bulletin board has been shown in the figure below.
Where the width of the board AB = DC = 
= 4.5 feet
and the length of the board AD = BC = 6 feet
As Ms. Berkin is dividing the board by stretching the ribbons to the opposite corners so the length of ribbons will be AC and BD.
In right angle triangle <em>ADC</em>, using Pythagorean Theorem,
= 
feet
Similarly in triangle <em>BDC</em>,
feet
Thus, total length of the ribbon used = AC + BD = 7.5 + 7.5 = 15 feet
The root sof this quadratic equation are -4 and 2.5.
The roots of any quadratic can be found by using the quadratic equation. The equation is below for you.
In this equation you use the number attached to x^2 as the a, which in this case is -2. The number attached to x as b, which is in this case -3. And the number at the end as c, which is 20. From there you solve for the answers.
Now you separate and get the two separate answers. First the positive.
4
Now the negative
-2.5
In order to construct this equation, we will use the variables:
V to represent mixture volume (40 ml)
C to represent mixture concentration (0.32)
v₁ to represent volume of first solution (40 / 4 = 10 ml)
c₁ to represent concentration of first solution (0.2)
v₂ to represent the volume of the second solution (40 * 3/4 = 30 ml)
c₂ to represent the concentration of the second solution
We know that the total amount of substance, product of the volume and concentration, in the final solution is equal to the individual amounts in the two given solutions. Thus:
VC = v₁c₁ + v₂c₂
40(0.32) = 10(0.2) + 30c
Answer:
StartFraction negative 1 Over k cubed EndFraction
Step-by-step explanation:
3k / (k + 1) × (k²- 1) / 3k³
= 3k(k² - 1) / (k + 1)(3k³)
= 3k³ - 3k / 3k⁴ + 3k³
= -3k / 3k⁴
= -1/k³
StartFraction k + 1 Over k squared EndFraction
(k + 1) / k²
StartFraction k minus 1 Over k squared EndFraction
(k - 1)/k²
StartFraction negative 1 Over k cubed EndFraction
= -1/k³
StartFraction 1 Over k EndFraction
= 1/k
Tada, Its on the Image. Hoped I helped :)
