f(x)= x^2 -6x +21
0 =x^2-6x+21
subtract 21 from each side to prepare for completing the square
-21 = x^2 -6x
completing the square (b/2)^2
(-6/2) ^ =3^2 = 9
add 9 to each side
-21 +9 = x^2 - 6x + 9
-21 +9 =(x-3) ^2
-12 = (x-3)^2
take the square root of each side
+- sqrt(-12) = x-3
add 3 to each side, take out the negative inside the square root
3 +- i sqrt(12)=x
simplify the square root sqrt(12)= sqrt(4)sqrt(3) =2sqrt(3)
3 +- i 2sqrt (3) = x
Answer: 3+2isqrt(3)
3-2isqrt(3)
∵ The formula of the compound interest is
→ A is the new amount
→ P in the initial amount
→ r is the interest rate in decimal
→ n is the number of periods
→ t is the time
∵ The initial amount is 800 dollars
∵ The annual rate is 3% = 3/100 = 0.03
∵ It is a compounded annually
∴ n = 1
∵ t = 5 years
→ Substitute all of these values in the formula above
→ Use the calculator to find the answer
∴ A = 927.4192594 dollars
I presume you mean 9 'square'
9^2= 9 X 9 = 81
Cheerio ✌️
Answer:
The volume of the prism is 72 cubic cm.
Step-by-step explanation:
This we know because a triangle with sides of 3 units, 4 units, and 5 units must be a 3–4–5 right triangle, the catheti (“legs”) of which are 3 and 4 units. So the area of the base is
3 cm. * 4 cm. / 2 = 6 square cm.
Lastly, the volume of the prism is the base area multiplied by the height:
6 square cm. * 12 cm. = 72 cubic cm.
Answer:
The average interest rate will be approximately 9.64%
Step-by-step explanation:
Enrique borrowed $23000
2% interest on $4500 will be
4500 × 2/100
= 45 × 2
= $90
On the rest, which is
$23000 - $4500 = $18500
11.5% interest on $18500 will be
18500 × 11.5/100
= 185 × 11.5
= $2127.50
The total interest will be
$90 + 2127.50 = $2217.50
The average interest will be Total interest multiply by 100, divide by principal
That is Interest = pr/100, where t = 1
r = (I × 100)/p
r = (2217.50 × 100)/23000
r = 221750/23000
r ≈ 9.64%
