* Developing and Applying the Quadratic Formula
- The solution of a quadratic equation, a𝑥² + b𝑥 + c = 0, where a,b, and c constants a ≠ 0, is given by the quadratic formula: 𝑥= -b ±√b² – 4ac ∕ 2a
- 3𝑥² + 6𝑥 – 4 = 0
a = 3, b = 6, b = -4
𝑥 = -6 ±√6² – 4(3)(-4) / 2(3)
𝑥 = -6 ±√36 + 48 / 6
𝑥 = -6 ±√84 / 6
𝑥 = -1 ±√14
Solving Radical Equation
How to solving radical equation
- Isolate the radical expression
- Square both sides of the equation: If x = y then x² = y²
- Once the radical is removed, solve for the unknown
- Check all answers.
- 𝒙² – 3 =13
√𝒙² = √16
𝒙 = 4
𝒙 = 4
2. √𝒙+8 = 3
(√𝒙+8)² = 3²
𝒙 + 8 = 9
𝒙 = 1
2.3 Adding and Subtracting Radical Expression
- When adding and subtracting radical the startegies for simplyfying polynomials can be used to symplify sums and differences of radicals. Like terms or like radicals in a sum or difference of radicals have the same radicand and the same index
- 7√9 – 4√9 = 3√9
- 7√9 and 4√9 are like terms becasue they have the same radicand and the same index. combine like terms.
2. ∛384 – ∛162 + ∛750
= 4∛6 – 3∛6 + 5∛6
= ∛6 + 5∛6
- The radicands are different , so simplyify each radical, then solve it
This week I learned about absolute value of a real number. Every real number can be represented as a point on a number line. The sign of the number indicates its position relative to 0. The magnitude of the number indicates its distance from 0.
The absolute value of -6 is |-6|=6
|6-4| (7+9) – 6 (4-6)
= |2| (16) – 6 (-2)
= 2(16) – (-12)
= 32 +12
Infinite geometric series
S∞= a/1-r a=7, r=0.2 or 1/5 3, 3/5, 3/25, 3/125…..
This week , I learn Infinite Geometric Series. An infinite geometric series has an infinite number of terms. To determine the sum of an infinite geometric series, we need to know a, a is the t1. Common ratio is -1 < r < 1 . The sum of the series, S∞ is : S∞=a/1-r
Arithmetic sequence – 3, 7, 11, 15, 19……
Formula – tn= t1+(n-1)d
t50=3+(49 x 4) (49×4=196)
Sum of 50
Formula – Sn = n/2 (t1 + tn)
S50 = 50/2 (t1 + t50)
S50 = 25 (3 + 199)
S50 = 25 x 202
S50 = 5050
: I tried to make a successful life, so I gots successful career, and I still dream. I am relatively successful in my job, but I don’t know why he always has unrealistic dreams. His expectations ever hurt me, so every time I feel extremely lonely, and The terrifying thing about me is that I have tried so far and it will not work. To be scary. But when I heard about my father ‘s suicide, I shocked. What should I do?
( A brief description of the Island with quotes)
- The platform and meeting place
“Here the beach was interrupted abruptly by the square motif of the landscape; a great platform of pink granite thrust up uncompromisingly through forest and terrace and sand and lagoon to make a raised jetty four feet high. The top of this was covered with a thin layer of soil and coarse grass and shaded with young palm trees” (Golding 13).
“Ralph grasped the idea and hit the shell with air from his diaphragm. Immediately the thing sounded. A deep, harsh note boomed under the palms, spread through the intricacies of the forest and echoed back from the pink granite of the mountain” (Golding 21).
“The beach between the palm terrace and the water was a thin stick, endless apparently, for to Ralph’s left the perspectives of palm and beach and water drew to a point at infinity; and always, almost visible, was the heat” (Golding 10).
3. Site where Ralph and Piggy find the conch
“Ralph had stopped smiling and was pointing into the lagoon. Something creamy lay among the ferny weeds” (Golding 18).
4. The lagoon