Answer:
The factorized form of the given expression is ![4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]](https://tex.z-dn.net/?f=4%20%5B%28a-1%29%5E2%20-%20b%28a%20-%201%20%2B%20%5Cfrac%7Bb%7D%7B4%7D%29%5D)
Step-by-step explanation:
Given;
4a² + b² - 4ab - 8a + 4b + 4
This expression is factorized as follows;
(4a² - 8a + 4) + (b² - 4ab + 4b)
(4a² - 4a - 4a + 4) + b² - 4b(a - 1)
(4a - 4)(a - 1) + b² - 4b(a - 1)
(4a - 4)(a - 1) - 4b(a - 1) + b²
4(a - 1)(a - 1) - 4b(a - 1) + b²
4(a - 1)² - 4b(a - 1 + b/4)
![4(a- 1)^2 - 4b(a - 1 + \frac{b}{4} )\\\\4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]](https://tex.z-dn.net/?f=4%28a-%201%29%5E2%20-%204b%28a%20-%201%20%2B%20%5Cfrac%7Bb%7D%7B4%7D%20%29%5C%5C%5C%5C4%20%5B%28a-1%29%5E2%20-%20b%28a%20-%201%20%2B%20%5Cfrac%7Bb%7D%7B4%7D%29%5D)
Answer:
975 students
Step-by-step explanation:
This is a dense question. Let's look at it piece by piece:
1. The ratio of boys to students in the class is 10/25. If there are 25 students and 15 girls, that leaves 10 boys.
2. The question says that the ratio is in proportion of boys to total students in the school. "In proportion" in this case means that if we convert 10/25 to a fraction with numerator 390, the denominator is the amount of students in school.
3. 10x39=390. What you do the numerator you must do to the denominator: 25x39=975.
4. This means 975 students go to the school.
Answer:
x^2 + y^2 = 36
Step-by-step explanation:
Just add 36 to both sides. This is a circle with the center at the origin and radius 6.
4z+2(z-4)=3z+11 perform indicated multiplication on left side
4z+2z-8=3z+11 combine like terms on left side
6z/-8=3z+11 add 8 to both sides
6z=3z+19 subtract 3z from both sides
3z=19 divide both sides by 3
z=19/3
z=6 1/3
So there is only one solution when z=6 1/3
Answer:
25 minutes
Step-by-step explanation:
50÷10=5
5×5=25
hopefully this helps :)
