Answer:
the answer is C
Step-by-step explanation:
We can only solve it is equal to something
if we assume that it eausl zero, then if we factor it we can assume the factors eqal zero
xy=0, then assume x and y=0
so what we do is if we have
ax^2+bx+c
we factor a and take the factors closest together
then place them with the x
then factor c and chose the closest ones
then try them and see if it works
so if we had
6x^2+20x+16
6=2 times 3
(2x+ )(3x+ )
we know that they are both + because the middle terms is positive and the end terms is positive
16=4 times 4
(2x+4)(3x+4)=6x^2+12x+8x+16=6x^2+20x+16
th easy way to check is we know that teh end terms will be right since we made them that way
to check the middle terms
if we have
(ax+b)(cx+d)
to check what the middle term is we do
bcx+dax
and see if that equals the middle term
so
2. 6x^2+20x+16
6=2 times 3
(2x+ )(3x+ )
we know that they are both + because the middle terms is positive and the end terms is positive
16=4 times 4
(2x+4)(3x+4)=6x^2+12x+8x+16=6x^2+20x+16
facored is (2x+4)(3x+4)=0
2x+4=0
x=-2
3x+4=0
x=-4/3
3. 5x^2+21x+4
5=1 times 5 prime is nice since we only have 1 option
(x+ )(5x+ )
we know they are both pluss since middle and end term is positive
4=2 times 2
(x+2)(5x+2)
(2 times 5x)+(x times 2)=10x+2x=12x, we need 21 so this wrong
change end term
(x+4)(5x+1)
(4 times 5x)+(1 times x)=20x+x=21x correct
factore form
(x+4)(5x+1)=0
x+4=0
x=-4
5x+1=0
x=-1/5
4.
-7x^2+59x-24
-7=-1 and 7 or -7 and 1
we pick -1 and 7 since we want the middle term to be positive
(7x- )(-x+)
signs are differenc since end term is negaive
-24=8 and -3
(7x-3)(-x+8)
(7x times 8)+(-3 times -x)=56x+3x=59x
correct
(7x-3)(-x+8)=0
7x-3=0
x=3/7
-x+8=0
x=8
OK, so I am getting tired of this so I will just do the rest in factored form isnce you probably shoud have figured out how to do it from the previous examples
5. (x-3)(3x-5)
6. (x-1)(2x+13)
7. (x-2)(3x+8)
8. 2x^2+17x-20 cannot be factored but 2x^2+18x-20 can maybe typing mistake
9. (x+3)(11x-8)
answers:
2.(2x+4)(3x+4)
3.(x+4)(5x+1)
4.(7x-3)(-x+8)
5. (x-3)(3x-5)
6. (x-1)(2x+13)
7. (x-2)(3x+8)
8. 2x^2+17x-20 cannot be factored but 2x^2+18x-20 can maybe typing mistake
9. (x+3)(11x-8)
Answer:
20/41
Step-by-step explanation:
The total of all students is ...
7 + 2 + 5 + 6 + 3 + 4 + 6 + 8 = 41
The total of students not studying chemistry is ...
7 + 2 + 5 + 6 = 20
Then the probability that a randomly-chosen student does not study chemistry is ...
p(not studying chem) = 20/41
Answer:
0.3056 or 30.56%
Step-by-step explanation:
The volume of the grapefruit with the peel is:
![V_p=\frac{4 \pi (d/2)^2}{3}\\V_p=\frac{4 \pi (12/2)^2}{3}\\V_p=48 \pi](https://tex.z-dn.net/?f=V_p%3D%5Cfrac%7B4%20%5Cpi%20%28d%2F2%29%5E2%7D%7B3%7D%5C%5CV_p%3D%5Cfrac%7B4%20%5Cpi%20%2812%2F2%29%5E2%7D%7B3%7D%5C%5CV_p%3D48%20%5Cpi)
When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:
![V_n=\frac{4 \pi (d/2)^2}{3}\\V_n=\frac{4 \pi (10/2)^2}{3}\\V_n=33.333 \pi](https://tex.z-dn.net/?f=V_n%3D%5Cfrac%7B4%20%5Cpi%20%28d%2F2%29%5E2%7D%7B3%7D%5C%5CV_n%3D%5Cfrac%7B4%20%5Cpi%20%2810%2F2%29%5E2%7D%7B3%7D%5C%5CV_n%3D33.333%20%5Cpi)
The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:
30.56% of volume of the grapefruit is the peel.