Answer:
1)6x^2+7x-24
2) x-4
3) f(-3)=-14 g(-3)=2 f(-3)/g(-3)=-7 and p(-3)=-3-4=-7
f(-11)=90 g(-11)=-6 f(-11)/g(-11)=-15 and p(-11)=-11-4=-15
4)f'(x)=(x-7)/3
Step-by-step explanation:
1) f(x)=2x-3 g(x)=3x+8
f(x)*g(x)=m(x)=(2x-3)(3x+8)=6x^2+16x-9x-24=6x^2+7x-24
2) f(x)=x^2+x-20 g(x)=x+5
f(x)/g(x)=p(x)=(x^2+x-20)/(x+5)=> by finding the roots of f(x) we obtain =
(x-4)(x+5)/(x+5)--->f(x)/g(x)=p(x)=(x-4)
3) f(-3)=-14 g(-3)=2 f(-3)/g(-3)=-7 and p(-3)=-3-4=-7
f(-11)=90 g(-11)=-6 f(-11)/g(-11)=-15 and p(-11)=-11-4=-15
4) If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back x
y=3x+7
(y-7)/3=x=--> f'(x)=(x-7)/3
Answer: Train A = 50 mph; Train B = 30 mph
Step-by-step explanation:
In this case, let's call the speed of both trains as:
Va: speed of train A
Vb: speed of train B
As train A is faster than train B, let's call speed of train B as X; So if Vb is X, then Va would be:
Vb = X
Va = X + 20
If we combine both Speed, we have:
V = Va + Vb = X + X + 20 = 2X + 20
Now that we have an expression for the combined speed, let's recall the formula for speed in general:
V = d/t
Where:
d: distance = 240 miles
t: time = 3 hours
Combining all the data we have:
V = 240/3
but V is 2X + 20 so:
2X + 20 = 240/3
Solving for X:
2X + 20 = 80
2X = 80 - 20
2X = 60
X = 60/2
X = Vb = 30 mph
Now that we know speed of one train, we can know the speed of the other train:
Va = 30 + 20 = 50 mph
Answer:
Step-by-step explanation:
The total number of cats in a local cat show is 250
Of these, 73 are orange, 11 are white, 80 are black, 27 are calico, 50 are gray, and 9 are tuxedo.
The probability of a
randomly selected cat from the show will be gray or tuxedo is
We simplify to get:
Answer:
The answer is option D.
Step-by-step explanation:
You have to add up both functions :
g(a) + h(a) = (g+h)(a)
(g+h)(a) = 3a + 4a + 1
(g+h)(a) = 7a + 1
For the first one, you have to convert the fractions to an improper fraction. To do that you need to multiply the bottom denominator number (3) by the whole number (1) then you need to add the numinator, so 3x1+2= 5. You have to keep the denominator so 1 2/3 is equal to 5/3. Then do the same to 2 1/5, and you get 11/5. Now you have to find a common denominator, that's basically the smallest number that both numbers can go Into, the lowest common denominator for 3 and 5 is 15. So 3x5= 15, so we have to multiply the top number by 5 which is 25. So 5/3 is equal to 25/15, then 5x3= 15, so you need to multiply 11 by 3 which is 33. So 11/5 is equal to 33/15. Then you add them. Add the numinators (25+33=58. Then you keep the denominator 15. So when u add it it's 58/15 then you need to simplify that and you get 3 13/15.
The second one you turn them into improper fractions like I told you how to before (multiply the bottom number by the whole number then add he top number, then add he same denominator.) do that for both. Then you line them right next to each other and multiply across. (I just realized that they were the same number so they are equal to 5/3 and 11/5)
Then you do 5x11 and you get 55 then do 3x5 and you get 15. 55/15 is your answer, but you need to simplify it, you need to divide 55 by 15, (not all the way just the first number) so you do 15x3 and that's 45, then you subtract that from 55, and you get 10, so then you take your denominator (15) and you answer is 3 10/15. But when you simplify it it's 3 and 2/3
Hope I helped sorry it's so long and sorry for any typos it's so long I didn't go back and check