Answer:
40 girls 20 boys i think / guess
Step-by-step explanation:
Answer:
x = ±2
Step-by-step explanation:
3x ^2 -4 = 8
Add 4 to each side
3x ^2 -4+4 = 8+4
3x^2 =12
Divide each side by 3
3x^2 =12
3x^2/3 = 12/3
x^2 = 4
Take the square root of each side
sqrt(x^2) = ±sqrt(4)
x = ±2
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
Given: cos A = 5/13 = adj side / hypotenuse
The the opp side is given by (hypo)^2 = (adj)^2 + (opp)^2. Here,
13^2 = 5^2 + (opp)^2, so that
(opp)^2 = 169 - 25 - 144. Then opp = +12. All of these lengths are in Q I.
opp 12
Then sin A = -------- = -------- (answer)
hyp 13
Answer: Andrew = 20
Jimmy = 25
Richard = 100
Step-by-step explanation:
Let the number of Andrew's comic books be y.
Jimmy has five more comic books than Andrew. This means Jimmy has: y+5
Richard has four times as many comic book as jimmy. This means Richard has: 4(y+5) = 4y + 20
Since there are 145 comic books together. This can be rewritten as:
y + (y+5) + (4y+20) = 145
6y+25 = 145
6y = 145 - 25
y = 120/6
y = 20
Andrew has 20 comic books
Jimmy has five more comic books than Andrew. Jimmy has: 20+5 = 25
Richard has: 4y + 20 = 4(20) + 20 = 100
