The answer is 5 large, 25 medium, 70 small dogs.
x - the number of large dogs
y - the number of medium dogs
z - the number of small dogs
<span>There are 100 dogs at Pampered Paws Kennel:
</span>x + y + z = 100
<span>Each day, the dogs eat 100 lb of food. Large dogs eat 3 lb, medium dogs eat 2 lb, and small dogs eat 0.5 lb:
3x + 2y + 0.5z = 100
</span><span>There are five times as many medium dogs as large ones:
x = 5y
</span>x + y + z = 100
3x + 2y + 0.5z = 100
y = 5x
____
Substitute y in the first two equations:
x + 5y + z = 100
3x + 2*5x + 0.5z = 100
___
6x + z = 100
13x + 0.5z = 100
____
z = 100 - 6x
13x + 0.5z = 100
____
13x + 0.5(100 - 6x) = 100
13x + 50 - 3x = 100
13x - 3x = 100 - 50
10x = 50
x = 50/10 = 5
y = 5x = 5 * 5 = 25
x + y + z = 100
5 + 25 + z = 100
30 + z = 100
z = 100 - 30
z = 70
As is shown in the figure attached:
1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
2. "D" and "x" are congruents,
because they are Alternate Interior angles, so x=38º.
3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
76º+38º+B=180º
B=180º-76º-38º
B=66º
4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
The opposite angles are: 76º and 66ª. Then, we obtain:
y=76º+66º
y=142º
Therefore, the answer is: The value of y is 142º.
The surface area formula for a cube is: 6 * s^2, where s is the side length.
The two surface areas are:
6 * 3^2 = 54
and
6 * 8^2 = 384
The ratio of their surface areas, from the surface area of the smaller cube to the surface area of the larger cube is:
54/384 = 9/64
The answer is 9/64.
Note that another way to to find the ratio of the squares of the side lengths of the cubes.
Okay YAS, I loove linear equations... moving on.
OKAY, so I'm going to start with Q2 (not 100% sure how to work out 1, but lets use process of elimination). Firstly, the rule is y=mx+c So, start with the first line y=2x-3, from this the first thing you need to do is find the y-intercept (m) and the gradient (c). So, this is very simple 2 is m and -3 is c (if you look at the rule it matches up).
m=2/1(this is rise/run, rise is how much you go up by, and run is how much you go left or right by (left if positive, right if negative))
c=-3
Now, go to your graph, and look on the y line and go to -3. Then go left, 1, and up 2. IS THERE A LINE CROSSING THROUGH THIS POINT? Yes? Good.
Now for y=-1/2+1. Looking at the rule again (y=mx+c),
m=-1/2 (rise/run)
c=1
NOW, once again go to your graph, and look on the y line and go to 1 (in this case the line actually passes through this point), now go right 2 places and up 1. IS THERE A LINE? Yes? Good!
NOOOW, for Q3, use the same steps and you will have the answer.
y=1/4x-2
m=1/4 (rise/run)
c=-2
Look at graph C, start at -2 on the y line, go left 4, and up 1? Yes? Line crossing through this point? good!!
Now for the 2nd one,
y= -2/5x+4
m=-2/3
c=4
Look at the same graph start at 4 on the y line, go right 5 and up 2! Got it? There's a line crossing through this point, yes? YAY
Now I have no idea how to do Q1, but by process of elimination it's pretty obvious. I hope this is right! Okay, bye!! :D
Answer:
Step-by-step explanation:
The base case in the recursive function are:
The recursive case is equal to:
So replace 
for 
:
In the new expression 
is a base case so you don't have to worry for that part, but 
is still the recursive case so evaluate again in
and 
are define as base cases so you replace for it's numbers:
Now return to and replace for the new values:
So the final answer is 20
