Answer:
in the space of x we'll equate it to 5-y
2(5-y)+3y=12
10-2y+3y=12
-2y+3y=12-10
y=2
subt y into first equation (x=5-y)
x=5-2
x=3
Answer:
32
Step-by-step explanation:
(-8 × -6) - 4²
48 - 4²
48 - 16 = 32
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
What you do here is replace is the given x value to find the y one
Like for the first box the y (top-to-down) would be found using y=3(-2)+4 which is gives y=-2
Applying the same for each in order:
(-2,-2)
(-1,0)
(0,4)
(1,7)
(2,10)
Ordered pairs are typed in (x,y) format like the answers I gave above
Answer:
D.
Step-by-step explanation:
Remember that the limit definition of a derivative at a point is:
![\displaystyle{\frac{d}{dx}[f(a)]= \lim_{x \to a}\frac{f(x)-f(a)}{x-a}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28a%29%5D%3D%20%5Clim_%7Bx%20%5Cto%20a%7D%5Cfrac%7Bf%28x%29-f%28a%29%7D%7Bx-a%7D%7D)
Hence, if we let f(x) be ln(x+1) and a be 1, this will yield:
![\displaystyle{\frac{d}{dx}[f(1)]= \lim_{x \to 1}\frac{\ln(x+1)-\ln(2)}{x-1}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%281%29%5D%3D%20%5Clim_%7Bx%20%5Cto%201%7D%5Cfrac%7B%5Cln%28x%2B1%29-%5Cln%282%29%7D%7Bx-1%7D%7D)
Hence, the limit is equivalent to the derivative of f(x) at x=1, or f’(1).
The answer will thus be D.
Answer:
Step-by-step explanation:The surface area of a sphere (the shape of a baseball) is given by the formula, SA = 4 (pi) r^2. Given the circumference of the circle, you can solve for the radius.
The formula for circumference is C = 2 x pi x r.
So input 9 for C and solve. 9 = 2 x pi x r.
You will get that r is equal to about 1.43 in.
Now put that r value into the surface area equation: SA = 4 (pi) 1.43^2
You will get a surface area equal to about 25.7 in^2.
Now multiply that number by the number of baseballs you need to cover, 100.
I'll let you do that step by yourself since it's simple algebra and you're smart enough to figure it out ;)
