Answer:
Inequality: 2x + 2 ≤ 5•2x - 50
Solution: x ∈ <6.5, ∞)
Step-by-step explanation:
2x - the smaller of consecutive even integers
2x+2 - the greater of consecutive even integers
5•2x - five times the smaller number
5•2x-50 - fifty less than five times the smaller number
"is at most" means is less or equal
2x + 2 ≤ 5•2x - 50
2x + 2 ≤ 10x - 50
-2 -2
2x ≤ 10x - 52
-10x -10x
-8x ≤ -52
÷(-8) ÷(-8)
x ≥ 6.5
<u>x ∈ <6.5, ∞)</u>
F(9) = 2/3 (9) -5 = 1 I am assuming f(x) = 2/3x-5 if it is -2/3x then it is -11
Answer:
there are 25 boys and 35 girls
Step-by-step explanation:
if you draw out 5 lines to represent the boys and 7 lines each to represent girls to equal enough to make 60 you need 5 times of this. 5x5=25 boys. 7x5=35 girls. 25+35=60
The differnce quotient is basically taking the derivitive (result will be f'(x)=5, but anyway)
here is the disffernce quotient
![lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h}](https://tex.z-dn.net/?f=lim_%7Bh%5Crightarrow0%7D%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D)
so
for your equation
![lim_{h\rightarrow0}\frac{(5(x+h)+4)-(5x+4)}{h}](https://tex.z-dn.net/?f=lim_%7Bh%5Crightarrow0%7D%5Cfrac%7B%285%28x%2Bh%29%2B4%29-%285x%2B4%29%7D%7Bh%7D)
![lim_{h\rightarrow0}\frac{5x+5h+4-5x-4}{h}](https://tex.z-dn.net/?f=lim_%7Bh%5Crightarrow0%7D%5Cfrac%7B5x%2B5h%2B4-5x-4%7D%7Bh%7D)
![lim_{h\rightarrow0}\frac{5h}{h}](https://tex.z-dn.net/?f=lim_%7Bh%5Crightarrow0%7D%5Cfrac%7B5h%7D%7Bh%7D)
h's cancel and you are left with 5
the differnce quotient is 5