1. 10
2. 5√2 in
1. The ratio for a 30-60-90 triangle is x:x√3:2x
x is the shortest leg so 2*x =2*5 = 10
2. the ratio of a 45-45-90 triangle is x:x:x√2
x is one leg so x * √2 = 5*√2 = 5√2
<h3>
Answer:</h3>
- x-intercept: 82.75
- y-intercept: -2.15
<h3>
Step-by-step explanation:</h3>
To find the x-intercept, set y=0 and solve.
... 0 = log(12x +7) -3
... 3 = log(12x +7) . . . . add 3
... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)
... 993 = 12x . . . . . . . .subtract 7
... 82.75 = x . . . . . . . . divide by 12
To find the y-intercept, set x=0 and solve.
... y = log(12·0 +7) -3
... y = log(7) -3 . . . . . . simplify
... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function
We notice that for x = 2 , or x = 4, the value of y=0 (x intercept),
replace x by any of the latter value in y=a(x-3)² -1
===> 0= a( 2-1)² - 1====>a=1
1.77 if you need more just tell me. have a nice day