Answer:
x = 3
Step-by-step explanation:
ΔABC is 45 45 90 right triangle
The ratio of leg: hypo = a : a√2
Given: hypo AC = 6√2; so AB = BC = 6
ΔBCD is 30 60 90 right triangle
The ratio of short leg : long leg : hypo = x : x√3 : 2x
Hypo. BC = 6 = 2 (3)
So short leg BD = x = 3
Activity 3
1) 2m^2(4m^2 + 3m + 2)
2) (x + 4)^2 (x - 4)
3) (x + 9)(x - 7)
4) 5y(17y - 4z)
5) (2x - y)(6x + 5y)
Activity 4
1) 80 units because when you sub h = 9, you get 400 as the answer and because it’s a square, you square root 400 which is 20 units per side.
2) x = 7cm because when you multiply (x + 5)(x - 3), you get x^2 + 2x - 15 = 48 and when you solve it you get x is equal to 7, -9, because the length of the rectangle is positive x is equal to 7.
3) the binomial would be (9x + 1)^2.
Answer: The three consecutive odd integers are: -15, -13, and -11 .
_______________________________________________________
Explanation:
_____________________________________________
x + (x + 2) + (x + 4) = -39 ;
_____________________________________________
in which "x" is one of the integers,
"(x + 2)" is the next consecutive odd integer;
"(x + 4)" is the third consecutive odd integer.
__________________________________________
By solving for "x", we can solve for each of three (3) consecutive odd integers.
________________________________________________________
x + (x + 2) + (x + 4) = -39 ;
_________________________________________________________
1x + 1x + 2 + 1x+ 4 = -39 ;
_____________________________________________________
3x + 6 = -39 ;
______________________________________________
Subtract "6" from EACH side of the equation:
______________________________________________
3x + 6 − 6 = -39 <span>− 6 ;
____________________________________________________
to get: 3x = -45 ;
____________________________________________________
Divide EACH side of the equation by "3" ;
____________________________________________________
3x / 3 = -45 / 3 ;
_____________________________________________________
to get: x = -15 ;
______________________________________________________
x + 2 = -15 + 2 = -13 ;
_______________________________________________________
x + 4 = -15 + 4 = -11 .
___________________________________________________
Are: -15, -13, and -11 ; Consecutive odd integers? YES!
___________________________________________________
Does: -15 + (-13) + (-11) =? = -39 ??
_____________________________________________________
-15 </span>− 13 <span>− 11 = ? 39 ?? YES!
____________________________________________________
Answer: The three consecutive odd integers are: -15, -13, and -11.
_______________________________________________________</span>
Answer:
Initial value is 
.
Step-by-step explanation:
Let us assume that the exponential function is 
...... (1)
Now, the point 
will satisfy the above equation.
Now, this point on the graph of the exponential function will be sufficient to find the initial value of the function (1) i.e. a.
Now, putting the value x = 0 and 
in the equation (1) we get,
⇒ 
⇒ 
(Answer)
