Answer:
Step-by-step explanation:
Hypotenuse² =base² + altitude²
(3x + 4)² = (2x + 1)² + (3x)²
{Use (a+b)² = a² + 2ab + b²}
(3x)² + 2*3x+4 + 4² = (2x)² + 2*2x*1 + 1² + 9x²
9x² + 24x + 16 = 4x² + 4x + 1 + 9x²
9x² + 24x + 16 = 13x² + 4x + 1
0 = 13x² + 4x + 1 - 9x² - 24x - 16
13x² - 9x² + 4x - 24x +1 - 16 = 0
4x² - 20x - 15 = 0
a = 4 ; b =-20 ; c = -15
D = b² - 4ac = (-20)² - 4*4*(-15) = 400 + 240 = 640
√D = √640 = 25.30
x = 5 .66 ; x = -0.66
Ignore x = -0.66 as length of a side cannot be negative
Answer : x = 5.66
The answer to the question
Answer:
m = -1
Step-by-step explanation:
12 times the number is 12m
17 less than that is 12m -17.
23 less than 6 times the number is 6m-23.
These expressions are said to be the same:
12m -17 = 6m -23
6m -17 = -23 . . . . . . . . subtract 6m from both sides
6m = -6 . . . . . . . . . . add 17 to both sides
m = -1 . . . . . . . . . divide both sides by 6
The value of m is -1.
(x^12)^5=x^(12*5)=x^60
(x^(-2))^9=x^(-18)
x^60*x^(-18)=x^(40) and we need to find x^a such that
x^(42)*x^a=x^(40)^5
x^a=x^(40)^5*x^(-42)
x^a=x^(200)x^(-42)
x^a=x^(200-42)
x^a=x^158
so the missing term is x^158
The range of a function is the set of the all values taken by the function, for all possible inputs.
When you watch this from a graphical point of view, the range is the portion of the y axis that the graph spans.
In this case, you can see that the lowest point reached by the function (its minimum) is 
. You can also see that the function is unbounded upwards.
So, the range is 
, and the lowest value is thus 2.
