Solve the inequality.<br> 2(4x - 3)2-3(3x) + 5x?<br> x 20.5<br> x 22<br> (-0, 0.5)<br> O (-0, 2]

The sum of two sides of a triangle must be greater than the third side
1) 5+9>14
14>14 It is incorrect so you can’t have these lengths

2)7+7>15
14>15 X

3)1+2>4
3>4 X

4)3+6>8
9>8

6+8>3
14>3

8+3>6
11>6

So the fourth choice is correct

8 0

3 years ago

What is the range of the following function:<br> y = 2(5^x) - 1

Orlov [11]

<h2>Hello!</h2>

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

$y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)$

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

5 0

3 years ago

Solve the inequality. 2(4x - 3)2-3(3x) + 5x? x 20.5 x 22 (-0, 0.5) O (-0, 2]