When you have your log base 4, the way you cancel that out is by making 4 the base on both sides, so you get 4^(log4) to reduce to 1, and you're left with:

2x + 3 = 4^(1/2) ... Simplify

2x + 3 = 2

2x = -1

x = -1/2

If you plug that back in, everything checks out. Maybe double check your use of logarithm/exponent properties?

4 0

2 years ago

Jeffery babysits for 4 dollars per hour, he also works as a math tutor for 7 dollars per hour. He is only allowed to work 13 hou

Oksana_A [137]

Given:

Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.

He is only allowed to work 13 hours total per week.

He wants to make at least 65 dollars.

To find:

The system of inequalities to represent this situation.

Solution:

Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.

He is only allowed to work 13 hours total per week. It means sum of x and y must be less than or equal to 13.

$x+y\leq 13$

He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.

$4x+7y\geq 65$

Number of hours can not be negative.

$x\geq 0, y\geq 0$ .

Therefore, the required system of inequalities contains some equations, $x+y\leq 13,4x+7y\geq 65$ and $x, y\geq 0$ .

4 0

2 years ago

Approximately how long is a leg of an isosceles right triangle that has a hypotenuse of length 11.31

Lapatulllka [165]

Answer:

Leg of an isosceles right triangle is 7.99 long.

Step-by-step explanation:

Given:

Length of the hypotenuse =11.31

To find:

Length of the leg of an isosceles right triangle =?

Solution:

According to Pythagorean's Theorem, we have

$a^2 +b^2 = c^2$ -----------------------------(1)

Here were are given as isosceles triangle, so the two sides will be of same length

So equation 1 can be rewritten as

$a^2 +a^2 = c^2$

$2a^2 = c^2$

Substituting the value of hypotenuse

$2a^2 = (11.31)^2$

$2a^2 = 127.91$

$a^2 = \frac{127.91}{2}$

$a^2 =63.955$

$a = \sqrt{63.955}$

a = 7.99

7 0

2 years ago