What is the domain of the function below?

Mathematics

2 answers:

amm18123 years ago

8 0

$f(x)=\log(x-4)+4\\\\The\ domain:\\\\x-4 > 0\qquad\text{add 4 to both sides}\\\\x > 4\\\\Answer:\ \boxed{x > 4\to x\in(4,\ \infty)}\to\boxed{D.}$

natulia [17]3 years ago

3 0

Answer:

(4, oo)

Step-by-step explanation:

i just took the test on plato and it is he correct answer if you have any more questions dm me personally and ill try to help!!! hopefully this helps

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The square of the sum of two numbers is 144 and the sum of of their square is 180, find the number... Please I really need the a

mr Goodwill [35]

Answer:

The numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

Step-by-step explanation:

Let the two numbers be 'x' and 'y'.

Given:

The squares of the sum of two numbers = 144

The sum of their squares = 180

The sum of the numbers = $x+y$

The square of the sum of numbers = $(x+y)^2$

Square of first number = $x^2$

Square of second number = $y^2$

The sum of their squares = $x^2+y^2$

Now, as per question:

$(x+y)^2=144---(1)\\\\x^2+y^2=180---(2)$

Expanding equation (1) using the formula $(a+b)^2=a^2+b^2+2ab$

This gives,

$(x+y)^2=144\\\\x^2+y^2+2xy=144\\\\\textrm{Plug in the value of }x^2+y^2\textrm{ from equation (2)}\\\\180+2xy=144\\\\2xy=144-180\\\\2xy=-36\\\\xy=-\frac{36}{2}\\\\xy=-18\\\\y=-\frac{18}{x}---(3)$

Plug in the value of 'y' from equation (3) in equation (1). This gives,

$x^2+(-\frac{18}{x})^2=180\\\\x^2+\frac{324}{x^2}=180\\\\x^4+324=180x^2\\\\x^4-180x^2+324=0\\\\\textrm{On solving, we get:}\\\\x^2=178.2\ or\ x^2=1.8\\\\\textrm{Square root both sides, we get:}\\\\x=\pm13.35\ or\ x=\pm1.35$