Answer:
- 8
Step-by-step explanation:
Given
x² - 64 = 0 ( add 64 to both sides )
x² = 64 ( take the square root of both sides )
x = ±
= ± 8
Solutions are x = 8 and x = - 8
Answer:
Triangle KLM
Step-by-step explanation:
Firstly, we need to write the coordinates of triangle NPQ
We have this as;
(-7,-6) for N
(-4,-3) for P
(-4,-6) for Q
Now, we are going to use the given translation formula;
(x + 8, y + 1)
N’ will be (-7+ 8, -6 + 1) = (1,-5)
P’ will be (-4+ 8, -3+1) = (4,-2)
Q’ will be (-4+ 8, -6+1) = (4,-5)
Now, we need to find the triangle with the exact given transformation coordinates calculated above;
We have the triangle as;
KLM
With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)
Answer:
In general gf(x) is not equal to fg(x)
Some pairs of functions cannot be composed. Some pairs of functions can be composed only for certain values of x.
Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.
Step-by-step explanation:
g(x) = 3x + 6 - 8, f(x) = √x.
The domain of a composed function is either the same as the domain of the first function, or else lies inside it
The range of a composed function is either the same as the range of the second function, or else lies inside it.
Or vice versa
Now only positive numbers, or zero, have real square roots. So g is defined only for numbers
greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or
equal to zero. You can work out that
f(x) ≥ 0 only when x ≥3/2
.
Answer:
The number of bracelets with she start are 48.
Step-by-step explanation:
Given:
Julia was recently given 9 bracelets. She plans to give 1/3 of her bracelets. She will be left with 23.
Now, we need to find with how many did she start.
Let the bracelets with she start be
.
She plans to give
=
.
According to question:

On solving the equation:

<em>Multiplying both sides by 3 we get:</em>


<em>Adding both sides by 27 and then dividing by 2 we get:</em>

Therefore, the number of bracelets with she start are 48.
Answer:
The volume of the cylinder is 367.6 M^3
Step-by-step explanation:
Mathematically, we have the volume of a cylinder calculated as follows;
V = pi * r^2 * h
r is the base radius given as 3 m
h is the height given as 13 m
So, we have the volume as;
V = 22/7 * 3^2 * 13 = 367.6 M^3