<h2>
Answer:</h2>
The correct options are:
Choice A
Choice C
and Choice E
<h2>
Step-by-step explanation:</h2>
We are asked to find the value of:
60% of 94
We know that: it is represented as:
Choice A)
We know that:
could also be written as:
Since we multiplied and divide by 10 such that:
Hence, option: A is correct.
Choice B)
This option is incorrect.
Since by choice A we get that the correct expression is:
Choice C)
We get:
This option is correct.
Since,
Choice D)
This option is incorrect because the actual expression is:
Choice E)
[/tex]\dfrac{60}{100}\cdot 94[tex]
This is the correct expression.
Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>
Step-by-step explanation:
Given the function j(x) = 11.6
and k(x) = 
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) = are inverse functions.
Answer:
so that number becomes divisible by 3, 6 and 9.
Step-by-step explanation:
In Number Theory there is a rule of thumb which states that sum of digits of a multiple of 3 equal 3 or a multiple of three. If we know that 
, then its sum of digits is:
(Eq. 1)
We have to determine which digits corresponds to multiples of three, there are four digits:
N = 0
(
)
N = 3
(
)
N = 6
(
)
N = 9
(
)
We get the following four distinct options: 154038, 154338, 154638, 154938. Now we find which number is divisible by 6 and 9 by factor decomposition:
It is quite evident that so that number becomes divisible by 3, 6 and 9.
Answer:
The length is 
and the breadth is 
Step-by-step explanation:
Let
x ----> the length of a rectangular campsite
y ----> the breadth of a rectangular campsite
we know that
The perimeter of a rectangle is equal to
so
------> equation A
The area of a rectangle is equal to
so
-----> equation B
substitute equation A in equation B
Solve the quadratic equation by graphing
The solution is 
( I assume that the length is greater than the breadth)
see the attached figure
Find the value of y
therefore
The length is and the breadth is
Answer:
29.15 km
Step-by-step explanation:
Given;
George walks; 25km west and then 15 km south
Resolving the directions to x and y axis;
North and South represent positive and negative y axis.
East and West represent positive and negative x axis respectively.
25km west
Rx = -25 km
15 km south
Ry = -15 km
The resultant displacement from the house is;
R = √(Rx^2 + Ry^2)
Substituting the values;
R = √((-15)^2 + (-25)^2)
R = √(225+625)
R = √(850)
R = 29.15 km
Therefore, he is 29.15 km from house
