Answer:
6 or -1.5
Step-by-step explanation:
We can let this integer be x.
Therefore, according to the question we have:
Subtracting 9x, we have a quadratic:
Plugging into the quadratic equation:
the square root of 81+144 is 15, so the answer is either 6 or -1.5
1 5/6 + 1/2
= 11/6 + 3/6
= 14/6 answer
The given equation is a combined variation.
We have been given an equation is
This is an equation in which we have three variables and one constant.
This can not be the case of direct or inverse variation because in direct or inverse variation we have only two variables. Whereas, here we have three variables.
So, Direct and inverse options are discarded.
So, either It can be joint or combined
In joint variation both the variables are directly proportional
Hence, given equation is not joint because if we rewrite the equation we will get both the variables are not directly proportional.
In combined, one variable is directly proportional and the other one is inversely proportional.
From we can see that z is directly proportional and x is inversely proportional.
Hence the answer is, the given equation is combined variation.
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(Please check the attachment for the diagram which will support the answer)
The regular pentagon is made up of five triangles as shown in the diagram. Let us now take the case of the bottom triangle ODC. We know from basic geometry that the area of any triangle is half times base times height. So, the area of the triangle will be half times DC (which is the base) times OP (which is the height).
Now, if we take into account all the triangles that make the pentagon we will get similar areas. The height of all such triangles will remain the same as OP because this is a regular pentagon.
Adding all these areas will give us the area of the pentagon which will come out to be:
Area of Pentagon=Area of Triangle OCD + Area of Triangle OBC +Area of Triangle OAB + Area of Triangle OAE + Area of Triangle OED
(Please see attachments for complete solution)
As we can see from the last attachment, the sum in the parenthesis is the perimeter of the pentagon and thus we get the area of the pentagon as
1/2 times apothem times Perimeter