Answer:
(1/3)(3x+12)
Step-by-step explanation:
1/3
times (3x+12)
3x+12 will be three times the number x + 12
1) First try to find a perfect square number that divides evenly into the number under the square root. Perfect square numbers include 4, 9, 16, 25, 36, 49, etc. because they are squares of the numbers 2, 3, 4, 5, 6, 7, etc., respectively.
2) Separate the root expression into the two numbers you found as factors, with each number now under its own square root symbol. For example, sqrt(12) = sqrt(4) times sqrt(3).
3) Keep simplifying. The square root of a perfect square becomes just a number, without the radical square root symbol. sqrt(4)*sqrt(3) becomes 2*sqrt(3).
4) Check to see if anymore simplifying can be done, either by combining constants or finding another perfect square number that divides evenly into your factors. If no more simplifying can be done, you have your final "simplified radical form" (SRF) answer, 2*sqrt(3).
If there is a square root anywhere in the DENOMINATOR, you must "rationalize" the denominator, in other words, somehow get rid of the root in the bottom, in order for the expression to be considered simplest. For example, if you have 4/sqrt(2) you must use the trick of simplifying by multiplying the expression by sqrt(2)/sqrt(2). This will clear the square root in the bottom. If you multiply straight across, you would get 4*sqrt(2)/2, which simplifies again to 2*sqrt(2).
<span>If you have a more complicated fraction with a square root in the denominator, like (4+sqrt(3))/(5-sqrt(3)), you will need to use the "conjugate" to simplify. This means multiplying top and bottom by the expression in the denominator, but with the middle sign flipped. Here you would multiply by (5+sqrt(3))/(5+sqrt(3)), multiply straight across on top and bottom using FOIL-ing and distribution. Some terms will cancel in the bottom, leaving you with a simpler denominator that has no square roots.</span>
The answer should be 42.
Since there are 60 questions in the test and she managed to answer 70% of the questions correctly, that means that she answered 70% out of 60 questions correctly.
So you need to calculate how much 70% out of 60 is. Since % is always measured on a base from 0 (%) to 100(%), then 70% is equal to the fraction 70/100, simplified to 7/10. To know how much 7/10 out of 60 is,you just multiplie them and your answer will be 42.
I hope this helps you forward.
Answer:
The tangent line to the point P(x0,y0) and the line OP are perpendicular
Step-by-step explanation:
To show that the tangent line to the point P(x0,y0) is perpendicular to the line OP, of the circle with center at 0(0,0), you first use implicit differentiation on the equation of a circle, as follow:
(1)
equation of a circle with center at (0,0) and constant radius r.
The implicit derivative of the equation (1) is:
You solve the previous equation for dy/dt:
The derivative dy/dx is also the slope of the tangent line, for the point P(x0,y0) you obtain:
The slope m' of the OP line is given by:
for the point P(x0,y0) you obtain:
In order to know if the lines OP and tangent line to the point P, are perpendicular between them, the you verify the following relation:
(2)
In fact, you relace the values of m and m':
The tangent line to the point P(x0,y0) and the line OP are perpendicular
