What is the y-intercept of the line perpendicular to 2x + y + 5 = 0 at (-1 , -3)?
1 answer:
Answer: -2.5
Step-by-step explanation:
Given that the slope of the first line is and the slope of the second line is
,if the two lines are perpendicular then
= -1 ,
The line given is 2x + y + 5 =0 , to find the slope of the line , we will need to make y the subject of the formula
2x + y +5 = 0
y = -2x -5
comparing the solution to the equation of line in slope - intercept form , which is given as y = mx + c , where m is the slope and c is the y-intercept. This means that the slope of the given line is -2.
Therefore , the slope of the line perpendicular to this line is given as . The point given is (-1 , -3 ). Thus , to find the equation of the new line , we will use the formula for finding equation of line in slope-point form , which is given as :
y - = m ( x -
)
m =
= -1
= -3
substituting into the formula , we have
y - ( -3 ) = ( x - {-1} )
y + 3 = (x + 1)
y + 3 = x +
making y the subject of the formula in order to write the equation in slope - intercept form , we have
y = x +
- 3
y = x -
Therefore , the y - intercept is - 2.5
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Answer:
256
Step-by-step explanation:
A calculator works well for this.
_____
None of the minus signs are subject to the exponents (because they are not in parentheses, as (-1)^5, for example. Since there are an even number of them in the product, their product is +1 and they can be ignored.
1 to any power is still 1, so the factors (1^n) can be ignored.
After you ignore all of the things that can be ignored, your problem simplifies to ...
(2^2)(2^-3)^-2
The rules of exponents applicable to this are ...
(a^b)^c = a^(b·c)
(a^b)(a^c) = a^(b+c)
Then your product simplifies to ...
(2^2)(2^((-3)(-2)) = (2^2)(2^6)
= 2^(2+6)
= 2^8 = 256
Answer:
Step-by-step explanation:
refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;
The factorial of an integer n is evaluated as;
Using this concept, the above expression can now be simplified as follows;
Therefore, the permutations of 5 items taken 3 at a time is 60.
The next expression, refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;
Therefore, the combinations of 6 items taken 4 at a time is 15.
The final step is to evaluate the product;