Write the equation of the line that contains the point (-2 , 5) and is perpendicular to the line y = 1/2x + 3

The line has the same slope as 7x-y=5 and the same y intercept as the graph 3y-11x=15

scoundrel [369]

7x - y= -5. Standard form is when it is written with x and y on the same side, but x is not negative or a fraction. To find the slope and y intercept, you must change the first two equations to slope intercept. You get y=7x-5 for the first one and y=11/3x+5 for the seccond equation. Take the 5 as your y intercept and the 7 as your slope and you get y=7x+5. Now you need to change it into standard form. When all is said and done, your final answer should be 7x - y = -5.

4 0

2 years ago

Read 2 more answers

What Numbers Go Into The Venn Diagram

antiseptic1488 [7]

Answer:

(a)The total number of outcomes where the sum is 9 or

greater than 9 is 10

(b)Total number of outcomes where the sum is odd = 18

(c)Total number of outcomes where the sum greater or equal to 9 and is

also odd = 6

Step-by-step explanation:

Here, Sample Space = { Sum of the two digits when two dices are thrown together}

or, S = {2,3,4,5,6,7,8,9,10,11,12}

(a) The number of ordered pairs where sum is 9 or greater than 9

= { sum is 9 , Sum is 10 , Sum is 11, Sum is 12}

= {(6,3)(3,6),(4,5)(5,4) , (5,5), (6,4),(4,6) , (6,5)(5,6), (6,6)}

Hence the total number of outcomes where the sum is 9 or

greater than 9 is 10

(b) The number of ordered pairs where sum is odd.

= { Sum is 3 , Sum is 5, Sum is 7, Sum is 9, Sum is 11}

= {(1,2)(2,1), (4,1)(1,4),(2,3)(3,2) , (6,1), (1,6),(5,2),(2,5),(4,3)(3,4) ,

(6,3)(3,6), (4,5)(5,4), (6,5),(5,6)} = 18

Hence total number of outcomes where the sum is odd = 18

(c) Intersection point refers the outcomes which have sum greater or equal to 9 and is odd

Here, the possible outcomes are = { Sum is 9 , Sum is 11}

={ (6,3)(3,6), (4,5)(5,4), (6,5),(5,6)} = 6

Hence total number of outcomes where the sum greater or equal to 9 and is also odd = 6

6 0

2 years ago

Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)