Find the coordinates of the image’s vertices.

a triangle with vertices l(–1, 5), m(–1, 7), and n(–8, 5) is rotated 270 counterclockwise about the origin.

a. l’(–5, 1), m’(–7, 1), and n’(–5, 8)
b. l’(1, 5), m’(1, 7), and n’(8, 5)
c. l’(5, 1), m’(7, 1), and n’(5, 8)
d. l’(5, –1), m’(7, –1), and n’(5, –8)

C. L' (5,1), M'(7,1) and N'(5,8)

Explanation:

For the rotation of a point 270° counterclockwise about the origin, the following rule applies:

(x , y) > (y , -x)

This means that, to get the image point:

1- We swap the values of the x and y coordinates in the original point

2- We change the sign of the x-coordinate of the original point (which is the y-coordinate in the image)

Now, for the givens, we simply apply the above rule to get the image:

L is (-1 , 5) > L' is (5 , 1)

M is (-1 , 7) > M' is (7 , 1)

N is (-8 , 5) > N' is (5 , 8)

Hope this helps :)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.