The figure shows a line graph and two shaded triangles that are similar: A line is shown on a coordinate grid. The x-axis values are from negative 30 to positive 30 in increments of 6 for each grid line. The y-axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 24, negative 4, and 0, 0, and 24, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to 12, 2 labeled as A, one leg is from 0, 0 to 12,0 and the second leg is from 12,0 to 12, 2. Another shaded right triangle is formed with the hypotenuse from 12, 2 and 18, 3 labeled as B, one leg is from 12, 2 to 18, 2 and the second leg is from 18, 2 to 18, 3.
Which statement about the slope of the line is true? (1 point)

Group of answer choices

It is 6 throughout the line.

The slope from point O to point A is fraction 1 over 6 times the slope of the line from point A to point B.

It is fraction 1 over 6 throughout the line.

The slope from point O to point A is six times the slope of the line from point A to point B.

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:

chiken

step-by-step explanation:

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.