Find the perimeter of the shape. A four sided figure JKLM is shown. J is located at negative 3, 4. K is located at negative 1, 6. L is located at 1, 1. M is located at negative 1, 3

9.4 units
11.5 units
13.3 units
15 units
Question 11(Multiple Choice Worth 4 points)
(04.03 MC)

Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (2, −1). She wants to align an important detail on the left edge of her stencil at (4, 1). She knows this is 1:4 of the way to where she wants the end of the stencil. Where is the end of the stencil located?

(12, 9)
(10, 7)
(3.5, 0.5)
(2.5, −0.5)
Question 12(Multiple Choice Worth 4 points)
(04.02 MC)

Randolph is creating rectangle WXYZ so that WX has an equation of y = 1 over 4x + 4. Segment XY must pass through the point (−2, 6). Which of the following is the equation for XY?

y − 6 = 1 over 4(x − (−2))
y − (−2) = 1 over 4(x − 6)
y − 6 = −4(x − (−2))
y − (−2) = −4(x − 6)
Question 13(Multiple Choice Worth 4 points)
(04.03 MC)

Calculate the area of triangle ABC with altitude CD, given A (−7, −1), B (−1, 5), C (0, 0), and D (−3, 3).

9 square units
18 square units
18.5 square units
21 square units
Question 14(Multiple Choice Worth 4 points)
(04.02 MC)

Write an equation of a line parallel to line EF in slope-intercept form that passes through the point (2, 6).

Line EF is shown. E is at negative 2, 5. F is at 1, 3.

y = 2x + 3
y = 3x + 6
y = negative two over 3x + twenty two over three
y = − two over threex + 6
Question 15(Multiple Choice Worth 4 points)
(04.01 MC)

Carla and Jonah are working together to determine if quadrilateral CDEF with coordinates C(2, 3), D(1, 2), E(4, 1), and F(5, 3) has perpendicular sides.

Carla sets up the following equations:
slope of segment CD equals 2 minus 3 all over 1 minus 2
slope of segment DE equals 1 minus 2 all over 4 minus 1

Jonah sets up the following equations:
slope of segment CD equals 2 minus 3 all over 1 minus 2
slope of segment EF equals 3 minus 1 all over 5 minus 4

Who is on track to get the correct answer, and why?

Carla is on the right track because she is finding the slopes of consecutive sides to check for perpendicular sides.
Carla is on the right track because she is finding the slopes of the opposite sides to check for perpendicular sides.
Jonah is on the right track because he is finding the slopes of the opposite sides to check for perpendicular sides.
Jonah is on the right track because he is finding the slopes of consecutive sides to check for perpendicular sides.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

i can you with this sweetie!

step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: