1) Approximating slopes of tangent lines using the process shown last week for the function f(x) = 3-x at the point (2, -1). Using a straightedge, draw a tangent line as accurately as possible at
the point (2, - 1). Then draw a secant line through the points (2, -1) and (3, -6). We will refer to that as
the right secant line. Draw another secant line, this time through the points (1, 2) and (2, - 1). This is the
left secant line. Answer the following questions.
a. What is the slope of the left secant line?
b. What is the slope of the right secant line?
c. Using the results above, fill in the blanks with numerical values:
< slope of tangent line <
d. Based on the foregoing, what is your best numerical estimate of the tangent line.

Scale factor of 2 is used to enlarge a figure as shown below the area of is 18 in.²

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.

Examine the paragraph proof. which theorem does it offer proof for? prove jnm – nmi according to the given information in the image. jk | hi while jnm and lnk are vertical angles. jnm and lnk are congruent by the vertical angles theorem. because lnk and nmi are corresponding angles, they are congruent according to the corresponding angles theorem. finally, jnm is congruent to nmi by the transitive property of equality alternate interior angles theorem gorresponding angle theorem vertical angle theorem o same side interior angles theorem