Marrisa added 1.56 and 13.47. She got 29.07. What mistake could Marrisa have made? She forgot to move the decimal point to the left after she added. She lined up the front numbers instead of the decimal places. She lined up the last numbers instead of the decimal places. She didn’t carry correctly between place values.

without an explanation your answer is (B) She lined up the front numbers instead of the decimal places.

if you need an explanation here:

For a problem with a decimal in the numbers, you ALWAYS have to line them up or your answer will be incorrect.

She should have put: 13.47

                                 +  1.56

                                    15.03

therefore, 15.03 would have been her correct answer. :-)

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d