Consider the sequence of steps to solve the equation:
5(x - 3) = 7x/2
step 1 ⇒ 10(x - 3) = 7x
step 2 ⇒ 10x - 30 = 7x
step 3 ⇒ 3x - 30 = 0
step 4 ⇒ 3x = 30
step 5 ⇒ x = 10
identify the property of equality which gets us from step 3 to step 4.
a) division property
c) subtraction property
b) addition property
d) multiplication property

Acone with volume 1350 m³ is dilated by a scale factor of 1/3. what is the volume of the resulting cone? enter your answer in the box. m³

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

The equation shown below represents function f. f(x)= -2x+5 the graph shown below represents function g. which of the following statements is true? a. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is less than the y-intercept of function g. b. over the interval [2, 4], the average rate of change of f is greater than the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. c. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. d. over the interval [2, 4], the average rate of change of f is less than the average rate of change of g. the y-intercept of function f is the same as the y-intercept of function g.