Answer:
Step-by-step explanation:
The slope of the line joining the 2 points is a measure of the average rate of change.
Calculate slope m using the slope formula
m =
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 3, - 2)
m = = = ← average rate of change
Answer:
3
Step-by-step explanation:
The expression is . To find the value, substitute the values x = 3 and y =-2 then follow order of operations.
20x - 30y = -50 ⇒ 20x - 30y = -50
x + 2y = -1 ⇒ <u>20x + 40y = -20</u>
<u>-70y</u> = <u>-30</u>
-70 -70
y = ³/₇
20x - 30(³/₇) = -50
20x - 12⁶/₇ = -50
<u> + 12⁶/₇ + 12⁶/₇
</u> <u>20x</u> = <u>47¹/₇
</u> 20<u /> 20<u>
</u> x = 2⁷/₂₀
(x, y) = (2⁷/₂₀, ³/₇)
Answer:
<em>Option A; the tournament did begin with 128 teams</em>
Step-by-step explanation:
We can see that this equation is represented by compound interest, in other words an exponential function, either being exponential growth or exponential decay;
f ( x ) = a + ( b )^x, where a ⇒ start value, b ⇒ constant, x ⇒ ( almost always considered ) time, but in this case rounds
Option A; The equation is given to be t ( x ) = 128 * ( 1/2 )^x. Given by the above, 128 should represent the start value, hinting that the tournament <em>did indeed begin with 128 teams</em>
Option B; As the rounds increase the number of teams approach 128. Now mind you 128 is the start value, not the end value, which would mean that <em>this statement is false</em>
Option C; The tournament began with 1/2 teams. Theoretically that would not be possible, but besides that the tournament began with 128 teams, only differed by 1/2 times as much every round. <em>This statement is thus false</em>
Option D; This situation actually represents exponential decay. If each round the number of teams differed by 1/2 times as much, the number of teams remaining is less than before, and thus this models exponential decay, not growth<em> ( statement is false )</em>
<em>Answer : Option A; the tournament did begin with 128 teams</em>
(2 x 2) + (4 x 4 x 4) x (4 x 4 x 4) =
4 + 64 x 64 =
4 + 4096 =
4100