Answer:
3/16
Step-by-step explanation:
16 pupils, 11 play both, 1 plays piano only and 1 flute only
⇒ 11 + 1 + 1 = 13 pupils who play at least one instrument
⇒ 16 - 13 = 3 pupils who don't play either instrument
⇒ Out of the 16 total pupils, 3 play neither, putting this into numbers:
which is then also the answer.
Keep in mind both of these angles are equal to each other meaning the equation will have a = So...
4x+7=5(x-4)
Now multiply 5 to x and 4
4x+7=5x-20
Now subtract 4x from 5x
7=1x-20
Now add 20 to both sides
27=x
So x=27
This must be FALSE, because:
7 players x 4(which is the range) = 28 which means that the total number of baskets made is 28.
If the greatest is 8, we must do 28 - 8, which gives us 20. This means that the remaining 6 players (7 - 1 = 6) made a total of 20 baskets.
However, if the fewest is 4 baskets, this means that the remaining 5 players (6 - 1 = 5) must have made a total of 16 baskets (20 - 4 = 16) and that each player must have scored 4 or more baskets each (since 4 was the fewest number of baskets made).
But this is impossible because if the remaining 5 players scored 4 (fewest number possible) each, it would give us 20 (4 x 5). But they should have made 16, or else the total of all the baskets would not be 28 (look back at start).
This means that the statement is impossible and therefore FALSE.
Hope this helped :)
You need to find points where the line g(x) intercepts the quadratic function f(x) in one and only one point.
Then 3x^2 + 4x -2 = mx - 5
solve 3x^2 + 4x - mx -2 + 5 = 0
3x^2 + (4 - m)x + 3 = 0
In order to there be only one solution (one intersection point) the radicand of the quadratic formula must be 0 =>
b^2 - 4ac = (4 - m)^2 - 4(3)(3) = 0
(4 - m)^2 = 24
4 - m = +/- √(24)
m = 4 +/- √(24) = 4 +/- 2√(6)
Then m, the slope of the line, may be 4 + 2√6 and 4 - 2√6
It should be 10...because the 2 angles in the base are the same so the length is mirrored
