Answer:
-15x^2 +8x -1
Step-by-step explanation:
(3x – 1)(-5x + 1)=
3x(-5x) + 3x(1) - 1(-5x) -1 =
-15x^2 +3x +5x -1 =
-15x^2 +8x -1
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Answer:
∠ ABC = 116°
Step-by-step explanation:
Since the angles are supplementary, they sum to 180° , that is
8x - 36 + 4x - 12 = 180
12x - 48 = 180 ( add 48 to both sides )
12x = 228 ( divide both sides by 12 )
x = 19
Then
∠ ABC = 8x - 36 = 8(19) - 36 = 152 - 36 = 116°
We are to find how long will it take to return to the ground?
Answer:
t = 0.48 sec
Step-by-step explanation:
We are given;
initial velocity; vi = 40 ft/s
hi = 70 ft
acceleration due to gravity; a = 32 ft/s²
Now, we are given that the rocket's height as a function of time is;
h = -12at² + vit + hi
At ground, h = 0
Plugging in the relevant values to obtain ;
0 = -12(32)t² + 40t + 70
-384t² + 40t + 70 = 0
The roots of the equation gives; t = 0.48 sec
Since this is multiple choice ...
• check if B is correct:
x = 0, y = 4, z = 1 ⇒ 3x - y + 4z = -4 + 4 = 0 ≠ -10
(it's not)
• check if C is correct:
x = -2, y = 4, z = 0
⇒ 3x - y + 4z = -6 - 4 + 0 = -10
⇒ 3x - y + 4z = 2 + 4 + 0 = 6
⇒ 3x - y + 4z = -4 - 4 + 0 = -8
While this solution does satisfy the system, it can still have infinitely many other solutions that would work.
• check if D is correct:
Eliminate one of the variables from each equation. For instance,
(3x - y + 4z) + (-x + y + 2z) = -10 + 6
2x + 6z = -4
x + 3z = -2
and
(2x - y + z) + (-x + y + 2z) = -8 + 6
x + 3z = -2
but now it's impossible to eliminate one of the variables.
Therefore there are infinitely many solutions to the system [D].
It sounds like your book is asking "what is the probability that the card is either a black card or a 9"
If so, there are 26 black cards (13 spades and 13 clubs) and four cards that have "9" on them (one in each suit). We have 26+4 = 30 cards that are either one or the other. There is overlap though. Namely the 2 black cards that have "9" on them (we count them twice), so we should subtract to get 30-2 = 28
There are 28 cards that either have a '9' on them, they are black, or both
This is out of 52 cards total
Divide the two values: 28/52 = 14/26 = 7/13 = 0.53846
Answer as a fraction: 7/13
Answer in decimal form: 0.53846
Answer as a percentage: 53.846%
Side note: the decimal form and percentage form are approximate
