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Answer:
a = √11 and b = 6
Step-by-step explanation:
Refer to attached picture for reference
for an right triangle with angle θ
we are given
cos θ = 5/6 = length of adjacent side / length of hypotenuse
hence
adjacent length = 5 units
hypotenuse length = 6 units
the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:
hypotenuse ² = adjacent ² + opposite² (rearrange)
opposite ² = hypotenuse ² - adjacent ²
opposite ² = 6² - 5²
opposite = √ (6²-5²) = √11
sin θ = opposite length / hypotenuse (substitute values above)
sin θ = √11 / 6
hence a = √11 and b = 6
the answer is x is equal to -4
x=-4
It's simply 4,2,0,-2..... the pattern is just subtracting two as you go on.
Answer:
B.a=b, c≠0
C.a=b, c=0
D.a-b=1, c≠1
Step-by-step explanation:
The equation given is c = ax - bx. We can factor the right-hand side to obtain an equivalent equation which is c = (a-b)x
Let’s explore each answer choice given. We are looking for cases where there is no one solution for the equation.
A
a-b = 1 so the right-hand side becomes 1x and we have x=c. Since c is 0 we have one solution that is x=0
B
a=b so a-b =0 and the equation becomes 0=c but the answer choice says c does not equal zero. So in this case there is no solution. This is a correct answer to the problem.
C
This is the same as choice B but since C =0 both sides of the equation equal zero. We get 0=0 but notice that this is true no matter what the value of x is so this equation is called identity and any value of x will do so there isn’t one solution but rather infinitely many. This is another right answer.
D
Here a-b=1 so we end up with x = c and since c doesn’t equal one any value of x except 1 is a solution so there isn’t one solution but infinitely many. This too is an answer to the question.
E
Since a doesn’t equal b and since c = 0 we have (a-b)x = 0 so. Either a-b is zero but since a and b are different this can’t be or x is zero. This there is one solution: x=0.
<em>From the above, the answer to the question is choices </em><em>B, C, and D</em>
