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
Answer:
5.2 × 
Step-by-step explanation:
a number in scientific notation is expressed as
a × 
where 1 ≤ a < 10 and n is an integer
write 0.0052 as a number between 1 and 10, that is 5.2
we have to the move the decimal point 3 places to the left to retain it's value
3 places left means n is - 3
0.0052 = 5.2 ×
Answer:
The team has 92 wins and 38 losses.
Step-by-step explanation:
In a season 130 games are played by a baseball team.
Let us assume that the team wins x games and losses y games.
Therefore, we can write, x + y=130....... (1)
It is given that if the team won sixteen more games twice as many games as it lost.
So, we can conclude that x =2y+16 ......(2)
Hence, solving equations (1) and (2) we get, (2y+16) + y =130
⇒ 3y = 114
⇒ y =38
And from equation (2), x = 2×38 + 16 = 92
Therefore, the team has 92 wins and 38 losses. (Answer)
Answer:
We multiplied by a negative number (-8)
We divided by a negative number (-8)
Step-by-step explanation:
Multiplying or dividing both sides of an equation by a negative number changes the inequality of the equation, because it changes the sign of each side of the equation
the solutions to a general quadratic equation is
X=-b±√b²-4ac/2a ,, When ax²+bx+c=0
the discriminant is the expression under the radical b²−4ac
Part A:
discriminant is (-16)² - 4(9)(60) = -1904
there are two complex solutions
Part B:
4x² + 8x − 5 = 0
4x² + 10x -2x - 5=0
2x ( 2x + 5) - 1(2 x + 5) =0
(2x + 5)(2x-1) = 0
/ \
/ \
2x+5 = 0 2x-1 =0
x = -5/2 x = 1/2
