Answer:
<em>A) The reference angle should be </em><u><em>
,</em></u><em> and the sign of the value should be </em><u><em>negative.</em></u>
Step-by-step explanation:
cos(
)
Remove full rotations of 2π until the angle is between 0 and 2
.
cos(
)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.
-cos(
)
The exact value of cos(
) is
.
−
Answer:
15% = $5100
7% = 900
Step-by-step explanation:
With simultaneous equations we can take the easier number like numbers that end in 0 or 5 or 2 etc.
We have 7% which is a prime and 15 so we call and name 'x' = amount
invested at 15%
x = the amount invested at 15%
Then 6000-x = the amount invested at 7%
The total interest earned is $710.
Therefore solve the simultaneous equation by substituting the 6000-x
0.15x + 0.08 (6000-x) = 710
Solve for x:
0.15x - 0.07x + 353 = 780 -> x = 357/0.07= $5100
Therefore the amount invested at 7% interest = 6000 - 5100 = $900
and here, 6000-900 = 5100 = 15%
Answer:
( 1+t , -1+t , 5-t )
Step-by-step explanation:
Direction vector:
( 5-1, 3+1, 1-5) = (4, 4, -4)
You can also take a scalar multiple
So, I'm using (1, 1, -1) as the direction vector
x(t) = 1+t
y(t) = -1+t
z(t) = 5-t
Answer: ![x + 18.99 \leq 24](https://tex.z-dn.net/?f=x%20%2B%2018.99%20%5Cleq%2024)
Step-by-step explanation:
Since, the cost of bus fair = x dollars,
Also, a baseball cap which is $18.99 is needed to buy with the given money,
Hence, total expenditure = x + 18.99
While the given money for spending = 24 dollars,
That is, the expenditure can not be exceeded to $ 24.
Thus, the required inequality,
![x + 18.99 \leq 24](https://tex.z-dn.net/?f=x%20%2B%2018.99%20%5Cleq%2024)
Answer:
Step-by-step explanation:
We have given a parallelogram ABCD.
For a parallelogram,
Opposite pair of sides are parallel to each other.
i.e AD is parallel to BC and AB is parallel to CD.
From the attached figure,
∡1 = ∡4 and ∡2 = ∡3 {If two parallel lines cut by a transversal line then alternate interior angles are congruent }
Next, AC ≅ AC {Reflexive identity}
hence, ΔABC ≅ ΔCDA , By Angle-Side-Angle(ASA) congruent property of triangle.
Therefore, AB = CD and AD = BC {Proved}