Over which interval(s) is the function decreasing?
Answer:
25X + 25Y = 1700
25X + 100Y = 3200
Step-by-step explanation:
Given that the principal of a high school spent $1700 for X desk and Y chairs at $25 each. Then, the equation will be
25X + 25Y = 1700 ....... (1)
If he had bought half the number of desk in twice the number of chairs he would have spent 1600. That is
25(X/2) + 25(2Y) = 1600
25X/2 + 50Y = 1600
Find the LCM and cross multiply
25X + 100Y = 3200 ........(2)
Step-by-step explanation:
The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
How to determine the value of sin(2x)
The cosine ratio is given as:
\cos(x) = -\frac 14cos(x)=−
4
1
Calculate sine(x) using the following identity equation
\sin^2(x) + \cos^2(x) = 1sin
2
(x)+cos
2
(x)=1
So we have:
\sin^2(x) + (1/4)^2 = 1sin
2
(x)+(1/4)
2
=1
\sin^2(x) + 1/16= 1sin
2
(x)+1/16=1
Subtract 1/16 from both sides
\sin^2(x) = 15/16sin
2
(x)=15/16
Take the square root of both sides
\sin(x) = \pm \sqrt{15/16
Given that
tan(x) < 0
It means that:
sin(x) < 0
So, we have:
\sin(x) = -\sqrt{15/16
Simplify
\sin(x) = \sqrt{15}/4sin(x)=
15
/4
sin(2x) is then calculated as:
\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)
So, we have:
\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗
4
15
∗
4
1
This gives
\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
Answer: (-0.5, 4)
Step-by-step explanation:
Midpoint formula: 
(x1, x2)=(2, -3)
(y1, y2)=(2, 6)
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Hope this helps!! :)
Please let me know if you have any question or need further explanation
