Answer:
We have 6y² + 13y - 8. We can rewrite this as 6x² + 16x - 3x - 8. Grouping terms we get 2x(3x + 8) - (3x + 8) and since both terms have the common factor of (3x + 8) the answer is (3x + 8)(2x - 1).
Styline menswear ordered short-sleeve shirts for $23 each and long-sleeve shirts for $28.50
short-sleeve shirts for $23
long-sleeve shirts for $28.50
Total cost = $9,862.50
Let x be the number of short - sleeve
and y be the number of long - sleeve
Total shirts = 375
x + y = 375
23x + 28.50y = 9862.50
Now we solve for x
x + y = 375 ( subtract x on both sides)
So y = 375 - x
Now plug in 375 -x for y in second equation
23x + 28.50y = 9862.50
23x + 28.50(375 - x ) = 9862.50
23x + 10687.5 - 28.50x = 9862.50
subtract 10687.5 from both sides
23x - 28.50x = -825
-5.5x = -825 (divide -5.5 on both sides)
x = 150
So number of short-sleeve = 150
-4.5x-2y=-12.5 and 3.25x-y=-0.75
we first multiply the second equation by -2
(-2)*(3.25x-y=-0.75)=-6.5x+2y=-1.5
add the equation to eliminate the y
so yo get (-4.5x-6.5x)=(-12.5-1.5)
-11x=-11
x=1
now we plug in x into any equation to solve for y
-45x-2y=-12.5 and x=1
(-45*1)-2y=-12.5
-4.5-2y=-12.5
-2y=-12.5+4.5
-2y=-8
y=4
then your answer is x=1 and y=4
The drawbridge will be at an incline of 10.56 degrees. That is 5.56 degrees more than it's initial incline of 5 degrees.
If you draw a picture of this situation, you will see that you can write a sine ratio with the 11 and 60 (opposite over hypotenuse)
sin(x) = 11/60 Solve the equation for x
x = 10.56
M∠ rst + m∠ vst = 180°
3 x + 7° + 9 x + 17° = 180°
12 x + 24° = 180°
12 x= 180° - 24°
12 x = 156°
x = 156° : 12
x = 13°
m ∠ rst = 3 · 13° + 7° = 39° + 7° = 46°
m ∠ vst = 180° - 46° = 134°
Answer:
A ) 46° and 134°
