<span>2.5 – 1.2x < 6.5 – 3.2x
-1.2x + 3.2x < 6.5 - 2.5
3.2x - 1.2x < 4
2x < 4
x < 4/2
x < 2</span>
Answer:
Step-by-step explanation:
The axis of symmetry can be calculated using the formula:
First we must determine a and b from the quadratic: 
. This is in standard form, with the highest power first in descending order.
Standard form is also: 
If we compare this to the quadratic given, we can conclude that:
Substitute the values for a and b into the formula.
Multiply in the denominator.
Divide.
This can also be determined from the graph. It is the x-coordinate of the vertex or the maximum/minimum. It divides the quadratic into 2 symmetrical halves.
2 cups of flour x cups of flour
–––––––––––– = –––––––––––––
24 cookies 54 cookies
cross multiply
2*54=24x
24x=108
x=4.5
4.5 cups of flour
Answer: Choice C
7 divided by cosec 50 degrees
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Explanation:
Abbreviations:
sec = secant
cot = cotangent
cosec = cosecant (csc is also a widely used abbreviation)
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Let the horizontal leg be x
This leg is opposite the angle 50 degrees. The hypotenuse is 7
Opposite = x
Hypotenuse = 7
We'll either use the sine rule or the cosecant (csc) rule
sine = opposite/hypotenuse
cosecant = hypotenuse/opposite
Since "sine" is nowhere to be found in the answer choices, we'll use the cosecant rule
-----------
cosecant = hypotenuse/opposite
csc(angle) = hypotenuse/opposite
csc(50) = 7/x
x*csc(50) = 7
x = 7/csc(50)
This is why the answer is choice C
