X = height of pole (in meters)
With respect to the 50 degree angle, the side x is the opposite leg. It is the leg furthest from the reference angle. The hypotenuse is 5 meters.
The trig function sine ties together the opposite and hypotenuse
sin(angle) = opposite/hypotenuse
sin(50) = x/5
5*sin(50) = x .... multiply both sides by 5
x = 5*sin(50)
------------------
Since x = 5*sin(50) isn't listed as an answer choice, let's try using cosine. We can't use it right away because we don't know the adjacent side. What we can do is change the reference angle. The missing angle of the triangle is 90-50 = 40 degrees. Let's make the 40 degree angle the reference angle
So x is now the adjacent side with respect to the 40 degree reference angle. The hypotenuse is always the longest side. The hypotenuse stays at 5.
cos(angle) = adjacent/hypotenuse
cos(40) = x/5
5*cos(40) = x
x = 5*cos(40)
This expression is listed. The answer is choice B
Answer: 10 inches × 14 inches
Work:
length = x inches
width = x - 4 inches
perimeter = 2(l+w)
48 = 2[(x)+(x - 4)]
48 = 2(2x - 4)
24 = 2x - 4
28 = 2x
14 = x
length = x inches = 14 inches
width = x - 4 inches = 14 - 4 = 10 inches
Answer:
$1.25
Step-by-step explanation:
divide 10/8
equals $1.25
1.25x8=$ 10
First term: a1 = 151
common difference: d = -14 (we decrease by 14 each time, eg, 151-14 = 137)
nth term of this arithmetic sequence is...
an = a1+d(n-1)
an = 151+(-14)(n-1)
an = 151-14n+14
an = -14n+165
This will be used in the formula below
Sn = n*(a1+an)/2
<span>Sn = n*(151+(-14n+165))/2
</span><span>S26 = 26*(151+(-14*26+165))/2 ... replace every n with 26
</span>S26 = -624
The final answer here is choice C) -624
<span>
</span>
ANSWER
EXPLANATION
The given function is:
Factor -3 for the first 2 terms.
We add and subtract the square of the coefficient of x.
Factor the perfect square trinomial.
The vertex form is:
