Answer: rational
Step-by-step explanation:
-6 can be written as such an infinite number of ways (just as any rational can be). For example, -6/1, 6/-1, 12/-2, -666/111 and so indeed -6 is rational.
Answer:
23
Step-by-step explanation:
5x6-c
5x6=30
30-c
c=7
30-7=23
9514 1404 393
Answer:
(A) -4 and -2
Step-by-step explanation:
The constant in the function tells you f(0) = 5.
You know that the positive leading coefficient means the value of f(x) will be negative for x-values smaller than some number. The offered answer choices indicate the value x = -4 is a lower bound on the value of c. So, -4 < c < 0, for sure.
To further refine the interval, you would need to know f(-2) and/or f(-1).
f(-2) = (-2)³ -2(-2) +5 = -8 +4 +5 = 1
Then -4 < c < -2.
_____
I find a graphing calculator to be very helpful locating zeros of polynomials.
<span> sin20 * sin40 * sin60 * sin80
since sin 60 = </span><span> √3/2
</span>√3/<span>2 (sin 20 * sin 40 * sin 80)
</span>√3/<span>2 (sin 20) [sin 40 * sin 80]
</span>
Using identity: <span>sin A sin B = (1/2) [ cos(A - B) - cos(A + B) ]
</span>√3/<span>2 (sin 20) (1 / 2) [cos 40 - cos 120]
</span>√3/4<span> (sin 20) [cos 40 + cos 60]
</span>
Since cos 60 = 1/2:
√3/4<span> (sin 20) [cos 40 + (1/2)]
</span>√3/4 (sin 20)(cos 40) + √3/8<span> (sin 20)
</span>
Using identity: <span> sin A cos B = 1/2 [ sin(A + B) + sin(A - B) ]
</span>√<span>3/4 (1 / 2) [sin 60 + sin (-20)] + </span>√3/8<span> (sin 20)
</span>
Since sin 60 = √3/<span>2
</span>√3/8 [√3/2 - sin 20] + √3/8 (sin 20)
3/16 - √3/8 sin 20 + √3/8<span> sin 20
</span>
Cancelling out the 2 terms:
3/16
Therefore, sin20 * sin40 * sin60 * <span>sin80 = 3/16</span>
Answer:
x = 42
Step-by-step explanation:
Cross multiplying is done as follows:
<em>the </em><em>denominator </em><em>of the second </em><em>fraction </em><em>is </em><em>multiplied </em><em>with the </em><em>numerator </em><em>of the first </em><em>equation</em> and <u>denominator of the first fraction is multiplied with the numerator of the second equation</u>
5(3x+6) = 4(4x-3) multiply inside the parenthesis
15x + 30 = 16x - 12 transfer like terms to same side of the equation
30 + 12 = 16x - 15x
42 = x
