Answer:

Step-by-step explanation:
A regular polygon is a shape with equal sides and angles. Because of this, we can write the following equation to set two sides equal to each other:

Solving, we will get a in terms of b:

Now we can substitute a for (b+3) into our equation:

Therefore, the length of each side of this polygon is
.
Since the perimeter of the polygon consists of all five sides, the perimeter is:

Answer: k = -1 +/- √769
<u>Step-by-step explanation:</u>
48x - ky = 11
<u>-48x </u> <u> -48x</u>
-ky = -48x + 11
Slope:
*************************************************************************
(k + 2)x + 16y = -19
<u>- (k + 2)x </u> -<u>(k + 2)x </u>
16y = -(k + 2)x - 19


Slope: 
**********************************************************************************
and
are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.
*
= -1
= 1
Cross multiply, then solve for the variable.
(k + 2)(k) = 16(48)
k² + 2k - 768 = 0
Use quadratic formula to solve:
k = -1 +/- √769
Answer:
0, for q ≠ 0 and q ≠ 1
Step-by-step explanation:
Assuming q ≠ 0, you want to find the value of x such that ...
q^x = 1
This is solved using logarithms.
__
x·log(q) = log(1) = 0
The zero product rule tells us this will have two solutions:
x = 0
log(q) = 0 ⇒ q = 1
If q is not 0 or 1, then its value is 1 when raised to the 0 power. If q is 1, then its value will be 1 when raised to <em>any</em> power.
_____
<em>Additional comment</em>
The applicable rule of logarithms is ...
log(a^b) = b·log(a)
Answer:
MK
Step-by-step explanation:
ML is the short side of right triangle MLK. MJ is the hypotenuse of right triangle MKJ. This gives you a clue that the ratios of interest are the short side to the hypotenuse. All these right triangles are similar, so ...
ML/MK = MK/MJ . . . . . ratio of short side to hypotenuse is the same
ML·MJ = MK² . . . . . . . cross multiply
MK = √(ML·MJ) . . . . . the geometric mean of ML and MJ is MK
Answer:
10.92
Step-by-step explanation:
turn the percent into a decimal, .28
.28×39=10.92