Answer:
Step-by-step explanation:
ΔPQS, ΔRQP and ΔRPS are similar (AA). Therefore the sides are in proportion:
We have:
Substitute:
<em>cross multiply</em>
Use the Pythagorean theorem:
Substitute:
A = -16 b = 0 c = 541
Use the quadratic formula which is
x = [-b +- sq root (b^2 -4*a*c)] / 2*a
x = [-0 +-sq root (0 -4*-16*541)] / 2 * -16
x = + - sq root (0 -4*-16*541) / -32
x = + - sq root (34,624) / -32
x = + - 186.075 / -32
x1 = 186.075 / -32 =
<span>
<span>
<span>
-5.81484375
</span>
</span>
</span>
x2 = -186.075 / -32 =
<span>
<span>
<span>
5.81484375
</span>
</span>
</span>
The decay factor of the equation given in the task content is; 0.87.
<h3>What is the decay factor from the equation?</h3>
According to the task content; the equation given is; y = 453(0.87)^4.
By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.
Read more on decay factor;
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Answer:
1. Dave worked for 34 hours.
2. Perimeter of the rectangle is 172 cm.
Step-by-step explanation:
1. Determination of the hours Dave worked.
Let D represent Dave.
Let M represent Mike.
Let J represent John.
Tota time worked by Dave, Mike and John is 56 hours. This can be written as:
D + M + J = 56 ..... (1)
Dave worked 6 more than 4 times as many hours as Mike. This can written as:
D = 6 + 4M .....(2)
John worked 6 less than 3 times as many hours as Mike. This can be written as:
J = 3M – 6 ........ (3)
Substituting the value of F and J into equation 1, we have:
D + M + J = 56
D = 6 + 4M
J = 3M – 6
6 + 4M + M + 3M – 6 = 56
6 – 6 + 4M + M + 3M = 56
8M = 56
Divide both side by 8
M = 56/8
M = 7
Substitute the value of M into equation (2) to obtain the value of D.
D = 6 + 4M
M = 7
D = 6 + 4(7)
D = 6 + 28
D = 34
Therefore, Dave worked for 34 hours .
2. Determination of the perimeter.
Length (L) = 64 cm
Width (W) = 22 cm
Perimeter (P) =?
P = 2(L + W)
P = 2 (64 + 22)
P = 2 (86)
P = 172 cm
Therefore, the perimeter of the rectangle is 172 cm
