Answer:
a = 2
b = 5
Step-by-step explanation:
Given :
(ar^b)^4 = 16r^20 ; a and b are positive integers :
Opening the bracket :
a^4r^4b = 16r^20
a^4 = 16 - - - - - (1)
r^4b = r^20 - - - (2)
a^4 = 16
Take the 4th root of both sides :
(a^4)^(1/4) = 16^1/4
a = 2
From (2)
r^4b = r^20
4b = 20
Divide both sides by 4
4b/4 = 20/4
b = 5
Hence ;
a = 2
b = 5
You can write two equations using the given information:
.. L = W +8
.. L * W = 609
Using substitution, you get a quadratic.
.. (W +8) * W = 609
.. W^2 +8W -609 = 0
Not surprisingly, you're looking for factors of 609 that differ by 8.
.. 609 = 1*609 = 3*203 = 7*87 = 21*29
The last two are the factors of interest.
.. (W +29)(W -21) = 0
The width of the rectangle is 21 feet, the length is 29 feet.
_____
Sometimes it is easier to work with the average dimension. Here, let that be x. Then you have
.. (x +4)(x -4) = 609
.. x^2 -16 = 609
.. x^2 = 625 = 25^2 . . . . . . . one of your memorized math facts
So, the dimensions are
.. 25 +4 = 29 by 25 -4 = 21, that is, 29 ft by 21 ft.
Answer:
C. 24 and 96
Step-by-step explanation:
He starts with 3 and follows the rules. multiply by 2
which numbers could be in devons pattern?
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48
48 × 2 = 96
96 × 2 = 192
The numbers that could be in Devon's pattern includes: 6, 12, 24, 48, 96, 192 etc
Therefore, the answer is C. 24 and 96
Answer:
Option (D).
Step-by-step explanation:
If the graph of a relation has two output values for a single input value, relation will not be considered to be a function.
Option (A).
For the input values of x = -1, there are two output values, y = -1, 1.
Therefore, given relation is not a function.
Option (B).
Since, all the parabolas don't represent a function, given parabola in the graph is not a function.
Option (C).
Not a function. It's a relation.
Option (D).
Line plotted in the graph has a distinct output value for every input value.
Therefore, the given graph represents a linear function.
