9514 1404 393
Answer:
(c) Yes, because angle 3 and angle 6 are congruent
Step-by-step explanation:
Angles 3 and 6 are "alternate interior" angles. When those angles are congruent, as these are, then the lines crossed by the transversal are parallel.
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We expect angles 5 and 6 to be supplementary because they are a linear pair. That fact says nothing about the relationship of line d to line c.
Mike has 78 feet of fencing available for his garden, this is the perimeter (P) of the rectangle:
Perimeter: P=78 feet
The formula of Perimeter is:
P=2(W+L), where W is the width and L is the length, then:
P=78→2(W+L)=78
Dividing both sides of the equation by 2:
2(W+L)/2=78/2
W+L=39
If the shape is of a golden rectangle, we know:
L=1.6W
Replacing this above:
W+1.6W=39
Adding similar terms:
2.6W=39
Solving for W
2.6W/2.6=39/2.6
W=15 feet
L=1.6W=1.6(15)→L=24 feet
Answer: T<span>he dimensions of the garden are: Width=15 feet and Length=24 feet. </span>
We could do it with algebra. But we can also do it the long way, which is
shorter than the algebraic way.
The digit in the tens place is 3 times the digit in the units place.
So the number MUST be
31, or
62, or
93 .
It can't be anything else.
Now here they are again, with the reverse of each one:
31 . . . 13 The new number is 18 less.
62 . . . 26 The new number is 36 less.
93 . . . 39 The new number is 54 less.
Obviously, the original number is 62.
