Please answer this like I
1 answer:
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<h2>Answer:</h2>
Option: D is the correct answer.
D. The slope of is 3, and passes through O.
<h2>Step-by-step explanation:</h2>It is given that:
AB is dilated by a scale factor of 3 to form AB .
Also, the line AB pass through the origin.
So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:
( Since, it is given the slope of AB is 3 )
Now , if AB is dilated to A'B' by a scale factor of 3 then
(0,0) → (0,0)
and
(x,y) → (3x,3y)
i.e. (0,0) and (3x,3y) will lie on A'B'.
Hence, the slope of line A'B' is given by:
Hence, both have the same slope.
The answer is : Option: D
Check the picture below.
of course, that's the slope simplified, now, taking a peek at the non-simplified slopes that are shaded, the larger triangle will have a larger "run" and a larger "rise" and thus a larger slope than the smaller one.
So we can say that from the origin to A, the non-simplified slope is larger than from A to B.
<h3>Given</h3>
72 blue, 42 red beads
beads are used to make identical necklaces
<h3>Find</h3>(a) the greatest number of necklaces that can be made
(b) the number of each color bead in each necklace
<h3>Solution</h3>You can write and factor the equation
... necklaces = 72 blue + 42 red
... necklaces = 6(12 blue + 7 red)
where 6 is the greatest common factor (GCF) of 72 and 42.
(a) You can make up to 6 identical necklaces. 6 is the largest common factor of 72 and 42. If you were to try to make more, they could not be identical.
(b) Each necklace can consist of 12 blue and 7 red beads. These are the numbers obtained when the total bead count is divided into 6 equal groups.
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There are several ways you can find the GCF of two numbers. For small numbers, it is generally feasible to use your knowledge of multiplication tables and factors to choose the largest common factor of two numbers. You can also use Euclid's algorithm, which is to repeatedly compute
... (largest number) modulo (smallest number)
until the result is zero. The final "smallest number" is the GCF.
Here, that looks like
... 72 mod 42 = 30
... 42 mod 30 = 12
... 30 mod 12 = 6
... 12 mod 6 = 0 . . . . . . . so 6 is the GCF
___
Of course, you know that
... 72 = 2³×3²
... 42 = 2×3×7
so, the largest set of common factors is 2×3 = 6.
___
Your graphing calculator may have a function for computing the greatest common divisor (GCD), too. The TI-84 does, for example.