Lcm and gcf of 8 and 18
2 answers:
Step-by-step explanation: To find the least common multiple or (lcm) of 8 and 18, begin by listing the multiples of each number.
<u>Multiples of 8</u>
1 × 8 = 8
2 × 8 = 16
3 × 8 = 24
4 × 8 = 32
5 × 8 = 40
6 × 8 = 48
7 × 8 = 56
8 × 8 = 64
9 × 8 = 72
Notice that we did not list 0 × 8 in our list of multiples and that's because 0 multiplied by 8 is 0 and 0 cannot be our least common multiple.
Now, let's list the multiples of 18. When listing the multiples of 18, it's a good idea to keep an eye on the list of multiples for 8 so that we will notice when we find a least common multiple.
<u>Multiples of 18</u>
1 × 18 = 18
2 × 18 = 36
3 × 18 = 54
4 × 18 = 72
Now, we can stop here because we found the least common multiple of 8 and 18 which is 72.
Greatest common factor is provided in the image attached.
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When two lines intersect, the angles across from the intersection (the "X") are congruent (equal), and referred to as "vertical angles."
So by the rule of vertical angles are congruent, we can set them equal:
to factor we need the factors of 84:
1×84, 2×42, 3×28, 4×21, 6×14
Now we need one of those factors ×2 ( from the x^2 term) minus the other factor to equal 13 (the middle term)
it turns out that if we use 4×21: 4×2 = 8
and 21-8 = 13. Woohoo! we got it
So now we have:
Now set each factor = 0
1) 2x - 21 = 0 and 2) x + 4 = 0
1) 2x - 21 = 0, 2x = 21, x = 21/2 = 10.5
2) x + 4 = 0, x = -4
Now we plug in each answer to check:
1) x = 10.5
1/2x + 42 = 1/2(10.5) + 42 = 5.25 + 42 = 47.25
47.25 = 47.25
BAM SO IT LOOKS LIKE THAT'S IT!!
But let's check 2) first:
2) x = -4
1/2x + 42 = 1/2(-4) + 42 = -2 + 42 = 40
40 = 40, so both work!!
But it asks for m<1, and <1 is supplementary because it lies on same line, meaning the sum of both = 189
Therefore m<1 = 180 - 47.25 = 132.75°
OR m<1 = 180 - 40 = 140°
So by the rule of vertical angles are congruent, we can set them equal:
to factor we need the factors of 84:
1×84, 2×42, 3×28, 4×21, 6×14
Now we need one of those factors ×2 ( from the x^2 term) minus the other factor to equal 13 (the middle term)
it turns out that if we use 4×21: 4×2 = 8
and 21-8 = 13. Woohoo! we got it
So now we have:
Now set each factor = 0
1) 2x - 21 = 0 and 2) x + 4 = 0
1) 2x - 21 = 0, 2x = 21, x = 21/2 = 10.5
2) x + 4 = 0, x = -4
Now we plug in each answer to check:
1) x = 10.5
1/2x + 42 = 1/2(10.5) + 42 = 5.25 + 42 = 47.25
47.25 = 47.25
BAM SO IT LOOKS LIKE THAT'S IT!!
But let's check 2) first:
2) x = -4
1/2x + 42 = 1/2(-4) + 42 = -2 + 42 = 40
40 = 40, so both work!!
But it asks for m<1, and <1 is supplementary because it lies on same line, meaning the sum of both = 189
Therefore m<1 = 180 - 47.25 = 132.75°
OR m<1 = 180 - 40 = 140°
Answer:
k=17
Step-by-step explanation:
Given F(x)=2x+3 shifts 10 units when it is replaced with the graph f(x)=2x-k.
The method to solve this kind of questions is find where the graph meets the x axis then add ten units to it .The obtained x coordinate is the point where the second graph meets the x axis.
Now first find where the F(x)=2x+3 meets the x axis by substituting F(x)=0.
Now add 10 to this x coordinate , we get x1==
this is x coordinate where the second line meets the x-axis.
The second line is F(x)=2x-k.
now f(x)=0 and x=17/2
On substitution we get
k=17