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3 years ago

Given ΔKLM with lengths as marked, what is the relationship of segment NO to segment KL?

Mathematics

1 answer:

Oliga [24]3 years ago

6 0

Segment NO is parallel to the segment KL.

Solution:

Given KLM is a triangle.

MN = NK and MO = OL

It clearly shows that NO is the mid-segment of ΔKLM.

By mid-segment theorem,

The segment connecting two points of the triangle is parallel to the third side and is half of that side.

⇒ NO || KL and $NO = \frac{1}{2}KL$

Therefore segment NO is parallel to the segment KL.

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Generate the nest three terms of each arithmetic sequence shown below.

o-na [289]

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

A)a1=-2 and d=4

We know that the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{2}=a_{1}+(2-1)d$

$a_{2}=a_{1}+(1)d$

Substituting the given value we get

$a_{2}= -2+(1)4$

$a_{2}= -2+4$

$a_{2}= 2$

------------------------------------------

Similarly

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the given value we get

$a_{3}= -2+(2)4$

$a_{3}= -2+8$

$a_{3}= 6$

-------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the given value we get

$a_{4}= -2+(3)4$

$a_{4}= -2+16$

$a_{4}= 10$

-------------------------------------------------------------------------------------------

B $a_n=a_{(n-1)}-8$ with $a_1=10$

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

$a_4= -14$

-------------------------------------------------------------------------------------------

C) $a_1=3, a_2=1$

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

$a_{4}= 3+(3)-2$

$a_{4}= 3-6$

$a_{4}= -3$

----------------------------------------------------------------------------------

$a_{5}=a_{1}+(5-1)d$

$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

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Answer:

Step-by-step explanation:

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2 years ago

Expressed as a product of its prime factors in index form, a number N is

Elena-2011 [213]

ANSWER

$5N^2=3^{2} \times 5^{5} \times x^{6}$

EXPLANATION

$N=3\times5^2 \times x^3$ .

$5N^2=5(3\times5^2 \times x^3)^2$

Recall this property of exponents;

$(a^m)^2=a^{m} \times a^m$

So our product becomes;

$5N^2=5(3\times5^2 \times x^3) \times (3\times5^2 \times x^3)$

$5N^2=5\times 3\times 3 \times 5^2 \times 5^2 \times x^3 \times x^3$

$5N^2=3\times 3\times 5 \times 5^2 \times 5^2 \times x^3 \times x^3$

Recall this law of exponents:

$a^m \times a^n =a ^{m+n}$

$5N^2=3^{1+1} \times 5^{1+2+2} \times x^{3+3}$

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3 years ago

1. Which description best describes the solution to the following system of equations?

Alisiya [41]

1. The best answer is A since a solution is where 2 lines intersect. Whether or not they intersect the x or y axis is completely irrelevant (so is whether they intersect the origin).

2. y=-x+5
-x+5=1/2x+2
-x+3=1/2x
3=3/2x
2=x

y=-(2)+5
y=3

Answer: (2,3)

3. It seems like the lines are completely on top of each other (coinciding) so there are infinitely many solutions.

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3 years ago

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