2 years ago

Graph the system of equations on graph paper to answer the question.

Mathematics

1 answer:

Digiron [165]2 years ago

7 0

Answer:

(7,-5)

Step-by-step explanation:

See attached graph.

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3 years ago

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These triangles are congruent by which triangle congruence postulate ?

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(a) SSS (side side side)
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3 years ago

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MArishka [77]

Answer:

The slope of the line segment CD = 9

Hence, option 'D' is true.

Step-by-step explanation:

Given that the slope of line segment = 9

We know that two triangles would be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given that the line segments AB and CD are both parts of the same non-vertical line. It means their slopes must be the same.

Thus, the slope of the line segment CD = 9

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3 years ago

Given that k is a positive integer. Find, in terms of k, an expression for Sn, which is the sum of the integers from 2k to 4k in

Elden [556K]

Answer:

$S_n=3k\cdot (2k+1)=6k^2 +3k$

Step-by-step explanation:

k is a positive integer.

Consider an arithmetic sequence:

$a_1=2k\\ \\a_n=4k\\ \\d=1$

First, find n:

$a_n=a_1+(n-1)\cdot d\\ \\4k=2k+(n-1)\cdot 1\\ \\2k=n-1\\ \\n=2k+1$

Now, find the sum of these 2k+1 terms:

$S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_n=\dfrac{2k+4k}{2}\cdot (2k+1)=\dfrac{6k}{2}\cdot (2k+1)=3k\cdot (2k+1)=6k^2 +3k$

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3 years ago