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3 years ago

Linear equation of line with slope 1/4

Mathematics

1 answer:

MrRa [10]3 years ago

4 0

Answer:

1/4x

Step-by-step explanation:

1/4x is a linear equation because it has a constant slope, and the slope of a line is shown before the x.

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For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of

Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is $(-1)^{k+1}(\frac{1}{2^{k}})$ .

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as $(-1)^{k+1}(\frac{1}{2^{k}})$ .

where k is from 1 to 10.

By the given expression sequence will be $\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......$

In this sequence first term "a" = $\frac{1}{2}$

and common ratio in each successive term to the previous term is 'r' = $\frac{\frac{(-1)}{4}}{\frac{1}{2} }$

r = $-\frac{1}{2}$

Since the sequence is infinite and the formula to calculate the sum is represented by

$S=\frac{a}{1-r}$ [Here r is less than 1]

$S=\frac{\frac{1}{2} }{1+\frac{1}{2}}$

$S=\frac{\frac{1}{2}}{\frac{3}{2} }$

S = $\frac{1}{3}$

Now we are sure that the sum of infinite terms is $\frac{1}{3}$ .

Therefore, sum of 10 terms will not exceed $\frac{1}{3}$

Now sum of first two terms = $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

Now we are sure that sum of first 10 terms lie between $\frac{1}{4}$ and $\frac{1}{3}$

Since $\frac{1}{2}>\frac{1}{3}$

Therefore, Sum of first 10 terms will lie between $\frac{1}{4}$ and $\frac{1}{2}$ .

Option D will be the answer.

3 0

3 years ago

Find the midpoint of the segment with the given endpoints.

andrew-mc [135]

To solve for the midpoint of the segment we use the equation that is given as:

(x1 + x2 / 2) , (y1 + y2 / 2)

For the points given,

(x1 + x2 / 2) , (y1 + y2 / 2)
(3+ 2 / 2) , (-5 + 9 / 2)
(5/2 , 2) or (2.5 , 2)

Hope this answers the question. Have a nice day. Feel free to ask more questions.

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3 years ago

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Marc left his house to drive to work. As he heads down his street, his speed increases steadily until he sees the stop sign at t

Anna35 [415]

The third graph is the correct answer :)

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3 years ago

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4x+10= 34<br>can someone help me?

vazorg [7]

Answer: