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laila [671]
3 years ago
10

Simplify the expression using the distributive property. 42+7a

Mathematics
2 answers:
Evgesh-ka [11]3 years ago
5 0

Answer:

  7(a +6)

Step-by-step explanation:

7 is a factor of both terms, so we can factor that out.

  42 +7a = 7·6 +7·a = 7(6 +a)

Viefleur [7K]3 years ago
3 0

Answer:

7(6+a)

Step-by-step explanation:

When you are doing this, you have to first find a common factor. In this case it is 7 because 7*6=42 and 7*a=7a. So the common factor is 7 because it has it in both numbers when factoring. You then take the common factor out and see what is left.

So you the the 7 out and whats left is 6+a.

You then write this into an expression. 7(6+a)

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CaHeK987 [17]

Answer:

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5 0
2 years ago
For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

1=a(1+4)\implies a=\frac15

This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
George is reading a book. At the end of 3 hours he has read 90 pages, and at the end of 5
jeka94

Answer:

74 pages/hour

Step-by-step explanation:

The average rate of change is the difference in the numbers of pages  divided by the difference in the numbers of hours.

At the end of 3 hours, 90 pages were read.

At he end of 5 hours, 238 pages were read.

Difference in hours: 5 hours - 3 hours = 2 hours.

Difference in pages: 238 pages - 90 pages = 148 pages

The average rate of change is the difference in pages divided by the difference in hours.

average rate of change = (148 pages)/(2 hours) = 74 pages/hour

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3 years ago
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anzhelika [568]

Answer:

67

Step-by-step explanation:

A linear pair is two angles which form a straight angle when combined (or 180 degrees). Thus do 180 - 113 to get 67 degrees for Angle 2

6 0
3 years ago
Suppose you roll a special 31-sided die. What is the probability that one of the following numbers is rolled?
madreJ [45]

Answer:

34.78 is the answer to ur question

4 0
2 years ago
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