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iren [92.7K]
3 years ago
8

Find a_1 and d for an arithmetic sequence with these terms. a_4=9and a_7=18

Mathematics
1 answer:
jonny [76]3 years ago
3 0
\bf \begin{array}{llll}
term&value\\
-----&-----\\
a_4&9\\
a_5&9+d\\
a_6&(9+d)+d\\
&9+2d\\
a_7&(9+2d)+d\\
&9+3d=\underline{18}
\end{array}\\\\
-------------------------------\\\\
9+3d=18\implies 3d=9\implies d=\cfrac{9}{3}\implies \boxed{d=3}

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=3
\end{cases}
\\\\\\
a_7=a_1+(7-1)d\implies 18=a_1+(7-1)3\implies 18=a_1+18
\\\\\\
18-18=a_1\implies \boxed{0=a_1}
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An automotive technician has two job offers. Shop A would pay him a straight salary of $900 per week. Shop B would pay him $25 p
JulsSmile [24]

Given,

The salary for the technician from shop A is $900 per week.

The salary for the technician from shop B is $25 per hour.

The equation for the total pay for shop B is,

\text{Total pay= salary of per hour}\times number\text{ of hour worked}

Taking the total pay as 900. As, to make the shop A and shop B equal.

\begin{gathered} 900=25\times Number\text{ of hour worked} \\ Number\text{ of hour worked}=\frac{900}{25}=36 \end{gathered}

Hence, he would have to log 36 hours during a week at Shop B in order to match the salary at Shop A.

7 0
1 year ago
What is the ratio between 5 footballs and 9 baseballs
____ [38]

Answer:

5:9

Step-by-step explanation:

It's just a way to set up ratios. Whichever number is said first gets put down first, then the number after gets put after.

So, 5:9

Or, you could write it as 5 footballs to 9 baseballs.

This is just my simple understanding of what you're asking since you asked what the ratio is.

Hope I helped!

7 0
3 years ago
What is the solution to 2/3a - 1/6 = 1/3
konstantin123 [22]
The solution would be: a = 3/4
4 0
2 years ago
Read 2 more answers
** 30 POINTS ** <br><br> Anyone got an idea for 7 and 8?
Harrizon [31]
7. i would guess 95-100 people were surveyed. the way you estimate this is by adding the number of students in each category. ex. about 3 in the first bar, about 9 in the next
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5 0
2 years ago
Emily reads a story book. o the first day, she reads 1/9 of the whole book, and on the second day, she reads 24 pages. The ratio
Marina86 [1]

There are 270 pages in this book.

Given that,

Emily reads a storybook the first day,

She reads 1/9 of the whole book, and on the second day, she reads 24 pages.

The ratio of the number of pages read to the remaining pages in the two days is 1:4.

We have to find

How many pages are there in this book?

According to the question,

Let, P is the number of pages,

The first day Emily reads p/9 pages of the whole book,

And the second day she read 24 pages.

The ratio of the number of pages read to the remaining pages in the two days = 1;4 = p/5.

Therefore,

The number of pages reads first day + the number of pages read the second day = The ratio of the number of pages read to the remaining pages in the two days

\rm \dfrac{p}{9} + 24 = \dfrac{p}{5}\\\\ \dfrac{p}{5} - \dfrac{p}{9} = 24\\\\\dfrac{p \times 9 - p\times 5}{45} = 24\\\\ \dfrac{9p-5p}{45} = 24\\\\\dfrac{4p}{45} = 24\\\\4p = 24\times 45\\\\4p = 1080\\\\p = \dfrac{1080}{4}\\\\p = 270 \ pages

Hence, there are 270 pages in this book.

For more details refer to the link given below.

brainly.com/question/14505922

8 0
2 years ago
Read 2 more answers
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