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2 years ago

12

The flagpole casts an 8 foot shadow as shown in the table at the same time the oak tree casts 12-foot shadow how tall is the oak

tree

1 answer:

jolli1 [7]2 years ago

3 0

How tall is the flagpole?

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If this particular arithmetic sequence, a7=34 and a15=74. What is the value of a21

Ilya [14]

This is an arithmetic sequence, meaning, to get the next term, you simply add some value to the current one, namely the "common difference" "d".

now, we know the 17th term is 34, let's go to the 15term then

34 + d
34 + d + d
34 + d + d + d
34 + d + d + d + d
34 + d + d + d + d + d
34 + d + d + d + d + d + d
34 + d + d + d + d + d + d + d
34 + d + d + d + d + d + d + d + d

now, notice, we got to the 15th term, which is 34 + d + d + d + d + d + d + d + d, or namely 34 + 8d, it just so happen we know is 74, therefore,

$\bf 34+8d=74\implies 8d=40\implies d=\cfrac{40}{8}\implies \boxed{d=5}$

ok, now that we know what the common difference is, let's find the first term in the sequence using the 7th term of 34,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=7\\
d=5\\
a_7=34
\end{cases}
\\\\\\
a_7=a_1+(7-1)5\implies 34=a_1+(7-1)5
\\\\\\
34=a_1+30\implies \boxed{4=a_1}$

and now let's use those 2 found folks, to get the 21st term,

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=4\\
d=5\\
n=21
\end{cases}
\\\\\\
a_{21}=4+(21-1)5\implies a_{21}=4+100\implies a_{21}=104$

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2 years ago

Aisha helps out at a petting zoo over the summer. She makes some changes where the animals are kept.

adoni [48]

I believe the awnser is A

3 0

2 years ago

Math 9:The floor of conference hall can be covered completely with tiles. Its length is 36 ft longer than its width. The area of

valentina_108 [34]

What is the question?
I'm assuming it is to find the length and width.
+_= plus or minus
(X+36)
____________
| |
(X) | |
|____________|

X^2+36X-2040<0
X<-36+_(36^2-4*-2040)^(1/2)
-----------------------------------
2
X<-18+_2((591)^(1/2))
This is probably not what you wanted, sorry

8 0

2 years ago

In a recreation park a children's slide is 27 feet long and makes an able of 39 degrees with the ground. Its top is reached by a

timurjin [86]

Each angle on a triangle would add up to 180 degrees. Since a ladder goes straight up, that angle would be 90 degrees. If you add that with the 39 degree angle, you'd get 129. Subtract that from 180 and you have your answer.

3 0

2 years ago

A homemade lip balm consists of coconut oil and beeswax. Coconut oil costs $0.50 per ounce and beeswax costs $2.00 per ounce. If

Alika [10]

Let

a--------> the total cost in dollars of $6$ ounces of coconut oil

b--------> the total cost in dollars of $5$ ounces of beeswax

we know that

$a=0.50 \frac{\$}{ounce}*6=\$3$

$b=2.00 \frac{\$}{ounce}*5=\$10$

therefore

<u>the answer is</u>

the total cost in dollars of $6$ ounces of coconut oil is $a=\$3$

the total cost in dollars of $5$ ounces ofbeeswax is $b=\$10$

7 0

2 years ago

Read 2 more answers