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1 year ago

Write an explicit equation for the following sequence. 100, 97, 94, 91, ...

Mathematics

1 answer:

pishuonlain [190]1 year ago

6 0

Answer:

$a_{n}$ = 103 - 3n

Step-by-step explanation:

there is a common difference between consecutive terms , that is

97 - 100 = 94 - 97 = 91 - 94 = - 3

This indicates the sequence is arithmetic with explicit equation

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 100 and d = - 3 , then

$a_{n}$ = 100 - 3(n - 1) = 100 - 3n + 3 = 103 - 3n

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Please help!!!!!!!!!!!!!

aivan3 [116]

Answers:

Step-by-step explanation:

We must simplify each option to see if they are equivalent to $-\frac{3}{8}$ .

Lets try A.

$-\frac{6}{16}$ can be simplified to $-\frac{3}{8}$ by dividing both the numerator and denominator by 3.

$-\frac{6}{16}$ ÷ $\frac{3}{3} = -\frac{3}{8}$

A is correct!

Lets try B

$\frac{12}{32}$ simplifies to $\frac{3}{8}$ . However, because this answer is not negative, it is not equivalent.

Lets try C

There is a negative in the numerator, making this fraction negative. So yes, $\frac{-3}{8} = -\frac{3}{8}$ .

Bonus Info: If there was a negative in both the numerator and denominator, the two negatives would cancel eachother out, making the fraction positive

C is correct!

Lastly, Lets try D

There is a negative in the denominator, so this fraction is negative. $\frac{9}{-24}$ can be simplified by dividing by 3 to $-\frac{3}{8}$ .

$\frac{9}{-24}$ ÷3 = $-\frac{3}{8}$

D is correct!

Hope this helped you!~

6 0

3 years ago

Joel can run around a 14– mi track in 81 sec, and Jason can run around the track in 69 sec. If the runners start at the same poi

Alenkasestr [34]

Answer:37.2 sec

Step-by-step explanation:

Given

Joel takes 81 sec for 14 mile long track

speed of joel $\frac{14}{1.35}$ mi/min=10.37 mi/min

Jason takes 69 sec for 14 mi track

so jason speed is $\frac{14}{1.15} mi/min=12.17 mi/min$

if both starts from same spot in opposite direction then

$\frac{x}{10.37}=\frac{14-x}{12.17}$

where x is distance covered by Joel

then x=6.44 miles

therefore time required

$t=\frac{6.44}{10.37}=0.621 min\approx 37.2 sec$

8 0

3 years ago

If P is parentheses and M is Multiplication and S is subtraction, what is EDA In PEMDAS? Very confused!

Studentka2010 [4]

E is exponents, D is division, A is addition

5 0

3 years ago

Read 2 more answers

A farmer owns 70 acres of land. Of the 70 acres, only 65% can be farmed. How many acres are available for farming? acres are ava

denis-greek [22]

45.5 acres of land can be farmed and 24.5 cannot be farmed.

4 0

2 years ago

Please please help me please help please please help me please help please

AVprozaik [17]

Answer:

Perimeter is 17.07

Step-by-step explanation:

We know that DF = EF = 5 cm, since D and E are the midpoints of AC and AB, both of which are 10 cm in length.

We need to use the Pythagorean theorem to get the length of DE.

$DE = \sqrt{5^{2} +5^{2}}=\sqrt{50} = 7.07\\$

So the perimeter of DEF is 5 + 5 + 7.07 = 17.07

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3 years ago