All categories

3 years ago

What is the 30th term of the arithmetic sequence?

Mathematics

2 answers:

ELEN [110]3 years ago

8 0

Answer:

C. $a_3_0=-101$

Step-by-step explanation:

We have the arithmetic sequence 15,11,7,3,-1,...

Where,

$a_1=15,\\a_2=11,\\a_3=7,\\a_4=3,\\a_5=-1,...$

You can see that the common difference d=(-4), or if you couldn't see the common difference you can calculate it with the formula:

$d=a_n_+_1-a_n$

Then,

$d=a_2-a_1\\d=11-15\\d=(-4)$

Now to find the 30th term of the arithmetic sequence we can use the following formula:

$a_n=a_1+(n-1).d$

Replacing n=30, $a_1=15$ and d=(-4):

$a_n=a_1+(n-1).d\\a_3_0=15+(30-1)(-4)\\a_3_0=15-29.4\\a_3_0=15-116\\a_3_0=-101$

Then the correct option is C. $a_3_0=-101$

anyanavicka [17]3 years ago

7 0

The correct answer is:

C.) -101

You might be interested in

Ana dives into a pool off of a springboard high dive. Her height (in meters above the water), x xx seconds after diving, is mode

vovikov84 [41]

Answer: Ana will hit the water after 3 seconds.

Step-by-step explanation:

The exercise gives you the following function which models Anna's height above the water (in meters) after diving "x" seconds:

$h(x)=-5(x+1)(x-3)$

You can rewrite the function with $h(x)=y$ :

$y=-5(x+1)(x-3)$

In order to calculate the number of seconds Ana will hit the water after diving, the procedure is:

- Substitute $y=0$ into the function:

$0=-5(x+1)(x-3)$

- Solve for "x".

By the Zero Product Property, you know that if $a* b = 0$ , then $a=0$ or $b=0$ .

Then you get:

$x=-1\ or\ x=3$

- Choose the positive value ( $x=3$ )

Then, Ana will hit the water after 3 seconds.

6 0

4 years ago

Find the positive value of X that makes the following equation a true number sentence. X to the power of 2 = 4/49

nasty-shy [4]

Answer:

x = $\frac{2}{7}$

Step-by-step explanation:

Given

x² = $\frac{4}{49}$ ( take the square root of both sides )

x = $\sqrt{\frac{4}{49} }$ = $\frac{\sqrt{4} }{\sqrt{49} }$ = $\frac{2}{7}$

8 0

3 years ago

Please Please Please Help Me

maks197457 [2]

Answer:

(x-y^2)(x^2 +xy^2 +y^4)
(a^2 +b)(a^4 -a^2b +b^2)
(m^3-n)(m^6 +m^3n +n^2)
(p+k^3)(p^2 -pk^3 +k^6)
(a^2+b^3)(a^4 -a^2b^3 +b^6)
(x-y)(x^2 +xy +y^2)(x^6 +x^3y^3 +y^6)

Step-by-step explanation:

In every case, the factorization makes use of the standard form for factoring the sum or difference of cubes:

a^3 +b^3 = (a +b)(a^2 -ab +b^2)
a^3 -b^3 = (a -b)(a^2 +ab +b^2)

1. a=x, b=y^2. Use the formula for the difference.

2. a^2 ⇒ a, b = b. Use the formula for the sum.

3. a=m^3, b=n. Use the formula for the difference.

4. a=p b=k^3. Use the formula for the sum.

5. a^2 ⇒ a, b^3 ⇒ b. Use the formula for the sum.

6. a=x^3, b=y^3. Use the formula for the difference. When you do, the first factor is the difference x^3 -y^3, which can be factored using the difference formula again with a=x, b=y.

4 0

4 years ago

One track coach wants her athletes to race 2 miles around a track to measure how fast each person can run?If the track is 2/3 of

Zina [86]

3 times.

If you use cross multiplication and using 2/3 and 2/1, you would get 6/2, which is equal to 3.

6 0

4 years ago

You're playing a game where you defend your village from an orc invasion. There are 333 characters (elf, hobbit, or human) and 5

zvonat [6]

Answer with explanation:

→Number of characters in the game =3 (elf, hobbit, or human)

→Number of defense tools in the game =5 (magic, sword, shield, slingshot, or umbrella)

⇒Total number of elements in the set ,which consist of 3 characters and 5 defense tools = 3 × 5=15→→{(elf,magic),(elf,sword),(elf,shield),(elf,slingshot),(elf,umbrella),(Hobbit,magic),(Hobbit,sword),(Hobbit,shield),(Hobbit,slingshot),(Hobbit,Umbrella),(Human,magic),(Human,sword),(Human,shield),(Human,slingshot),(Human,Umbrella)}

→Out of 15 different ,pairs of Characters and tools,there are 7 pairs in which ,Hobbit as a character and umbrella as a defense tool is used. (Hobbit,magic),(Hobbit,sword),(Hobbit,shield),(Hobbit,slingshot),(Hobbit,Umbrella), (Human,Umbrella), (elf,umbrella).

Then, required probability

$=\frac{\text{Total favorable outcome}}{\text{Total Possible outcome}}\\\\=\frac{15-7}{15}=\frac{8}{15}$

7 0

3 years ago

Read 2 more answers