Create 2 new equivalent fractions by multiplying the numberator and denominator of the given fractions by a non-zero number.

PLEASE HELP!!!!! 3, 8, 13, 18, 23, ....<br><br> The recursive formula for this sequence is:

rodikova [14]

Answer:

a₈ = 37

Step-by-step explanation:

The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .

The recursive formula for the sequence is: $a_n = a_{n - 1} + 5$

Here, $a_n$ represents the $n^{th}$ of the sequence.

And, $a_{n - 1}$ represents the $(n - 1)^{th}$ of the sequence.

'+5' denotes that '5' is added to the $(n - 1)^{th}$ term to get the $n^{th}$ term. In other words, the difference between two consecutive numbers in the sequence is 5.

Now, we are asked to find a₈ i.e., n =8.

Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.

So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.

⇒ a₆ = 23 + 5 = 28.

⇒ a₇ = 28 + 5 = 32.

⇒ a₈ = 32 + 5 = 37.

Therefore, the $8^{th}$ term of the sequence is 37.

8 0

3 years ago

If the ratio of a to b is 2.3 and the ratio

viva [34]

Answer:5.7 D

Step-by-step explanation:

4 0

3 years ago

Which statement describes the translation of y = −1/5 (x + 5)2 + 2 from standard position? Standard position is when the vertex

stellarik [79]

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

f(x + n) - move the graph n units to the left

f(x - n) - move the graph n units to the right

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$f(x)=-\dfrac{1}{5}x^2\\\\f(x+5)=-\dfrac{1}{5}(x+5)^2\\\\f(x+5)+2=-\dfrac{1}{5}(x+5)^2+2$

<h3>B. Moved 2 units up and 5 units to the left.</h3>

3 0

3 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Juliette [100K]

Hello,
Please, see the attached files.
Thanks.

3 0

3 years ago

Find the minimum and maximum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f

nata0808 [166]

Via Lagrange multipliers:

$L(x,y,\lambd)=x^2y+x+y+\lambda(xy-5)$
$L_x=2xy+1+\lambda y=0$
$L_y=x^2+1+\lambda x=0$
$L_\lambda=xy-5=0$

$\underbrace{10}_{2xy}+1+\lambda y=0\implies \lambda=-\dfrac{11}y$
$xy=5\implies y=\dfrac5x\implies\lambda=-\dfrac{11}5x$

$\impliesx^2+1+\left(-\dfrac{11}5x\right)x=0\implies x^2=\dfrac56\implies x=\pm\sqrt{\dfrac56}$
$xy=5\implies y=\pm\sqrt{30}$

At these points, we get local minima of $f\left(\pm\sqrt{\dfrac56},\pm\sqrt{30}\right)=\pm2\sqrt{30}$ .

- - -

Another way to do this is to make $f(x,y)$ a function independent of $y$ , which is made possible by the constraint.

$xy=5\implies y=\dfrac5x$
$\implies f(x,y)=f\left(x,\dfrac5x\right)=F(x)=6x+\dfrac5x$
$\implies F'(x)=6-\dfrac5{x^2}=0\implies x=\pm\sqrt{\dfrac56}$

and so on.

8 0

3 years ago

Create 2 new equivalent fractions by multiplying the numberator and denominator of the given fractions by a non-zero number.​

Create 2 new equivalent fractions by multiplying the numberator and denominator of the given fractions by a non-zero number.