3 years ago

Identify the vertex of the function, f(x) = 3(x - 1)² + 5.

Mathematics

1 answer:

Otrada [13]3 years ago

3 0

Answer:

(1,5)

Step-by-step explanation:

You might be interested in

For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

7 0

3 years ago

Find the product ( x ≠ ? )

dsp73

Answer:

-3

Step-by-step explanation:

if x= -3

the denominator becomes 0 and the fraction becomes undefined.

8 0

3 years ago

What is the quotient when 2x + x + 3 is divided by x + 1?

Nat2105 [25]

Answer:

answer is 3

there are two ways to solve it. I hope you understand.

4 0

3 years ago

last year, total sales for your grocery store were $10,342 with returns of $214 and discounts of $599. the linear feet of shelvi

kompoz [17]

Answer:

The answer would be A. $16.6 per linear foot

8 0

3 years ago

Read 2 more answers

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

schepotkina [342]

I need you to be more specific

8 0

3 years ago

Read 2 more answers

Identify the vertex of the function, f(x) = 3(x - 1)² + 5.​

Identify the vertex of the function, f(x) = 3(x - 1)² + 5.