All categories

4 years ago

Find the sum of the constants a, h, and k such that

Mathematics

1 answer:

ra1l [238]4 years ago

6 0

Answer:

Step-by-step explanation:

The value of "a" is the coefficient of x^2, so we know that is 2.

Solve for h

Now, we have ...

2x^2 -8x +7 = 2(x -h)^2 +k

Expanding the right side gives us ...

= 2(x^2 -2hx +h^2) +k

= 2x^2 -4hx +2h^2 +k

Comparing x-terms, we see ...

-4hx = -8x

h = (-8x)/(-4x) = 2

Solve for k

Now, we're left with ...

2h^2 +k = 7 = 2(2^2) +k = 8 +k

Subtracting 8 we find k to be ...

k = 7 -8 = -1

And the sum of constants a, h, and k is ...

a +h +k = 2 +2 -1 = 3

The sum of the constants is 3.

You might be interested in

Solve the inequality. 4x+6<3x-5

Scrat [10]

Answer:

4x+6<3x-5

4x+6 =3x-5

collect like terms

4x-3x =3x-5

x= -11

x<-11

5 0

3 years ago

2 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Ivanshal [37]

Answer:

This series is divergent

Step-by-step explanation:

we are given a series

Firstly, we will find nth term

Numerator:

3, 4, 5,...

so, nth term will be

$a_n=n+3$

Denominator:

4,5,6,....

so, nth term will be

$b_n=n+4$

so, we can find it's nth term as

$c_n=\frac{n+3}{n+4}$

we can use divergent test

$\lim_{n \to \infty} c_n=\lim_{n \to \infty} \frac{n+3}{n+4}$

we can divide top and bottom by n

$\lim_{n \to \infty} c_n= \lim_{n \to \infty} \frac{n/n+3/n}{n/n+4/n}$

$\lim_{n \to \infty} c_n= \lim_{n \to \infty} \frac{1+3/n}{1+4/n}$

now, we can plug n=inf

$\lim_{n \to \infty} c_n= \frac{1+0}{1+0}$

$\lim_{n \to \infty} c_n=1$

Since, it is non-zero value

so, this series is divergent

8 0

3 years ago

The area of a regular octagon is 35 cm squared what is the area of a regular octagon with sides five times as long

KATRIN_1 [288]

The answer would be 875cm squared

7 0

3 years ago

Read 2 more answers

A submarine at a depth of -25 2/3feet descended 5 1/3. How many feet must the submarine rise to reach the surface?

zheka24 [161]

Answer:

it descended 31 Feet b b b b b b b b b bb b b b b b b b b b b

7 0

3 years ago

Mr. Cornapple is the fruit & vegetable buyer for a large school district. In a given week, he has a budget of $6,550. Bushel

Nina [5.8K]

Answer:

40x + 30y ≤ 6,550

Step-by-step explanation:

Given:

Cost of each apple bushels = $40

Cost of each corn bushels = $30

Total budget = $6,550

Find:

Inequality

Computation:

Assume;

Total number of apple bushels = x

Total number of corn bushels = y

So,

40x + 30y ≤ 6,550

6 0

3 years ago