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3 years ago

HElp fasttttttttttttttttttttttttt

Mathematics

1 answer:

Eduardwww [97]3 years ago

7 0

9514 1404 393

Answer:

-0.16

Step-by-step explanation:

The 'a' value can be found by looking at the difference between the y-value of a point 1 unit from the vertex, and the y-value of the vertex.

Here, that is a negative fraction of a unit. If we assume the value is a rational number that can be accurately determined from this graph, then we can find it by looking for a point where the graph crosses a grid intersection. It looks like such grid points are (-7, 0) and (3, 0). The vertex is apparently (-2, 4), so the vertex form of the equation is ...

y = a(x +2)^2 +4

Using the point (3, 0), we have ...

0 = a(3 +2)^2 +4 . . . . . fill in the values of x and y

-4 = 25a . . . . . . . . . . subtract 4; next, divide by 25

a = -4/25 = -0.16

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Monica [59]

Expand f(z) into partial fractions:

$\dfrac1{z(z-2)} = \dfrac12 \left(\dfrac1{z-2} - \dfrac1z\right)$

Recall that for |z| < 1, we have the power series

$\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n$

Then for |z| > 2, or |1/(z/2)| = |2/z| < 1, we have

$\displaystyle \frac1{z-2} = \frac1z \frac1{1 - \frac2z} = \frac1z \sum_{n=0}^\infty \left(\frac 2z\right)^n = \sum_{n=0}^\infty \frac{2^n}{z^{n+1}}$

So the series expansion of f(z) for |z| > 2 is

$\displaystyle f(z) = \frac12 \left(\sum_{n=0}^\infty \frac{2^n}{z^{n+1}} - \frac1z\right)$

$\displaystyle f(z) = \frac12 \sum_{n=1}^\infty \frac{2^n}{z^{n+1}}$

$\displaystyle f(z) = \sum_{n=1}^\infty \frac{2^{n-1}}{z^{n+1}}$

$\displaystyle \boxed{f(z) = \frac14 \sum_{n=2}^\infty \frac{2^n}{z^n} = \frac1{z^2} + \frac2{z^3} + \frac4{z^4} + \cdots}$

6 0

2 years ago

If f(x) = -2x + 4, then f^-1(x) =

Nadusha1986 [10]

Answer:

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

Step-by-step explanation:

Consider the real number y such that f ⁻¹(x) = y

$f^{-1}\left( x\right) =y\Longleftrightarrow f\left( y\right) =x$

We need to find y in order to determine the expression of f ⁻¹(x)

f(y) = x ⇔ -2y + 4 = x

⇔ 4 - x = 2y

⇔ y = (4 - x)/2

$\Longleftrightarrow y=-\frac{x}{2} +2$

7 0

2 years ago

Multiply. Enter the product in the simplest form.

vaieri [72.5K]

Answer:

2/15

Step-by-step explanation:

1/5 x 2/3 = 2/15 which can't be simplified so 2/15 is the correct answer

6 0

3 years ago

Read 2 more answers

Peggy had three times as many quarters as nickels. She had $1.60 in all. How many nickels and how many quarters did she have?

saul85 [17]

Answer:

<em>3n; 2 nickels and 6 quarters</em>

Step-by-step explanation:

"Peggy had three times as many quarters as nickels."

Whatever number of nickels she has, the number of quarters is 3 times as many.

Since she has n nickels, she has 3 times n quarters.

The number of quarters is 3n.

A nickel is worth $0.05, so n nickels are worth 0.05n.

A quarter is worth $0.25, so 3n quarters are worth 0.25(3n).

0.05n + 0.25(3n) = 1.60

0.05n + 0.75n = 1.6

0.8n = 1.6

n = 2

She has 2 nickels.

3n = 3(2) = 6

She has 6 quarters.

5 0

4 years ago

Read 2 more answers

Ten times the square of a non-zero number is equal to forty times the number

S_A_V [24]

To convey as an algebraic expression simply break down the statements and use any variable to represent the number in the sentence.

10 • x^2 = 40x
10x^2 = 40x
10x^2 - 40x = 0
10(x^2 - 4x) = 0
X(x - 4) = 0

X = 0

X - 4 = 0
X = 4.

Here are two possibilities of what the number can be, but because it is a nonzero number, I believe it would be 4.

7 0

4 years ago