Which of the following is equivalent to (x^2 − 9)(x + 2) − (x^2 + 4x + 4)(x − 5)?

ivolga24 [154]

Let's first find the slope. This is (y_2 - y_1)/(x_2 - x_1), where (x_1, y_1) and (x_2, y_2) are points.

For this problem, our slope is (0 - 2)/(3 - 0) = -2/3.

We can now use the point-slope formula to find the equation of our line:
(y - y_1) = m(x - x_1)
(y - 2) = -2/3(x - 0)
y - 2 = (-2/3)x
y = (-2/3)x + 2

The equation of our line is $\boxed{y = -\frac{2}{3}x + 2}$ .

8 0

3 years ago

List the first 4 terms of the sequence 3n² + 1

Ganezh [65]

Answer:

4, 13, 28, 49

Step-by-step explanation:

1st term = 3 × (1)² + 1 = 4

2nd term = 3 × (2)² + 1 = 13

3rd term = 3 × (3)² + 1 = 28

4th term = 3 × (4)² + 1 = 49

3 0

2 years ago

Read 2 more answers

A cryptographic hash takes a message as input and produces a fixed-length string as output, called the digital fingerprint. A br

Allushta [10]

Answer:

$1.85x10^{19}$ attempts are required to find a matching pair if the digital fingerprint is 64 bits long.

$3.40*10^{38}$ attempts are required to find a matching pair if the digital fingerprint is 128 bits long.

Step-by-step explanation:

Each bit has two options. So

How many attempts are required to find a matching pair if the digital fingerprint is 64 bits long?

So for each of the 64 bits, we have the following number of options.

2 - 2 - 2 - 2 -... - 2

So, in all, there are

$T = 2^{64} = 1.85x10^{19}$

options.

So, $1.85x10^{19}$ attempts are required to find a matching pair if the digital fingerprint is 64 bits long.

128 bits long?

Using the same logic as the first question.

$T = 2^{128} = 3.40*10^{38}$

So, $3.40*10^{38}$ attempts are required to find a matching pair if the digital fingerprint is 128 bits long.

5 0

3 years ago

Find The value of x, y and z

Ratling [72]

Answer:

x = 18 ; y = 10 ; z = 102°

Step-by-step explanation:

The triangle in the pic is an isosceles triangle.

As it is an isosceles triangle , it's two sides will be equal .

$= > 3x - 42 = 12$

$= > 3x = 42 + 12 = 54$

$= > x = \frac{54}{3} = 18$

Also, both the base angles will be equal.

$4y - 1 = 39$

$= > 4y = 39 + 1 = 40$

$= > y = \frac{40}{4} = 10$

According to angle sum property of a triangle , sum of measure of all the angles of a triangle is equal to 180°. So,

$z + 39 + 39 = 180$

$= > z + 78 = 180$

$= > z = 180 - 78 = 102$

5 0

2 years ago

Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function int

melisa1 [442]

Answer:

Vertex form: $f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}$

The vertex is $(-\frac{7}{2},-\frac{53}{4})$

Step-by-step explanation:

For a general quadratic function the form is:

$ax ^ 2 + bx + c$

For the function

$f(x) = x ^ 2+ 7x -1$

The values of the coefficients for the function are the following: $a = 1$ , $b =7$ , $c = -1$

Take the value of b and divide it by 2. Then, the result obtained squares it.

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

$(\frac{b}{2})^2=(\frac{7}{2})^2=\frac{49}{4}$

Add and subtract $\frac{49}{4}$

$f(x) = (x ^ 2 +7x +\frac{49}{4}) -\frac{49}{4}- 1$

Write the expression of the form

$f(x) = (x+\frac{b}{2})^2 +k$

$f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}$

The vertex is $(-\frac{7}{2},-\frac{53}{4})$

6 0

3 years ago