Find the exact value by using a half-angle identity. sin 22.5°

Cody stamped 460 envelopes in 30 minutes. How many envelopes per minute did Cody stamp?

Leokris [45]

Answer:

15 1/3 envelopes in 1 minutes

Step-by-step explanation:

Take the number of envelopes and divide by the number of minutes

460 envelopes / 30 minutes

15.333333.... envelopes per minute

15 1/3 envelopes in 1 minutes

3 0

3 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

The living room in a new house has the dimensions shown. What is the volume of the room?

Savatey [412]

Add the sides then what ever you got add that up with 9 yd

5 0

3 years ago

Which equation represents the data in

klasskru [66]

Answer:

y = 2x - 4

Step-by-step explanation:

The equations are put in slope intercept form

Slope intercept form: y = mx + b

Where m = slope and b = y intersect

So in order to find the equation of the data represented by the table we will have to find the slope and y intercept

Let's begin!

First let's find the slope

We can find the slope by using the slope formula

m = (y2 - y1) / (x2 - x1) where the x and y values are derived from coordinates from the table

The points chosen may vary but I have chosen the points (0,-4) and (1,-2)

Now that we have chosen the points we will use to find the slope let's define the variables

remember coordinates are written like this: (x,y)

The x value of the second coordinate is 1 so x2 = 1

The x value of the first coordinate is 0

So x1 = 0

The y value of the second coordinate is -2 so y2 = -2

The y value of the first coordinate is -4

So y1 = -4

Now that we have defined each variable let's plug in the values into the formula

Formula: m = (y2 - y1) / (x2 - x1)

Variables: x2 = 1, x1 = 0, y2 = -2, y1 = -4

Substitute values

m = (-2 - (-4) / ( 1 - 0 )

Evaluate

The negative signs cancel out on top and it changes to +4

m = (-2 + 4)/(1-0)

Add top values

m = 2/(1-0)

Subtract bottom numbers

m = 2/1

Simplify fraction

m = 2

So we can conclude that the slope (m) = 2

Now let's find the y intercept or "b"

The y intercept is the value of y when x = 0

If you look at the table when x = 0 y = -4 meaning that the y intercept or "b" is -4

Now that we have found everything let's find the equation of the data represented by the table

The equation is in slope intercept form

y = mx + b

Define variables

m = 2 and b = -4

Substitute values

y = 2x - 4

The equation is y = 2x - 4

4 0

3 years ago

Identify the percent of change as an increase or a decrease. 24 songs to 78 songs Increase Decrease Question 2 Find the percent

algol [13]

1)increase
2)225%
Thats the answers

6 0

3 years ago