I need help with this question 2x + 1/2 = -5

2x+2y=8 in function form step by step please?

nasty-shy [4]

You could get two different functions out of this:

2x + 2y = 8

1). 'y' as a function of 'x'

Subtract 2x from each side: 2y = -2x + 8

Divide each side by 2 :  y = -x + 4

2).  'x' as a function of 'y' :

Subtract 2y from each side: 2x = -2y + 8

Divide each side by 2 :  x = -y + 4

Those two functions look the same, but that's just because the original
equation given in the problem was so symmetrical. In general, they're
not the same function.

7 0

3 years ago

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A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an a

Scrat [10]

Answer:

The answer is (C) 8

Step-by-step explanation:

First, let's calculate the length of the side of the square.

$A_{square}=a^2$ , where $a$ is the length of the side. Now, let's try to build the square. First we need to find a point which distance from (0, 0) is 10. For this, we can use the distance formula in the plane:

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ which for $x_1=0$ and $y_1 = 0$ transforms as $d=\sqrt{(x_2)^2 + (y_2)^2}$ . The first point we are looking for is connected to the origin and therefore, its components will form a right triangle in which, the Pythagoras theorem holds, see the first attached figure. Then, $x_2$ , $y_2$ and 10 are a Pythagorean triple. From this, $x_2= 6$ or $x_2=8$ while $y_2= 6$ or $y_2=8$ . This leads us with the set of coordinates:

$(\pm 6, \pm 8)$ and $(\pm 8, \pm 6)$ . (A)

The next step is to find the coordinates of points that lie on lines which are perpendicular to the lines that joins the origin of the coordinate system with the set of points given in (A):

Let's do this for the point (6, 8).

The equation of the line that join the point (6, 8) with the origin (0, 0) has the equation $y = mx +n$ , however, we only need to find its slope in order to find a perpendicular line to it. Thus,

$m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{8-0}{6-0} \\m = 8/6$

Then, a perpendicular line has an slope $m_{\bot} = -\frac{1}{m} = -\frac{6}{8}$ (perpendicularity condition of two lines). With the equation of the slope of the perpendicular line and the given point (6, 8), together with the equation of the distance we can form a system of equations to find the coordinates of two points that lie on this perpendicular line.

$m_{\bot}=\frac{6}{8} = \frac{8-y}{6-x}\\ 6(6-x)+8(8-y)=0$ (1)

$d^2 = \sqrt{(y_o-y)^2+(x_o-x)^2} \\(10)^2=\sqrt{(8-y)^2+(6-x)^2}\\100 = \sqrt{(8-y)^2+(6-x)^2}$ (2)

This system has solutions in the coordinates (-2, 14) and (14, 2). Until here, we have three vertices of the square. Let's now find the fourth one in the same way we found the third one using the point (14,2). A line perpendicular to the line that joins the point (6, 8) and (14, 2) has an slope $m = 8/6$ based on the perpendicularity condition. Thus, we can form the system:

$\frac{8}{6} =\frac{2-y}{14-x} \\8(14-x) - 6(2-y) = 0$ (1)

$100 = \sqrt{(14-x)^2+(2-y)^2}$ (2)

with solution the coordinates (8, -6) and (20, 10). If you draw a line joining the coordinates (0, 0), (6, 8), (14, 2) and (8, -6) you will get one of the squares that fulfill the conditions of the problem. By repeating this process with the coordinates in (A), the following squares are found:

(0, 0), (6, 8), (14, 2), (8, -6)

(0, 0), (8, 6), (14, -2), (6, -8)
(0, 0), (-6, 8), (-14, 2), (-8, -6)
(0, 0), (-8, 6), (-14, -2), (-6, -8)

Now, notice that the equation of distance between the two points separated a distance of 10 has the trivial solution $(\pm10, 0)$ and $(0, \pm10)$ . By combining this points we get the following squares:

(0, 0), (10, 0), (10, 10), (0, 10)
(0, 0), (0, 10), (-10, 10), (-10, 0)
(0, 0), (-10, 0), (-10, -10), (0, -10)
(0, 0), (0, -10), (-10, -10), (10, 0)

See the attached second attached figure. Therefore, 8 squares can be drawn

8 0

3 years ago

Which functions have an additive rate of change of 3? Select TWO options

Pachacha [2.7K]

Answer:

Second table.

Step-by-step explanation:

A function has an additive rate of change if there is a constant difference between any two consecutive input and output values.

The additive rate of change is determined using the slope formula,

$m = \frac{y_2-y_1}{x_2-x_1}$

From the first table we can observe a constant difference of -6 among the y-values and a constant difference of 2 among the x-values.

$m = \frac{ - 9- - 3}{4-2} = - 3$

For the second table there is a constant difference of 3 among the y-values and a constant difference of 1 among the x-values.

The additive rate of change of this table is

$m = \frac{ - 1 - - 4}{3 - 1} = 3$

Therefore the second table has an additive rate of change of 3.

5 0

3 years ago

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Math. please help me!!!

d1i1m1o1n [39]

Part A.

In this part we have to find the increasing interval .

Increasing interval is that interval where graph goes up. And from the graph we can say that the graph goes up in the interval

$(-1,0)U (1, \infty)$

And that's the increasing interval .

Part B.

Correct option is B

x and y intercepts

x intercept is the point where graph touches the x axis. And the graph touches the x axis at x=-1 and 1 .

So the x intercepts are

$(-1,0) ,(1,0)$

y intercepts are the point, where the graph touches or crosses the y axis.

Therefore the y intercept is (0,1)

So the correct option is D .

4 0

3 years ago

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The image below shows the graph of a sound recorded on an oscilloscope. What are the period and the amplitude? (Each unit on the

Serhud [2]

Remember that the period of a sinusoidal function is the vertical distance between the t-axis and one of the extreme points. From the graph we can infer that the period of the function is 4.5.

Also, the amplitude is the distance between two consecutive maximum or two consecutive minimum points. From the graph we can infer that the amplitude of the function is 0.05 seconds.

We can conclude that the correct answer is: 0.05 seconds; 4.5

7 0

3 years ago

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