What is the value of x?

Do the following scenarios model the equation y=2x+5

Volgvan

The slope is 2 and y-intercept (0,5).
The graph is given down below.

4 0

3 years ago

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What is the type of conic section given by the equation x^2 - 9y^2 = 900 and what is the domain and range?

Valentin [98]

A conic section is a curve obtained by the intersection of the surface of a cone with a plane. A conic section can be a circle, a hyperbola, a parabola, and an ellipse.

For a circle, the general equation of a circle with center, (a, b), and a radius, r, is of the form
$(x-a)^2+(y-b)^2=r^2$

For a hyperbola, the general equation of a hyperbola with center (h, k), and a and b half the lengths of the major and the minor axis respectively is of the form.
$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} =1$

For a parabola, the general equation of a parabola with center (h, k), and a multiplier a is of the form
$y-k=a(x-h)^2$

For an ellipse, the general equation of an ellipse with center (h, k), and a and b half the lengths of the major and the minor axis respectively.
$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1$

Given the equation
$x^2-9y^2=900$
It can be rewritten as
$\frac{(x-0)^2}{900} - \frac{(y-0)^2}{100} =1 \\ \\ \frac{(x-0)^2}{30^2} - \frac{(y-0)^2}{10^2} =1$
This gives an equation of a hyperbola with center (0, 0), half the length of the major axis = 30 and half the length of the minor segment = 10.

The domain of the equation is all real values of x.

8 0

4 years ago

Tylond puts $5,000 into a savings account that earns 4%

MariettaO [177]

Answer:

125,000

Step-by-step explanation:

7 0

3 years ago

If an image is to be reflected in the line y = x and the x-axis, does the order of the reflections affect the final image? Expla

OverLord2011 [107]

Answer:

Affects

Step-by-step explanation:

Consider point (2,-1).

1. Reflect it in the line y=x, then the image point will have coordinates (-1,2). Now reflect it in the x-axis, then the image point will have coordinates (-1,-2).

2. Reflect the point (2,-1) in the x-axis. Its image is point (2,1). Reflect this point in the line y=x, then its image will be point (1,2).

Since images in 1st case and 2nd case differ, the order affects the final image.

4 0

3 years ago

A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an

slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Horizontal distance from the start line, measured in meters.

$y$ - Height of the long jumper, measured in meters.

$a$ , $b$ , $c$ - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m)$ , $(x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m)$ , this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0$ (Eq. 1)

$81\cdot a + 9\cdot b + c = 0$ (Eq. 2)

$64\cdot a + 8\cdot b + c = 0.05$ (Eq. 3)

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}$ , $b = \frac{3}{25}$ , $c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}$ .

But we need $y$ measured in centimeters, then, we use the following conversion:

$y = 100\cdot y'$

Then, we get that:

$y = -x^{2}+12\cdot x -27$

Where $x$ and $y$ are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2}+12\cdot x -27$ .

4 0

3 years ago