Use the distributive property to write the products as sums: 3(2x -1)

Mathematics

1 answer:

GaryK [48]2 years ago

6 0

Multiply each of "2x" and "-1" by 3 in turn: 6x - 3 (answer)

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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

3 years ago

Find the surface area of the rectangular prism.

Nataly_w [17]

Answer:

130 ft^2

Step-by-step explanation:

SA= surface area

SA= 2*l*w + 2*l*h + 2*w*h

l= length = 10

w= width =5

h = height = 1

SA= 2*l*w + 2*l*h + 2*w*h

SA= 2*10*5 +2*10*1+2*5*1

SA= 100+20+10

SA= 130 ft^2

4 0

3 years ago

The cylindrical container is four-fifths full of powder. Round to the nearest tenth if necessary. a. The total capacity of the c

mezya [45]

Answer:

a. $\pi r^2h$

b. $\frac{4\pi r^2h}{5}$

Step-by-step explanation:

Volume of the container denotes its quantity. It is a three-dimensional space.

Let V denotes the volume of the container, h denotes the height of the container and r denotes the radius of the container.

The total capacity of the container in terms of π is $\pi r^2h$ <u />

As the cylindrical container is four-fifths full of powder, so the volume of the powder in terms of π is $\frac{4}{5}\times$ volume of the container i.e., $\frac{4\pi r^2h}{5}$