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2 years ago

A new cell phone is on sale for 40% off its original price. The sale price is $48.

1 answer:

7 0

If it is 40% off, it is selling at 60% of it original price.

The sales price is $48
60% = 58
1% = 58 ÷ 60 = 0.93
100% = 0.93 x 100 = $93

The original price is $93

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Hello I need help Find the missing side lengths, leave your answers as radicals in simplest form

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$y = \frac{1}{2} \times \frac{8 \sqrt{3} }{3} \\$

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2 years ago

Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic

Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

$(x-a)^2+(y-b)^2+(z-c)^2=r^2$

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

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3 years ago

A theater sells adult tickets for $8.00 and Children's tickets for 5.50. Sally bought some of each kind (not the same number) an

sdas [7]

8x +(5.5)y=78.50 is the equation.

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Factor completely 121x^2 - 16.

Sindrei [870]

Assuming you meant the x2 as x squared, then:

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All these appear to be physic phenomena because they do not change the composition of the matter.

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3 years ago