4) The diameter of a circle is 32m. The radius is represented by 4(x + 2).

Mathematics

1 answer:

vaieri [72.5K]2 years ago

3 0

Answer:

The value of x is 2

Step-by-step explanation:

Diameter = 2r -------------------------------------------------------------------(1)

where r is the radius

The value of the diameter = 32 m and radius is given to be 4(x+2)

substitute the above into equation (1) and then solve for x

32 = 2 [ 4(x + 2)]

first open the inner bracket

32 = 2[4x + 8}

then open the outer bracket

32 = 8x + 16

subtract 16 from both-side of the equation

32 - 16 = 8x +16 - 16

16 = 8x

Divide both-side of the equation by 8

16/8 = 8x/8

2 = x

x = 2

Therefore, the value of x is 2

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I NEED HELP PLEASE, THANKS! :)

Alenkasestr [34]

Answer:

Option A

Step-by-step explanation:

This is a great question!

The first thing we want to do here is to graph the system of " inequalities " -

$\begin{bmatrix}2x+9y\le \:100\\ 9x+y\le \:54\end{bmatrix}$

As x is ≥ 0, respectively y ≥ 0, it makes things a lot simpler, as it kind of restricts us to quadrant 1, but not entirely.

First change each inequality to " slope - intercept " form, as such -

$2x + 10y \leq 100,\\10y \leq 100 - 2x,\\y \leq - 1 / 5x + 10\\----------\\9x + y \leq 54,\\y \leq - 9x + 54$

The graphed solutions would be in the attachment. I have colored the region with which the two intersect, and the fact that we are limited to quadrant 1. In this colored region there are 3 major points, ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ). We have to determine which of these are are maximum points, as the minimum are the same. Substitute these values ( ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ) ) into the equation f( x, y ) = 10x + 4y,

$f ( x, y ) = 10( 5 ) + 4( 9 ),\\f ( x, y ) = 86 -\\f ( x, y ) = 10( 0 ) + 4( 10 ),\\f ( x, y ) = 40 -\\f ( x, y ) = 10( 6 ) + 4( 0 ),\\f ( x, y ) = 60$