ANSWER
Possible rational roots: <span><span>±1,±2,±3,±4,±6,±12</span><span>±1,±2,±3,±4,±6,±12</span></span>
Actual rational roots: <span><span>1,−1,2,−2,−3</span></span>
<span><span>see attachments for all steps.</span></span>
a counterclockwise rotation about the origin of 90°
The coordinates of P(3, 3), Q(5, 3), R(5, 7)
The coordinates of P'(- 3, 3 ), Q'(- 3, 5), R'(- 7, 5)
Note that the y-coordinate of the image is the negative of the original, while the x-coordinate of the original becomes the y-coordinate of the image
The rotation which does this is a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x )
given that
4112/5 = 822 remainder 2
to get the correct way and incorrect way.
so
For,
822 x 5 = 4110
For,
822 x 2 + 5 = 1649
For,
822 x 5 + 2 = 4112
therefore,
The correct way to check The incorrect way to way to check
822 x 5 + 2 822 x 5
822 x 2 + 5
Thwre are 28 clients who don not play any of the instrument using the principle of Venn distribution.
<u>Using a Venn diagram analogy</u> :
- Total number of client, U = 108
- Piano, P = 42
- Guitar, G = 51
- Piano and Guitar, (PnG) = 13
- None =?
<u>From the information given</u> :
- P only = 42 - 13 = 29
- G only = 51 - 13 = 38
<u>The total number of clients can be related thus</u> :
- Total = P only + G only + PnG + None
108 = 29 + 38 + 13 + None
108 = 80 + None
None = 108 - 80
None = 28
Therefore, the number of clients who do not play any of the instruments is 28
Learn more :brainly.com/question/12570490
In triangle ABC,
AC = 12/ (sin30) = 12 / (1/2) = 24
DC = 24-x
DB = DC tan 30 = (24-x) tan30 <span>=(24−x)/</span><span>√3
</span>
In triangle ADB using Pythagorean Theorem<span><span>x2</span>+((24−x)/<span>√3</span><span>)2</span>=<span>12^2</span></span><span><span>x2</span>+(24−x<span>)^2</span>/3=<span>12^2</span></span><span>3<span>x2</span>+(24−x<span>)^2</span>=432</span><span>4<span>x2</span>−48x+576=432</span><span>4<span>x2</span>−48x+144=0</span><span><span><span>x2</span>−12x+36=0
x1 = x2 =6
AD = AC - DC = 24- (24-x) = 6</span></span>
