This is the concept of algebra, suppose that the number of cats is x;
number of cats will be x-20
number of rabbits will be 3/2x
thus the total number of animals will be:
x+(x-20)+3/2x=350
7/2x=350+20
7/2x=370
x=370*2/7
x=105.7=106
therefore we conclude that there we 106 cats in the shelter
I have encountered this problem before. The figure gave out 3 chords, 2 of which are diameters, and 1 radius.
A chord is a line segment that joins any two points on a circle.
A diameter is the longest chord on a circle. It originates at one side of the circle, passes through the middle point of the circle, and end on another side of the circle.
The chords in the figure area: AD, BE, and DE. AD and BE are diameters, they pass through F.
Among the choices: A.) AD and B.) BE are the chords.
CF and DF are radii. They only end up in the middle point of the circle.
By the polynomial remainder theorem, the remainder is
<em>f</em> (2) = 2⁵ + 5×2³ + 4 = 32 + 40 + 4 = 76
(The theorem says a polynomial <em>p(x)</em> has remainder <em>p(c)</em> upon dividing it by <em>x</em> - <em>c</em>.)
The value of line AL is 21. 51cm
<h3>How to determine the length</h3>
To find line AL,
Using
Sin α = opposite/ hypotenuse to find line AB
Sin 90 = x/ 24
1 = x/24
Cross multiply
x = 24cm
Now, let's find line AC
Sin angle B = line AC/24
Note that to find angle B
angle A + angle B + angle C = 180
But angle B = 2 Angle A
x + 2x + 90 = 180
3x + 90 = 180
3x = 180-90
x = 30°
Angle B = 2 × 30 = 60°
Sin 60 = x/ 24
0. 8660 = x/24
Cross multiply
x = 24 × 0. 8660
x = 20. 78cm
We have the angle of A in the given triangle to be divide into two by the bisector, angle A = 15°
To find line AL, we use
Cos = adjacent/ line AL
Cos 15 = 20. 78/ line AL
Line AL = 20. 78/ cos 15
Line AL = 20. 78 / 0. 9659
Line AL = 21. 51 cm
Thus, the value of line AL is 21. 51cm
Learn more about trigonometry ratio here:
brainly.com/question/24349828
#SPJ1
1.)
=(x-8i)(x+8i)
x^2+8ix-8ix-64i^2
x^2-64i^2
x^2-64(-1)
x^2+64
2.)
=(4x-7i)(4x+7i)
16x^2+28ix-28ix-49i^2
16x^2-49i^2
16x^2-49(-1)
16x^2+49
3.)
=(x+9i)(x+9i)
x^2+9ix+9ix+81i^2
x^2+18ix+81(-1)
x^2+18ix-81
4.)
=(x-2i)(x-2i)
x^2-2ix-2ix+4i^2
x^2-4ix+4(-1)
x^2-4ix-4
5.)
=[x+(3+5i)]^2
(x+5i+3)^2
(x+5i+3)(x+5i+3)
x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9
x^2+6x+10ix+30i+25i^2+9
x^2+6x+10ix+30i+25(-1)+9
x^2+6x+10ix+30i-25+9
x^2+6x+10ix+30i-16
Hope this helps :)
