The first letter can be any one of 8. For each of those . . .
The second letter can be any one of the remaining 7. For each of those . . .
The third letter can be any one of the remaining 6. For each of those . . .
The fourth letter can be any one of the remaining 5. For each of those . . .
The fifth letter can be any one of the remaining 4.
The total number of possibilities is (8 x 7 x 6 x 5 x 4) = <em>6,720</em> .
(That's 8! / 3! .)
Note:
If you're allowed to use the same letter more than once,
then there are 8 choices for each of the 5 letters.
The total number of possibilities then is (8 x 8 x 8 x 8 x 8) = 32,768 .
(That's 8⁵ or 2¹⁵ .)
Complete Question
Which of the following statements are true and which are false? Give reasons for your answers.
(i) Only one line can pass through a single point.
(ii) There are an infinite number of lines which pass through two distinct points.
(iii) A line can be produced indefinitely on both sides.
(iv) If two circles are equal, then their radii are equal.
(v) if AB=PQ and PQ=XY, then AB=XY.
A (i),(ii) - True
(iii),(iv),(v)-False
B(i),(ii),(iii) -True
(iv),(v)-False
C (i),(ii) -False
(iii),(iv),(v)-True
D (i),(ii),(iii) -False
(iv),(v)-True
Answer:
The correct option is C
Step-by-step explanation:
i is false because several lines can pass through a single point
ii is false because only one line can pass through two distinct points
iii is true because you can extend a line from both points (start and end points )
iv is true because when two equal circle are placed together and radius is trace we will discover that they are equal
v is true because from Euclid's First Axiom , if a= c and c = d the a = d
<h2>
Answer:</h2>
The possible formula for a fourth degree polynomial g is:
<h2>
Step-by-step explanation:</h2>
We know that if a polynomial has zeros as a,b,c and d then the possible polynomial form is given by:
Here the polynomial g has a double zero at -2, g(4) = 0, g(3) = 0.
This means that the polynomial g(x) is given by:
![g(x)=m(x-(-2))^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x+2)^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x^2+2^2+2\times 2\times x)(x(x-3)-4(x-3))\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-3x-4x+12)\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-7x+12)\\\\i.e.\\\\g(x)=m[x^2(x^2-7x+12)+4(x^2-7x+12)+4x(x^2-7x+12)]\\\\i.e.\\\\g(x)=m[x^4-7x^3+12x^2+4x^2-28x+48+4x^3-28x^2+48x]\\\\i.e.\\\\g(x)=m[x^4-7x^3+4x^3+12x^2+4x^2-28x^2-28x+48x+48]\\\\i.e.\\\\g(x)=m[x^4-3x^3-12x^2+20x+48]](https://tex.z-dn.net/?f=g%28x%29%3Dm%28x-%28-2%29%29%5E2%28x-4%29%28x-3%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%2B2%29%5E2%28x-4%29%28x-3%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B2%5E2%2B2%5Ctimes%202%5Ctimes%20x%29%28x%28x-3%29-4%28x-3%29%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B4%2B4x%29%28x%5E2-3x-4x%2B12%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%28x%5E2%2B4%2B4x%29%28x%5E2-7x%2B12%29%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E2%28x%5E2-7x%2B12%29%2B4%28x%5E2-7x%2B12%29%2B4x%28x%5E2-7x%2B12%29%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-7x%5E3%2B12x%5E2%2B4x%5E2-28x%2B48%2B4x%5E3-28x%5E2%2B48x%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-7x%5E3%2B4x%5E3%2B12x%5E2%2B4x%5E2-28x%5E2-28x%2B48x%2B48%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cg%28x%29%3Dm%5Bx%5E4-3x%5E3-12x%5E2%2B20x%2B48%5D)
Also,
i.e.
Hence, the polynomial g(x) is given by:
Answer:
The proper answer is in the picture.
Step-by-step explanation:
<u><em>PLEASE MARK BRAINLIEST</em></u>
ABC is a right triangle right-angled at B.
AC is the hypotenuse, length 96cm
Angle C=30 degrees, therefore AB is the short leg opposite angle C.
sin(30)=opp/hyp=AB/AC=AB/96
=>
AB=96sin(30)=96(1/2)=48 cm.
