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mafiozo [28]
3 years ago
11

What is the value of x?

Mathematics
1 answer:
Alexus [3.1K]3 years ago
5 0

Answer:

x = 22.5

Step-by-step explanation:

\frac{BH}{DH}  =  \frac{HM}{HT}  \\  \frac{6}{15 + 6}  =  \frac{9}{9 + x}  \\  \frac{6}{21}  =  \frac{9}{9 + x}  \\ 6(9 + x) = 9 \times 21 \\ 54 + 6x = 189 \\ 6x = 189 - 54 \\  6x = 135 \\ x =  \frac{135}{6}  \\ x = 22.5

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Q(x)=x^3+ax^2+2b is divided by (x-3) and has a remainder of 4. Find the values of "a" and "b"​
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Answer:

Let p(x) = x3 + ax2 + bx +6

(x-2) is a factor of the polynomial x3 + ax2 + b x +6

p(2) = 0                                                                                      

p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 0

7 +2 a +b = 0

b = - 7 -2a -(i)                                                                              

x3 + ax2 + bx +6 when divided by (x-3) leaves remainder 3.

p(3) = 3                                                                                      

p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 3

11+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii)                                    

Equating the value of b from (ii) and (i) , we have

(- 7 -2a) = (-10 - 3a)

a = -3                                                                                          

Substituting a = -3 in (i), we get

b = - 7 -2(-3) = -7 + 6 = -1

Thus the values of a and b are -3 and -1 respectively.

Step-by-step explanation:

4 0
2 years ago
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