Question

2.)A BUS TRAVEL 300 KILOMETERS AT GIVEN SPEED. IF THE SPEED IS INCREASED BY 10 KILOMETERS PER HOUR, THE TRIP WILL BE REDUCED BY ONE HOUR. FIND THE SPEED

3.)THE AREA OF A RECTANGULAR GARDEN IS 84 SQUARE METERS AND ITS PERIMETER IS 8 METERS. FIND THE DIMENSIONS OF THE GARDEN.

4) THE SUM OF TWO NUMBERS IS 18. THE SUM OF THEIR SQUARES IS 4 MORE THAN 16 TIMES THE LARGER NUMBER. FIND THE NUMBERS

Answer 1

Step-by-step explanation:

Q4 ) x + y = 18

x^2 + y^2 = 4 + 16x

Substitute x = 18 - y into the second equation

(18 - y)^2 + y^2 = 4 + 16(18-y)

(18-y)(18-y) + y^2 = 4 + 288 - 16y

324 - 18y - 18y + y^2 + y^2 = 292 - 16y

324 - 36y + 2y^2 = 292 - 16y

32 - 20y + 2y^2 = 0

Rearrange

2y^2 - 20y + 32

2(y^2 - 10y + 16)

2(y - )(y - ) both minus as the - 10y and + 16

multiples of 16: 16,1; 4,4; 8,2

choosing 8,2 as they add up to 10

2(y-8)(y-2)=0

(y-8)(y-2)=0*2

y=8

y=2

x=18-8 = 10

x=18-2 = 16

Could be 8 and 10

Could also be 2 and 16

Proof

8+10 = 18; 8^2 + 10^2 = 164

16*10 = 160 + 4= 164

2+16 = 18; 2^2 + 16^2 = 260

16*16 = 256 + 4 = 260