Math Challenge? Click to See? Solve and get 10 pts?

Question

Q:7) A rail journey of 300 km cost £84. At the same rate per km
a)what would be the cost of traveling 250 km.
b)How far could you travel for £63?

Q:8) Do this question on a sheet of graph paper. Do not shade the defined by the inequalities.
x+y < 6, 3x+y ≥ 3, y ≥ -1

Q:9) Find, an expression for the nth term

i)5,10,15,20,………...
ii)1,8,27,64, …………
iii)2,4,7,11,16……..

Q:10) Factorize
a)x2 – 7x
b)x2 + 12x + 20
c)x2 – 4
d) 552 - 452
e) Find the value of p and q, for all values of x.
x2– px + 12 = (x – 6)(x-q)

Q: 11) When three times a number, x, is added to a second number, y, the total is 33. The
first number added to three times the second number is 19.
a)Form two equations connecting x and y.
b)Find the two numbers.

Q:11) Ahmed is x years old and his father is x2 years old. The sum of their ages is 56
years. Form an equation in x and solve it to find the age of each.

Answer 1

7a) 84/300=x/250
84*250=300x
7*2*2*3*5*5*5*2=3*2*2*5*5*x
7*5*2=x
x=70
Therefore, it would cost 70 pounds

7b) 300/84= 100/26, which is the distance one can travel in km for 1 pound.
That means that the distance would be 6300/26 km for 63 pounds. That simplifies to 3150/13, or 242 4/13 km.

8) If we drew it on graph paper, we wouldn't be able to post it. Besides, that second sentence is so ambiguous, I can't tell what you are asking.

9i) 5n
9ii) n^3
9iii) When 0 2n+(1+2...+n-2)

(By the way, it's called 'factor', not 'factorize')
10a) x(x-7)
10b) (x+2)(x+10)
10c) (x-2)(x+2)
10d) Don't need to, it's just 100
10e) p=8, q=2

11a)
3x+y=33
x+3y=19
11b) x=10, y=3

I'm assuming this was supposed to be 'Q:12'
12) x+x^2=56
x(x+1)=56
x=7

Therefore, Ahmed is 7 and his father is 49.

Answer 2

1) A = P( 1+r)^t A = 410(1+.07)² A = 410(1.07)² A= $469.41 2) Draw 3 overlapping circles. Label 1 circle basketball, one volleyball and one soccer. Put 2 in the region where all 3 overlap. Put 1 where only basketball and soccer overlap. Put 2 where volleyball and soccer overlap. Put 1 where basketball and volley ball overlap (I think you have a typo here). Add up what is already in the basketball circle (4) so only 4 are left to just play basketball. Add up what is already in the volleyball circle(5) so only 4 are left to just play volleyball. Add up what is already in the soccer circle(5) so only 5 are left to just play soccer. Now find the total of all your numbers and that is your answer.

Answer 3

7(a).
300Km = £84 (÷ 300)
1Km = £0∙28 (x 250)
250Km = £70

7(b).
300Km = £84 (÷ 84)
3∙571 428 571...Km = £1 (x 63)
225Km = £63.

8.
It will be best to draw this out yourself.

9.
(i). n+5

Answer 4

7a) ... 66