If f(x) = |x – 10 – x2| evaluate f(-7)
Solution
f(x) = |x - 10 – x2|
f(-7) = |-7 - 10 – (-7)2|
f(-7) = |-17 – (-7)2| (since -7 - 10 = -17)
f(-7) = |-17 – 49| since
f(-7) = |-66| = 66 since any number out of absolute
signs is +ve.
Hence
f(-7) = 66
TRY THIS..................
If f(x) = | x – 60 – x2| evaluate f(-8)
If 5x + 13y= 8 + 6x; find the x intercept.
Solution
x-intercept
is when y=0.
5x
+ 13(0)= 8 + 6x.
5x
- 6x + 13(0)= 8
-x
+ 0 = 8
-x
= 8.
-x = 8
dividing by -1 both sides.
-1 -1
x =
-8
Hence x-intercept is (-8,0)
TRY
THIS………………………
If
11x - 3y= 33 + 13x; find the x intercept.
Rayan deposited the amount of 20,000/=
in a bank for 5 years and got a profit of 1500/=. Find the interest rate?
Solution
I = 1500/=, P = 20,000/=, T = 5 years,
R = ?
I = PRT
100
1500 = 20000 x R x 5
100
1500 = 20000 x R x 5
100
1500 = 200 x R x 5
1500 = 1000R
1.51500
= 1000R
1000
1000
Hence the interest rate was 1.5%
TRY THIS………….
Rayan deposited the amount of 6,000/=
in a bank for 5 years and got a profit of 4200/=. Find the interest rate?
A man got a profit of 7400/=
after selling an item. Find the buying price if the percentage profit was 10%.
Solution
%’ge profit = Profit X
100 where B. P. represents
Buying Price.
B.P
10% = 7400 X
100
B.P.
B.P. x 10% = 740,000 x B.P. [multiplying by B.P. both sides]
B.P.
B.P. x 10 = 740,000
B.P. x 101 = 740,000
110 10
B.P. =74,000
Hence Buying Price was 74,000/=
TRY THIS………………
A man got a profit of 90,500/=
after selling an item. Find the buying price if the percentage profit was 20%.
9x
=3x +72; find x
Solution
9x
=3x +72
9x
- 3x = 72 taking 3x on the
left side
9x
- 3x – 72 = 0. Taking 72 on
the left side as well
32x
- 3x – 72 = 0. Rewriting 9x
as 32x.
(3x)2
– (3x) – 72 = 0. Factoring 3x
out.
Let
u = 3x ……… (i)
(u)2
– (u) – 72 = 0.
u2
– 9u + 8u – 72 = 0 [Factorizing by
splitting the middle term].
(u2
– 9u) + (8u – 72) = 0
u(u
– 9) + 8(u – 9) =0
(u
– 9)(u + 8) =0
u – 9 = 0 or
u + 8 =0
u
= 9 or u =-8
We
neglect the –ve answer and we stick with the positive one.
Now from (i) u = 3x
9
= 3x
32
= 3x equal bases they cancel
out.
x = 2
TRY
THIS………….
9x =3x + 111/4;
find x
4
Log327 + Logx =8. Find x
Solution
Log327
+ Logx =8
Log333
+ Logx =8
3Log33
+ Logx =8
(3
x 1) + Logx =8
3
+ Logx =8
Logx
=8 - 3
Logx
=5
Log10x
=5 [Since
any log without a base it is a base 10 logarithm]
x
= 105 [after
changing logarithmic form into exponential form]
x
= 100,000 answer.
TRY
THIS………….
Log5625
+ Logu =9. Find u
There are 37 villagers at the meeting. 12 are farmers and 18 are workers and 8 are both farmers and workers. How many villagers are
i)
Either
farmers or workers.
ii)
Neither
farmers nor workers
Solution
n(U)=37
n(F)=12
n(W)=18
n(FnW)=8
n(FuW)=?
n(FuW)’=?
i) n(FuW) = n(F) + n(W) - n(FnW)
n(FuW)
= 12 + 18 - 8
n(FuW)
= 30 – 8
n(FuW)
= 22
----------------------------------------
n(U)
= n(FuW) + n(FuW)’
37
= 22+ n(FuW)’
37
- 22=n(FuW)’
15=n(FuW)’
Hence those who are neither farmers nor workers are 15
TRY THIS.....................
There are 40 villagers at the meeting. 12 are farmers and 18 are workers and 6 are both farmers and workers. How many villagers are
i) either farmers or workers.
ii) neither farmers nor workers
=========================
Expand
y(y – 4)(y – 10)
Solution
=
y(y – 4) (y – 10)
=
y[y (y – 10) – 4 (y – 10)]
=
y[y2 – 10y – 4y + 40]
=
y3 – 14y2 + 44y
=
y3 – 14y2 + 44y answer
TRY THIS………..
Expand
w(w – 9) (w – 10)
Jemson
bought a radio at 50,000/= and after one year he sold it at a loss of 14%. Find
the price of a radio after a year.
Solution
=
50,000 - (14% of 50,000)
=
50,000 - (0.14 of 50,000) after dividing
14% by 100
=
50,000 - 7,000
=
43000/=
Hence the new price
is 43000/=
TRY
THIS………….
Patson
bought a radio at 70,000/= and after one year he sold it at a loss of 24%. Find
the price of a radio after a year.
