Question

i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 =

ii) Solve 3x – 2 divided by 2= 4x - 5 divided by 4 (5marks)

c) Solve the following pairs of simultaneous equations 2x + y = 7 and x - 2y = -1

Answer #1

i) 3(2x-5) - 2(5x-7) + 9 = 0

So, 6x - 15 - 10x + 14 + 9 = 0

So, - 4x + 8 = 0

So, 4x = 8

So, x = 2

c) 2x + y = 7 & x - 2y = - 1

So, 2(2x + y) + (x - 2y) = 2.7 - 1

So, 4x + 2y + x - 2y = 14 - 1

So, 5x = 13

So, x = 13/5

So, from, 2x + y = 7, we get,

2(13/5) + y = 7

So, y + 26/5 = 7

So, y = 7 - 26/5 = (35-26)/5 = 9/5

So, x = 13/5 & y = 9/5

Note : question number (ii) is incomplete or there is some mistake in the values.

Please let me know the correct values the comments section & I will update the answer.

Also, if there is some mistake in the 2 questions I have solved, let me know & recheck the values you entered.

I will edit the solution if needed.

Thank you.

solve the following pairs of simultaneous equations
a) x=7y+3
y=3x-7
b) 2x+5y =23
5x-2y=14

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

1) a) From the set {-8, -2/3, 5i, √(-9), √2, 0, 3+3i, -2.35,
7}
i) List the set of Natural Numbers
ii) List the set of Integers
iii) List of the set of Rational Numbers
vi) List the set of Real Numbers
2)Solve the following pairs of simultaneous equations 3x + y = 7
and 2x - 2y = 2
b) i) -30 ÷ -6 - (-12 + 8) – 4 x 3 =
c)Calculate the simple interest earned if...

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

Consider the linearly independent set of vectors
B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4,
1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4)
in P4(R), does B form a basis for P4(R) and why?

find y' for the function
1. (y-2)^7=3x^2+2x-2
2. 3y^3+2x^3=3
3.(4y^2+3)^4+3x^5-5=0
4. 4x^2+3x^2y^2-y^3=3x

solve for x using the factor theorem and long division. a.
2x^3-3x^2-5x+6=0 b. 8x^3+4x^2-18x-9=0 c.
2x^3+10x^2+13x+5=0 d. -2x^3-12x^2+x+60=0

solve the equations
a). 4x-(-3x-3) =2x +1-1/2x+1
b) 8x-x^2=2 solvee by completing square
c) x-2x^2=5 solve by quadraticformula

for 7-9 you will solve the following system of equation :
2x+3u+z=17 x-3y+2z=-8 5x-2y+3z=5 7) what is the solution for x? a)2
b)1 c)infinitely many solution d)no solution 8)what is the solution
for y? a)4 b)2 c)inifinitely many solutions d)no solution 9) what
is the solution for z? a)9 b)1 c)inifinitely many solutions d)no
solution

solve the system of equations
1: y=3x^2-2x-1
2x+3y=2
2: x^2+(y-2)^2=4
x^2-2y=0

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