17. Solve for x and y
x^2 = 4 – y x = y + 2
18. Expand the following
i) 4x(3x +2)
ii) (4x + 7)(4x + 7)
iii) (4x + 7)(3x +2)
b) Find the roots of the equation 2x^2 – 11x -21 = 0
19. Solve, for 0◦ < Ө < 360◦, giving your answer to 1 decimal place where appropriate
i) 2 sin Ө = 3 cos Ө
ii) 2 – cos Ө = 2 sin^2 Ө
20.Using lasers, a surveyor makes the measurements shown below, where B and C are in a marsh. The angle PAC is 90 degrees. Find the distance between B and C.
PA = 265.74
angle APB 21.66 degrees
angle APC 8.85 degrees
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4x(3x+2)= (4x*3x) + (4X*2)= 12x^2+ 8x
ReplyDeletestep1: multiply 4x by 3x
4x*3x=12x^2
step2: multiply 4x by 2
4x*2= 8x
step3: add produts
12x^2 + 8x
(18)(ii)(4x+7)(4x+7)
ReplyDeletestep1: multiply 4x from the first bracket by everything in the second bracket
4x(4x+7)= (4x*4x)+(4x*7)=16x^2+28x
step2: multiply 7 from the first bracket by everything in the second bracket
7(4x+7)= 28x+49
step3: add the both produts
16x^2+28x+28x+49= 16x^2+56x+49
(18)(iii)(4x+7)(3x+2)
ReplyDeletestep1: multiply 4x from the first bracket by everything in the second bracket
4x(3x+2)= 12x^2+12x
step2: multiply 7 from the first bracket by everything in the second bracket
7(3x+2)= 21x+14
step3: add the both products
12x^2 + 12x + 21x + 14 = 12x^2+33x+14
4x(3x+2)=4x(3x)=12x^2
ReplyDelete4x(2)=8x
hence ans=12x^2+8x
(4x+7)(4x+7)=
ReplyDelete4x(4x)+4x(7)+4x(7)+7(7)=
16x^2+56x+49
(4x+7)(3x+2)=
ReplyDelete4x(3x)+4x(2)+7(3x)+7(2)=
21x^2+8x+21x+14=
21x^2+29x+14
(19)number 2
ReplyDelete2-cos@=2sin^2@
2-cos@=2(1-cos^2@) i used this rule sin^2@+cos^2@=1
2-cos=2-2cos^2@
2cos^2@-cos@=0
cos@=0 (2cos@-1)=0
@=cos0 cos@=1/2
@=9o, 270 @=60,300
miss you brought back memories but i am not sure if it correct someone correct me please
@=cos
num (20)
ReplyDeletea/sina=b/sinB
b=265.74*sin8.85/sin90=40.9
sin=opp/hyp hyp=40.4/sin8.85=262.6
all angles in a triangle=180 8.85+90-180=81.15
40.9sin81.15=40.4
262.6cos8.85=259.5
tan=21.66*259.5=103
103+40.4=143.4
correct me if i am incorrect
Solve:
ReplyDeletex^2=4-yx=y+2
x^2=4-yx-y-2
x=^2 4-yx-y-2
sub. values of x to find valu for y.
18. expand:
4x(3x+2)
(4x*3x)+ (4x*2)
12x^2+ 8x
i do not think you could solve an equation with 2 equal signs because then how wold you know what side it is on...
ReplyDelete18.
ReplyDeletei
4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
18
ReplyDeleteii
(4x+7)(4x+7)
4x(4x)+4x(7)+7(4x)+7(7)
16x^2+28x+28x+49
16x^2+56x+49
which is the same as (4x+7)^2
18
ReplyDeleteiii
(4x+7)(3x+2)
4x(3x)+4x(2)+7(3x)+7(2)
12x^2+8x+21x+14
12x^2+29x+14
18
ReplyDeleteb
2x^2-11x-21=0
factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
2-cosӨ=2sin^2Ө
ReplyDelete2-cosӨ=2(1-cos^2Ө) recall sin^2Ө+cos^2Ө=1
2-cosӨ=2-2cos^2Ө
2cos^2Ө-cosӨ=2-2
2cos^2Ө-cosӨ=0
cosӨ=0 (2cosӨ-1)=0
cosӨ=0 and 2cosӨ=0
Ө=cos-1(0)=90,270
Ө=cos-1(1/2)=60,300
i dont know how to solve an equation with 2 equal signs
ReplyDeletei thought that it waz 2 seperate equations...jus she probably placed them wrong!!
ReplyDeletecuz an equation cant have 2 equal signs
i think miss knows better than that.
2x^2-11x-21=0
ReplyDelete(2x+3)(x-7)=0
2x+3=0:x=-3/2
x-7=0
x=7
x=-3/2
x=7
ques 19 i
ReplyDelete2sin* = 3cos*
sin*/cos* = 3/2
tan* = 1.5
* = tan^-1 1.5
56.3,236.3
to expand
ReplyDelete4x(3x+2)
we multiply 4x by everything in the brackets
=12x^2+8x
(4x+7)(4x+7)
we multiply each term in one bracket and multiply it by each term in the other bracket
=16x^2+56x+49
we do the same for
(4x+7)(3x+2)
=12x^2+29x+14)
i)4x(3x +2)=
ReplyDelete12x^2+8x.
ii)(4x + 7)(4x + 7)=
16x^2+28x+28x+49=
16X^2+56x+49.
iii)(4x + 7)(3x +2)=
12x^2+8x+21x+14=
12x^2+29x+14
Roots of the equation 2x^2 – 11x -21 = 0
factoring (2x+3)(x-7)=0
2x+3=0 or x-7=0
x=-3/2 x=7
"roots are the solution to the equation."
4x(3x +2)
ReplyDelete(4x*3x)+(4x*2)
12x^2+8x
(4x + 7)(4x + 7)
ReplyDelete4X*4X+4X*7+7*4X+7*7
8X^2+56X+49
(4x + 7)(3x +2)
ReplyDelete(4x*3x + 4x*2 +7*3x + 7*2)
12x + 8x + 21x + 14
12x + 29x + 24
if jonh bought two hot dogs and three sodas and it cost $12 and then he bought six hot dogs and 9 sodas and it cost $36. john has to buy six hot dogs and 12 sodas how much will cost????.
ReplyDelete18)Expand
ReplyDeletei)4x(3x+2)
=12x^2+8x
ii)(4x+7)(4x+7)
=16x^2+28x+28x+49
=16x^2+56x+49
iii)(4x+7)(3x+2)
=12x^2+21x+8x+14
=12x^2+29x+14
2x^2-11x-21=0
ReplyDelete(x-7)(2x+3)
x=7, x=/3/2
Ques 18B
question 18
ReplyDelete(i) 4x(3x+2)
=12x^2+8x
question 18
ReplyDelete(ii) (4x+7)(4x+7)
4x(4x+7)+7(4x+7)
16x^2+28x+28x+49
16x^2+56x+49
question 18
ReplyDelete(iii) (4x+7)(3x+2)
4x(3x+2)+7(3x+2)
12x^2+8x+21x+14
12x^2+29x+14
Question 20
ReplyDeleteFact is that B and C are on the same level
But it is assumed that B is on the right of c so:
Finding for AC where we have a right angle triangle
tan Q(theta/Angle)=opp/adj
tan 8.85=opp/265.74
265.74tan8.85=opp
opp=41.38 This is also known as AC
Finding for AB where a bigger right angle is present
tan Q=opp/adj
tan(21.66+8.85)=opp/adj
Note- that angles are integrated to form APB
265.74tan30.51=opp
opp=156.6
or known as AB
AB-AC=CB
156.6-41.38=115.22
18.i. 4x(3x+2)
ReplyDelete=12x^2 + 8x.
ii. (4x+ 7) (4x+ 7)
ReplyDelete16x^2 + 28x + 28x + 49.
16x^2 + 56x+ 49.
18.b.
ReplyDelete2x^2-11x-21.
2x^2 + 3x - 14x - 21=0
x(2x+3) -7(2x+3)=0.
(2x+3) (x-7)=0.
2x+3=0 or x-7=0
2x=-3 or x =7.
x= -3/2.
roots of the equation is (-3/2,0)
(7,0)
4x(3x+2)
ReplyDeleteTo expand this first multiply 4x by everything inside the brackets
(4x*3x)
(4X*2)
Now add them together
(4x*3x) + (4X*2)
Hence: 4x(3x+2) = 12x^2+ 8x
19 (ii)
ReplyDeletefor 0<@<360
2-cos@=2sin^2@
2-cos@=2(sin^2@)
recall sin^2@=cos^2@=1
therefore; sin^2@=1-cos^2@ sub into eq'n
2-cos@=2(1-cos^2@)
2-cos@=2-2cos^2@
2cos^2@-cos@+2-2=0
2cos^2@-cos@=0
cos@(2cos@-1)=0
then; cos@=0
@=90
and; 2cos@=1
cos@=1/2
@=60
cos is positive in 1st and 4th quadrant
@=90, 360-60
@=90, 300
17. x^2 = 4 – y x = y + 2
ReplyDeletex^2 = 4 - y x = y + 2
>> -y = x^2 - 4 >> y = x - 2
>> y = -x^2 + 4
y = -x^2 + 4 = x - 2
y = -x^2 + 4 = x - 2
ReplyDeletey = -x^2 + 2 = x
y = -x^2 - x + 2
y = -x^2 -2x +1x +2
ReplyDelete-x(x + 2) +1(x + 2)
(-x + 1)(x + 2)
x= 1, x= -2
substitute x values into Y = -x^2 -x + 2
ReplyDelete1) y = -1^2 - 1 + 2 >>>> y = 0
2) y = -(-2)^2 - 2 + 2 >>>> y = -4
Question 18
ReplyDelete(i) 4x(3x+2)
Multiply 4x by 3x and 2
(4x*3x)+(4x*2)
=12x^2+8x
(ii) (4x+7)(4x+7)
also equal to (4x+7)^2
4x(4x+7)+7(4x+7)
16x^2+28x+28x+49
=16x^2+56x+49
(iii) (4x+7)(3x+2)
4x(3x+2)+7(3x+2)
12x^2+3x+21x+14
12x^2+29x+14
(b)2x^2-11x-21=0
2x^2-14x+3x-21=0
(2x^2-14x)(3x-21)=0
2x(x-7)+3(x-7)=0
0=(2x+3)(x-7)
18) mul.... whatever is in front the brackets by what is inside the brackes
ReplyDelete4x(3x+2)
4x*3x+4x*2
12x^2+8x
mul the 1st term in the first bracket by everything indise the second bracket. then mul.... the 2nd term in the 1st bracket by everything inside the second bracket. and add
(4x+7)(4x+7)
4x(4x+7)+7(4x+7)
16x^2+28x+28x+49
16x^2+56x+49
same procedure as stated above
(4x+7)(3x+2)
4x(3x+2)+7(3x+2)
12x^2+8x+21x+14
12x^2+29x+14
for ques 18 B
ReplyDelete2x^2-11x-21=0
1st factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
17) solving for x and y
ReplyDeletex^2=4-yx=y+2
X^2-4+yx=y+2
x^2-4+yx/y+2=y+2/y+2
Note- we divide by (y+2)
It is assumed that when two same numbers/variable is canceled we remain with one so we use it as part of the equation.
x^2+x-1=1
x^2+x-2=0
(x-1)(x+2)=0
X=1, x=-2
18
ReplyDeletei) 4x(3x+2)=12x^2+8x
ii) (4x+7)(4x+7)=4x(4x+7)+7(4x+7)
ReplyDelete=16x^2+28x+28x+49
=16x^2+56x+49
iii)
ReplyDelete(4x+7)(3x+2)
4x(3x+2)+7(3x+2)
12x^2+8x+21x+14
12x^2+29x+14
18)1.
ReplyDelete4x(3x+2)= 12x^2+8x
18.ii)
ReplyDelete(4x + 7)(4x + 7)
=16x^2+28x+28x+49
=16x^2+56x+49
18.iii)
ReplyDelete(4x + 7)(3x +2)
12x^2+8x+21x+14
12x^2+29x+14
(17)
ReplyDeletex^2= 4 – y x = y + 2
x^2= 4 - y x = y + 2
-y= x^2 - 4 >> y = x - 2
y= -x^2 + 4
y= -x^2 + 4 = x - 2
18)
ReplyDelete=4x(3x+2)
multiply the 4x by eveything in the bracket
so therefore the resulting answer will be
=12x^2+8x
18)
ReplyDeletemultiply each value in the barackets by the other
(4x+7)(4x+7)
=4x(4x) +4x(7) +7(4x) +7(7)
=16x^2 +28x +28x +49
=16x^2 +56x +49
18)
ReplyDeletesimilar to the above equation multiply each value by the other. expand the brackets.
(4x+7)(3x+2)
=4x(3x) +4x(2) +7(3x) +7(2)
=12x^2 +8x +21x +14
=12x^2 +29x +14
19)(i) 2 sin *= 3 cos *
ReplyDelete2 sin *= 3 cos *
sin * /cos *= 3/2
recall: tan * =sin */ cos *
therefore tan *= 3/2
*= tan^-1 (3/2)
*= 56.31
0<*<360
*= 56.31, (180 + 56.31)
*= 56.31, 236.31
This comment has been removed by the author.
ReplyDelete18)b
ReplyDelete2x^2-11x-21= 0
multiply 2x^2 by -21
answer wil be 42
then u get factors of 42 to make up -11
the factors are -14x and 3x
2x^2-14x+3x-21=0
2x(x-7)+3(x-7)=0
0=(2x+3)(x-7)
2x+3=0
x=3/2
x-7=0
x=7
19) (ii)
ReplyDelete2 - cos *= 2 sin^2 *
recall: sin^2 *+ cos^2 *=1
therefore;sin^2* = -cos^2* + 1
so
2 - cos *= 2(-cos^2 * +1)
2 - cos *= -2cos^2 * + 2
0= 2cos^2 * - cos *
0= cos *(2 cos *- 1)
0= cos *
*= cos^-1 (0)
*= 90, (360-90)
*= 90, 270
2 cos * - 1=0
2cos*=1
cos *= ½
*= cos^-1 (1/2)
*= 60, (360-60)
*= 60, 300
18.(i) 4x( 3x+ 2)
ReplyDeleteexpand the bracket by multiplying it contents by 4x
so. = 4x* 3x + 4x* 2
= 12x ^2 + 8x
18) (ii) (4x + 7) (4x + 7)
ReplyDeleteyou use the crab law for this equation by multiplying each term in the first bracket with the two terms in the other bracket.
so. = (4x* 4x)+ (4x *7) + (7* 4x) + ( 7* 7)
= 16x^2 + 28x + 28x + 49
= 16x^2 + 56X + 49
18. Expand the following
ReplyDeletei) 4x(3x +2)
ii) (4x + 7)(4x + 7)
iii) (4x + 7)(3x +2)
b) Find the roots of the equation 2x^2 – 11x -21 = 0
(18)(iii)
(4x + 7)(3x + 2)
you can use the crab law for this equation also by multiplying each term in the first bracket with the two terms in the other bracket.
s0. = (4x + 7)(3x + 2)
=( 4x *3x)+ (4x* 2) + (7 * 3x) + (7 * 2)
= 12x^2 + 8x + 21x + 14
= 12 x^2 + 29 x + 14
18)(b)
ReplyDelete2x^2 - 11x -21=0
a=2, b= -11, c= -21
a*c= 2 * -21=- 42
-42= 2 * -21
3 * -14- this could be used to satisfy the equation
2x^2 - 14x + 3x -21=0
2x( x - 7) + 3(x - 7)=0
(2x + 3) ( x -7)=0
2x + 3=0
2x= 3
x= 3/2
x= 1.5
x -7=0
x=7
the roots are therefore : x= 1.5, x= 7
18. Expand the following
ReplyDeletei) 4x(3x +2) = 12(x^2) + 8x
ii. (4x +7)(4x + 7)
ReplyDelete= 16(x^2) + 56x + 49
iii. (4x + 7)(3x + 2)
ReplyDelete= 12(x^2) + 8x + 21x + 14
= 12(x^2) + 29x + 14
18)
ReplyDeletei)
4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
19)
ReplyDeleteii)
2-cosӨ=2sin^2Ө
2-cosӨ=2(1-cos^2Ө) recall sin^2Ө+cos^2Ө=1
2-cosӨ=2-2cos^2Ө
2cos^2Ө-cosӨ=2-2
2cos^2Ө-cosӨ=0
cosӨ=0 (2cosӨ-1)=0
cosӨ=0 and 2cosӨ=0
Ө=cos-1(0)=90,270
Ө=cos-1(1/2)=60,300
18 (i)
ReplyDelete4x(3x +2)
12x^2+8x
18 (ii)
ReplyDelete(4x + 7)(4x + 7)
16x^2+28x+28x+49
16x^2+52x+49
and a quadratic is formed
18 (iii)
ReplyDelete(4x + 7)(3x +2)
12x^2+21x+8x+14
12x^2+29x+14
i dont understand question one can some1 please explain.....thanks
ReplyDeletei) 4x(3x +2)
ReplyDelete12x^2 + 8x
ii) (4x + 7)(4x + 7)
ReplyDelete= 16X^2 + 28X + 28X + 49
= 16X^2 + 56X + 49
4x(3x+2)
ReplyDelete(4x*3x) + (4x*2)
=12x^2 + 8x
roots of an equation =b^2-4ac
ReplyDelete(4x + 7)(4x + 7)
ReplyDelete= (4x*4x)+(4x*7) +(7*4x)+(7*7)
= 16x^2 +28x +28x+ 49
= 16x^2 + 56x + 49
1).
ReplyDeletex^2=4-yx=y+2
x^2-4+yx=y+2
x^2-4+yx-y-2=0
x^2-6+yx-y=0
1(x^2-6)+y(x-1)=0
(x^2-6)(x-1)(1+y)=0
so therefore x^2-6=0
x^2=6
x=sqrt6
x=2.45
x-1=0
x=1
y+1=0
y= -1
2.(1)
ReplyDelete4x(3x+2)
first you multiply 4x by 3x, and then 4x by 2.
12x^2+8x
2.(2)
ReplyDelete(4x+7)(4x+7)
first you multiply 4x by 4x, 4x by 7, 7 by 4x and 7 by 7.
16x^2+28x+28x+49
16x^2+56x+49
2.(3)
ReplyDelete(4x+7)(3x+2)
first you multiply 4x by 3x, 4x by 2, 7 by 3x and 7 by 2.
12x^2+8x+21x+14
12x^2+29x+14
b).
ReplyDelete2x^2-11x-21=0
2x^2-14x+3x-21=0
2x(x-7)+3(x-7)=0
(x-7)(2x+3)=0
so therefore x-7=0 and 2x+3=0
x=7 and 2x= -3
x= -3/2
20.
ReplyDeleteIF PAC is 90 degrees,
angle APB 21.66 degrees,
angle APC 8.85 degrees and
PA is 265.74.
therefore angle ACP is 81.15 degrees,
angle ABP IS 68.34 degrees.
USING tan angle= opp/adj.
tan angle= AC/a
tan 8.85= AC/265.74
AC= tan 8.85*265.74
AC= 41.38
tan angle= AB/a
tan 21.66= AB/265.74
AB= tan 21.66*265.74
AB= 105.54
so therefore BC= AB-AC
BC= 105.54-41.38
BC= 64.16
iii) (4x + 7)(3x +2)
ReplyDelete= 12x^2 + 8x + 21x + 14
= 12x^2 + 29x + 14
You have to answer instantly. You can't take time, answer it immediately. OK
ReplyDeleteLet's find out just how clever you really are Ready? GO!!!
You are participating in a race. You overtake the second person. What position are you in?
18)i)
ReplyDelete4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
18)i)
ReplyDelete(4x+7)(4x+7)
4x(4x)+4x(7)+7(4x)+7(7)
16x^2+28x+28x+49
16x^2+56x+49
18)iii)
ReplyDelete(4x+7)(3x+2)
4x(3x)+4x(2)+7(3x)+7(2)
12x^2+8x+21x+14
12x^2+29x+14
18)b)
ReplyDelete2x^2-11x-21=0
then factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
can someone please help me understand number 17???
ReplyDeletethanks....
question 18
ReplyDelete(i)4x(3x+2)
=(4x x 3x) + (4x x 2)
= 12x^2 + 8x
question 18
ReplyDelete(ii)(4x+7) (4x+7)
= (4x x 4x + 4x x 7) + (7 x 4x + 7 x 7)
= 16x^2 + 28x + 28x + 49
= 16x^2 + 56x + 49
question 18
ReplyDelete(iii)(4x+7) (3x+2)
= (12x^2 + 8x) (21x + 14)
= 12x^2 + 8x + 21x + 14
= 12x^2 + 29x + 14
18.
ReplyDeletei
4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
18
ReplyDeleteii
(4x+7)(4x+7)
4x(4x)+4x(7)+7(4x)+7(7)
16x^2+28x+28x+49
16x^2+56x+49
which is the same as (4x+7)^2
18
ReplyDeleteiii
(4x+7)(3x+2)
4x(3x)+4x(2)+7(3x)+7(2)
12x^2+8x+21x+14
12x^2+29x+14
18
ReplyDeleteb
2x^2-11x-21=0
factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
i do not think you could solve an equation with 2 equal signs because then how wold you know what side it is on...
ReplyDelete18.
ReplyDeletei
4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
18
ReplyDeleteiii
(4x+7)(3x+2)
4x(3x)+4x(2)+7(3x)+7(2)
12x^2+8x+21x+14
12x^2+29x+14
18
ReplyDeleteb
2x^2-11x-21=0
factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
2-cosӨ=2sin^2Ө
ReplyDelete2-cosӨ=2(1-cos^2Ө) recall sin^2Ө+cos^2Ө=1
2-cosӨ=2-2cos^2Ө
2cos^2Ө-cosӨ=2-2
2cos^2Ө-cosӨ=0
cosӨ=0 (2cosӨ-1)=0
cosӨ=0 and 2cosӨ=0
Ө=cos-1(0)=90,270
Ө=cos-1(1/2)=60,300
question 18(i)
ReplyDelete4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
question 18(ii)
ReplyDelete(4x+7)(4x+7)
4x(4x)+4x(7)+7(4x)+7(7)
16x^2+28x+28x+49
16x^2+56x+49
question 18(iii)
ReplyDelete(4x+7)(3x+2)
4x(3x)+4x(2)+7(3x)+7(2)
12x^2+8x+21x+14
12x^2+29x+14
question 18(b)
ReplyDelete2x^2-11x-21=0
factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
question 20
ReplyDeletea/sinA=b/sinB
b=265.74*sin8.85/sin90=40.9
sin=opp/hyp hyp=40.4/sin8.85=262.6
all angles in a triangle=180 8.85+90-180=81.15
40.9sin81.15=40.4
262.6cos8.85=259.5
tan=21.66*259.5=103
103+40.4=143.4
i stand to be corrected for the above answers!!!!
ReplyDelete19)i)
ReplyDelete2 sin *= 3 cos *
2 sin *= 3 cos *
sin * /cos *= 3/2
recall: tan * =sin */ cos *
therefore tan *= 3/2
*= tan^-1 (3/2)
*= 56.31
0<*<360
*= 56.31, (180 + 56.31)
*= 56.31, 236.31
19)ii)
ReplyDelete2-cosӨ=2sin^2Ө
2-cosӨ=2(1-cos^2Ө) recall sin^2Ө+cos^2Ө=1
2-cosӨ=2-2cos^2Ө
2cos^2Ө-cosӨ=2-2
2cos^2Ө-cosӨ=0
cosӨ=0 (2cosӨ-1)=0
cosӨ=0 and 2cosӨ=0
Ө=cos-1(0)=90,270
Ө=cos-1(1/2)=60,300
Does question 1 have two equal signs or is it two separate equations:
ReplyDeletex^2 = 4 – y
x = y + 2
????????????????????????????????????????
i) 4x(3x + 2)
ReplyDelete4x(3x) + 4x(2)
12x^2 + 8x
ii) (4x + 7)(4x + 7)
ReplyDelete4x(4x) + 4x(7) + 7(4x) + 7(7)
16x^2 + 28x + 28x + 49
16x^2 + 56x + 49
hmmmmm...are there any adventurous types on this blogg who wish to solve 16x^2 + 56x + 49 ??????????????????????????????????????????????
ReplyDeleteiii) (4x + 7)(3x + 2)
ReplyDelete4x(3x) + 4x(2) + 7(3x) + 7(2)
12x^2 + 8x + 21x + 14
12x^2 + 29x + 14
open question:
ReplyDeleteagain...anyone wants to test there intelligence ???? Solve 12x^2 + 29x + 14
Question 18
ReplyDelete(i) 4x(3x+2)
Multiply 4x by 3x and 2
(4x*3x)+(4x*2)
=12x^2+8x
(ii) (4x+7)(4x+7)
also equal to (4x+7)^2
4x(4x+7)+7(4x+7)
16x^2+28x+28x+49
=16x^2+56x+49
(iii) (4x+7)(3x+2)
4x(3x+2)+7(3x+2)
12x^2+3x+21x+14
12x^2+29x+14
(b)2x^2-11x-21=0
2x^2-14x+3x-21=0
(2x^2-14x)(3x-21)=0
2x(x-7)+3(x-7)=0
0=(2x+3)(x-7)
18)
ReplyDeletei)4x(3x+2)
12x^2+8x
18
ReplyDeleteii)(4x+7)(4x+7)
16x^2+28x+28x+49
16x^2+56x+49
18)
ReplyDeleteiii)(4x+7)(3x+2)
12x^2+8x+21x+14
12x^2+29x+14
18)b)
ReplyDelete2x^2-11x-21
2x^2-14x+3x-21
2x(x-7)+3(x-7)
(x-7)(2x+3)
x=7, x=-3/2
question 18 b)
ReplyDeleteby factorization
2x^2-11x-21=0
(2x+3)(x-7)=0
either or
2x+3=0
2x+3-3=0-3
2x=-3
x=-3/2
x-7=0
x-7+7=0+7
x=7
x=-3/2 or x=7
number (18)
ReplyDeletei
4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
number (18)
ReplyDeletepart ii
(4x+7)(4x+7)
4x(4x)+4x(7)+7(4x)+7(7)
16x^2+28x+28x+49
16x^2+56x+49
number (18)
ReplyDeletepart iii
(4x+7)(3x+2)
4x(3x)+4x(2)+7(3x)+7(2)
12x^2+8x+21x+14
12x^2+29x+14
number (18)
ReplyDeletepart b
2x^2-11x-21=0
factorize
(2x+3)(x-7)
2x+3=0 and x-7=0
2x=-3 x=7
x=-3/2 x=7
number (19)
ReplyDelete2-cosӨ=2sin^2Ө
2-cosӨ=2(1-cos^2Ө) recall sin^2Ө+cos^2Ө=1
2-cosӨ=2-2cos^2Ө
2cos^2Ө-cosӨ=2-2
2cos^2Ө-cosӨ=0
cosӨ=0 (2cosӨ-1)=0
cosӨ=0 and 2cosӨ=0
Ө=cos-1(0)=90,270
Ө=cos-1(1/2)=60,300
number (20) part 1
ReplyDeleteIF PAC is 90 degrees,
angle APB 21.66 degrees,
angle APC 8.85 degrees and
PA is 265.74.
therefore angle ACP is 81.15 degrees,
angle ABP IS 68.34 degrees.
number (20) part 2
ReplyDeleteUSING tan angle= opp/adj.
tan angle= AC/a
tan 8.85= AC/265.74
AC= tan 8.85*265.74
AC= 41.38
tan angle= AB/a
tan 21.66= AB/265.74
AB= tan 21.66*265.74
AB= 105.54
so therefore BC= AB-AC
BC= 105.54-41.38
BC= 64.16
for ques 18(i)
ReplyDelete4x(3x+2)
4x(3x)+4x(2)
12x^2+8x
expand
ReplyDelete18
1) 4x(5x + 2)
20x^2 +8x
expand
ReplyDelete18
111)
(4x + 7) (3x + 2)
4x(3x + 2) +7 (3x+2)
12x^2 +8x +21x +14
19. 0◦ < Ө < 360
ReplyDeletei) 2 sin Ө = 3 cos Ө
2sin@ = 3cos @
2sin@/cos@ = 3cos@/cos@
2tan@=3
tan@=3/2
@=tan^-1 (1.5)
@=56.3
@ for 0◦ < Ө < 360
=56.3 and 236.3
18. Expand the following
ReplyDeletei) 4x(3x +2)
= (4x*3x)+ (4x*2)
= 12x^2 + 8x
ii) (4x + 7)(4x + 7)
ReplyDelete= (4x*4x) + (4x*7) + (7*4x) + (7*7)
= 16x^2 + 28x + 28x + 49
= 16x^2 + 56x + 49
iii) (4x + 7)(3x +2)
ReplyDelete= (4x*3x) + (4x*2) + (7*3x) + (7*2)
= 12x^2 + 8x + 21x + 14
= 12x^2 + 29x + 14
17.
ReplyDeletex^2 = 4 – y x = y + 2
x^2 = 4 - y x = y + 2
y = x^2 - 4 >> y = x - 2
y = -x^2 + 4
y = -x^2 + 4 = x - 2