test revision for year 10 and 11..Please help me..please?

Question

1) The weekly wage, $w, of a salesman consists of a fixed component of $200 then $10 commission for each unit he sells.
a)If he sells n units in a week, find a rule for his weekly wage w, in terms of the number of units sold.
b)Find his wage if he sells 30 units.

c)How many units does he sell if his weekly wage is $550?

2) A parabola has x –intercepts of 2 and 7 and passes through the point (3, 6). Find the equation of the parabola.


3) For each of the following make the symbol indicated in brackets the subject:
a)H=20 – 2T
b) S=P(I+rt) +7



4) Find the equation of the line that passes through the point with coordinates (–2, 6)and is :
a)parallel to the line with equation y =–3x + 4
b)perpendicular to the equation y =–3x + 4



5) Find the x–intercepts of the graphs of:
a)y = -(x - 2)² + 4
b)y = 25 – x²

Answer 1

1a) he earns $200 plus $10 for each unit so he earns. so that's $200 plus $10x(# of units sold). if he sells n units then that's 200+10n units.
So w=200+10n

1b)find his wage when he sells 30 units. that's n=30, so using our result from part a 200+10x30=200+300=500 dollars

1c)how many units does he sell if his wage is 550? that's w=550 so using part a we get
550=200+10n
subtract 200
350=10n
divide by 10
35=n
he sold 35 units

2)parabola has x-intercepts 2 and 7 and passes through (3,6).
parabolas have the form y=ax²+bx +c. Because the x intercepts are 2 and 7 we know that (x-2) and (x-7) are factors so that gives us a(x-2)(x-7). We still don't know what a is. so we have a(x-2)(x-7)
which is a(x²-2x-7x+14)=a(x²-9x+14). Now to find a, we know that it passes through the point (3,6) so that means x=3 y=6 is a solution. So 6=a(3²-9•3+14) 6=a(9-27+14) 6=a(-4) a=-6/4=-3/2
therefore, our parabola is y=(-3/2)x²+(27/2)x-21

3) I don't see any brackets

4) parallel lines have the same slope, perpendicular lines have opposite reciprocal slopes.
a) parallel to y=-3x+4 and passes through (-2,6)
It has the same slope so it looks like y=-3x+b, we just need to find b. it passes through (-2,6) so that means x=-2 y=6 is a solution, so 6=-3(-2)+b 6=6+b subtract 6: 0=b so the line is y=-3x

b) perpendicular to y=-3x+4, and goes through (-2,6)
It's going to have opposite reciprocal slope so the slope is 1/3 and the equation is going to look like y=(1/3)x+b. Once again it passes through (-2,6) so x=-2 y=6 is a solution and 6=(1/3)•-2+b so 6=(-2/3)+b add 2/3: 6+(2/3)=b 20/3=b
so the equation is y=(1/3)x+20/3

5) x intercepts are where y=0
a) 0=-(x-2)²+4
subtract 4
-4=-(x-2)²
divide by -1
4=(x-2)²
Square root
±2=x-2
add 2
2±2=x
therefore x=4 or 0

b)0=25-x²
add x²
x²=25
square root
x=±5
therefore x=5 or -5


Hope that helps! good luck on your test. sorry I couldn't help on #3 the answer involves basic algebra, I'm sure you can get it if you try.

Answer 2

1)a) 200 + 10n = w
b) 200 + 10(30) = 200 + 300 = 500
c) 200 + 10n = 550; 10n = 350; n = 35

Answer 3

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