I dont have options but i can sayEach of these questions is asking you to figure out how g(x) would be graphed based on some other function, f(x), except we're gonna make some changes to f(x) first. For example, let's look at part (a). You're told that g(x) = 2f(x)+3. 1. Whatever f(x) is, 2f(x) would take all of the y values and double them.2. Whatever that turns out to be, "+3" would add 3 to every y value. So, to translate (1, -2), first we double the y value...so that'd be -2 * 2, or -4. Then we add 3, which gives 1. So, the point (1, -2) becomes (1, 1). [EDIT: Um, no, -4 + 1 isn't 1. It's -1. My bad! MBW] Part (b) is a little bit trickier: 1. Whatever f(x) is, by adding 1 to x, it actually shifts the graph left by 1, even though it sorta feels like you should be shifting it 1 to the right. Let's not get too far into the details here, so for the moment, f(x+1) means "shift the graph of f to the left by 1." In other words, subtract 1 from x to get the new point. 2. Whatever f(x+1) is, then the "-3" would subtract 3 to every y value. So, if (1, -2) was on the original graph, then f(x+1) would be shifted to the left by 1...so that's (0, -2). And then, we subtract 3 from y, so that'd be (0, -5). Basically, anything inside the parentheses, like f(x+1), messes with the x coordinate of the point, and anything outside the parentheses, like -f(x) or f(x) + 3, messes with the y coordinate. For the last two, I'll give you a few hints and see if you can take it from there. For part (c): f(2x), even though you think it might double the value of x, actually divides the value of x by 2.For part (d): the trick here is to ignore the "-x" until the last step. Deal with the f(x-1) first (which shifts the x coordinate...which way?), then the negative outside of f(x) (which flips the sign of the y coordinate), then the +3 outside of f(x)...and then, at the end, the "-x" would flip the sign of the x coordinate. I hope this helps point you in the right direction!
From the last answer
angle CPD = 38°
agian,
angle BPC + angle CPD = 90° ( sum of complementary angles)
or, angle BPC + 38 = 90
or, angle BPC = 90 - 38
or, angle BPC = 52°
therefore BPC = 52
I'll be honest, this is a pretty interesting question. I've never seen anything like it before!
We can start off by making equations with the given. If there are 100 heads, that means that the total number of chickens and pigs combined is 100. Thus, we can form our first equation:
p + c = 100
('p' represents number of pigs, and 'c' represents number of chickens)
We also know that there are 270 legs total. Since chickens have 2 and pigs have 4, we can make the following equation:
2c + 4p = 270
I suppose the quickest way to solve for this equation is to use the subtraction method. Put the equations on top of each other:
2c + 4p = 270
c + p = 100
___________
Multiply the bottom equation by -2;
2c + 4p = 270
-2c -2p = 100
____________
"Add" these two equations together:
2c + 4p = 270
-2c -2p = -200
___________
2p = 70
Divide both sides by 2:
p = 35
Ah, finally. Now that we know that there are 35 pigs, input this variable into the first equation to find the number of chickens:
c + 35 = 100
Subtract:
c = 65
There are 35 pigs and 65 chickens
-T.B.
Answer:
Average speed v = 83.8 km/h
Step-by-step explanation:
Given;
Distance travelled = 95 km
Time taken t = 12.23 - 11.15 = 1 hour 8 minutes
t = 1 + 8/60 hours = 1.133 hours.
Average speed v = distance travelled/time taken
substituting the values;
v = 95 km ÷ 1.133 hours
Average speed v = 83.8 km/h
