How would you model the function rule Y=-2x-3 with a table of values. can you pretty please show your work i just need help i've
been on this problem for like 20 mins
1 answer:
Y = -2x - 3
First make a table, then start inserting the x's you choose and figure out the y's.
x y
----------------------
-2 -2(-2) -3
4 - 3
1
-----------------------
-1 -2(-1) - 3
2 - 3
-1
------------------------
0 -2(0) - 3
0 - 3
-3
-------------------------
1 -2(1) - 3
-2 - 3
-5
--------------------------
2 -2(2) - 3
-4 - 3
-7
--------------------------
Now you can plot the points into a graph.
(-2, 1), (-1, -1), (0, -3), (1, -5), (2, -7)
First make a table, then start inserting the x's you choose and figure out the y's.
x y
----------------------
-2 -2(-2) -3
4 - 3
1
-----------------------
-1 -2(-1) - 3
2 - 3
-1
------------------------
0 -2(0) - 3
0 - 3
-3
-------------------------
1 -2(1) - 3
-2 - 3
-5
--------------------------
2 -2(2) - 3
-4 - 3
-7
--------------------------
Now you can plot the points into a graph.
(-2, 1), (-1, -1), (0, -3), (1, -5), (2, -7)
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The two original functions are 4x+9y=7 and 4x-9y=9
To use the combination method, add all the values of the two equations together to cancel out one of the variables
4x+4x+9y-9y=7+9
8x=16
8x/8=16/8
x=2
4(2)+9y=7
8+9y=7
8-8+9y=7-8
9y=-1
y=-
To use the combination method, add all the values of the two equations together to cancel out one of the variables
4x+4x+9y-9y=7+9
8x=16
8x/8=16/8
x=2
4(2)+9y=7
8+9y=7
8-8+9y=7-8
9y=-1
y=-
ANSWER
EXPLANATION
The given binomial expansion is:
Compare this to
we have a=2x , b=-3y and n=10
We want to find the coefficient of the term
This implies that, r=5.
The terms in the expansion can be obtained using
We substitute the given values to obtain;
Hence the coefficient is;
To begin with, the question is asking for the answer in days, so let's change 3 weeks to days. There are 7 days in 1 week; 3 weeks times 7 days = 21 days.
21 total days of vacation.
Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)
M + J + W = 21 [This is the equation we'll be coming back to]
Now, we can use the clues given in the question to have an equation for each variable/boy.
Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.
So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W
To have an equation for each individual boy, we must rearrange the last two equations in the list.
First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J
Second, <span>M = (1/2)W
Multiply both sides by 2
2M = W
New equations:
</span><span>M + J + W = 21 [From the old list]
</span>J = (1/2)W
W = 2M
Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
<span>(7/2)M = 21
</span>
Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
M = 6
Now we know Max was on vacation for 6 days.
If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.
So...
<span>J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days
</span>
Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.
Let's double check our answer:
M + J + W = 21 days<span>6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!</span>
21 total days of vacation.
Max + Jared + Wesley = 21 days
(Let's use the first letter of their name to represent their vacation time)
M + J + W = 21 [This is the equation we'll be coming back to]
Now, we can use the clues given in the question to have an equation for each variable/boy.
Max was on vacation twice as long as Jared. We can interpret this as M= 2J Max was on vacation only half as long as Wesley. We can interpret this as M = (1/2)W.
So far we have these three equations: M + J + W = 21M = 2J M = (1/2)W
To have an equation for each individual boy, we must rearrange the last two equations in the list.
First, M = 2J.
Divide both sides by 2
M/2 = 2J/2
(1/2)M = J
Second, <span>M = (1/2)W
Multiply both sides by 2
2M = W
New equations:
</span><span>M + J + W = 21 [From the old list]
</span>J = (1/2)W
W = 2M
Now we can substitute the last two equations into the first one.
M + J + W = 21
M + (1/2)W + 2M = 21
[Combine Like Terms]
<span>(7/2)M = 21
</span>
Then, solve for M (Max's vacation days):
Multiply both sides by 2/7
M = 6
Now we know Max was on vacation for 6 days.
If Max was on vacation twice as long as Jared, that means Jared was on vacation HALF as long as Max.
So...
<span>J = (1/2)M
J = (1/2) * 6
J = 3
Jared was on vacation for 3 days
</span>
Wesley was on vacation twice as long as Max so... W = 2M
W= 2*6
W = 12
Wesley was on vacation for 12 days.
Let's double check our answer:
M + J + W = 21 days<span>6 + 3 + 12 = 21
The numbers work out so the math is correct. Hope this helps and makes sense!</span>