If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
<em>X' = (3, -1)</em>
<em>Y' = (2, -2)</em>
<em>Z' = (-1, -3)</em>
<h3>Rotation of coordinates</h3>
If the coordinates (x, y) is rotated 270° counterclockwise, the resulting coordinate point will be;
(x, y) - > (y, -x)
From the given triangles, the coordinate points are expressed as
<em>X = (1, 3)</em>
<em>Y = (2, 2)</em>
<em>Z = (3, -1)</em>
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
<em>X' = (3, -1)</em>
<em>Y' = (2, -2)</em>
<em>Z' = (-1, -3)</em>
Learn more on rotation here: brainly.com/question/26249005
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Let's start by writing a system of linear equations:
c -> cookies
cb -> candy bars
(You can use any abbreviations to your preference)
Abby:
4 cookies
3 candy bars
$10.25 per bag
The equation would be:
4c+ 3cb = $10.25
Marissa:
2 cookies
7 candy bars
$14.75 per bag
The equation would be:
2c + 7cb = $14.75
So our linear equation system would be:
<span>4c+ 3cb = $10.25
</span><span>2c + 7cb = $14.75
I would try to get rid of one variable so I can solve for the other variable. In this case, it is easier to get rid of c since I can multiply the second equations by 2. Then it would subtract the two equations.
(2c + 7cb = $14.75) 2 = 4c + 14 cb = $29.50
4c + 3cb = $10.25
- 4c+14 cb = $29.50 (4c would get canceled.)
---------------------------------
-11 cb = - $19.25 (Divide by -11 to solve for cb)
</span> --------- -------------
-11 -11
cb = $1.75
Now we know cb (candy bar) cost, we would substitute this value into cb into one of the equations. It doesn't matter which equation you put it in. I will substitute it in the first equations.
4c + 3 (1.75) = $10.25
4c + 5.25 = $10.25 (Multiply 3 by 1.75)
-5.25 -5.25 (Subtract 5.25 on both sides)
4c = 5 (Divide by 4 on both sides to get c)
---- ---
4 4
c= 1.25
Check the work:
4(1.25) + 3(1.75)
= $10.25
2(1.25) + 7(1.75)
= $14.75
Total cost:
cookies = $1.25
candy bars = $ 1.75
Hope this helps! :)
Answer:
answers and work are shown below:)
Step-by-step explanation:
The domain is talking about the "range" of the horizontal axis therefore you will be focusing on the x-intercepts.
The answer will be All non-negative real numbers less than or equal to 18
because the x-intercepts lies at 0 and 18. The answer makes sense because the furthest you can go is 18 ft and the closest you could go is 0 ft. The "all non-negative real numbers" puts a restriction on the least distance it could travel so that means that it stops at 0 ft because if you go any further, you will end up in the negatives and it clearly states "non-negative".
Answer:
27 4th root (x^3)
Step-by-step explanation:
(81x) ^ 3/4
We know (ab) ^c = a^c b^c
81 ^ (3/4) * x^3/4
We can rewrite 81 as 3^4
(3^4)^(3/4) * x^3/4
We know that a^b^c = a^ (b*c)
3^(4*3/4) * x^3/4
3^(3) * x^3/4
27 * x^3/4
27 4th root (x^3)
