Answer:
Brandon has <u>18 Dimes and 33 Quarters</u> [Beware: The problem does not state that Brandon owns the coins - he just has them. Check your pockets]
Step-by-step explanation:
Let D and Q stand for the numbers of Dimes(D) and Quarters(Q). <u>I'll use pennies instead of dollars, so avoid the clutter of decimal points</u>.
We are told that:
Q = 2D - 3 [The number of quarters is 3 less than twice the number of dimes.]
and
25Q + 10D = 1005 [total value of $10.05]
Substitute the value of Q in the first equation in the second, so that we have an equation with just one unknown, D.
25(2D-3) + 10D = 1005
50D - 75 + 10D = 1005
60D = 1080
<u>D = 18</u>
<u></u>
Q = 2D - 3
Q = 2(18) - 3
<u>Q = 33</u>
=============================
Check
25Q + 10D = 1005
25(33) + 10(18) = 1005 ?
825 + 180 = 1005 <u>YES</u>
----
Q = 2D - 3 ?
33 = 2(18) - 3 <u>YES</u>
X<4 represents "all numbers smaller than 4, including all negative numbers."
In interval notation, this comes out to (-infinity, 4).
9514 1404 393
Answer:
(3, 2)
Step-by-step explanation:
Reflection across y=x swaps the coordinates:
(x, y) ⇒ (y, x)
Dilation by a factor of 1/2 multiplies each coordinate by 1/2.
(x, y) ⇒ (x/2, y/2)
The combination of these transformations gives you ...
(x, y) ⇒ (y/2, x/2)
(4, 6) ⇒ (3, 2)