Answer:
x = -36, y = 6, z = -6
Step-by-step explanation:
The requirement x/z = -z means x = -z².
The requirement x/y = z means x = yz.
These two requirements together mean yz = -z², or y = -z.
The requirements that z/2 and z/3 are integers mean that z is a multiple of 2·3 = 6. The smallest magnitude non-zero multiple is z=-6 (since we also require z < -z).
Using z=-6, we have x = -z² = -36; y = -(-6) = 6.
For some positive integer n, ...
... x = -36n², y = 6n, z = -6n.
The first equation is 6x - 2y = 10. To solve for y, you will use inverse (opposite) operations to undo what is happening to y. Please see the steps below for the work.
6x - 2y = 10
-6x -6x
<u>-2y </u>= <u>(-6x + 10)</u>
-2 -2
y = 3x - 5
Answer:
$35,75
Step-by-step explanation:
55 . 35 / 100 = 19,25
55 - 19,25 = 35,75
Answer:
3 years
Step-by-step explanation:
As with many age problems, you can reason it without equations. If Tom is 13 now, 2 years ago he was 11. If the total age of the two cats at that time was 15, then Tim was 15 -11 = 4.
That means Tim is now 4+2 = 6, so will be 9 in 3 years.
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<em>Additional comment</em>
If you want to write equations, there are several ways you can do it. We often like to use variables to represent the current age. We can assign ...
x = Tim's current age; y = Tom's current age.
The sum of their ages 2 years ago was ...
(x -2) +(y -2) = 15
Tom's current age is 13, so we have y=13. Using that in the equation gives ...
x -2 +13 -2 = 15
x = 6 . . . . . . . . . . subtract 9, collect terms
That's Tim's current age, so Tim will be 9 years old in 3 years.
<h3>
Answer: Rhombus and square</h3>
Explanation:
Any rhombus has its diagonals meet at 90 degree angles. The proof for this is a bit lengthy, so I'll let you handle it. The basic idea is to draw in the diagonals, which forms smaller triangles. Proving those triangles to be congruent leads to supplementary congruent angles, which in turn leads to the 90 degree angles needed.
A square is a special type of rhombus where all four angles are the same (each 90 degrees). Put another way, a square is both a rectangle and a rhombus at the same time.
Some rectangles are not squares, so the non-square rectangles will have the diagonals not be perpendicular.
