Answer:
1.The ratio of dogs to cats is 3 to 4
2. For every 3 dogs there are 4 cats.
Step-by-step explanation:
The solution of the equation is x = -4/3.
<h3>What does it mean to solve an equation?</h3>
An equation represents equality of two or more mathematical expression.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
WE have been given an equation as;
|x - 4| = 5x + 12
In an absolute value equation, we solve the original expression as our first equation. Our second one is that we multiply the right side by -1.
Case 1: original equation
|x - 4| = 5x + 12
x - 4 = 5x + 12
x - 5x = 12 + 4
-4x = 16
x = -4
Case 2: Opposite equation
|x - 4| = 5x + 12
x - 4 = - (5x + 12)
x - 4 = - 5x - 12
x + 5x = -12 + 4
6x = -8
x = -4/3
Now we have two solutions. We need to check for extraneous solutions because of all the manipulations;
Check:
|x - 4| = 5x + 12
use x = -4
|-4 - 4| = 5(-4) + 12
| -8 | = -20 + 12
8 = -8
Thus, it is Not a solution
Now, |x - 4| = 5x + 12
use x = -4/3
| -4/3 - 4| = 5( -4/3) + 12
|-16/3 | = -20/3 + 12
|-16/3 | = 16/3
16/3 = 16/3
Thus, it is the Solution.
Learn more about solving equations here:
brainly.com/question/18015090
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Answer:
By S.S.S. congruence property; ΔTZW ≅ ΔVZU
Step-by-step explanation:
Given:
TUVW is a rectangle.
To Prove : TZW ≅ UZV
Proof:
Since TUVW is a rectangle, and we know that opposite side of a rectangle is equal.
So,
And also TV and WU are the diagonals of the rectangle.
And the diagonals of rectangle bisects each other.
Therefore;
Now In ΔTZW and ΔVZU
TW = UV (from 1)
TZ = ZV (from 2)
WZ = ZU (from 3)
So, by S.S.S. congruence property;
ΔTZW ≅ ΔVZU
Hence proved.
Answer:
500.61
Step-by-step explanation:
5 multiplied by 100 = 500
1/10 = 0.1, So 6 multiplied by 0.1 = 0.6
1/100 = 0.01, So 1 multiplied by 1 = 0.01
500 + 0.6 + 0.01 = 500.61
11, add six and a half to four and a half.
