Answer:
(-7, -1)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
5x - 9y = -26
-2x + 3y = 11
<u>Step 2: Rewrite Systems</u>
-2x + 3y = 11
- Multiply everything by 3: -6x + 9y = 33
<u>Step 3: Redefine Systems</u>
5x - 9y = -26
-6x + 9y = 33
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Combine 2 equations: -x = 7
- Divide -1 on both sides: x = -7
<u>Step 5: Solve for </u><em><u>y</u></em>
- Define equation: 5x - 9y = -26
- Substitute in <em>x</em>: 5(-7) - 9y = -26
- Multiply: -35 - 9y = -26
- Add 35 on both sides: -9y = 9
- Divide -9 on both sides: y = -1
Answer:
A general way of explaining this is
Suppose that we have a given property (or a pattern if we are working with a series of numbers):
Now, if that property is true, for example, for the numbers 1, 2, 3... etc. Then we can suppose that the property is also true for an unknown number N.
Now, if using the hypothesis that the property is true for N, we can prove that the property is also true for N + 1, then we actually proved that the property is true for all the set.
We actually can use any set, not only the natural numbers.
For example, we can use the set of the even numbers {2, 4, 6, 8....}, suppose that the property is true for a random number N, that is even, and then see if using that hypothesis we can prove that the property is also true for the next number in the set; N + 2.
Multiply 5.8 by 100 to convert to percent:
<span>5.8 × 100 = </span>580 %
Answer:
1:4:12
Step-by-step explanation:
George = x
Alex = 12 + x
Carl = 3(12 + x) = 36 + 3x
x + 12 + x + 36 + 3x = 68
5x + 48 = 68
5x = 20
x = 4
George = x = 4
Alex = 12 + x = 12 + 4 = 16
Carl = 36 + 3x = 36 + 3(4) = 48
4:16:48 = 1:4:12
The ratio is 1:4:12.
First, multiply the top equation by 2 and bottom by -3.
60x+60y=900
-60x-75y=-1035
————————
-15y=-135
—————-
-15=-15
y=9
So the answer should be 9.
