1 Subtract
9
y
9y from both sides
4
x
=
6
3
−
9
y
4x=63−9y
2 Divide both sides by
4
4
x
=
6
3
−
9
y
4
x=
4
63−9y
3 Factor out the common term
9
9
x
=
9
(
7
−
y
)
4
x=
4
9(7−y)
Done
Eas
permutations
5 digits
5*4*3*2*1=120 ways
if you count 0 in front of the number as a whole number
if you don't, then there are 96 ways
Answer: -20/21
Step-by-step explanation:
Using the Pythagorean identity, we can get that the sine of angle theta is .
But since theta terminates in Quadrant II, the sine of angle theta is positive, meaning that it has a value of 20/29.
Now, since tan = sin/cos, tan theta = (20/29)/(-21/29) = -20/21
Answer:
(a) x + 3(x + 4) = 5(x + 2) - 5
(b) youngest: 7 years old
middle: 9 years old
oldest: 11 years old
Step-by-step explanation:
(a)
We know that x is the youngest child's age. Since the sisters' ages are consecutive odd integers, we know that the ages differ by 2. So, the middle sister's age is x + 2 and the oldest sister's age is x + 4.
Our equation to model the sentence "the sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister's age" would be:
x + 3 * (x + 4) = 5 * (x + 2) - 5
x + 3(x + 4) = 5(x + 2) - 5
(b)
Now, we can just solve the equation above:
x + 3(x + 4) = 5(x + 2) - 5
x + 3x + 12 = 5x + 10 - 5
4x + 12 = 5x + 5
x = 12 - 5 = 7
So, the youngest sister is 7 years old.
That means the middle sister is 7 + 2 = 9 years old, and the oldest sister is 9 + 2 = 11 years old.
The ages, then, are:
youngest: 7 years old
middle: 9 years old
oldest: 11 years old
Answer:
(-3, 1)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations by substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
x = 2y - 5
-2x + 5y = 11
<u>Step 2: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: -2(2y - 5) + 5y = 11
- Distribute -2: -4y + 10 + 5y = 11
- Combine like terms: y + 10 = 11
- Isolate <em>y</em>: y = 1
<u>Step 3: Solve for </u><em><u>x</u></em>
- Define original equation: x = 2y - 5
- Substitute in <em>y</em>: x = 2(1) - 5
- Multiply: x = 2 - 5
- Subtract: x = -3