6x^2 + 4(x^2 - 1) =
6x^2 + 4x^2 - 4 =
10x^2 - 4 <===
To determine the correct statement in the choices presented, we first have to solve the area of the tray. We assume it to be in a rectangular form so the area is:
Area = 10 in x 10 in x 7/2.54 in = 275.59 in³ for the paint tray
1 gallon paint = 231 in³ paint
Therefore, the correct answer is the first option. <span>The paint will not fill the tray by 44.59 in</span>³<span>.</span>
Answer:
(2, 5)
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 using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y - 3x = 1
2y - x = 12
<u>Step 2: Rewrite Systems</u>
y - 3x = 1
- Add 3x on both sides: y = 3x + 1
<u>Step 3: Redefine Systems</u>
y = 3x + 1
2y - x = 12
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 2(3x + 1) - x = 12
- Distribute 2: 6x + 2 - x = 12
- Combine like terms: 5x + 2 = 12
- Isolate <em>x</em> term: 5x = 10
- Isolate <em>x</em>: x = 2
<u>Step 5: Solve for </u><em><u>y</u></em>
- Define equation: 2y - x = 12
- Substitute in <em>x</em>: 2y - 2 = 12
- Isolate <em>y </em>term: 2y = 10
- Isolate <em>y</em>: y = 5
Formula of the slope of a linear function:
m = (y₂ - y₁)/(x₂ - x₁)
m= (-1 - 6)/[0- (-5)]
m= -7/5 This is the slope requested
Answer:
-1
f (x) = -3(x + 5)
Step-by-step explanation:
1) in f(x) = 1/3x-5, replace f(x)= with y= as follows: y = (1/3)x - 5
2) interchange x and y, obtaining: x = (1/3)y - 5
3) solve this result for y: (1/3)y = -x - 5, or -(x + 5). Next, multiply both sides by 3 to eliminate the fraction (1/3): y = -3(x + 5)
4) replace y with the symbol for "inverse of f(x);
-1
f (x) = -3(x + 5)
