Answer:
A≈113.1
Step-by-step explanation:
Answer:
t=x+44
Step-by-step explanation:
the x ounces are being added to the vase's pre-existing 44 ounces so therefore the equation is t=x+44
Looking at the problem statement, this question states for us to determine the range of the function that is provided in a graph is. Let us first determine what range is.
- Range ⇒ Range is what y-values can be used in the function that is graphed. For example, if a line just goes up and down all the way to negative and positive infinity, then the range would be negative infinity to positive infinity as it includes all of the y-values in it's solutions.
Now moving back to our problem, we can see that we have a vertex at (2, -5) and that the lowest y-values is at y = -5. Therefore the y-values would be anything greater than or equal to -5 and less than infinity because the lines go forever up in the positive-y-direction.
Therefore, the option that would best match the description that we provided would be option B, -5 ≤ y < ∞.
Answer:
The area is 7.5 square units
Answer:
No solutions.
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
- Solving systems of equations by graphing
- Expanding
- Finding roots of a quadratic
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:

Step-by-step explanation:
<u>Step 1: Define systems</u>
2x - y = 9
4x² + 3y² - 2x + y = 16
<u>Step 2: Rewrite systems</u>
2x - y = 9
- Subtract 2x on both sides: -y = 9 - 2x
- Divide -1 on both sides: y = 2x - 9
<u>Step 3: Redefine systems</u>
y = 2x - 9
4x² + 3y² - 2x + y = 16
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 4x² + 3(2x - 9)² - 2x + (2x - 9) = 16
- Expand: 4x² + 3(4x² - 36x + 81) - 2x + (2x - 9) = 16
- Distribute 3: 4x² + 12x² - 108x + 243 - 2x + 2x - 9 = 16
- Combine like terms: 16x² - 108x + 234 = 16
- Factor GCF: 2(8x² - 54x + 117) = 16
- Divide 2 on both sides: 8x² - 54x + 117 = 8
- Subtract 8 on both sides: 8x² - 54x + 109 = 0
- Define variables: a = 8, b = -54, c = 109
- Resubstitute:

- Exponents:

- Multiply:

- Subtract:

Here we see that we start to delve into imaginary roots. Since on a real number plane, we do not have imaginary roots, there would be no solution to the systems of equations.
<u>Step 5: Graph systems</u>
<em>We can verify our results.</em>