let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:
2p + 3d = 18.25
4p + 2d = 27.50
From this, we can use substitution or elimination to solve:
For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.
For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.
I'll be using elimination in this case:
-2(2p + 3d = 18.25) --> -4p - 6d = -36.50
-4p - 6d = -36.50
4p + 2d = 27.50
-4d = -9.00
d = 2.25
4p + 2 * 2.25 = 27.50
4p + 4.50 = 27.50
4p = 23.00
p = 5.75
Now let's check our answer:
2 * 5.75 + 3 * 2.25 = 18.25
11.50 + 6.75 = 18.25
18.25 = 18.25
So drinks cost $2.25 and popcorn $5.75
The answer is B.
Breaking down the operation:
NUmerators:
x × x = x² and
+3 × -3 = -9Denumerators:
x × x = x² and
+2 × -2 = -4Answer:
×
Hope it helped,
Happy homework/ study/ exam!
Answer:
<u>p = 21.4 cm</u>
<u>∠P = 44°</u>
Step-by-step explanation:
Apply the Pythagorean Theorem to solve for the length of p.
- p² + 21² = 30²
- p² = 900 - 441
- p² = 459
- p = √459
Now, take the inverse sine function to find angle P :
- sin⁻¹ (opposite side / hypotenuse)
- sin⁻¹ (21/30)
- sin⁻¹ (0.7)
(approximately)
Answer: 28 in.
Step-by-step explanation:
The perimeter is the total distance around the entire figure. Because all the lengths of the sides are already given, you just have to add them all up.
P = 4 in. + 8 in. + 8 in. + 4 in. + 4 in. = 28 in.
Answer:
The roots of the given equation are x = 0 and x = -8.
General Formulas and Concepts:
<u>Algebra I</u>
Terms/Coefficients
Quadratic Equations
- Solving quadratic equations
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
y = x² + 8x
<u>Step 2: Find Roots</u>
- [Quadratic] Factor: y = x(x + 8)
- [Quadratic] Set up [Solve]: 0 = x(x + 8)
- [Quadratic] Define: x = 0, -8
∴ the roots of the quadratic equation y = x² + 8x is equal to 0 and -8.
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Topic: Algebra I
