Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
Point (-4, 7)
Point (2, -8)
<u>Step 2: Find slope </u><em><u>m</u></em>
- Substitute:
- Subtract/Add:
- Simplify:
Answer:
Step-by-step explanation:
Answer:
(0, 2 ) and (- 
, 
)
Step-by-step explanation:
Given the 2 equations
2x² + 4x - y = - 2 → (1)
x² + y = 2 → (2)
subtract x² from both sides in (2)
y = 2 - x² → (3)
Substitute y = 2 - x² into (1)
2x² + 4x - (2 - x²) = - 2
2x² + 4x - 2 + x² = - 2
3x² + 4x - 2 = - 2 ( add 2 to both sides )
3x² + 4x = 0 ← in standard form
x(3x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x = 0
3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = -
Substitute these values into (3) for corresponding values of y
x = 0 : y = 2 - 0² = 2 - 0 = 2 ⇒ (0, 2)
x = - : y = 2 - (- )² = 2 - 
= ⇒ ( - , )
10 pounds of candy costing $1.20 per pounds must be mixed with 40 pounds of candy costing $ 0.95 per pound to obtain a 50 pounds of candy costing $ 1 per pound
<em><u>Solution:</u></em>
Let "x" be the pounds of candy at $ 1.20 per pound
Then (50 - x) is the pounds of candy at $ 0.95 per pound ( since 95 cents is equal to 0.95 pound)
Therefore, x pounds of candy costing $1.20 per pounds must be mixed with (50 - x) pounds of candy costing $ 0.95 per pound to obtain a 50 pounds of candy costing $ 1 per pound
Then the equation becomes,
1.20x + (50 - x)0.95 = 50 x 1
On expanding we get,
1.20x + 47.5 - 0.95x = 50
0.25x = 50 - 47.5
0.25x = 2.5
x = 10
Then (50 - x) = 50 - 10 = 40
So we need 10 pounds of candy worth $ 1.20 per pound and 40 pounds of candy worth $ 0.95 to obtain 50 pounds of candy worth a dollar a pound
