A cell phone plan charges $30 per month plus $0.10 per text. Which equation represents the monthly cost C for t texts?
AC = 0.10(30 + t)
BC = 30 + 0.10t
CC = 30.10t
DC = 30t + 0.10
Explanation
📌 Fixed cost = $30 (base monthly charge) Variable cost = $0.10 per text = 0.10t Total: C = 30 + 0.10t
💡 This is a linear equation in slope-intercept form: y = mx + b where m = 0.10 and b = 30.
Question 5 of 10
Florida standards 6A-6CMedium Calc
Factor: x² + 5x + 6
A(x+3)(x+3)
B(x−2)(x−3)
C(x+1)(x+6)
D(x+2)(x+3)
Explanation
📌 Find two numbers that multiply to 6 and add to 5: 2 and 3. (x + 2)(x + 3)
Question 6 of 10
Florida standards 8A-8BMedium Calc Diagram
For a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac. It tells us how many times the related parabola y = ax² + bx + c crosses the x-axis — and therefore how many real solutions the equation has.
The discriminant's sign matches the number of x-axis crossings.
Which statement about D = 0 is TRUE?
ATwo real solutions — the parabola crosses the x-axis twice
BThe number of solutions can't be determined from D alone
CNo real solutions — the parabola doesn't reach the x-axis
DExactly one real solution — the parabola is tangent to the x-axis
Explanation
The discriminant b² − 4ac counts how many real solutions a quadratic equation has by reflecting how many times the parabola y = ax² + bx + c crosses the x-axis.
The three cases: • D > 0: parabola crosses the x-axis at TWO different points → 2 real solutions. • D = 0: parabola is *tangent* to the x-axis — it touches at exactly ONE point (the vertex itself sits on the x-axis) → 1 real solution (often called a *double root*). • D < 0: parabola sits entirely above or below the x-axis, never touching it → 0 real solutions (the roots are complex / imaginary).
Application: D = 0 is the borderline case useful for problems like "for what value of c does ax² + bx + c = 0 have exactly one solution?" — set b² − 4ac = 0 and solve.
Question 7 of 10
Florida standards 7A-7CEasy Calc Word
The vertex of y = (x − 3)² + 2 is:
A(2, 3)
B(3, 2)
C(3, −2)
D(−3, 2)
Explanation
📌 Vertex form: y = a(x−h)² + k. Vertex = (h, k) = (3, 2).
Question 8 of 10
Florida standards 5A-5CMedium Calc Word Diagram
The system of equations is graphed below. How many solutions does it have?
AOne solution
BTwo solutions
CNo solution
DInfinitely many solutions
Explanation
📌 The lines are parallel (same slope, different y-intercepts). Parallel lines NEVER intersect → NO solution.
Systems with no solution are called 'inconsistent.'
Question 9 of 10
Florida standards 6A-6CHard Calc Word
Use quadratic formula: 2x²−5x−3=0
Ax=2 or x=−3
Bx=3 or x=−1/2
Cx=−3 or x=1/2
Dx=5 or x=−3
Explanation
📌 x=(5±√(25+24))/4=(5±7)/4. x=3 or x=−1/2
Question 10 of 10
Florida standards 7A-7CEasy Calc Word Diagram
Which graph represents a quadratic function?
ANeither
BBoth
CB
DA
Explanation
📌 Quadratic = U-shaped parabola. Graph A shows a parabola. Graph B is a straight line → linear, not quadratic.