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 = 30t + 0.10
CC = 30.10t
DC = 30 + 0.10t
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 2 of 10
Florida standards 5A-5CHard Calc
Solve: 3x+4y=10, 2x−4y=−5
A(1, 1.75)
B(1, 2)
C(2, 1)
D(0, 2.5)
Explanation
📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75
Question 3 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
BNo real solutions — the parabola doesn't reach the x-axis
CThe number of solutions can't be determined from D alone
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 4 of 10
Florida standards 1A-1GMedium Calc Word
A ball is thrown upward. Its height is h = −16t² + 48t. When does it hit the ground?
A4 sec
B1 sec
C2 sec
D3 sec
Explanation
📌 h = 0: −16t² + 48t = 0 → t(−16t + 48) = 0 → t = 0 or t = 3 seconds
Question 5 of 10
Florida standards 6A-6CHard Calc Word
Use quadratic formula: 2x²−5x−3=0
Ax=5 or x=−3
Bx=2 or x=−3
Cx=3 or x=−1/2
Dx=−3 or x=1/2
Explanation
📌 x=(5±√(25+24))/4=(5±7)/4. x=3 or x=−1/2
Question 6 of 10
Florida standards 6A-6CMedium Calc Word
Use the quadratic formula for x² − 4x + 3 = 0
Ax = 0, 4
Bx = 2, 4
Cx = −1, −3
Dx = 1, 3
Explanation
📌 a=1, b=−4, c=3. x = (4 ± √(16−12))/2 = (4±2)/2 → x=3 or x=1
Question 7 of 10
Florida standards 7A-7CEasy Calc Word
The vertex of y = (x − 3)² + 2 is:
A(3, −2)
B(−3, 2)
C(3, 2)
D(2, 3)
Explanation
📌 Vertex form: y = a(x−h)² + k. Vertex = (h, k) = (3, 2).
The scatter plot shows the relationship between hours studied and test scores. What type of correlation is shown?
ANo correlation
BPositive correlation
CCannot determine
DNegative correlation
Explanation
📌 Points trend upward from left to right → positive correlation. As hours studied increases, test score increases. The trend line slopes upward → positive relationship.
Question 10 of 10
Florida standards 2A-2HMedium Calc Word Diagram
Which line has a negative slope?
ANeither
BBoth
CA
DB
Explanation
📌 Negative slope = line goes DOWN from left to right (↘). Positive slope = line goes UP from left to right (↗). Graph B has negative slope.