equations
inequalties
slope
functions
geometry
100

x + 5 = 12

x = 12 - 5 = 7

100

\(3x-4<8\)x

  • \(x < 4\)



100

Find the slope of a line that goes up \(3\) units for every \(4\) units it moves to the right.

 m = 3/4

100

\(f(x) = 3x - 5\), find \(f(4)\).

  •  \(f(4) = 7\)



100

Two angles of a triangle measure \(50^{\circ }\) and \(70^{\circ }\). Find the third angle \(x\)

  • : \(x = 60^\circ\)



200

3x - 4 = 11

3x = 15 x = 5

200

-5 <2x+1 <7

  •  \(-3 \le x < 3\)
200

Find the slope of the line passing through \((2, 5)\) and \((6, 13)\)

m = 2

200

Find the domain of \(g(x) = \frac{5}{x - 3}\).

  • All real numbers except \(x = 3\) (or \((-\infty, 3) \cup (3, \infty)\))



200

A right triangle has a leg of length \(5\) cm and a hypotenuse of length \(9\) cm. Find the exact length of the missing leg \(b\).

 \(b = 2\sqrt{14}\) cm

300


\(5x + 2 = 2x + 14\)





3x = 12 x = 4 

300


 \(-1 < 4x + 2 < 10\)



-1 + 3x =2 <5x

300

Find the slope of the line given by the equation \(3x + 4y = 12\).

  • \(m = -\frac{3}{4}\)



300

If \(f(x) = x^2\) and \(g(x) = 2x + 1\), find \((f \circ g)(x)\).

  • \((f \circ g)(x) = 4x^2 + 4x + 1\)



300

Find the total surface area of a closed cylinder with a radius of \(3\) cm and a height of \(7\) cm. Leave the answer in terms of \(\pi \).

  • \(60\pi\) \(\text{cm}^{2}\)



400


 \(x^2 - 5x + 6 = 0\)


\(x = 2\) or \(x = 3\) [1, 2, 3, 4, 5]

400


\(|2x - 5| \ 9\)




(\(-2 \leq x \leq 7\)

400

Line \(A\) passes through \((-1, 4)\) and \((2, 10)\). Find the slope of Line \(B\) if it is perpendicular to Line \(A\).

  • \(m_B = -\frac{1}{2}\)



400

Find the inverse function \(f^{-1}(x)\) for \(f(x) = \frac{2x + 1}{3}\).

  •  \(f^{-1}(x) = \frac{3x - 1}{2}\)



400

Inside a circle, chord \(AB\) and chord \(CD\) intersect at point \(E\). If \(AE = 4\), \(EB = x\), \(CE = 3\), and \(ED = 8\), find \(x\).

x = 6

500

x2 + y2 = 25

x + y = 7

3, 4 or 4,3

500


 \(x^2 - 6x - 16 > 0\)




\(x < -2\) or \(x > 8\)

500

The slope of a line passing through \((3, y)\) and \((9, 4)\) is \(\frac{2}{3}\). Find the value of \(y\).

y = 0

500

Find the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for \(f(x) = x^2 - 3x\).

  • \(2x + h - 3\) (where \(h \neq 0\))


500

A circle is centered at the origin \((0,0)\). Find the equation of the line tangent to this circle at the point \((3, 4)\).

\(3x + 4y = 25\) (or \(y = -\frac{3}{4}x + \frac{25}{4}\))

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