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equations

100

3x+4=25 

3x=21

200

x+6=0

x=2

300

x+6=10

x=4

400

x+y=3

x=9

inequalities

200

2<= -4-x

x>=-6

300

x/2+4<9

x<= 10

400

2x+9<26

x<8

500

-2>=x/-4-2

x>=4

slope

100

plumber charges a flat fee plus $50 per hour. If you graph the total cost vs. hours worked, what is the slope?

50

200

Find the slope of the line: y = -7x + 12.

m=-7

300

Find the slope of a line passing through (5, 10) and (8, 1).

m=-3

400

ou have a line \(y = \frac{2}{3}x - 4\).

-3/2

500

A line has a slope of 4. It passes through (x, 2) and (5, 10). Solve for x

x-3

functions

100

Given \(f(x) = 3x + 5\), find the value of \(f(4)\)

17

200

Given \(g(x) = x^2 - 1\), find the value of \(x\) when \(g(x) = 24\).

• 
  

5 or -5

300

If \(f(x) = 2x\) and \(g(x) = x + 7\), find the value of \(f(g(3))\).

20

400

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

 = 2x + 3\) [1, 2, 3, 4]

500

Evaluate \(h(-2)\) for the following function:
\(h(x)=\begin{cases}x^{2}&\text{if\ }x<0\\ 2x+1&\text{if\ }x\ge 0\end{cases}\)

• 
  

4

geometry

100

60m 20m in a retangular box

a² +b^{2 =}c²

63.25

200

Find the slope of a treadmill that rises 1 foot for every 4 feet of horizontal length.

• Equation: \(m = \frac{\text{rise}}{\text{run}}\)
• Solution:
  • \(m = \frac{1}{4}\)

 

m= 0.25

300

Find the slope of a line passing through the points \(A(2, 3)\) and \(B(5, 12)\). [1]

• Equation: \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
• Solution:
  • \(m = \frac{12 - 3}{5 - 2}\)
  • \(m = \frac{9}{3}\)

3

400

Find the slope of the line given by the equation: \(3x + 4y = 12\). [1, 2]

• Method: Rewrite the equation into \(y = mx + b\) form.
• Solution:
  • Subtract \(3x\) from both sides: \(4y = -3x + 12\)
  • Divide everything by 4: \(y = -\frac{3}{4}x + 3\)

-3/4

500

ind the slope of the line passing through \((k, 5)\) and \((3, k)\) if the slope is known to be \(2\). Solve for \(k\).

• Equation: \(2 = \frac{k - 5}{3 - k}\)
• Solution:
  • Multiply both sides by \((3 - k)\): \(2(3 - k) = k - 5\)
  • Expand: \(6 - 2k = k - 5\)
  • Add \(2k\) to both sides: \(6 = 3k - 5\)
  • Add 5 to both sides: \(11 = 3k\)
  • Divide by 3: \(k = \frac{11}{3}\)

11/3