Question

1. add: $20\angle70^{\circ} + 10\angle40^{\circ}$
2. write $4r - 4u$ in polar form.
3. solve: $\

$$\begin{cases}\\frac{3}{8}x - \\frac{1}{2}y = 2 \\\\ 0.06x - 0.2y = -0.64\\end{cases}$$

$

1. solve $3x^2 - 2x + 5 = 0$ by completing the square.
2. use similar triangles to find $a$ and $b$.

triangle image with right angle, angle 30°, side 11, and sides $a$, $b$

1. the data shown came from an experiment that involved lead (pb) and boron (b). write the equation that expresses lead as a function of boron: $pb = mb + b$.

scatter plot with line of best fit, x-axis: boron in milligrams, y-axis: lead in milligrams
simplify:

1. $\sqrt{81\sqrt{3}}$
2. $\sqrt3{x^5y^6}\sqrt{xy^3}$
3. $3\sqrt{\frac{2}{5}} + 3\sqrt{\frac{5}{2}} - 6\sqrt{40}$
4. expand: $(x - 2)^3$
5. simplify: $\frac{x^2y - \frac{1}{y}}{\frac{x^2}{y} - 6}$
6. use a calculator to simplify. estimate first.

(a) $\frac{-471,635 \times 10^5}{0.0071893 \times 10^{-14}}$
(b) $(2.4)^{-3.06}$

1. use similar triangles to solve for $b$ in terms of $x$, $y$, and $z$.

circle with intersecting chords, segments labeled $x$, $y$, $b$, $z$

Explanation:

Since there are multiple questions, let's solve question 20 first (solving the system of linear equations):

Step1: Simplify the first equation

The first equation is $\frac{3}{8}x - \frac{1}{2}y = 2$. Multiply both sides by 8 to eliminate denominators:
$3x - 4y = 16$ (Equation 1)

Step2: Simplify the second equation

The second equation is $0.06x - 0.2y = -0.64$. Multiply both sides by 100 to eliminate decimals:
$6x - 20y = -64$ (Equation 2)

Step3: Solve the system using elimination

Multiply Equation 1 by 2: $6x - 8y = 32$ (Equation 3)
Subtract Equation 2 from Equation 3:
$(6x - 8y) - (6x - 20y) = 32 - (-64)$
$12y = 96$
$y = 8$

Step4: Substitute $y = 8$ into Equation 1

$3x - 4(8) = 16$
$3x - 32 = 16$
$3x = 48$
$x = 16$

Answer:

$x = 16$, $y = 8$