$\displaystyle yt - 3x= 100$

$\displaystyle yt - 3x+ 3x = 100 + 3x$

$\displaystyle yt = 100 + 3x$

$\displaystyle \frac{yt}{y} = \frac{100 + 3x}{y}$

$\displaystyle t= \frac{100 + 3x}{y}$

$\displaystyle 0.01M + 0.01N$

$\displaystyle =0.01(M + N)$

$\displaystyle =0.01 \cdot 1,000$

$\displaystyle =10 > 1$

This makes (A) greater.

$\displaystyle 5x + 9 = 64$

$\displaystyle 5x + 9 -9 = 64-9$

$\displaystyle 5x = 55$

$\displaystyle 5x \div 5 = 55 \div 5$

$\displaystyle x = 11$

$\displaystyle 4y -7 = 37$

$\displaystyle 4y -7 + 7 = 37+ 7$

$\displaystyle 4y = 44$

$\displaystyle 4y \div 4 = 44 \div 4$

$\displaystyle y = 11$

The quantities are equal.

To solve this problem, simply plug the numbers into the equation: $\displaystyle 1^2-4(3)$. Then, just simplify. This gives you $\displaystyle 1-12$, which is $\displaystyle -11.$

$\displaystyle f(-2)$ and $\displaystyle f(-2)$ mean that you must plug in what it's inside the parantheses to x in the function. Therefore, when you plug in -2 to the function, you get $\displaystyle 3(-2^2)-1$, which is 11. Then, plug in 2 to the function, which gives you $\displaystyle 3(2^2)-1$, which is also 11. Therefore, the columns are equal.

The slope of the line $\displaystyle y=4x-3$ is 4. You can determine this by remembering the y=mx+b slope-intercept form. "M" is slope, so the number in front of x is the slope. Therefore, it's 4. The slope of a line perpendicular to the line is the negative reciprocal of the first slope. Therefore, if the slope of the first line is 4, then the slope of the perpendicular line is $\displaystyle \frac{-1}{4}$ . Therefore, Column A is greater.

First, calculate the price of the jacket in Column A. If the $30 jacket is on sale for 10% off, that means that it is $3 lower. (10% of $30 is $3). Therefore, the price of the jacket is $27. The quantities in both columns are equal.

The point $\displaystyle \left ( 9, y\right )$ is on the line of the equation $\displaystyle 4x-5y = 20$. Finding the $\displaystyle y$-coordinate of this point is the same as evaluating $\displaystyle y$ for $\displaystyle x= 9$.. Substitute, and we get: 

$\displaystyle 4x-5y = 20$

$\displaystyle 4 \cdot 9 -5y = 20$

$\displaystyle 36 -5y = 20$

$\displaystyle 36 -5y- 36 = 20 - 36$

$\displaystyle -5y = - 16$

$\displaystyle -5y \div (-5) = - 16 \div (-5)$

$\displaystyle y = 3 \frac{1}{5}$

The $\displaystyle x$-intercept of any line is the point at which the line intersects the $\displaystyle x$-axis; therefore, its $\displaystyle y$-coordinate is 0. Similarly, the $\displaystyle x$-coordinate of the $\displaystyle y$-intercept is 0. The quantities are equal.

The $\displaystyle y$-coordinate of the $\displaystyle x$-intercept of the line is 0, so to find the $\displaystyle x$-coordinate, set $\displaystyle y = 0$ and solve for $\displaystyle x$:

$\displaystyle 0.5x+ 0.4y = -400$

$\displaystyle 0.5x+ 0.4 \cdot 0 = -400$

$\displaystyle 0.5x+ 0 = -400$

$\displaystyle 0.5x = -400$

$\displaystyle 0.5x \div 0.5 = -400 \div 0.5$

$\displaystyle x = -800$

Similarly, to find the $\displaystyle y$-coordinate of the $\displaystyle y$-intercept, set $\displaystyle x= 0$ and solve for $\displaystyle y$:

$\displaystyle 0.5x+ 0.4y = -400$

$\displaystyle 0.5 \cdot 0+ 0.4y = -400$

$\displaystyle 0+ 0.4y = -400$

$\displaystyle 0.4y = -400$

$\displaystyle 0.4y \div 0.4 = -400 \div 0.4$

$\displaystyle y = -1,000$

(A), the $\displaystyle x$-coordinate of the $\displaystyle x$-intercept of the line, is greater.