We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:
Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:
Now, we have our final range: -5 < x < 9
Answer:2 pizzas
Step-by-step explanation:
2 2/3 and 2 5/6 can both be rounded to 3. Double that and you get 6. Since there were 8 pizzas originally,subtract 6 from 8 to get 2 remaining pizzas.
Answer:
3/4
Step-by-step explanation:
Constant of Proportionality is just a fancy way of saying slope (for a line passing through (0, 0), at least).
You can find it by looking at y/x, which will be equal at any point on the line (which is why it is a "constant").
So, for multiple points on the line:
1.5 / 2 = 3/4
3 / 4 = 3/4
4.5 / 6 = 3/4
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
