Answer:
9x,2,8y
Step-by-step explanation:
Aida did not correctly divide by the common factor to get (4+8).
9 3/10- 1 7/10 is 7.6 or 7 3/5
If you're only provided with the lengths of a triangle, and you're asked to determine whether or not the triangle is right or not, you'll need to rely on the Pythagorean Theorem to help you out. In case you're rusty on it, the Pythagorean Theorem defines a relationship between the <em>legs</em> of a right triangle and its <em>hypotenuse</em>, the side opposite its right angle. That relationship is a² + b² = c², where a and b are the legs of the triangle, and c is its hypotenuse. To see if our triangle fits that requirement, we'll have to substitute its lengths into the equation.
How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.
So, substituting our values in, we have:
(2.6)² + (8.1)² = (8.6)²
Performing the necessary calculations, we have:
6.76 + 65.61 = 73.96
72.37 ≠ 73.96
Failing this, we know that our triangle cannot be right, but we <em>do </em>know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of <em>increasing the angle between a and b</em>. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be <em>obtuse</em>, which is to say: yes, there's an angle in it larger than 90°.
Answer:
17. See below
18. 750
Step-by-step explanation:
17. Since the lollipops are being sold at the same price, 50 cents, for each one sold, they make a constant amount of money. For each increase in lollipops sold, there is a constant increase in money made, and thus the situation is a linear function.
18. To solve this equation, let's say y is the money made at the convention in dollars and x is the number of lollipops sold. If the principal gave them 125 dollars before they sold any lollipops (0 lollipops sold), then 125 is the y-intercept of the function, and in the equation y=mx+b, b=125. If each lollipop costs 50 cents (half of a dollar), then for each lollipop, x, sold, .5 dollars are made and are added to the profit, y. Thus, .5 dollars is the slope. The equation then becomes:
Now, if they need 500 dollars, y is thus equal to 500 dollars. Solving the equation:
Thus, 750 lollipops must be sold.
