Answer:
Simplify the expression.
−
1b^{2}+
13
b
Step-by-step explanation:
The answer to this question is the first item in the choices which is "The teacher should use the mean for both Amo and Javier" when computing and comparing their grades. The mean is the average grade while the median is the center of the grade. It would be wrong to apply median in computing their grades and it would be also wrong when the use two different methods when computing and comparing their grades.
The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width
Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!
1 pint = 2 cups or 1 cup = 1/2 pint
x pints = 12 cups
(12 cups) / 2 = 6 pints
12 cups is equivalent to 6 pints
