1. C. Rectangle
2. F. 160
3. D. Triangular prism
4. H. 30 boxes
5. C. Equilateral Triangle
Answer:
they are like terms
Step-by-step explanation:
the sign ± is not a matter only veriable and power
In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
This question boils down to this:
"What is the diagonal of a square with a side length of 90 ft?"
The key to this question is the properties of squares.
All of the angles in a square are right, (90°) but that diagonal is going to bisect two of those into 45° angles.
Now we have two triangles, each with angle measures of 45°, 45°. and 90°.
(an isoceles right triangle)
This 45-45-90 tirnalge is one of two special triangles (the other being the 30-60-90) and here is its special property: the sides opposite these angles can be put as x, x, and x√2 respectively. Why? Well, we know that our triangle is isoceles (the congruent base angles ⇔ congruent sides) and so we call those x...by the Pythagorean theorem...a² + b² = c²...2x² = c²...x√2 = c!
In our case here, that diagonal, being the hypotenuse of our triangle, is going to be 90√2 feet, or approximately 127.3 feet.
There are two ways you could go about solving this.
You could divide the length of the base (6mm) by 2 and use that to find the area or you could find the area of the whole triangle using 6mm and divide that by 2.
I will use the first method I described:
base = 6/2
base = 3 mm
height = 5.2 mm
area = bh/2
area = (3 * 5.2)/2
area = 7.8 square mm
(don't forget your units)
Using the other method would look like this:
area = bh/2
b = 6
h = 5.2
area = (6 * 5.2)/2
area = 15.6 square mm
area/2 = 7.8 square mm
As you can see either method yields the same result.
Hope this helped.
Cheers and good luck,
Brian
