Step-by-step explanation:
Equation: y = (x - 1)² + 4
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!
The answer to this question is 5,120 you have to multiply by 2
Answer:
5 degrees
Step-by-step explanation:
Corresponding angles in a transversal are congruent. This can be proved by using the alternate exterior angles theorem, which would make these two angles alternate interior angles. With this, we can form a new equation.
Solve Algebraically
5x+23=7x+13
5x+10=7x
10=7x-5x
10=2x
<h2>x=5</h2><h2 />
Some examples of geometric constraints include parallelism, perpendicularity, concentricity and symmetry. Parallelism occurs when two or more lines or axes of curves are equidistant from each other. Perpendicularity is a constraint in which lines or axes of curves intersect at right angles.
