The two triangles are similar but not drawn to scale. What is the scale factor needed to perform a dilation from the triangle with side length 26 inches to the triangle with side length 106.6 inches?
26in
106.6in
The scale factor to transform from the smaller triangle to the larger triangle is:
106.6/26 = 4.1
The two images below are similar (but absolutely not drawn to scale whatsoever, not even close). Find the value of x in the image. Round your answer to the nearest tenth.
31in,20.7in
x,14.6
Using the concept of similar triangles, we can set up the following proportion:
31 / 20.7 = x / 14.6
Cross multiplying gives us:
20.7x = 31 * 14.6
Simplifying further:
20.7x = 452.6
Dividing both sides by 20.7:
x = 452.6 / 20.7
x ≈ 21.9
Therefore, the value of x is approximately 21.9.
Fully simplify the following expression: 12/2*5*4/(7-3)
The expression simplifies to the number:
To fully simplify the expression 12/2*5*4/(7-3), we follow the order of operations (PEMDAS):
First, we simplify within the parentheses:
7 - 3 = 4
Now, we substitute that value back into the expression:
12/2 * 5 * 4/4
Next, we simplify the division and multiplication from left to right:
6 * 5 * 4/4
Then, simplify the remaining multiplication:
30 * 4/4
Finally, simplify the division and multiplication:
120/4
The expression simplifies to:
30
Simplify the following expression and leave your final answer in exponential form. (Example: write 5^2not 25).
y^19/y
The simplified expression is:
To simplify the expression y^19/y, we can use the rule of exponentiation which states that when dividing two terms with the same base, we subtract the exponents. In this case, y is our base.
So, y^19/y can be simplified as y^(19-1) = y^18.
Therefore, the simplified expression is y^18.