If you would like to dial a square with a side length of 8 units to create a square with the length of 20 units, what scale factors should you use? Write your answer in decimal form
To find the scale factor, we need to determine the ratio of the side lengths of the larger square to the smaller square.
The side length of the larger square is 20 units, and the side length of the smaller square is 8 units.
Therefore, the scale factor is given by:
(scale factor) = (larger square side length) / (smaller square side length)
= 20 / 8
= 2.5
So, the scale factor is 2.5.
You use the scale factor of 3/4 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle
To find the radius of the original circle, we need to multiply the radius of the dilated circle by the reciprocal of the scale factor.
The scale factor is 3/4, so the reciprocal is 4/3.
The radius of the dilated circle is 9 inches.
Therefore, the radius of the original circle is computed as:
(radius of original circle) = (radius of dilated circle) * (reciprocal of scale factor)
= 9 inches * (4/3)
= 12 inches
So, the radius of the original circle is 12 inches.
CDE PQR.m<C= 13, m<D= 65. What are the measures of angles P, Q and R
To find the measures of angles P, Q, and R, we need to determine their respective values using the given information.
We are given that m<C = 13 and m<D = 65.
Looking at triangle CDE, angle C and angle D are two of its interior angles. Since the sum of all interior angles of a triangle is 180 degrees, we can write the equation:
m<C + m<D + m<E = 180
Substituting the given values, we have:
13 + 65 + m<E = 180
78 + m<E = 180
m<E = 180 - 78
m<E = 102
Now, let's consider triangle PQR. Angle CDE (or angle E) is one of its interior angles. Since the sum of all interior angles of a triangle is 180 degrees, we can write the equation:
m<P + m<Q + m<R + m<E = 180
Substituting the given values, we have:
m<P + m<Q + m<R + 102 = 180
m<P + m<Q + m<R = 180 - 102
m<P + m<Q + m<R = 78
Therefore, the measures of angles P, Q, and R are as follows:
m<P = angle P
m<Q = angle Q
m<R = angle R
m<P + m<Q + m<R = 78
And angles P and Q are?
Apologies for the oversight.
To find the measures of angles P and Q, we need more information or additional equations to solve for the individual angles.
Given the current information (m<C = 13 and m<D = 65), we cannot determine the specific measures of angles P and Q. Further details or equations are required to solve for those angles.
Estimate
Based on the information provided (m<C = 13 and m<D = 65), we can make an estimate of the measures of angles P and Q.
Since the sum of all interior angles in a triangle is 180 degrees, we can estimate that angle P and angle Q would have measures close to 50 degrees each. This is just a rough estimate and may not be completely accurate without more information or equations to solve for the individual angles.