We understand that a rectangle has been altered into the one shown in Figure 1 using this rule:
It is known that the origin is the center of rotation and two rules apply to perform a rotation of 90 degrees, namely:
1. Clockwise
The rule to convert a point in this case is:
This rule has already been implemented to create the image, so we need to reverse the outcome using this formula, hence:
2. Counterclockwise
Applying the same concept as before but with new rules for the scenario:
Reversing the outcome gives us:
Answer:
The area calculates to 83.905 cm^3
Step-by-step explanation:
The overall ratio is 9 + 7 + 6 = 22
Thus, the side lengths are computed as follows;
9/22 * 44 = 18 cm
7/22 * 44 = 14 cm
6/22 * 44 = 12 cm
Heron’s formula allows us to determine the area of the triangle
First, we calculate s
s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22
Heron’s formula can be expressed as;
A = √s(s-a)(s-b)(s-c)
where a, b, and c are 18, 14, and 12 respectively
Plugging in the values, we obtain;
A = √22(22-18)(22-14)(22-12)
A = √(22 * 4 * 8 * 10)
A = √(7,040)
A = 83.905 cm^3
Answer:
Step-by-step breakdown:
The necessary formula for this problem is
which resolves to
leading to
36 + 6x = 40 + 5x, and consequently
x = 4
Thus, DG equals 5 + 4 + 3, resulting in 12
Response:
The coach should begin seeking players who weigh at least 269.55 pounds.
Step-by-step explanation:
We have these details from the question:
Average, μ = 225 pounds
Standard Deviation, σ = 43 pounds
The weights follow a bell curve, indicating a normal distribution.
Formula:
We need to establish the value of x that corresponds to a probability of 0.15
Review from the standard normal z table gives us:
Consequently, the coach should start recruiting players weighing at least 269.55 pounds.
I NEED ASSISTANCE! Please prepare a two-column proof in a word processing document or on paper, using the guide to demonstrate that triangle RST is congruent to triangle RSQ, provided that RS is perpendicular to ST, RS is perpendicular to SQ, and ∠STR is congruent to ∠SQR. Hand in the complete proof to your teacher.
Given:
RS ⊥ ST
RS ⊥ SQ
∠STR ≅ ∠SQR
Prove:
△RST ≅ △RSQ
