Answer:
- D(5, 4), E(14, 7), M(9.5, 5.5)
Step-by-step explanation:
As AD = 1/4AB and DE ║ AC, the ratio CE/CB = 1/4, or CE = 1/4CB
<u>Find the coordinates of D:</u>
- x = 1 + 1/4(17 - 1) = 1 + 4 = 5
- y = 5 + 1/4(1 - 5) = 5 - 1 = 4
<u>Find the coordinates of E:</u>
- x = 13 + 1/4(17 - 13) = 13 + 1 = 14
- y = 9 + 1/4(1 - 9) = 9 - 2 = 7
<u>Find the coordinates of the midpoint M of DE:</u>
- x = (5 + 14)/2 = 19/2 = 9.5
- y = (4 + 7)/2 = 11/2 = 5.5
Answer:
6 units
Step-by-step explanation:
(-4 , -10) ; (-4 , -4)
Distance = 
![= \sqrt{(-4-[-4])^{2}+(-4-[-10])^{2}}\\\\= \sqrt{(-4+4)^{2}+(-4+10)^{2}}\\\\=\sqrt{0+(6)^{2}}\\\\= \sqrt{36}\\\\= 6](https://tex.z-dn.net/?f=%3D%20%5Csqrt%7B%28-4-%5B-4%5D%29%5E%7B2%7D%2B%28-4-%5B-10%5D%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%20%5Csqrt%7B%28-4%2B4%29%5E%7B2%7D%2B%28-4%2B10%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B0%2B%286%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%20%5Csqrt%7B36%7D%5C%5C%5C%5C%3D%206)
Answer:
12 30
Step-by-step explanation:
The right answer for the question that is being asked and shown above is that: "D. a rectangle with a length of 20 units and a width of 11 units." This is the statement that <span>best describes the resulting cross-section of the prism</span>
Question: What value of c will complete the square below (
) and make the expression a perfect square trinomial?
Answer: c = 225
Step-by-step explanation:
Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that <u>a = x, and b² = c</u>, but we need to find the numerical value of 
.
To do this, note that the middle term, or <u>2ab, corresponds with (is equal to) 30x</u>. We know that a = x, and thus, <u>2ab = 2bx</u>. Now, 2bx and 30x are corresponding terms; thus, <u>2bx = 30x</u>.
Dividing by 
on both sides gives us <u>b = 15</u>. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)
