Answer:
The length of the rhombus is =![\frac{bc}{b+c}cm](https://tex.z-dn.net/?f=%5Cfrac%7Bbc%7D%7Bb%2Bc%7Dcm)
Step-by-step explanation:
It is given that the Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC.Then,
AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:
![\frac{BE}{CE}=\frac{BA}{AC}=\frac{c}{b}](https://tex.z-dn.net/?f=%5Cfrac%7BBE%7D%7BCE%7D%3D%5Cfrac%7BBA%7D%7BAC%7D%3D%5Cfrac%7Bc%7D%7Bb%7D)
⇒![\frac{BE}{CE}=\frac{c}{b}](https://tex.z-dn.net/?f=%5Cfrac%7BBE%7D%7BCE%7D%3D%5Cfrac%7Bc%7D%7Bb%7D)
⇒![\frac{BE}{BC}=\frac{c}{c+b}](https://tex.z-dn.net/?f=%5Cfrac%7BBE%7D%7BBC%7D%3D%5Cfrac%7Bc%7D%7Bc%2Bb%7D)
Now, ΔDBE is similar to ΔABC, then
DE=![(\frac{BE}{BC}){\times}AC](https://tex.z-dn.net/?f=%28%5Cfrac%7BBE%7D%7BBC%7D%29%7B%5Ctimes%7DAC)
=![(\frac{c}{c+b}){\times}b](https://tex.z-dn.net/?f=%28%5Cfrac%7Bc%7D%7Bc%2Bb%7D%29%7B%5Ctimes%7Db)
=![\frac{bc}{b+c}cm](https://tex.z-dn.net/?f=%5Cfrac%7Bbc%7D%7Bb%2Bc%7Dcm)
Thus, the length of the rhombus is =![\frac{bc}{b+c}cm](https://tex.z-dn.net/?f=%5Cfrac%7Bbc%7D%7Bb%2Bc%7Dcm)
Hello there! I can help you! So the centerpieces take 15 minutes to make, and x equals the amount of centerpieces. That part makes 15x. Just by looking at the answers, A and C are already eliminated. We are adding up the time. the florst has already spent 2 hours, which equals 120 minutes. She will spend no more than 6 hours or 360 minutes on creating the centerpieces. We add the time, not subtract. B is the only one that shows that. 120 + 15x ≤ 360. The answer is B. Your answer is correct.
The correct answer is C)
![a_n=2\times(-4)^{n-1}](https://tex.z-dn.net/?f=a_n%3D2%5Ctimes%28-4%29%5E%7Bn-1%7D)
.
Since it is a geometric sequence, we multiply by a constant, r, each time to find the next term.
g₂ = -8
g₅ = 512
g₂ * r * r * r = g₅
-8(r)(r)(r) = 512
-8r³ = 512
Divide both sides by -8:
-8r³/-8 = 512/-8
r³ = -64
Take the cubed root of both sides:
∛r³ = ∛-64
r = -4
Now we work backward from g₂ to find g₁:
-8/-4 = 2
We have that g₁ = 2 and r = -4. This gives us
A+B+C =180
7x+49+5y=180 ---> 7x+5y=131
7(15) +49+5(15)=180
180=180
(15)+7(15)+41=A
161=A
2(15)+13=B
43=B
B=C
43=C
A=161
B=43
C=43
The movies of 120 min or less than 120 mins are 100
Further explanation:
A histogram is a visual representation of data.
In the given histogram we can see that
5 movies are 0 to 30 minutes, 10 movies are 31 to 60 minutes, 30 movies are 61 to 90 minutes, 55 movies are 91 to 120 minutes, and 15 movies are over 120 minutes.
In order to find the number of movies which are 120 minutes long or less than 120 minutes we will add up all the number of movies with 120 length and less than that
So,
![No.\ of\ movies\ 120\ min\ long\ or\ less\ than\ that = 5+10+30+55\\=100\ movies](https://tex.z-dn.net/?f=No.%5C%20of%5C%20movies%5C%20120%5C%20min%5C%20long%5C%20or%5C%20less%5C%20than%5C%20that%20%3D%205%2B10%2B30%2B55%5C%5C%3D100%5C%20movies)
The movies of 120 min or less than 120 mins are 100
Keywords: Histogram, reading histograms
Learn more about histograms at:
#LearnwithBrainly