Answer:
Step-by-step explanation:
its 52cm
1) EF = 2 and DF = 4
2) KL = 4√3 and JL = 8
3) ST = 6 and RS = 6√3
4) PQ = 4.5√3 and RQ = 4.5
<u>Step-by-step explanation</u>:
<u>Rules for special triangles 30°,60°,90°</u> :
- The length of the side opposite to 30° is a.
- The length of the side opposite to 60° is a√3.
- The length of the side opposite to 90° is 2a.
1) DE = 2√3 is opposite to 60°
⇒ 2√3 = a√3
⇒ a = 2
EF = a which is opposite to 30°.
⇒ EF = 2
DF = 2a which is opposite to 90°.
⇒ DF = 4
2) KJ = 4 is opposite to 30°
⇒ a = 4
KL = a√3 which is opposite to 60°.
⇒ KL = 4√3
JL = 2a which is opposite to 90°.
⇒ JL = 8
3) RT = 12 is opposite to 90°
⇒ 2a = 12
⇒ a = 6
ST = a which is opposite to 30°.
⇒ ST = 6
RS = a√3 which is opposite to 60°.
⇒ RS = 6√3
4) PR = 9 is opposite to 90°
⇒ 2a = 9
⇒ a = 4.5
PQ = a√3 which is opposite to 60°.
⇒ PQ = 4.5√3
RQ = a which is opposite to 30°.
⇒ RQ = 4.5
Answer:
We conclude that the lifetime of tires is less than 30,000 miles.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 30,000 miles
Sample mean,
= 29,400 miles
Sample size, n = 54
Alpha, α = 0.05
Population standard deviation, σ =1200 miles
First, we design the null and the alternate hypothesis
We use One-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We reject the null hypothesis and accept the alternate hypothesis.
Thus, we conclude that the lifetime of tires is less than 30,000 miles.
Answer:
![x = 18](https://tex.z-dn.net/?f=x%20%3D%2018)
![\angle A = 166](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%20166)
Step-by-step explanation:
The question is properly presented in the attachment.
Given
![\angle A = 7x + 40](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%207x%20%2B%2040)
![\angle B = 3x + 112](https://tex.z-dn.net/?f=%5Cangle%20B%20%3D%203x%20%2B%20112)
Required
Solve for x and ![\angle A](https://tex.z-dn.net/?f=%5Cangle%20A)
From the attachment
and
are vertically opposite.
This means that:
= ![\angle B](https://tex.z-dn.net/?f=%5Cangle%20B)
Substitute values for
and ![\angle B](https://tex.z-dn.net/?f=%5Cangle%20B)
![7x + 40 = 3x + 112](https://tex.z-dn.net/?f=7x%20%2B%2040%20%3D%203x%20%2B%20112)
Collect Like Terms
![7x -3x = 112 - 40](https://tex.z-dn.net/?f=7x%20-3x%20%3D%20112%20-%2040)
![4x = 72](https://tex.z-dn.net/?f=4x%20%3D%2072)
Make x the subject
![x = \frac{72}{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B72%7D%7B4%7D)
![x = 18](https://tex.z-dn.net/?f=x%20%3D%2018)
Substitute 18 for x in ![\angle A = 7x + 40](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%207x%20%2B%2040)
![\angle A = 7 * 18 + 40](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%207%20%2A%2018%20%2B%2040)
![\angle A = 166](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%20166)
The angle for this triangle is more than 89°.
An acute triangle is a triangle that is smaller than an 90° triangle.