This is a lot of calculation.
So we know that the sum of angles for any heptagon is 900, because heptagon can be divided into five non-overlapping triangles and sum of angles of each triangle is 180.
Now you just add up all angles and simplify the equation:
900 = (6x - 8) + 120 + (7x - 64) + (5x - 4) + 135 + (3x + 31) + (4x + 15)
900 = <span>25x + 225
Now it's just regular algebra equation. You can solve for x:
675 = 25x
x = </span>27
So the value of x is 27
By proportion:-
4 / 30 = x / 75 where x is number needed for the '75' country
30x = 300
x = 10
They need 10 drivers.
<u>Solution-</u>
Given that,
In the parallelogram PQRS has PQ=RS=8 cm and diagonal QS= 10 cm.
Then considering ΔPQT and ΔSTF,
1- ∠FTS ≅ ∠PTQ ( ∵ These two are vertical angles)
2- ∠TFS ≅ ∠TPQ ( ∵ These two are alternate interior angles)
3- ∠TSF ≅ ∠TQP ( ∵ These two are also alternate interior angles)
<em>If the corresponding angles of two triangles are congruent, then they are said to be similar and the corresponding sides are in proportion.</em>
∴ ΔFTS ∼ ΔPTQ, so corresponding side lengths are in proportion.

As QS = TQ + TS = 10 (given)
If TS is x, then TQ will be 10-x. Then putting these values in the equation



∴ So TS = 3.85 cm and TQ is 10-3.85 = 6.15 cm
Answer: |3-(-8)|
Step-by-step explanation:
Given: Paige lives 3 miles east of her school. Diego lives 8 miles west of the school.
From the picture , the number line represents the position of the houses of the two friends such that position of Paige is 3 but position of Diego is (-8) [since east and west are opposite directions]
We know that, Distance between any two points from A to B= B-A
Since distance is a positive quantity, thus
The distance between them =
miles=11 miles
Answer:
Step-by-step explanation:
Consider the given expression is
![\ln (x\sqrt[3]{x^2+1})](https://tex.z-dn.net/?f=%5Cln%20%28x%5Csqrt%5B3%5D%7Bx%5E2%2B1%7D%29)
We need to rewrite the expression as a sum,difference,or multiple of logarithms.
![[\because \sqrt[n]{x}=x^{\frac{1}{n}}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%5Bn%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%5D)
Using the properties of logarithm we get
![[\because \ln (ab)=\ln a+\ln b]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%20%28ab%29%3D%5Cln%20a%2B%5Cln%20b%5D)
![[\because \ln (a^b)=b\ln a]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%20%28a%5Eb%29%3Db%5Cln%20a%5D)
Therefore, the simplified form of the given expression is
.