Mary's house is approximately 49.73 miles from her grandmother's house.
The distances the three drove were;
Mary drove for 49.73 miles, Theo drove 50 miles and Nancy drove 53.299 miles.
Explanation:
- The given triangle has a 13 mile long adjacent side, a 48 mile long opposite side and the distance of Mary's route is the hypotenuse. As we have two sides of the triangle, we can solve for the length of the other side by using Pythagoras' theorem.
- Assume the hypotenuse of the triangle measures x miles. According to Pythagoras theorem, x = √(13² + 48²) , x = √169 + 2,304 x = √2,473 = 49.729. Rounding this off, we get Mary's route was 49.73 miles long.
- Nancy drove √2,840 miles = 53.2916 miles.
- So Mary drove the shortest distance of 49.73 miles, second shortest was Theo who drove for 50 miles and the longest was Nancy who drove for 53.299 miles.
Answer:
<h2>x = -0.2</h2>
Step-by-step explanation:
![-1(x+5)=3[x+2x-1)]\\\\\text{for}\ -1(x+5):\ \text{distribtutive property}\\\text{for}\ [x+(2x-1)]:\ \text{associative property}\\\\(-1)(x)+(-1)(5)=3[(x+2x)-1]\\-x-5=3(3x-1)\\\\\text{for}\ 3(3x-1):\ \text{distributive property}\\\\-x-5=(3)(3x)+(3)(-1)\\-x-5=9x-3\\\\\text{for the equation}:\ \text{addition property of equality}\\\\-x-5=9x-3\qquad\text{add 5 to both sides}\\-x-5+5=9x-3+5\\-x=9x+2\\\\\text{for the equation:}\ \text{subtraction property of equality}\\\\-x=9x+2\qquad\text{subtract}\ 9x\ \text{from both sides}](https://tex.z-dn.net/?f=-1%28x%2B5%29%3D3%5Bx%2B2x-1%29%5D%5C%5C%5C%5C%5Ctext%7Bfor%7D%5C%20-1%28x%2B5%29%3A%5C%20%5Ctext%7Bdistribtutive%20property%7D%5C%5C%5Ctext%7Bfor%7D%5C%20%5Bx%2B%282x-1%29%5D%3A%5C%20%5Ctext%7Bassociative%20property%7D%5C%5C%5C%5C%28-1%29%28x%29%2B%28-1%29%285%29%3D3%5B%28x%2B2x%29-1%5D%5C%5C-x-5%3D3%283x-1%29%5C%5C%5C%5C%5Ctext%7Bfor%7D%5C%203%283x-1%29%3A%5C%20%5Ctext%7Bdistributive%20property%7D%5C%5C%5C%5C-x-5%3D%283%29%283x%29%2B%283%29%28-1%29%5C%5C-x-5%3D9x-3%5C%5C%5C%5C%5Ctext%7Bfor%20the%20equation%7D%3A%5C%20%5Ctext%7Baddition%20property%20of%20equality%7D%5C%5C%5C%5C-x-5%3D9x-3%5Cqquad%5Ctext%7Badd%205%20to%20both%20sides%7D%5C%5C-x-5%2B5%3D9x-3%2B5%5C%5C-x%3D9x%2B2%5C%5C%5C%5C%5Ctext%7Bfor%20the%20equation%3A%7D%5C%20%5Ctext%7Bsubtraction%20property%20of%20equality%7D%5C%5C%5C%5C-x%3D9x%2B2%5Cqquad%5Ctext%7Bsubtract%7D%5C%209x%5C%20%5Ctext%7Bfrom%20both%20sides%7D)
((-4)^5)^8 / ((-4)^7)^3
= (-4)^40 / (-4)^21
= (-4)^20
Answer:
4 2/3 cm
Step-by-step explanation:
When we have area, it is the related to the scale factor by the scale factor squared
Area large/ area of small = 49/9
Take the square root
sqrt(49/9) = 7/3
The scale factor is 7/3 large to small
The small side is 2 cm
large 7 x cm
-------- = ------ = -----------
small 3 2 cm
Using cross products
7*2 = 3x
Divide by 3
14/3 = 3x/3
14/3 = the large side
4 2/3 cm
