Given:
Consider the given equation is:
To find:
The missing exponent.
Solution:
Let x be the missing exponent. Then the given equation can be written as
It can be rewritten as:
![[\because a^ma^n=a^{m+n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5Ema%5En%3Da%5E%7Bm%2Bn%7D%5D)
On comparing the coefficient of m, we get
Therefore, the value of the missing exponent is 8. So, the complete equation is 
.
Answer:
Step-by-step explanation:
x + y = 10
22x + 14y = 172
-22x - 22y = -220
22x + 14y = 172
-8y = - 48
y = 6 ceramic vases
x + 6 = 10
x = 4 glass vases
I'm going to assume that the room is a rectangle.
The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle.
You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.
The dimensions of your room are 25ft (length) by 24ft (width).
It probably gos like this here's my answer for number 1 6/8 and 9/12. for number 3, 10/12 and 15/18.
