Answer:
   see attached
Step-by-step explanation:
Here's your worksheet with the blanks filled.
__
Of course, you know these log relations:
   log(a^b) = b·log(a) . . . . . power property
   log(a/b) = log(a) -log(b) . . . . . quotient property
   log(x) = log(y)   ⇔   x = y . . . . . . . . . equality property
 
        
             
        
        
        
Answer:
t= .43
Step-by-step explanation:
8t + 3 -t
8t - t = 7t
7t + 3
7t/7 = t
3/7 = .43
t= .43
 
        
             
        
        
        
Terrace, because area= length (l) * width (w). Since terrace's room is 9 by 8, you multiply 9*8 which gives you 72ft squared. Jody's bedroom id 7*10 which gives you 70 ft squared. 72 is greater than 70.
        
             
        
        
        
Answer:
<em>Beck actually caught 45 fish</em>
Step-by-step explanation:
<u>System of Equations</u>
We call the following variables:
x = number of fish Ally caught
y = number of fish Beck caught
They caught a total of 75 fish, thus:
x + y = 75      [1]
If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:
3y = 2x + 75      [2]
From [1]:
x = 75 - y      [3]
Substituting in [2]:
3y = 2(75 - y) + 75
Operating:
3y = 150 - 2y + 75
Simplifying:
5y = 225
Dividing by 5:
y = 45
Beck actually caught 45 fish
 
        
                    
             
        
        
        
Answer:
A. 162 m²
Step-by-step explanation:
==>Given:
Isosceles trapezoid with:
base a = 19m
base b = 35m
Perimeter = 74meters 
==>Required: 
Area of trapezoid 
==>Solution:
Recall: the length of the legs of an isosceles trapezoid are equal.
Perimeter of isosceles trapezoid = sum of the parallel sides + 2(length of a leg of the trapezoid)
Let l = leg of trapezoid.
Perimeter = 74m
Sum of parallel sides = a+b = 19+35 = 54m
Thus,
74 = 54 + 2(l)
74 - 54 = 2(l)
20 = 2(l)
l = 20/2 = 10m
Let's find area:
Area = ½(a+b)*h
a = 19
b = 35
h = ?
Using Pythagorean theorem, let's find h as follows:
h² = l² - [(35-19)/2)²
h² = 10² - [16/2]²
h² = 100 - 64
h² = 36
h = √36 = 6m
Area = ½ x (a+b) × h
= ½ × (19+35) × 6
= ½ × 54 × 6
= 27 × 6
Area = 162m²