Answer:
x=55
a=11.47
Step-by-step explanation:
To find x we add all the angles in the triangle. The three angles in a triangle add to 180 degrees
35+x+90 = 180
Combine like terms
125+x=180
Subtract 125 from each side
125-125+x=180-125
x= 55
To find a
sin 35 = opposite side/ hypotenuse
sin 35 =a/20
Multiply each side by 20
20sin35 =a
11.47152873 =a
Answer:
4 2/3 gallons of gas
Step-by-step explanation:
Step 1
Suppose a car gas tank holds 21 gallons of gas.
On a trip it uses 2/3 of a tank of gas on a trip.
= 2/3 × 21 gallons of gas
= 14 gallons of gas
Step 2
Then it uses 1/3 of what is left in the tank.
The number of gallons of gas left =
21 gallons of gas - 14 gallons of gas
= 7 gallons of gas
Hence, this is calculated as:
1/3 × 7 gallons of gas
= 2 1/3 gallons of gas
Step 3
How many gallons of gas are left in the tank?
This is calculated as:
7 gallons of gas - 2 1/3 gallons of gas
= 7/1 - 7/3
Lowest common denominator =
= 21 - 7/3
= 14/3
= 4 2/3 gallons of gas is left
Therefore, 4 2/3 gallons of gas is left.
We have this equation:
First, combine both logarithms using the multiplication property and simplify the expression.
![\log[x(x + 99)] = 2](https://tex.z-dn.net/?f=%5Clog%5Bx%28x%20%2B%2099%29%5D%20%3D%202)
![\log[ {x}^{2} + 99x ] = 2](https://tex.z-dn.net/?f=%5Clog%5B%20%7Bx%7D%5E%7B2%7D%20%2B%2099x%20%5D%20%3D%202)
Now, use the definition of logarithm to transform the equation.
Finally, use the quadratic formula to solve the equation.
With this, we can say that the solution set is:
We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.
Answer:
Step-by-step explanation:
Blank 1 = " x "
Blank 2 = " 3 "
Answer:
Step-by-step explanation:
Recall the exponent property 
.
Therefore, simplify:
