Solve for x in the equation 811(x+45)=2455.(1 point)%0D%0A$$
811(x+45) = 2455
Remove the parentheses by distributing the 811:
811x + 811(45) = 2455
Multiply 811 by 45:
811x + 36595 = 2455
Subtract 36595 from both sides:
811x = 2455 - 36595
Simplify:
811x = -34140
Divide both sides by 811:
x = -34140/811
Therefore, x ≈ -42.14
Solve for x in the equation 8/11(x+4/5)=24/55.(1 point)%0D%0A$$
To solve for x in the equation (8/11)(x + 4/5) = 24/55, we can follow these steps:
1. Distribute (8/11) to both terms inside the parentheses:
(8/11)(x) + (8/11)(4/5) = 24/55
2. Simplify the expressions inside the parentheses:
(8x/11) + (32/55) = 24/55
3. Combine like terms on the left side:
(8x/11) + (32/55) - (24/55) = 0
4. Combine the fractions on the left side with a common denominator:
(8x/11) + 8/55 = 0
5. Subtract 8/55 from both sides:
(8x/11) = -8/55
6. Multiply both sides by the reciprocal of 8/11 to isolate x:
x = (-8/55) * (11/8)
7. Simplify the right side:
x = -88/440
8. Simplify further by dividing both numerator and denominator by their greatest common divisor, 8:
x = -11/55
Therefore, x is equal to -11/55.
Solve for x in the equation −6.29(x+7.85)=−19.499.(1 point)%0D%0A$$
To solve for x in the equation -6.29(x + 7.85) = -19.499, we can follow these steps:
1. Distribute -6.29 to both terms inside the parentheses:
-6.29x - 6.29(7.85) = -19.499
2. Simplify the expressions inside the parentheses:
-6.29x - 49.3165 = -19.499
3. Add 49.3165 to both sides to isolate the variable term:
-6.29x = -19.499 + 49.3165
4. Simplify the right side:
-6.29x = 29.8175
5. Divide both sides by -6.29 to solve for x:
x = 29.8175 / -6.29
6. Simplify the right side:
x ≈ -4.74
Therefore, x is approximately equal to -4.74.
Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.(1 point)
Let's solve this problem algebraically.
Let c be the cost of one guitar pick.
The cost of 25 guitar picks would be 25c.
Since the cost of 25 guitar strings is $1 more than 25 guitar picks, the cost of 25 guitar strings would be 25c + $1.
We are told that Patrick spent a total of $40, so we can set up the following equation:
25c + (25c + $1) = $40
Combine like terms:
50c + $1 = $40
Subtract $1 from both sides:
50c = $40 - $1
50c = $39
Divide both sides by 50 to solve for c:
c = $39/50
Simplify fraction:
c = $0.78
Therefore, the cost of one guitar string would be $0.78.