1. What percent of 120 is 48? 57.6%?
2. collect like terms. 17T + T + 15/13T= 249/13T?
3. solve using the principles together. 3x-6=12 i am solving for x=6?
4. solve using the addition principle. -37+n=19 i am solving for n= -18?
5. solve using the multiplication principle. -9x=162 solving for x= -18?
1. To find the percentage of a number, you can use the formula:
(percentage / 100) x number = desired value
In this case, we want to find what percentage 48 is of 120. Let's plug in the values:
(percentage / 100) x 120 = 48
To solve for the percentage, divide both sides of the equation by 120:
(percentage / 100) = 48 / 120
Simplify the fraction:
(percentage / 100) = 2 / 5
Now, we can cross multiply and solve for the percentage:
5 x percentage = 2 x 100
5 x percentage = 200
Divide both sides of the equation by 5:
percentage = 200 / 5
percentage = 40
Therefore, 48 is 40% of 120, not 57.6%.
2. To collect like terms in an equation, you need to combine the terms that have the same variable and exponent.
In the given equation, we have:
17T + T + (15/13)T = (249/13)T
To combine the terms, add up the coefficients of the like terms:
17T + T + (15/13)T = (249/13)T
(17 + 1 + 15/13)T = (249/13)T
To simplify further, find a common denominator for 17 and 13:
(17 + 1 + (15/13))T = (249/13)T
(221/13)T = (249/13)T
The variables and exponents are the same on both sides of the equation, so we can cancel them out:
221/13 = 249/13
Since the fractions on both sides of the equation are equal, you can conclude that the equation is an identity. Therefore, the statement that 17T + T + (15/13)T = (249/13)T is true.
3. To solve the equation 3x - 6 = 12 for x using the principles together, you need to isolate the variable x by adding or subtracting the same values to both sides of the equation.
Given equation: 3x - 6 = 12
First, add 6 to both sides of the equation to remove the constant term on the left side:
3x - 6 + 6 = 12 + 6
Simplify:
3x = 18
Next, divide both sides of the equation by 3 to solve for x:
(3x) / 3 = 18 / 3
Simplify:
x = 6
Therefore, x = 6 is the solution to the equation.
4. To solve the equation -37 + n = 19 using the addition principle, you need to isolate the variable n by adding or subtracting the same values to both sides of the equation.
Given equation: -37 + n = 19
First, add 37 to both sides of the equation to remove the constant term on the left side:
(-37 + n) + 37 = 19 + 37
Simplify:
n = 56
Therefore, n = -18 is not the correct solution. The correct solution is n = 56.
5. To solve the equation -9x = 162 using the multiplication principle, you need to isolate the variable x by multiplying or dividing both sides of the equation by the same non-zero value.
Given equation: -9x = 162
First, divide both sides of the equation by -9 to solve for x:
(-9x) / (-9) = 162 / (-9)
Simplify:
x = -18
Therefore, x = -18 is the correct solution to the equation.