Changing The Subject Of A Formula

1. What is the subject of the following equation h=2x+7y

The subject of the equation h=2x+7y is h. This means that h is the variable that the equation is solving for or representing.

Explanation

The subject of the equation h=2x+7y is h. This means that h is the variable that the equation is solving for or representing.

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2. True or false: To get rid of the square root when transposing we square both sides of the equation.

True

False

When transposing an equation involving a square root, we square both sides of the equation in order to eliminate the square root. This is because squaring both sides of an equation cancels out the square root, leaving us with a simplified equation that is easier to solve. Therefore, the statement "To get rid of the square root when transposing we square both sides of the equation" is true.

Explanation

When transposing an equation involving a square root, we square both sides of the equation in order to eliminate the square root. This is because squaring both sides of an equation cancels out the square root, leaving us with a simplified equation that is easier to solve. Therefore, the statement "To get rid of the square root when transposing we square both sides of the equation" is true.

3. Make x the subject of the formula in the following equation x - 2c = b

X=b+2c

X=b-2c

X=2c/b

X=2b/ c

To make x the subject of the formula in the equation x - 2c = b, we need to isolate x on one side of the equation. By adding 2c to both sides of the equation, we get x = b + 2c.

Explanation

To make x the subject of the formula in the equation x - 2c = b, we need to isolate x on one side of the equation. By adding 2c to both sides of the equation, we get x = b + 2c.

4. The value of U in the equation r=2x+U when x =3 and r = 10.

When x = 3 and r = 10, we can substitute these values into the equation r = 2x + U and solve for U. By rearranging the equation, we have 10 = 2(3) + U, which simplifies to 10 = 6 + U. Subtracting 6 from both sides, we get U = 4. Therefore, the value of U in the equation is 4.

Explanation

When x = 3 and r = 10, we can substitute these values into the equation r = 2x + U and solve for U. By rearranging the equation, we have 10 = 2(3) + U, which simplifies to 10 = 6 + U. Subtracting 6 from both sides, we get U = 4. Therefore, the value of U in the equation is 4.

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5. True or false: To get rid of the square symbol when changing the subject of a formula we can cube root both sides of the equation.

True

False

To get rid of the square symbol when changing the subject of a formula, we can take the square root of both sides of the equation, not the cube root. The cube root is used to get rid of the cube symbol, not the square symbol.

Explanation

To get rid of the square symbol when changing the subject of a formula, we can take the square root of both sides of the equation, not the cube root. The cube root is used to get rid of the cube symbol, not the square symbol.

6. When changing the subject of an equation if you divide the left side of your equation by a Y what do you need to do to the right side of the equation?

Multiply by Y

Divide by Y

Add Y

Subtract Y

When changing the subject of an equation, if you divide the left side of the equation by Y, you need to do the same to the right side of the equation in order to maintain equality. This is because in mathematics, whatever operation is performed on one side of an equation must also be performed on the other side to keep the equation balanced. Therefore, the correct answer is to divide by Y on the right side of the equation.

Explanation

When changing the subject of an equation, if you divide the left side of the equation by Y, you need to do the same to the right side of the equation in order to maintain equality. This is because in mathematics, whatever operation is performed on one side of an equation must also be performed on the other side to keep the equation balanced. Therefore, the correct answer is to divide by Y on the right side of the equation.

7. Change the subject of this equation to C=2&pir

R=C/2π

R=2Cπ

R=2π/C

R=2Cπ

To change the subject of the equation to C=2πr, we need to isolate the variable r. By dividing both sides of the equation by 2π, we can eliminate it from the right side and obtain r = C/2π.

Explanation

To change the subject of the equation to C=2πr, we need to isolate the variable r. By dividing both sides of the equation by 2π, we can eliminate it from the right side and obtain r = C/2π.

8. The steps used when making x the subject of this formula 7x2-4r=k

Add 4r to both sides, divide both sides by 7 and square both sides of the equation.

Subtract 4r to both sides, divide both sides by 7 and square root both sides of the equation.

Add 4r to both sides, multiply both sides by 7 and square root both sides of the equation.

Add 4r to both sides, divide both sides by 7 and square root both sides of the equation.

To make x the subject of the formula 7x^2 - 4r = k, we need to isolate x on one side of the equation. Adding 4r to both sides cancels out the -4r term on the left side, leaving us with 7x^2 = k + 4r. Then, dividing both sides by 7 gives us x^2 = (k + 4r)/7. Finally, taking the square root of both sides allows us to solve for x, resulting in x = √((k + 4r)/7). Therefore, the correct steps are to add 4r to both sides, divide both sides by 7, and then take the square root of both sides.

Explanation

To make x the subject of the formula 7x^2 - 4r = k, we need to isolate x on one side of the equation. Adding 4r to both sides cancels out the -4r term on the left side, leaving us with 7x^2 = k + 4r. Then, dividing both sides by 7 gives us x^2 = (k + 4r)/7. Finally, taking the square root of both sides allows us to solve for x, resulting in x = √((k + 4r)/7). Therefore, the correct steps are to add 4r to both sides, divide both sides by 7, and then take the square root of both sides.