To solve for y in the equation 5(y + 3) = 2(y – 2) + 7, we can start by simplifying both sides of the equation: On the left side, we can distribute 5 to (y + 3): 5y + 15 = 2(y – 2) + 7 On the right side, we can distribute 2 to (y – 2): 5y + 15 = 2y – 4 + 7 Next, we simplify further by combining like terms: 5y + 15 = 2y + 3 To isolate the y term, we can subtract 2y from both sides: 5y – 2y + 15 = 2y – 2y + 3 3y + 15 = 3 Then, subtract 15 from both sides: 3y + 15 – 15 = 3 – 15 3y = -12 Finally, divide both sides by 3 to solve for y: 3y/3 = -12/3 y = -4 Therefore, the solution to the equation is y = -4.

The volume of a cube is calculated by multiplying the length of one side by itself three times. In this case, the volume is 64 cubic units. To find the length of one side, we take the cube root of the volume. The cube root of 64 is 4. Therefore, the correct answer is  4 units.

To simplify the expression (2x + 3) – (x – 5), we need to remove the parentheses and apply the negative sign to the terms inside the second parentheses. Distributing the negative sign, we get: (2x + 3) – x + 5 Now, we can combine like terms. Grouping the x terms together and the constant terms together, we have: 2x – x + 3 + 5 Simplifying further, we get: x + 8 Therefore, the simplified expression is x + 8.

To solve for x in the equation 4(2x – 3) = 3(5x + 2), we can start by simplifying both sides of the equation. Distributing 4 to (2x – 3) gives us 8x – 12, and distributing 3 to (5x + 2) gives us 15x + 6. The equation now becomes 8x – 12 = 15x + 6. Subtracting 8x from both sides and subtracting 6 from both sides, we get -18 = 7x. Finally, dividing both sides by 7 gives us x = -18/7. Therefore, the correct answer is -18/7.

To simplify the expression 5 – (2 – 3) + 4, we need to remove the parentheses and apply the negative sign to the term inside the parentheses. Inside the parentheses, we have 2 – 3, which simplifies to -1. Now, we can rewrite the expression without the parentheses: 5 – (-1) + 4 To remove the double negative, we can rewrite -(-1) as +1: 5 + 1 + 4 Combining the terms, we have: 10 Therefore, the simplified expression is 10.

The perimeter of a square is calculated by adding the lengths of all four sides. If we let s represent the length of one side of the square, then the perimeter can be expressed as 4s. In this case, we are given that the perimeter of the square is 32 units. Therefore, we can set up the equation: 4s = 32 To find the length of one side, we need to isolate s. We can do this by dividing both sides of the equation by 4: 4s/4 = 32/4 s = 8 Therefore, the length of one side of the square is 8 units.

To solve for y in the equation 3y + 7 = 2(4y – 1), we can follow these steps:

1. Distribute the coefficient on the right side of the equation: 3y + 7 = 8y – 2
2. Move all the terms with y to one side of the equation and the constant terms to the other side. We can do this by subtracting 3y from both sides and adding 2 to both sides: 3y – 8y = -2 – 7 Simplifying further: -5y = -9
3. Solve for y by dividing both sides of the equation by -5: y = (-9) / (-5) Simplifying further: y = 9/5 or y = 1.8

Therefore, the solution to the equation is y = 9/5 or y = 1.8.

To simplify the expression 2x – (3x + 4) – (5x – 1), we start by removing the parentheses and applying the negative sign to the terms inside. This gives us 2x – 3x – 4 – 5x + 1. Combining like terms, we have -6x – 3. Therefore, the correct answer is -6x – 3.

To simplify the expression 2(3x – 4) + 5(2x + 1), we can apply the distributive property. Distributing 2 to (3x – 4) gives us 6x – 8, and distributing 5 to (2x + 1) gives us 10x + 5. The expression now becomes 6x – 8 + 10x + 5. Combining like terms, we have 16x – 3. Therefore, the correct answer is 16x – 3.

To solve for x in the equation 4(2x + 1) + 5 = 3(3x – 2), we can start by simplifying both sides of the equation: On the left side, we can distribute 4 to (2x + 1): 8x + 4 + 5 = 3(3x – 2) Simplifying further, we have: 8x + 9 = 9x – 6 To isolate the x term, we can subtract 8x from both sides: 8x – 8x + 9 = 9x – 8x – 6 Simplifying further, we have: 9 = x – 6 Next, we can isolate x by adding 6 to both sides: 9 + 6 = x – 6 + 6 Simplifying further, we have: 15 = x Therefore, the solution to the equation is x = 15.

If the length of a rectangle is triple its width, and the width is 5 units, we can find the length by multiplying the width by 3. Length = 3 * Width Length = 3 * 5 Length = 15 Therefore, the length of the rectangle is 15 units.

If the length of a rectangle is 6 units more than its width and the width is 5 units, the length would be 5 + 6 = 11 units. The formula for the perimeter of a rectangle is P = 2(L + w). Plugging in the values, we have P = 2(11 + 5) = 2(16) = 32 units. Therefore, the correct answer is  32 units.

Apologies for the error. Let's simplify the expression correctly. To simplify 2(3x – 4) – 3(2x + 1), we can distribute the coefficients: 2(3x – 4) – 3(2x + 1) = 6x – 8 – 6x – 3 Next, we can combine like terms: (6x – 6x) + (-8 – 3) = 0 + (-11) = -11 Therefore, the simplified expression is -11.

To simplify the expression 2(5x – 3) + 3(2x + 4), we can apply the distributive property. Distributing 2 to (5x – 3) gives us 10x – 6, and distributing 3 to (2x + 4) gives us 6x + 12. The expression now becomes 10x – 6 + 6x + 12. Combining like terms, we have 16x + 6. Therefore, the correct answer is 16x + 6.

To simplify the expression 3(2x – 5) – 2(4 – 3x), we can follow these steps: 1. Distribute the coefficients: 3 * 2x – 3 * 5 – 2 * 4 + 2 * 3x 2. Simplify each term: 6x – 15 – 8 + 6x 3. Combine like terms: 6x + 6x – 15 – 8 4. Combine the constant terms: 12x – 23 Therefore, the simplified expression is 12x – 23.

Distributing 2 to (x – 3) gives us 2x – 6. The equation now becomes 2x – 6 = 4x + 8. To isolate x, we subtract 2x from both sides: -6 = 2x + 8. Subtracting 8 from both sides gives us -14 = 2x. Finally, dividing both sides by 2, we find x = -7.

The area of a square is calculated by multiplying the length of one side by itself. In this case, the area is 49 square units. To find the length of one side, we take the square root of the area. The square root of 49 is 7. Therefore, the correct answer is  7 units.

To solve for x in the equation 4(3x – 2) = 5(2x + 1), we can start by simplifying both sides of the equation. Distributing 4 to (3x – 2) gives us 12x – 8, and distributing 5 to (2x + 1) gives us 10x + 5. The equation now becomes 12x – 8 = 10x + 5. Subtracting 10x from both sides and adding 8 to both sides, we get 2x = 13. Finally, dividing both sides by 2 gives us x = 6.5. Therefore, the correct answer is 6.5.

To find the perimeter of the rectangle, we need to know the formula for the perimeter of a rectangle, which is P = 2(L + W), where P represents the perimeter, L represents the length, and W represents the width. In this case, we are given that the width is 6 units, and the length is 4 units more than the width. Therefore, the length would be 6 + 4 = 10 units. Now we can substitute the values into the perimeter formula: P = 2(10 + 6) = 2(16) = 32 units. Therefore, the perimeter of the rectangle is 32 units.

To solve for y in the equation 3(y – 2) + 4 = 2(y + 5) – 1, we can start by simplifying both sides of the equation. Distributing 3 to (y – 2) gives us 3y – 6, and distributing 2 to (y + 5) gives us 2y + 10. The equation now becomes 3y – 6 + 4 = 2y + 10 – 1. Combining like terms, we have 3y – 2 = 2y + 9. Subtracting 2y from both sides and adding 2 to both sides, we get y = 11. Therefore, the correct answer is  11.

Let's solve the equation step by step:

1. Distribute the coefficients: 2(x – 4) + 3 = 5(x + 1) – 2

Expanding the terms inside the parentheses: 2x – 8 + 3 = 5x + 5 – 2

2. Combine like terms: 2x – 5 = 5x + 3
3. Move all the terms with x to one side of the equation and the constant terms to the other side: 2x – 5x = 3 + 5

Simplifying further: -3x = 8

4. Solve for x by dividing both sides of the equation by -3: x = 8 / -3

Simplifying further: x = -8/3 Therefore, the solution to the equation is x = -8/3.

To simplify the expression 3x – (4x + 5) – (2x – 3), we need to remove the parentheses and apply the negative sign to the terms inside the parentheses. Distributing the negative sign, we get: 3x – 4x – 5 – 2x + 3 Now, we can combine like terms. Grouping the x terms together and the constant terms together, we have: (3x – 4x – 2x) – (5 – 3) Simplifying further, we get: -3x – 2 Therefore, the simplified expression is -3x – 2.

To simplify the expression (1/2) + (1/3) – (1/4), we need to find a common denominator for the fractions. The least common multiple of 2, 3, and 4 is 12. Multiplying the numerator and denominator of each fraction to have a denominator of 12, we get 6/12 + 4/12 – 3/12. Combining the numerators, we have 7/12. Therefore, the correct answer is  7/12.

To solve for y in the equation 2(y – 3) + 5 = 3(y + 2) – 1, we can follow these steps:

1. Distribute the coefficients on both sides of the equation: 2y – 6 + 5 = 3y + 6 – 1
2. Combine like terms: 2y – 1 = 3y + 5
3. Move all the terms with y to one side of the equation and the constant terms to the other side. We can do this by subtracting 3y from both sides and adding 1 to both sides: 2y – 3y = 5 + 1 Simplifying further: -y = 6
4. Solve for y by multiplying both sides of the equation by -1 to get rid of the negative sign: -1 * -y = -1 * 6 Simplifying further: y = -6

Therefore, the solution to the equation is y = -6.

The sum of the angles in a triangle is always 180°. Given that two angles measure 60° and 80°, we can find the missing angle by subtracting the sum of the given angles from 180°: 180° – (60° + 80°) = 180° – 140° = 40°. Therefore, the correct answer is (a) 40°.