Question

Translate the following verbal phrases into algebraic expressions using the symbols given.

1. Three-quarters the product of two numbers x and y.
2. Seven times the product of two numbers x and y, less 5, divided by thrice a third number z.
3. The cube of the sum of two numbers x and y.
4. The square of thrice a number a, take away double a second number b.
5.Half the sum of two numbers x and y, divided by twice third number z.

Answer 1

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Answer 2

Given,

A few verbal phrases,

1. Three-quarters the product of two numbers x and y.

2.seven times the product of two numbers x and y, less 5, divided by thrice a third number z.

3.The cube of the sum of two numbers x and y.

4.The square of thrice a number a, take away double a second number b.

5.Half the sum of two numbers x and y, divide by twice third number z.

To find,

Algebraic expressions for the given verbal phrases.

Solution,

1.

Three quarters is written as $\frac{3}{4}$.

Product of two numbers means their multiplication.

⇒$x$×$y=xy$

So, three quarters of the product of x and y will be,

⇒$\frac{3}{4}xy$

Therefore, answer is $\frac{3}{4}xy.$

2.

Product of x and y will be,

⇒$xy$

Seven times the product will be,

⇒$7xy$

Minus 5

⇒$7xy-5$

Thrice of z is written as,

⇒$3z$

Divided by $3z$

⇒$\frac{7xy-5}{3z}$

Therefore, the answer is $\frac{7xy-5}{3z}.$

3.

Sum of two numbers is their addition.

⇒$x+y$

Cube of them will be to the power three.

⇒$(x+y)^{3}$

Therefore, the answer is $(x+y)^{3}$.

4.

Thrice of a number a is given by,

⇒$3a$

Square of it will be,

⇒$(3a)^{2}$

Double of b can be written as,

⇒$2b$

Subtracting both, we'll get,

⇒$(3a)^{2}-2b$

Therefore, the answer is $(3a)^{2}-2b$.

5.

Sum of x and y will be,

⇒$x+y$

Half of their sum will be,

⇒$\frac{1}{2}(x+y)$

Twice of z will be,

⇒$2z$

Now diving the twice of z by the obtained half,

⇒$\frac{\frac{1}{2}(x+y) }{2z}$

⇒$\frac{x+y}{4z}$

Therefore, the answer is $\frac{x+y}{4z}$.