Question

A. Translate each of the following phrases into a mathematical expression. Use as few variables as possible:
1. The sum of a number and 10
2. The product of two numbers
3. The product of -1 and a number
4. One-half times the sum of two numbers
5. Twice a number
6. Five less than a number
7. A number less 8
8. Six more than a number
9. A number decreased by 6
10. The square of a number
11. Four times the square of a number
12. Three less than twice a number
13. Five more than three times a number
14. One-half of a number
15. The square of the sum of 5 and a number
16. The sum of the squares of two numbers
17. There are twice as many boys as there are girls.
18. There are 10 more cars than jeeps.
19. A man’s age 10 years ago
20. The area of a rectangle whose length is 7 more than its width

Answer 1

Step-by-step explanation:

1)z+10

2)x×y

3)-1×r

4)1/2(a+b)

5)2x

6)5<s

7)j<8

8)6+t

9)n-6

10)a²

11)4×m²

12)3-2u

13)5+3p

14)1/2q

15)(5+v)²

16)(x+y)²

17)2(mn)

18)10x>y

19)r-10

20)area=(7i+i)

Answer 2

Answer:

The mathematical expressions for the given phrases are given below:

Step-by-step explanation:

1) Mathematical Expression: $x+10$

The variable here is x.

2) Mathematical Expression: x×y

The variable here is x and y.

3) Mathematical Expression:$(-1)$×x

The variable here is x.

4) Mathematical Expression: $\frac{1}{2} (x+y)$

The variable here is x.

5) Mathematical Expression: 2×x

The variable here for the number is x.

6) Mathematical Expression: $x - 5$

The variable here for the number is x.

7) Mathematical Expression: $x - 8$

The variable here for the number is x.

8) Mathematical Expression: $x +6$

The variable here for the number is x.

9) Mathematical Expression: $x - 6$

The variable here for the number is x.

10) Mathematical Expression: $x^{2}$

The variable here for the number is x.

11) Mathematical Expression: $4x^{2}$

The variable here for the number is x.

12) Mathematical Expression: 2×x$-3$

The variable here for the number is x.

13) Mathematical Expression: $5 + 3$×x

The variable here for the number is x.

14) Mathematical Expression: $\frac{1}{2}$×x

The variable here is x.

15) Mathematical Expression:$(5+x)^{2}$

The variable here is x.

16) Mathematical Expression:$x^{2} + y^{2}$

The variable here is x and y.

17) Mathematical Expression: The number of boys = 2×x

The variable here is the number of girls which is taken to be x.

18) Mathematical Expression: The number of cars = $x+10$

The variable here for the number of jeeps is x.

19) Mathematical Expression: The age of man 10 years ago =  $x - 10$

The variable here for the man's present age is x.

20) Mathematical Expression for the area of rectangle = $(x +7)(x)$

The variable here for width is x.

Therefore length = $x + 7$