EVALUATE FOR GIVEN VALUE OF THE VARIABLES

Evaluate the following expressions when

x = 8, y = 9 and z = 10

Problem 1 :

2∛-x - √y

Solution :

= 2∛-x - √y

Substitute x = 8 and y = 9

= 2∛-8 - √9

= 2(-2) - 3

= -4 - 3

= -7

Problem 2 :

z² + (xy/y) - 5

Solution :

= z² + xy/y - 5

Substitute x = 8, y = 9 and z = 10

= (10)² + (8) (9) / 9 - 5

= 100 + 72 / 4

= 172/4

= 43

Problem 3 :

-5|x - z| + 1/2 z

Solution :

= -5|x - z| + 1/2 z

Substitute x = 8 and z = 10

= -5|8 - 10| + 1/2 (10)

= -5|-2| + 5

= -5(2) + 5

= -10 + 5

= -5

Problem 4 :

What is -4 - 2x + 7 when x = -5?

a. -7          b. 1         c. 13          d. 21

Solution :

= -4 - 2x + 7

By applying x = -5 in equation

= -4 - 2(-5) + 7

= -4 + 10 + 7

= -4 + 17

= 13

So, option (c) is correct.

Problem 5 :

What is 4∛a - c√b + 6 when a = 27, b = 64 and c = -2?

a. 2            b. 22            c. 26           d. 34

Solution :

= 4∛a - c√b + 6

Substitute a = 27, b = 64 and c = -2

= 4∛27 - (-2)√64 + 6

= 4(3) + 2(8) + 6

= 12 + 16 + 6

= 34

So, option (d) is correct.

Problem 6 :

What is

|-5x + 6y| + √z / 5^x - 22

when x = 2, y = -13 and z = 81

Solution :

= |-5x + 6y| + √z / 5^x - 22

Substitute x = 2, y = -13 and z = 81

= |-5(2) + 6(-13)| + √81 / 5² - 22

= |-10 - 78| + 9 / 25 - 22

= |-88| + 9 / 3

= 88 + 9 / 3

= 97/3

= 32.3

Problem 7 :

A playground is in shape of a square. The area of the square PQRS is 256 m² with each side (x + 2)m. One day Suraj along with his two friends Ajay and Aman went to play there with bicycle. Someone stole Suraj bicycle but Ajay and Aman helped him by contributing ₹ (4a + 60) and ₹ (6a + 10) respectively, to buy a new bicycle. The cost of bicycle was ₹ 4200.

On basis of this information given in passage answer following questions.

(a) Find the value of x

b) What is the value of a?

(c) What was the amount given by Ajay and Aman to Suraj?

(d) What is the perimeter of the playground?

Solution :

a) area of the square PQRS = 256 m²

Side length of square = x + 2

(x + 2)(x + 2) = 256

x²+ 4x + 4 = 256

x²+ 4x + 4 - 256 = 0

x²+ 4x - 252 = 0

x²+ 18x - 14x - 252 = 0

x (x + 18) - 14(x - 18) = 0 

(x + 18)(x - 14) = 0

x = -18 and x = 14

b) Amount contributed by Ajay = 4a + 60

Amount contributed by Aman = 6a + 10

4a + 60 + 6a + 10 = 4200

10a + 70 = 4200

10a = 4200 - 70

10a = 4130

a = 4130/10

a = 413

(c)

Amount spent by Ajay = 4a + 60

= 4(413) + 60

= 1652 + 60

= 1712

Amount spent by Aman = 6a + 10

= 6(413) + 10

= 2478 + 10

= 2488

(d) What is the perimeter of the playground = 4 (side length)

= 4 (x + 2)

Applying the value of x, we get

= 4 (14 + 2)

= 4(16)

= 64 m

So, the required perimeter is 64 m.

Problem 8 :

An online photo printing service charges $0.15 per photo and $2.99 for the shopping. The total cost c for printing and shipping any number of pictures p can be represented by the function c = 0.15p + 2.99

Part A :

a) What input values for p make sense in this situation ?

a) rational number    b) whole number

c) decimal       d) irrational number

Part B :

Complete the function table for c = 0.15p + 2.99

Solution :

Part A :

Here p represents number of photo. Then it must be a whole number. Option b is  correct.

Part B :

When p = 4

c = 0.15(4) + 2.99

= 0.6 + 2.99

= 3.59