Which of the following are used to represent unknown quantities in algebra?
In algebra, unknown quantities are represented by lower case letters.
What do literals usually represent?
Literals usually represent variables.
Convert in the simplest form.
On multiplying both sides of the ratio by 8, we get 1 on left sids and 4 on right side.
What is the equation for the statement 'half of a number added to 10 is 15'?
Write an equation for the statement 'thrice the length of a room is 340 metres'.
What is the method of finding a solution by trying out various values for the variable called?
A Find the value of 'a' that satisfies the equation 6a = −144.
Choose a value of 'a' that satisfies the equation 6a = -30.
6a = −30 ⇒ a = -30/6 = -5
What is the value of x if 3/4x +8 =17?
For what value of 'a' is 6(2a-1)+8 = 14 true?
Determine the value of x given 6x−1 = 2x+9.
Ramu's father is thrice as old as Ramu. If father's age is 45 years, how old is Ramu?
A number is multiplied by 6 and 12 is added to the product. The result is 84. What is the number?
Let the number be x. It is multiplied by
6 ⇒ 6x 12 is added to the product
The result is 84 ⇒ 6x+12 = 84 ⇒ 6x = 72
∴ x = 12
(By trial and error method).
Find the length of a side of an equilateral triangular garden whose perimeter is 66 m.
Let the side of an equilateral triangular garden be x m.
So, 3x = 66 ⇒ x = 22m
In the given figure, what are the magnitudes of the angles shown?
From the figure,x∘ + 3x∘ = 180∘ (straight angle)
⇒ 4x∘ =180∘
⇒x∘ = 45∘
∴ 3x∘ = 3×45∘ = 135∘
The length of a rectangle is twice its breadth. If its area is 72 sq. m, find the breadth of the rectangle.
Let the breadth of the rectangle be b units. The length is twice its breadth.
⇒ Its length = 2b units
∴ Area = b × 2b sq units
⇒2×b×b = 72 b × b= 72/2 ⇒b × b = 36 = 6 × 6
⇒ b = 6m
Which of the following is the perimeter of a regular hexagon of side 's' units?
A regular hexagon has 6 equal sides. Hence perimeter = 6s units.
Which of the following does 2n -1 represent?
2n - 1 is 1 subtracted from the product of 2 and n.
what is the value of p?
In a piggy bank the number of 25 paise coins is five times the number of 50 paise coins. If there are 120 coins, find the amount in the bank.
Let the number of 50 paise coins be x.
⇒ 25 paise coins = 5x
Given that total coins = 120
⇒ x + 5x = 120
⇒ 6x = 120
⇒ x = 120/6 = 20
∴ 50 paise coins = 20
⇒ Amount = 20×50 p = Rs. 10
Value of 25 paise coins = 25p × 5 × 20
= 25p × 100 = Rs. 25
Total amount Rs. (25 + 10) = Rs. 35