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There are 3 squares which are arranged in such a manner that it forms a triangle as shown in the figure below. If the area of square A and B is $81c{m}^2$ and $144c{m}^2$ respectively, then find the area of the third square C.

If triangle ABC is a isosceles triangle such that AB = AP is an altitude and AD bisects angle A.

Question 96

Solve the following:

Express as a power of a rational number with negative exponent.
$\left(a\right){\left({\left(\frac{-3}{2}\right)}^{-2}\right)}^{-3}\left(b\right)(2^5÷2^8)\times 2^{-7}$

What are joint and disjoint sets

F=(9/5)C+32

Is there a temperature which is numerically the same in both Fahrenheit and celcius? If yes,find it.

Explain the solution with reason.

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per $100c{m}^2$

How to find the root of √.037037037....is it irrational or rational?

If $x+\frac{1}{x}=11,$ find the value of $x^2+\frac{1}{x^2}$.

The cost of 3 books and 5 notebooks is Rs 250, while the cost of 4 books and 4 notebooks is Rs 280.

If the cost of a book is represented by x and the cost of a notebook is represented by y, then which set of equations represents the given information?

Virender Sehwag’s scorecard for a five-match ODI series is 23, 89, 76, 54, 102 runs respectively. What is Sehwag’s average score for the tournament?

The largest cube is carved out of a sphere of diameter $10\sqrt{3}cm$. Find the volume of the cube.

1. $180c{m}^3$

   
   

Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at$4\%$ per annum.

Given a circle with $O$ as the centre. Find the value of $x$.

In the following figure;

IA and IB are bisectors of $\angle CABand\angle CBA$repsectively.

CP is parallel to IA and CQ is parallel to IB.

The largest interval for which $x^{22}-x^{19}+x^{14}-x^5+1>0$ is

If $a+b+c=8$ and $ab+bc+ca=20$, the value of $a^3+b^3+c^3–3abc$ is ___

The equation $x=7$, in two variables can be written as ___.

$\sqrt{3}$ is a/an___number.

I don't understand the term collinear in a graph. Is that same to Three or more points lying on a straight and same line

₹ 9,000 was divided equally among a certain number of people. Had there been 20 more people, each would have got ₹ 160 less. Find the number of people.

A right circular cylinder has a base with radius of 4.2 cm and an altitude of 8.5 cm. It’s lateral surface area (or curved surface area) is

Segment of a circle is the region bounded by an arc and a ___ of the circle.

1. chord

   
   

If the supplement of an angle is two-third of itself. Determine the angle and its supplement.

Each interior angle of a regular polygon is 144°. The measure of each interior angle of a regular polygon which has double the number of sides as the first polygon is

Find the sum.

$10.1+\frac{1001}{100}+\frac{10001}{1000}+\frac{100001}{10000}$

In the given figure, equal chords AB and CD of a circle with centre O cut each other at right angles at E. If M and N are the mid-points of AB and CD respectively, then OMEN is a

The diagonals of a cyclic quadrliateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backwards, bisects the opposite side.

ABC is a triangle, D is a point on AB such that $AD=\frac{1}{4}AB$ and E is a point on AC such that $AE=\frac{1}{4}$ AC. Prove that DE = $\frac{1}{4}BC$

Of the three angles of a triangle, one is twice the smallest and another one is thrice the smallest.Find the angles.

$\text{A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and heigh 3cm.The number of such cones}\left(a\right)21\left(b\right)63\left(c\right)126\left(d\right)130$

Factorise:
$9x^2+18x+8$

A conical tent 10 m high and tha radius of its base is 24 m . Find the slant height of the rent. If the cost of $1m^2$ canvas is Rs70, find the cost of canvas required to make the tent.

In $\Delta ABC$, E is the mid -point of median AD such that BE produced meets AC at F. If AC = 10.5 cm, then AF =

If a - b = -8 and ab = -12 then $a^3-b^3=$

The value of : $(a^{\frac{1}{8}}+a^{\frac{-1}{8}})(a^{\frac{1}{8}}-a^{\frac{-1}{8}})(a^{\frac{1}{4}}+a^{\frac{-1}{4}})(a^{\frac{1}{2}}+a^{\frac{-1}{2}})$ is -

The mean $\overline{x}$ of the data is given by:

Question 158(i)

Find a single machine that will do the same job as the given hook-up.
$a(\times 2^3)machinefollowedby(\times 2^{-2})machine$.
Maya multiplied $(4^2\times 3^2)$ by thinking about stretching machines.

Use Maya's idea to multiply $5^3\times 2^3$.
Maya's idea is another product law of exponents.
Multiplying Expressions with the same Exponents
$a^c\times b^c=(a\times b{)}^c$
You can use this law with more than two expressions. If the exponents are the same, multiply the expressions by multiplying the bases and using the same exponent. e.g. $2^8\times 3^8\times 7^8=(2\times 3\times 7{)}^8={42}^8$.

In the following figure, ED = EC. Then, which of the options is/are true?