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Question 158

In the given figure, state the three pairs of equal parts in $\Delta ABC$ and $\Delta EOD$. Is $\Delta ABC\cong \Delta EOD$? Why?

David cuts a cake into two equal halves. He cuts one half into smaller pieces of equal size. Each of these smaller pieces weighs twenty grams. If he has seven pieces of the cake in all, how heavy is the original cake?

Evaluate prime factorisation of $729$ using step diagram method.

$\sum$fx = 5x + 2, $\sum$f = 12. If the mean of the distribution is 6, what is the value of x?

A spherical balloon is filled with $4500\pi$ cubic metres of Helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic metres per minute, then the rate at which the radius of the balloon decreases $49$ minutes after the leakage began is:

Question 17

Fill in the blanks to make the statement true.

On a number line, $\frac{-1}{2}$ is to the ___ of zero .

463.5 should be divided by _____ to get 4.635.

Solve the following problems.

A sum of Rs. 800 amounts to Rs. 1,160 in 4 years at a certain rate of interest. What is the amount for Rs. 640 at the same rate of interest?

Find the value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}.$

You are given the measurement of the two legs of a right angled triangle. What else do you need in order to draw a triangle?

1. 6

(x)^(-a) x (x)^(-b) = ___

Question 95

Measures (in degrees) of two complementary angles are two consecutive even integers. Find the angles.

On sale with a 20% discount, the price of a book is $40. What is the original price of the book?

If star is made following an unchanging relation an show below.

If the same unchanging relation is followed and a new star is made as shown, then the value of a & b will be equal to

In ΔABC,
∠A = 30°,
∠B = 40°
and ∠C = 110°

In ΔPQR,
∠P = 30°,
∠Q = 40°
and ∠R = 110°

A student
says that ΔABC ≅
ΔPQR by AAA congruence
criterion. Is he justified? Why or why not?

There is a park with two triangular jogging tracks. Rahul and his friend Arjun went for jogging. The park had a route map which mentioned that the sides of jogging tracks with the same color have the same length and nothing was mentioned about different colored sides.

Both of them started jogging at 7 AM on different tracks. Rahul finished his jogging at 7:40 AM. At what time will Arjun finish his jogging if both of them are jogging at the same speed,given that the triangular tracks are congruent to each other?

Consider the figure:

If $\angle$A = ${50}^{\circ }$​, $\angle$B = ${70}^{\circ }$​, and x = 2y, then, the value of x (in degrees) is___.

From the given information calculate the area of the triangle. Given the height of the triangle is 5 cm and it divides the base into two equal parts of 3 cm each. Express your answer in m${}^2$.

Question 26

In questions 24 to 59, fill in the blanks to make the statements true.
$30\%ofRs.360=$ ___

The capacities of two bottles are in the ratio 5: 3. If the smaller bottle is emptied thrice and the larger bottle once into a vessel; and in another vessel, only the larger bottle is emptied twice then find the ratio of the liquids in both the vessels.

The diameter of a circle is 10 cm. Its radius is ___.

Match the following monomial expressions with their corresponding degree.

One angle of a triangle is ${61}^{\circ }$ and the other two angles are in the ratio $\left(\frac{3}{2}\right):\left(\frac{4}{3}\right)$. Find the smallest angle in the triangle.

Tap on all the acute angles.

The perimeter of a triangular field is 90 m and the ratio of the sides is 3 : 5 : 7. Find the area of the field.

Give two examples for a cuboid.

If a polyhedron has 8 faces and 14 edges, then it will have _______ vertices

The base of a square pyramid is a ____.

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. $2^8\times 3^8\times 7^8=(2\times 3\times 7{)}^8={42}^8$.

During the sale time, a cereal box that normally costs $\$4$ is sold for $\$3.5$, the discount percentage offered on the original price is

Construct the right angled ΔPQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm.

What is the coefficient of $x$ in the algebraic expression $8z-5x+7y$?