State whether the lines y = x + 2, y = − x + 3 and y − x = 1 form a triangle or not. Explain why or why not.

Simplify using the laws of exponents: Find x so that $7 to the power of left parenthesis 2 x plus 1 right parenthesis end exponent divided by 49 equals 7 cubed$

The measures of the angles of a triangle are $2 square root of 2 x end root comma square root of 2 x end root text and end text 6 square root of 2 x end root$ .
Find the measure of each angle and classify the triangle by its angles.

The area of parallelogram is p sq.cm and height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first Obtain an expression in terms of p, q and r for the height of the second parallelogram.

A poster has an area of 432 square inches. The length , in inches, of the poster is 6 inches longer than the width of the poster. Which of the following equations can be solved to determine the length, in inches, of the poster?

Note:
The question can be further extended and ask us to find the length, breadth, or the perimeter of the poster. In that case, first we would solve the above equation to find the length of the poster and then use it to find the breadth. Finally we can find the perimeter easily by using the formula: perimeter $equals 2 to the power of cross times$ (length + breadth).

A poster has an area of 432 square inches. The length , in inches, of the poster is 6 inches longer than the width of the poster. Which of the following equations can be solved to determine the length, in inches, of the poster?

A Medicine Capsule is in the shape of a cylinder of diameter 0.5 cm with two hemi spheres stuck to each of its ends. The length of entire capsule is 2 cm. Find the capacity of capsule.

The measures of the angles of a triangle are $11 square root of x comma 5 square root of x text and end text 2 square root of x$ .
Write an equation to show the relationship of the angles and find the measure of each angle

An ecologist selected a random sample of 30 prairie dogs from a colony and found that the mean mass of the prairie dogs in the sample was 0.94 kilograms (kg) with an associated margin of error of 0.12kg. Which of the following is the best interpretation of the ecologist's findings?

Note:
There are many concepts and definitions used in solving this question. The student must be familiar with mean, sampling, random sample, margin of error and hoe any results derived from the sample relate to the population, to solve this problem correctly.

An ecologist selected a random sample of 30 prairie dogs from a colony and found that the mean mass of the prairie dogs in the sample was 0.94 kilograms (kg) with an associated margin of error of 0.12kg. Which of the following is the best interpretation of the ecologist's findings?

Find the missing values

In the first half of the journey a bus travelled with an average speed of 20 km/hr. If the given average speed for the complete trip made by the bus is 24 km/hr, then calculate the average speed covered by the bus in the second half of the trip.

Shop A and shop B are at an equal distance from shop C. Distances between shops are shown in the diagram. Classify the triangle formed by them based on the sides.

In the given figure ABCD is a rectangle. It consists of a circle and two semi circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures.

Find the missing values

The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. Find the capacity of the bucket.

The front row of an auditorium has 10 seats. There are 50 rows in total. If each row has 2 more seats than the row before it, which expression gives the total number of seats in the last row?