Question
Solve the equation 2x +1 = x - 3, and represent the solution(s) on the number line.
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If f(x) = x4 - 2x3 + 3x2 - ax - b when divided by x - 1, the remainder is 6, then find the value of a + b.
Factorise:
4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz
4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz
Read the Source/ Text given below and answer these questions:
Arun is participating in an 8 miles walk. The organizers used a square coordinate grid to plot the course. The starting point is at A (3, 1). At B (3, 4), there's a water station to make sure the walkers stay hydrated. From water station, the walkway turns right and at C (6,4) a garden is situated to keep walkers fresh. From the garden, the walkway turns left and finally, Arun reaches at destination D to complete 8 miles.
questions:
1. How far is the water station B from the starting point A?
2. How far is the water station B from garden C?
Arun is participating in an 8 miles walk. The organizers used a square coordinate grid to plot the course. The starting point is at A (3, 1). At B (3, 4), there's a water station to make sure the walkers stay hydrated. From water station, the walkway turns right and at C (6,4) a garden is situated to keep walkers fresh. From the garden, the walkway turns left and finally, Arun reaches at destination D to complete 8 miles.
questions:
1. How far is the water station B from the starting point A?
2. How far is the water station B from garden C?
Examine whether the following numbers are rational or irrational.
$\sqrt{7}\times\sqrt{343}$
→$\sqrt{7}\times\sqrt{343}$
Simplify:
$\Big(\frac{7776}{243}\Big)^{-\frac{3}{5}}$
→$\Big(\frac{7776}{243}\Big)^{-\frac{3}{5}}$
Find p(0), p(1) and p(2) of the polynomial: $p ( t ) = 2 + t + 2 t ^ { 2 } - t ^ { 3 }$
→In figure, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u.
Find four different solutions of the equation x + 2y = 6
Read the following statements which are taken as axioms:
- If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
- If a transversal intersect two parallel lines, then alternate interior angles are equal.
Rewrite the following polynomial in standard form.
x - 2x2 + 8 + 5x3
x - 2x2 + 8 + 5x3