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Kaylis [27]
2 years ago
5

1.Show that the statement p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by

Mathematics
1 answer:
Genrish500 [490]2 years ago
8 0

If x is a real number such that x3 + 4x = 0 then x is 0”.Let q: x is a real number such that x3 + 4x = 0 r: x is 0.i To show that statement p is true we assume that q is true and then show that r is true.Therefore let statement q be true.∴ x2 + 4x = 0 x x2 + 4 = 0⇒ x = 0 or x2+ 4 = 0However since x is real it is 0.Thus statement r is true.Therefore the given statement is true.ii To show statement p to be true by contradiction we assume that p is not true.Let x be a real number such that x3 + 4x = 0 and let x is not 0.Therefore x3 + 4x = 0 x x2+ 4 = 0 x = 0 or x2 + 4 = 0 x = 0 orx2 = – 4However x is real. Therefore x = 0 which is a contradiction since we have assumed that x is not 0.Thus the given statement p is true.iii To prove statement p to be true by contrapositive method we assume that r is false and prove that q must be false.Here r is false implies that it is required to consider the negation of statement r.This obtains the following statement.∼r: x is not 0.It can be seen that x2 + 4 will always be positive.x ≠ 0 implies that the product of any positive real number with x is not zero.Let us consider the product of x with x2 + 4.∴ x x2 + 4 ≠ 0⇒ x3 + 4x ≠ 0This shows that statement q is not true.Thus it has been proved that∼r ⇒∼qTherefore the given statement p is true.

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Lyrx [107]
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5 0
3 years ago
A triangle has a base length of 14cm greater than its height . If the area of the triangle is 48cm^2, find the height of the tri
irga5000 [103]
Area of triangle = base x height /2
48 = (a+14)a/2
a^2 +14a = 96
a^2 + 14a - 96 = 0
Solving for a = 5.04
5 0
3 years ago
I need help is for today!!!!
kaheart [24]

Answer:

angle b = 25°

for angle A = 180 - 50 (ie 25 + 25)

angle a =130°

3 0
2 years ago
Read 2 more answers
8×9=(5+3)×9 just need help with the answer
Svetllana [295]

Answer:

It is true.

Step-by-step explanation:

8 multiplied by 9 is 72.   5+3 is 8, which is multiplied by 9, giving the same answer on both ends.

3 0
2 years ago
Plz help me I dont get it
wlad13 [49]
So you have to decrease £30 by 20%

To do this, an easy way would be to first take away 100% from 20% because you are DECREASING :
100 - 20 = 80

Then divide your answer by 100 :
80 / 100 = 0.8

This means 0.8 is going to be your multiplier so you do
0.8 * 30 = 24

Answer = £24
5 0
3 years ago
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