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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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Nancy and seven of her friends shared the $101.20 dinner bill equally. How much did each person pay?
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12.65. Divide 101.20 by 8
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2 years ago
In which number does the digit 2 have a value that is ten times as great as the value of the digit 2 in the number 135,284?
Valentin [98]

Answer: See explanation

Step-by-step explanation:

You didn't give the options but let me help out.

First and foremost, we should note that the value of the digit 2 in the number 135,284 is 200. Therefore, the value that is ten times as great as the value of the digit 2 in the number 135,284 would be:

= 10 × 200

= 2000

Therefore, the 2 must be in the thousands place. This can be seen in numbers such as:

172748.

6 0
2 years ago
Please help explanation if possible
poizon [28]

Step-by-step explanation:

Hi there!

The given equation is:

y = -2x + 5………………(i)

Comparing the equation with y = mx+c, we get;

m1 = -2

Also another equation of the line which passes through point (-4,2), we get;

(y-2) = m2(X+4)............(ii) { using the formula (y-y1) = m2(x-x2)}

According to the question, they are perpendicular to eachother, So according to the condition of perpendicular lines;

m1*m2 = -1

-2*m2 = -1

or, m2 = 1/2.

Therefore, m2= 1/2.

Now, keeping the value of m2 in equation (ii).

(y-2) = 1/2(x+4)

y = (1/2)x + 4

Therefore, the required equation is: y = (1/2)x + 4.

<u>Hope</u><u> it</u><u> helps</u><u>!</u>

3 0
3 years ago
Firewood is stacked in a pile. The bottom row has 20 logs and the top row has 14 logs. Each row has one more log than the row ab
zavuch27 [327]

Answer:

19

Step-by-step explanation:

Add from numbers 14-20

8 0
3 years ago
Lily had 95 inches of yarn. After cutting 4 pieces that were each the same length, she had 15 inches of yarn left.
Anika [276]
Each was 10 inches because she had 95 and 95-15=40 divided by 4 = 10
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3 years ago
Read 2 more answers
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