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Kaylis [27]
3 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]3 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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The sum of four consecutive integers is 106. What is the largest number?
ratelena [41]

Answer:

28

Step-by-step explanation:

25+26+27+28=106

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3 years ago
Calculate the new balance of an account that has been sitting for three years with a 1.5% interest rate and had an initial depos
maksim [4K]

Answer:

$5225

Step-by-step explanation:

Use the formula for the amount after simple interest: A = P(1 + rt)

"A" is the final amount, or balance.

"P" is the principal, or the starting amount.

"r" is the rate of interest in decimal form.

"t" is the time.

What we know:

P = 5000

t = 3

r = 1.5%

Convert the rate to decimal form by dividing by 100, or moving the decimal place two places to the left.

1.5% => 0.015 = r

Substitute what we know into the formula:

A = P(1 + rt)

A = 5000(1 + (0.015)(3))     <=simplify

A = 5000(1 + 0.045)

A = 5000(1.045)

A = 5225     <= new balance

The new balance of an account is $5225.

4 0
3 years ago
37% of what number is 72?
tatiyna
The answer is 194.59

(72 x 100) / 37 = 194.59
4 0
2 years ago
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Which expression will help you find the area of the triangular bases?
AnnZ [28]

Answer:

The correct answer is 1/2×8×3.

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3 years ago
You are getting a car wash for $45.50. You have to pay 5% sales tax and you want to tip the person who washed your car 20%. How
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Answer:

$56.88

Step-by-step explanation:

amount paying for sales tax---> $2.28

amount paying for tip---> $9.1

amount paying for car wash---> $45.50

$2.28 + $9.1 + $45.50= $<u><em>56.88</em></u>

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3 years ago
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