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3 years ago

Answer the question below

Mathematics

1 answer:

lys-0071 [83]3 years ago

6 0

Answer:

A) -1

Step-by-step explanation:

$\frac{3 + 2\sqrt{5} }{2\sqrt{5}-3 } \\$

We can rewrite 2√5 - 3 as -(3 + 2√5)

Therefore,

$\frac{3+ 2\sqrt{5} }{-(3 + 2\sqrt{5} )} \\$

We can cancel out 3 + 2√5 both in the numerator and the denominator. So we get

= 1/-1

= -1

Answer : A) -1

Thank you.

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What is the smallest prime number p such that

Ne4ueva [31]

The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>

The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.

i.e.

p^3 + 4p^2 + 4p

By factorization, we have:

= p(p+2)²

Now, to get exactly 30 divisor.

(p+2)² requires to give us 15 factors.

Therefore, we can have an equation p + 2 = p₁ × p₂²

where:

p₁ and p₂ relate to different values of odd prime numbers.

So, for the least values of p + 2, Let us assume that:

p₁ = 5 and p₂ = 3

p + 2 = 5 × 3²

p + 2 = 5 × 9

p + 2 = 45

p = 45 - 2

p = 43

Therefore, we can conclude that the smallest prime number p such that

p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

Learn more about prime numbers here:

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Using properties to find the sum and product of 5 times 23 times 2

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what's the average temperature change in degrees Fahrenheit per hour if the temperature fell 22 degrees Fahrenheit in 10 hours

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Read 2 more answers

Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sid

lozanna [386]

L(1, -4)=(xL, yL)→xL=1, yL=-4
M(3, -2)=(xM, yM)→xM=3, yM=-2

Slope of side LM: m LM = (yM-yL) / (xM-xL)
m LM = ( -2 - (-4) ) / (3-1)
m LM = ( -2+4) / (2)
m LM = (2) / (2)
m LM = 1

The quadrilateral is the rectangle KLMN
The oposite sides are: LM with NK, and KL with NK
In a rectangle the opposite sides are parallel, and parallel lines have the same slope, then:
Slope of side LM = m LM = 1 = m NK = Slope of side NK
Slope of side NK = m NK = 1

Slope of side KL = m KL = m MN = Slope of side MN

The sides KL and LM (consecutive sides) are perpendicular (form an angle of 90°), then the product of their slopes is equal to -1:
(m KL) (m LM) = -1
Replacing m LM = 1
(m KL) (1) = -1
m KL = -1 = m MN

Answer:
Slope of side LM =1
Slope of side NK =1
Slope of side KL = -1
Slope of side MN = -1

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Answer:

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Step-by-step explanation:

To find the inverse of any function, start by switching the x and f(x) values.

f(x) = √(x + 3)

x = √(f(x) + 3)

Now solve for the new f(x). The result will be your inverse function.

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