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olga2289 [7]
2 years ago
11

Let m,n,p, and q represent nonzero positive integers. find a number in terms of m,n,p, and q that is halfway between m/n and p/q

.
Mathematics
2 answers:
alukav5142 [94]2 years ago
7 0
This is the same as averaging. You add them and divide by 2.

((m/n) + (p/q))/2 would be a number in between m/n and p/q.

Do note that n and q must be nonzero, but luckily that is a given.
bulgar [2K]2 years ago
6 0

Answer:

it is given that,m,n,p, and q represent nonzero positive integers.

A number between a and b is given by

  \frac{a+b}{2}

where, a and b are rational numbers ,having denominator ≠0.

A number between

 \frac{m}{n} \text{and} \frac{p}{q} \text{is equal to}\\\\=\frac{\frac{m}{n} + \frac{p}{q}}{2}\\\\=\frac{mq+np}{2nq}

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Solve the following inequality: 38 < 4x + 3 + 7 – 3x.
DochEvi [55]
38 < 4x + 3 +7 - 3x (original equation)
38 < 4x - 3x + 3 + 7 (combine like terms)
38 < x + 10 (simplify)
38 - 10 < x + 10 - 10 (subtract 10 from both sides to get (x) alone)
28 < x (simplify)
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7 0
2 years ago
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Tan 235° = 2tan20°+ tan215°​
Mariulka [41]

Given :  tan 235 = 2 tan 20 + tan 215

To Find : prove that

Solution:

tan 235 = 2 tan 20 + tan 215

Tan x = Tan (180 + x)

tan 235 = tan ( 180 + 55) = tan55

tan 215 = tan (180 + 35) = tan 35

=> tan 55 = 2tan 20 + tan 35

55 = 20 + 35

=> 20  = 55 - 35

taking Tan both sides

=> Tan 20 = Tan ( 55 - 35)

=> Tan 20  = (Tan55 - Tan35) /(1 + Tan55 . Tan35)

Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1

=> Tan 20  = (Tan 55 - Tan 35) /(1 + 1)

=> Tan 20  = (Tan 55 - Tan 35) /2

=> 2 Tan 20  = Tan 55 - Tan 35

=> 2 Tan 20 +  Tan 35 = Tan 55

=>  tan 55 = 2tan 20 + tan 35

=>  tan 235 = 2tan 20 + tan 215

QED

Hence Proved

5 0
1 year ago
which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 2x – 1 into the quadratic formula below
irinina [24]

0 = 4x^2+2x- 1

Quadratic formula is

x = \frac{-b+-\sqrt{b^2-4ac}}{2a}

'a' is the coefficient of x^2 = 4

'b' is the coefficient of x = 2

'c' is the constant = -1

Now we plug in all the values in quadratic formula

x = \frac{-b+-\sqrt{b^2-4ac}}{2a}

x = \frac{-2+-\sqrt{2^2-4(4)(-1)}}{2(4)}

x = \frac{-2+-\sqrt{18}}{8}

The above one is the substitution of values of a,b,c in quadratic formula.

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1 year ago
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The diagram shows the cross section of a cylindrical pipe with water lying in the bottom.
disa [49]
Hey 

So my brother posted this on Yahoo 
Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm. 

<span>What you do now is the following: </span>

<span>Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7) </span>

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<span>The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram. </span>

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<span>b) </span>

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<span>≃ 13.5 * 30 cm³ </span>
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Hoped it Helped
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Alika [10]

Let

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