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Viktor [21]
3 years ago
15

If two thirds of a number is decreased by 4, the result is 56. find the number

Mathematics
2 answers:
nikitadnepr [17]3 years ago
6 0
56+4=60\\\\60\times3=180\\\\180:2=\fbox{90}\\\\CHECK:\\\frac{2}{3}\times90-4=2\times30-4=60-4=56

=================================================

128-38=90\\\\90\times9=810\\\\810:5=\fbox{162}\\\\CHECK:\\\\38+\frac{5}{9}\times162=38+5\times18=38+90=128

=================================================

14.6-2.3=12.3\\\\12.3\times5=61.5\\\\61.5:3=\fbox{20.5}\\\\CHECK:\\\\\frac{3}{5}\times20.5+2.3=3\times4.1+2.3=12.3+2.3=14.6
tresset_1 [31]3 years ago
3 0
Let the number be x
There are actually 3 different statements - 

1. two-thirds of a number decreased by 5 is 56
2*x/3 - 4 =56
2*x/3=60
x=90

2. 38 added to 5/9 of number gives 128
i.e 5*x/9 + 38 = 128
5*x/9 = 90
x = 162

3. sum of 2.3 and 3/5 of number gives 14.6
i.e 2.3 + 3*x/5 = 14.6
3*x/5 = 12.3
x = 4.1*5
x = 20.5
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Each leg = 1 unit (and both legs are that way, since the triangle is isosceles - so two sides are the same)

Hypotenuse = √2 units.

So if we know either leg, we multiply by √2 to get the hypotenuse. In reverse, we divide by √2 if we know the hypotenuse to get the measurement of a leg.

Our problem tells us that the hypotenuse AC is 10 units. We divide 10 by √2 to get the measurement of leg AB. Since it's a 45 -45 - 90 triangle, AB = BC.

AB = \frac{10}{\sqrt{2}}

= \frac{10\sqrt{2}}{\sqrt{2}\sqrt{2}} to rationalize the radical

= \frac{10\sqrt{2}}{2} = 5\sqrt{2}

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3 years ago
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Assoli18 [71]
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3 years ago
The system of equations
cupoosta [38]

Answer:

z = -12

Step-by-step explanation:

The given system of equations is:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

But from (1): xy = x + y

Using this in (7), we have

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8)

Using this in (4)

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5..........................................(9)

Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

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Answer:

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Step-by-step explanation:

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