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Troyanec [42]
3 years ago
7

Solve The Equation 4x×9y=7 4x-9y=9

Mathematics
1 answer:
hoa [83]3 years ago
8 0

Answer:

\large\boxed{x=\dfrac{9}{8}-\dfrac{\sqrt{109}}{8},\ y=-\dfrac{1}{2}-\dfrac{\sqrt{109}}{18}}\\or\\\boxed{x=\dfrac{9}{8}+\dfrac{\sqrt{109}}{2},\ y=-\dfrac{1}{2}+\dfrac{\sqrt{109}}{18}}

Step-by-step explanation:

\left\{\begin{array}{ccc}4x\times9y=7&(1)\\4x-9y=9&(2)\end{array}\right\\\\(2)\\4x-9y=9\qquad\text{subtract}\ 4x\ \text{from both sides}\\-9y=-4x+9\qquad\text{change the signs}\\9y=4x-9\qquad\text{substitute it to (1)}\\\\4x(4x-9)=7\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\(4x)(4x)+(4x)(-9)=7\\(4x)^2-36x=7\\(4x)^2-2(4x)(4.5)=7\qquad\text{add}\ 4.5^2\ \text{to both sides}\\(4x)^2-2(4x)(4.5)+4.5^2=7+4.5^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

(4x-4.5)^2=7+20.25\\(4x-4.5)=27.25\to 4x-4.5=\pm\sqrt{27.25}\\\\4x-\dfrac{45}{10}=\pm\sqrt{\dfrac{2725}{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{2725}}{\sqrt{100}}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25\cdot109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{109}}{10}\\\\4x-\dfrac{45}{10}=\pm\dfrac{5\sqrt{109}}{10}\qquad\text{add}\ \dfrac{45}{10}\ \text{to both sides}\\\\4x=\dfrac{45}{10}\pm\dfrac{5\sqrt{109}}{10}

4x=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 4}\\\\x=\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\\\\\text{Put the values of}\ x\ \text{to (2):}\\\\9y=4\left(\dfrac{9}{8}\pm\dfrac{\sqrt{109}}{8}\right)-9\\\\9y=\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}-\dfrac{18}{2}\\\\9y=-\dfrac{9}{2}\pm\dfrac{\sqrt{109}}{2}\qquad\text{divide both sides by 9}\\\\y=-\dfrac{1}{2}\pm\dfrac{\sqrt{109}}{18}

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The rate of increase of population of Hermitville is given by:
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3 years ago
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Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, -6), B(5, -6), C(5, -2)
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Answer:

Step-by-step explanation:

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Please help Maggie's brother is 3 years younger than twice her age. The sum of their ages is 30.
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I’m not sure if this is correct but this is the way i would solve it.

first, make an equation with the given information

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x= 16.5


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7 0
3 years ago
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Answer:

The correct option is A) The growth factor of the investment.

Step-by-step explanation:

Consider the provided exponential function.

V(t) = 30,000(1.125)^t

Where V(t) is the total value  after t years.

Here the function is in the form of Exponential Growth:

y = a(b)^x

Where b value is the growth factor.

By comparing we get that the constant '1.125' represents the growth factor by which our value is increasing each year.

Constant '30,000' represents the initial value i.e. the investment made.

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3 years ago
A. x 1 2 3 y 1 4 9 B. x 1 2 3 y 2 5 10 C. x 1 2 3 y 3 6 9 D. x 1 2 3 y 0 3 8 Which table can be represented by a line? A) B) C)
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A.)
x  y
1  1
2  4
3  9
dx=2-1→dx=1   dy=4-1→dy=3
dx=3-2→dx=1   dy=9-4→dy=5 different to 3, then this table can not be represented by a line

B.)
x  y
1  2
2  5
3  10
dx=2-1→dx=1   dy=5-2→dy=3
dx=3-2→dx=1   dy=10-5→dy=5 different to 3, then this table can not be represented by a line

C.)
x  y
1  3
2  6
3  9
dx=2-1→dx=1   dy=6-3→dy=3
dx=3-2→dx=1   dy=9-6→dy=3, then this table can be represented by a line

D.)
x  y
1  0
2  3
3  8
dx=2-1→dx=1   dy=3-0→dy=3
dx=3-2→dx=1   dy=8-3→dy=5 different to 3, then this table can not be represented by a line

Answer: Option C. x 1 2 3 y 3 6 9
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