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3 years ago

Solve the equation graphically: √ x = - x.

Mathematics

1 answer:

Nikolay [14]3 years ago

6 0

Sqrt[x] = -x
x= x ^ 2
x - x^2 = 0
-x(x-1)=0
x(x-1)=0
x = 1 or x = 0
sqrt 1 isn not equal to 0

x= 0

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the length and width of a rectangle are consecutive even integers. the area of the rectangle is 80 square units. what are the le

nadya68 [22]

X(x + 2) = 120sq units

Set it equal to 0 
x^2 + 2x - 120 = 0 

factor 
(x + 12)(x - 10) 

For the shorter side: 
x - 10 = 0 
x = 10 

Now that you have x, solve for the longer side which we said was represented by 
x + 2 
10 + 2 = 12 

Proof 
A = L x W 
120 = 10 x 12 
120 = 120 
true 

Our length is 12 and our width is 10

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3 years ago

Solve The Equation 4x×9y=7 4x-9y=9

hoa [83]

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:

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

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

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

8 0

2 years ago

Does anyone know 1/4 x ? = -2?

SSSSS [86.1K]

Answer:

-8

Step-by-step explanation:

1/4 x = -2

You want the value of x. x is being multiplied by 1/4. To get x alone on the left side, you need to divide both sides by 1/4. Dividing by 1/4 is the same as multiplying by 4.

Multiply both sides of the equation by 4.

4 * 1/4 x = -2 * 4

4 * 1/4 = 1, so on the left side you get 1x which is just x.

x = 8

Answer: -8

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dedylja [7]

Answer:

157

Step-by-step explanation:

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2 years ago

What decimal is equal 35%

iren [92.7K]

Answer:

0.35

Step-by-step explanation:

Divide 35 by 100 and you get 0.35

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3 years ago

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