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3 years ago

10

(2x+1)/2=(x+2)/5if possible can you show me step by step how to get the answer

1 answer:

katrin2010 [14]3 years ago

8 0

Answer:

$\boxed{\bold{Decimal \ Form: \ x \ = \ -0.125}}$

$\boxed{\bold{Fraction \ Form:x=-\frac{1}{8}}}$

Step By Step Explanation:

Apply Fraction Cross Multiply: If $\bold{\frac{a}{b}=\frac{c}{d}:then\ a\cdot \:d=b\cdot \:c}$

$\bold{\left(2x+1\right)\cdot \:5=2\left(x+2\right)}$

$\bold{\left(2x+1\right)\cdot \:5: \ 10x+5}$

$\bold{2\left(x+2\right): \ 2x+4}$

$\bold{10x+5=2x+4}$

Subtract 4 From Both Sides

$\bold{10x+5-5=2x+4-5}$

Simplify

$\bold{10x=2x-1}$

Subtract 2x From Both Sides

$\bold{10x-2x=2x-1-2x}$

Simplify

$\bold{8x=-1}$

Divide Both Sides By 8

$\bold{\frac{8x}{8}=\frac{-1}{8}}$

Simplify

$\bold{x=-\frac{1}{8}}$

Turn Fraction Into Decimal

$\bold{-1 \ \div \ 8 \ = \ -0.125}$

$\bold{-0.125}$

Regards,

Mordancy

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If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?

kondaur [170]

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here, $x_1=-8, y_1=-6, x_2=-4, y_2=-14$

$$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)$

$$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)$

$$P(x, y) =(-6, -10)$

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here, $x_1=-6, y_1=-10, x_2=-8, y_2=-6$

$r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}$

$r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}$

$r=\sqrt{(-2)^{2}+(4)^{2}}$

$r=\sqrt{20}$ units

The standard form of the equation of a circle is

$(x-a)^{2}+(y-b)^{2}=r^{2}$ , where (a, b) are center and r is the radius.

Here, center = (–6, –10) and $r=\sqrt{20}$

$(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}$

$(x+6)^{2}+(y+10)^{2}=20$

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

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2 years ago

Read 2 more answers

If 40% of a number is 80 what is 25% of that number?

olga2289 [7]

Answer:

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Step-by-step explanation

40% of a number is 80

.40 * n = 80

Divide each side by .4

.40 n/.4 = 80/.4

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The number is 200

Now lets find 25 percent of that number

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