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Gala2k [10]
3 years ago
6

Double the sum of a double the number and quotient of five and two

Mathematics
1 answer:
Vika [28.1K]3 years ago
4 0

Answer:

The required expression is 2(2x+\frac{5}{2})

Step-by-step explanation:

Let the number be x

We are supposed to write the algebraic expression of given statement

Double the number = 2x

Quotient of five and two =\frac{5}{2}

Now we are given that Double the sum of a double the number and quotient of five and two

So, Sum of a double the number and quotient of five and two =2x+\frac{5}{2}

So, Double the sum of a double the number and quotient of five and two =2(2x+\frac{5}{2})

Hence The required expression is 2(2x+\frac{5}{2})

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a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l
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\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}

Step-by-step explanation:

The equation of a line:

y=mx+b

We have

m=\dfrac{2}{3}

substitute:

y=\dfrac{2}{3}x+b

The formula of a distance between a point and a line:

General form of a line:

Ax+By+C=0

Point:

(x_0,\ y_0)

Distance:

d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}

Convert the equation:

y=\dfrac{2}{3}x+b     |<em>subtract y from both sides</em>

\dfrac{2}{3}x-y+b=0    |<em>multiply both sides by 3</em>

2x-3y+3b=0\to A=2,\ B=-3,\ C=3b

Coordinates of the point:

(0,\ 0)\to x_0=0,\ y_0=0

substitute:

d=4

4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}

4=\dfrac{|3b|}{\sqrt{13}}\qquad|    |<em>multiply both sides by \sqrt{13}</em>

4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}   |<em>divide both  sides by 3</em>

b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}

Finally:

y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}

4 0
3 years ago
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