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3 years ago

14

Simply 4x2y2 + 8x3y5 2xy2

1 answer:

Setler [38]3 years ago

5 0

I’m not sure if you were using exponents, but if you were, this is it simplified.

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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

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

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

2 years ago

If the 7th of an AP is equal to 11 times the 11th term, find the 18th term

Zina [86]

Answer:

-33 or 33

Step-by-step explanation:

The seventh term of an AP is written as:

$a + 6d$

The eleventh term of an AP is written as:

$a + 10d$

If the 7th term is 11 times the 11th term, then;

$a + 6d = 11(a + 10d)$

Expand to get:

$a + 6d = 11a + 110d$

$11a - a = 6d - 110d$

$10a = - 104d$

$\frac{a}{d} = - \frac{104}{10}$

$\frac{a}{d} = - \frac{52}{5}$

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

$- 52 + 5 \times 17 = 33$

For the second case,

$52 - 5 \times17 = - 33$

3 0

3 years ago

. put these numbers in order, from least to greatest. if you get stuck, consider using a number line. 3.5 -1 4.8 -1.5 -0.5 -4.2

luda_lava [24]

-4.2, -3.5,-2.1,-1.5,-1,-0.5,0.5,2,3.5,4.8

7 0

1 year ago

From the sum of -16 and -11, subtract the sum of -20 and 10

Vika [28.1K]

Answer:

-37

Step-by-step explanation:

-16+-11=-27

-20+10=-10

-27+-10=-37

5 0

2 years ago

Y-5x=3 what does y equal

Tamiku [17]

Answer:

2

Step-by-step explanation:

because y-5x=3 its very simple math.

4 0

2 years ago