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3 years ago

Find the quotient: 15x^4y^2-30x^2y^3+45xy/5xy is ____. when this quotient is divided by _the result is x^3y-2xy^2+3

1 answer:

5 0

$\dfrac{15x^4y^2-30x^2y^3+45xy}{5xy}=\dfrac{15x^4y^2}{5xy}-\dfrac{30x^2y^3}{5xy}+\dfrac{45xy}{5xy}\\\\=3x^{4-1}y^{2-1}-6x^{2-1}y^{3-1}+9=3x^3y-6xy^2+9\\\\=3(x^3y-2xy^2+3)\\\\Used:\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\Answer:\\....\underline{3x^3y-6xy^2+9}...\ \ \ ...\underline{3}...$

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Vanyuwa [196]

The answer is 64. Hope it helps you

8 0

2 years ago

Write an inequality for x that would give this rectangle a perimeter of at least 300ft

Travka [436]

Answer:

The inequality for $x$ is:

$x\geq 142$

Step-by-step explanation:

Given:

Width of rectangle = 3 ft

Height or length of rectangle = $(x+5)$ ft

Perimeter is at least 300 ft

To write an inequality for $x$ .

Solution:

Perimeter of a rectangle is given as:

⇒ $2l+2w$

where $l$ represents length of the rectangle and $w$ represents the width of the rectangle.

Plugging in the given values in the formula, the perimeter can be given as:

⇒ $2(x+5)+2(3)$

Using distribution:

⇒ $2x+10+6$

Simplifying.

⇒ $2x+16$

The perimeter is at lest 300 ft. So, the inequality can be given as:

⇒ $2x+16\geq 300$

Solving for $x$

Subtracting both sides by 16.

⇒ $2x+16-16\geq 300-16$

⇒ $2x\geq284$

Dividing both sides by 2.

⇒ $\frac{2x}{2}\geq \frac{284}{2}$

⇒ $x\geq 142$ (Answer)

7 0

3 years ago

Which is a possible expression for the series <br> -6-12-24-48-96-192

iren [92.7K]

Answer:

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Step-by-step explanation:

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4 0

2 years ago

Simplify the following expression:<br><br> (4x+8) - 3(x+1)

Umnica [9.8K]

Answer:

x + 5

Step-by-step explanation:

$4x + 8 + (-3)(x) + (-3)(1)$
$4x + 8 -3x -3$
$(4x-3x) + (8-3)$
$x + 5$

Therefore, the answer is x + 5.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

8 0

2 years ago

Read 2 more answers

FURTHER MATHEMATICS Use determinants to solve the systems of equation:

maw [93]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}2x+1y+2z&=&13\\1x+1y-2z&=&8\\1x+2y+1z&=&11\\\end{array}\right.\\\\\\\Delta=\left| \begin{array}{ccc}2&1&2\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\0&\frac{1}{2}&-3\\0&1&3\end{array}\right| =2*(\frac{3}{2}+3)=9\\\\$

$\Delta_1=\left| \begin{array}{ccc}13&1&2\\8&1&-2\\11&2&1\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\8&1&-2\\\frac{11}{2}& 1&\frac{1}{2}\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\-5&0&-4\\\frac{-5}{2}& 0&\frac{5}{2}\end{array}\right| \\\\=2*(-1)*(\frac{-25}{2}-\frac{20}{2}) =45\\$

$\Delta_2=\left| \begin{array}{ccc}2&13&2\\1&8&-2\\1&11&1\end{array}\right| \\\\\\=\left| \begin{array}{ccc}3&21&0\\3&30&0\\1&11&1\end{array}\right| \\\\\\=1*(90-63) =27\\$

$\Delta_3=\left| \begin{array}{ccc}2&1&13\\1&1&8\\1&2&11\end{array}\right| \\\\\\=\left| \begin{array}{ccc}0&-1&-3\\0&-1&-3\\1&2&11\end{array}\right| \\\\\\=0\\$

$\left\{\begin{array}{ccc}x=\dfrac{\Delta_1}{\Delta}=\dfrac{45}{9}=5\\\\y=\dfrac{\Delta_2}{\Delta}=\dfrac{27}{9}=3\\\\z=\dfrac{\Delta_3}{\Delta}=\dfrac{0}{9}=0\\\end{array}\right.$

8 0

3 years ago

Find the quotient: 15x^4y^2-30x^2y^3+45xy/5xy is ________. when this quotient is divided by _____the result is x^3y-2xy^2+3

Find the quotient: 15x^4y^2-30x^2y^3+45xy/5xy is ____. when this quotient is divided by _the result is x^3y-2xy^2+3