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2 years ago

What is the distributive property of 6(2x + 5y).

Mathematics

2 answers:

zavuch27 [327]2 years ago

5 0

Answer:

12x+30y

Step-by-step explanation:

6(2x+5y)

The distributive property is used if a number is in the form

$a(b+c)$

To solve this problem, you need to multiply b and c by a.

$=ab+ac$

Now, let's plug in your numbers.

a = 6

b = 2x

c = 5y

$6(2x+5y)\\=(6)2x+(6)5y\\=12x+30y$

nikitadnepr [17]2 years ago

4 0

Answer:

12x+30y

Step-by-step explanation:

6*2x+6*5y

12x+30y

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A cone has a diameter of 3 inches the cone holds 12 cubic inches of water to the nearest in what is the height

LUCKY_DIMON [66]

Answer:

5 inches

Step-by-step explanation:

A cone's volume can be found using the formula $V = \frac{1}{3} \pi r^2 h$ . If the cone has a diameter of 3 inches then its radius is half r= 1.5 inches. Substitute r = 1.5 and V = 12 cubic inches.

$V = \frac{1}{3} \pi r^2 h \\12 = \frac{1}{3} \pi (1.5)^2 h \\12 = \frac{1}{3} \pi (2.25) h\\12 = 2.355h\\5.10 = h$

This means the height of the cone is 5.10 inches or to the nearest inch 5 inches.

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3 years ago

What three dimensional solid has 6 rectangular faces, 2 equal bases that are not rectangles, and 18 edges

lapo4ka [179]

A hexagonal prism should work! The two bases are hexagons, and there are 6 lateral faces that are rectangles. When you count the edges, there are 18

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3 years ago

Read 2 more answers

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amid [387]

Is there any way u can translate this

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3 years ago

Formulate the following problem as least squares problems. For each problem, give a matrixA and a vector b such that the problem

hammer [34]

Answer:

a) $A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right]$

$b=\left[\begin{array}{ccc}0\\1\end{array}\right]$

b) $||Ax-b||^{2} =(-bx_{2}+4)^{2} (-4x_{1} +3x_{2} -1)^{2} +(x_{1} +8x_{2} -3)^{2}$

c) $A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]$

$x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]$

Step-by-step explanation:

a) considering the equation:

Minimize $x_{1}^{2} +2x_{2}x^{2} +3x_{3}^{2}+(x_{1} -x_{2} +x_{3} -1)^{2} +(-x_{1} -4x_{2} +2)^{2}$

$A=\left[\begin{array}{ccc}1&2&3\\1&-1&1\end{array}\right]$ (matrix A)

vector b

$b=\left[\begin{array}{ccc}0\\1\end{array}\right]$

b) If Pxn is matrix B and p-vector d, we have:

minimize $(-6x_{2}+4)^{2} +(-4x_{1} +3x_{2} -1)+(x_{1} +8x_{2} -3)^{2}$

$Ax=\left[\begin{array}{ccc}0&-6&0\\-4&3&0\\1&8&0\end{array}\right]$

$\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-4\\1\\3\end{array}\right]$

$Ax-b=\left[\begin{array}{ccc}-bx_{2}+4 \\-4x_{1}+3x_{2}-1 \\x_{1}+8x_{2}-3 \end{array}\right] =1$

$||Ax-b||^{2} =(-bx_{2}+4)^{2} (-4x_{1} +3x_{2} -1)^{2} +(x_{1} +8x_{2} -3)^{2}$

c) minimize $2(-bx_{2}+4)^{2} +3(-4x_{1} +3x_{2} -1)^{2} +4(x_{1} -x_{2} -3)^{2} -(6\sqrt{2}x_{2} +4\sqrt{2} )^{2} +(-4\sqrt{3} x_{1} +3\sqrt{3}x_{2} -\sqrt{3})^{2} +(2x_{1} -16x_{2} -6)^{2}$

in matrix:

$A=\left[\begin{array}{ccc}0&6\sqrt{2} &0\\\sqrt{3} &3\sqrt{3} &0\\2&-16&0\end{array}\right]$

$x=\left[\begin{array}{ccc}x_{1} \\x_{2} \\x_{3} \end{array}\right]$

$b=\left[\begin{array}{ccc}-\sqrt{2} \\\sqrt{3} \\6\end{array}\right]$

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3 years ago

The perimeter of a rectangular town is 32 miles.its width is 5 miles find the length

son4ous [18]

The perimeter of a rectangle is expressed as:

P = perimeter

l = length

w = width

P = 2(l + w)

Plug in our values to the formula mentioned above

32 m = 2(l + 5).

Start by dividing each side by 2.

16 = l + 5.

Subtract 5 from each side.

11 = l.

The length of your town is 11 miles

8 0

3 years ago