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Greeley [361]
3 years ago
12

Simplify the expression.

Mathematics
1 answer:
Anna71 [15]3 years ago
5 0

Since we have a cubic root, we're interested in factoring cubes inside the root, so that we can take them out. If we factor 648, we have

648=2^3\times 3^4=2^3\times 3^3\times 3 = (2\times 3)^3\times 3 = 3\times 6^3

So, we have

3x\sqrt[3]{648 x^4 y^8} = \sqrt[3]{3\times 6^3\cdot x^3\cdot x \cdot y^6\cdot y^2}=3x\cdot 6\cdot x\cdot y^2\sqrt[3]{3\cdot x\cdot y^2}

And the result simplifies to

18x^2y^2\sqrt[3]{3xy^2}

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JulsSmile [24]

1,000,000,000 is the smallest one.

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Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 1
ser-zykov [4K]

Answer:100B + 50M ? 25000

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3 years ago
Find the midpoint of the segment having endpoints (0 ,1/8) and (-4/5 ,0)
kvasek [131]

Answer:

Mid point of the given end points = (\frac{-2}{5},\frac{1}{16} )

Step-by-step explanation:

Given the end points of the line segment are :

(0, \frac{1}{8}) & (\frac{-4}{5},0)

We will use the mid point formula when two points are: (x₁,y₁) & (x₂,y₂)

mid point = (\frac{x_{1} +x_{2} }{2},\frac{y_{1} +y_{2} }{2} )

now put the value of x₁ = 0

x₂ = \frac{-4}{5}

y₁ = \frac{1}{8}

y₂ = 0

mid point = (\frac{0-\frac{4}{5} }{2},\frac{\frac{1}{8}+0 }{2})

                = (\frac{-2}{5},\frac{1}{16} )

That's the final answer.

3 0
3 years ago
Area of a Triangle
jek_recluse [69]

Answer:

3.51 (round to the nearest hundreds)

Step-by-step explanation:

PART A

slope of the line passing through AC : (6-1)/(1-2) = 5/-1 = -5

equation of the line passing through B and perpendicular to AC:

y-3 = 1/5(x-3)

y-3 = 1/5x -3/5

y = 1/5 x - 3/5 + 3

y = 1/5 x + (-3+15)/5

y = 1/5 x + 12/5

PART B

line that passes through the points A and C

y-1 = -5(x-2)

y = -5x+10 + 1

y = -5x + 11

Interception of the lines

y = 1/5x + 12/5

y = -5x + 11

-5x + 11 = 1/5x + 12/5

-25x +55 = x + 12

26x = 43

x = 43/26

y = -5(43/26) + 11

y= -215/26 + 11

y = (-215+286)/26 = 71/26

D (1.65, 2.73)

PART C

AC = \sqrt{(1-2)^2 + (6-1)^2} = \sqrt{1 + 25} = \sqrt{26} = 5,09902

BD = \sqrt{(3-1.65)^2 + (3-2.73)^2} = 1,376735

PART D

AREA = (5,09902 * 1.376735)/2 = 3,509999

8 0
3 years ago
Which method would be best (quickest) for solving the system below:<br> 3x - 4y = -2<br> y = 2x + 1
taurus [48]
To solve with Elimination:

Write the equations under one another, like this:

2x - y = -1
+ 3x + 4y = 26

Ideally, we would like for one of the variables to be eliminated when we add vertically (straight down). But if we add them as they are this does not happen. We must manipulate one of the equations so that it will happen. Again, you can try to eliminate either x or y. I always look for a term that has a coefficient of 1 (or negative 1). So, let's use that y from the first equation again.

If the coefficient of the y in the other equation is POSITIVE 4, then I need the coefficient from the first equation to be its opposite, NEGATIVE 4. To do this, simply multiply the first equation by 4, this will create MAGIC!

4( 2x - y = -1)
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Be certain to Distribute across the entire first equation, so multiply all three terms by 4.

8x - 4y = -4
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Now add straight down (vertically). The y term will be eliminated.

11x = 22

Divide both sides of the equation by 11.

x = 2

Almost there! Now, substitute the 2 in for x in either of the original equations. Either one will work. I'm gonna use the second equation.

3x + 4y = 26

3(2) + 4y = 26

6 + 4y = 26

Subtract 6 from both sides of the equation.

4y = 20

Divide both sides of the equation by 4.

y = 5

That's it! There it is again. Put it all together. If x = 2 and y = 5, then the solution is the ordered pair, (2,5).
8 0
2 years ago
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