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2 years ago

What is the factored form of x^3 - 729

Mathematics

2 answers:

tensa zangetsu [6.8K]2 years ago

8 0

Answer:

(x - 9)(x^2 + 18x + 81).

Step-by-step explanation:

Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 - 729 = (x - 9)(x^2 + 18x + 81)

lawyer [7]2 years ago

7 0

Answer: $(x-9) (x^{2} +9x + 81)$

Step-by-step explanation:

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There are 80 guards and 32 forwards in Ben's basketball league.

xxTIMURxx [149]

Answer:

Step-by-step explanation:

The greatest common factor between 32 and 80 is 16 not 8.

32 (forwards) / 16 (teams) = 2 forwards on each team.

80 (guards) / 16 (teams) = 5 guards on each team.

6 0

3 years ago

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Rus_ich [418]

Answer:

the last one

Step-by-step explanation:

6 0

3 years ago

A recipe calls for 14cup of brown sugar for every 23cup of white sugar. How many cups of brown sugar are required for every cup

photoshop1234 [79]

Note: Consider all the numeric values are in the fraction form. Like $14\to \dfrac{1}{4}$ , $23\to \dfrac{2}{3}$ etc.

Given:

A recipe calls for $\dfrac{1}{4}$ cup of brown sugar for every $\dfrac{2}{3}$ cup of white sugar.

To find:

The number of cups of brown sugar that are required for every cup of white sugar.

Solution:

We know that,

Required brown sugar for $\dfrac{2}{3}$ cup of white sugar = $\dfrac{1}{4}$ cup

Using this, we get

Required brown sugar for 1 cup of white sugar = $\dfrac{\dfrac{1}{4}}{\dfrac{2}{3}}$ cup

$=\dfrac{1}{4}\times \dfrac{3}{2}$ cup

$=\dfrac{3}{8}$ cup

So, $\dfrac{3}{8}$ cup of brown sugar is required for every cup of white sugar.

Therefore, the correct option is B.

6 0

3 years ago

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and ro

Helga [31]

Answer:

Part 1) The shape is a trapezoid

Part 2) The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

Part 3) The area is $937.5\ units^2$

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

$P=AB+BC+CD+AD$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

$d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}$

$d=\sqrt{(-24)^{2}+(7)^{2}}$

$d=\sqrt{625}$

$d_A_B=25\ units$

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

$d=\sqrt{(-8+22)^{2}+(27+21)^{2}}$

$d=\sqrt{(14)^{2}+(48)^{2}}$

$d=\sqrt{2,500}$

$d_B_C=50\ units$

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

$d=\sqrt{(9+8)^{2}+(-4-27)^{2}}$

$d=\sqrt{(17)^{2}+(-31)^{2}}$

$d=\sqrt{1,250}$

$d_C_D=25\sqrt{2}\ units$

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

$d=\sqrt{(9-2)^{2}+(-4+28)^{2}}$

$d=\sqrt{(7)^{2}+(24)^{2}}$

$d=\sqrt{625}$

$d_A_D=25\ units$

Find the perimeter

$P=25+50+25\sqrt{2}+25$

$P=(100+25\sqrt{2})\ units$

simplify

$P=25(4+\sqrt{2})\ units$ ----> exact value

$P=135.4\ units$

therefore

The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

step 3

Find the area

The area of trapezoid is equal to

$A=\frac{1}{2}[BC+AD]AB$

substitute the given values

$A=\frac{1}{2}[50+25]25=937.5\ units^2$

4 0

3 years ago

What is the value of e to five decimal places

notsponge [240]

Using google calculator you can see that

e≈2.7 1 8 2 8 182846.....

Fifth decimal place is bold 8.

When we round up to 5th decimal place, we get

e≈2.7 1 8 2 8.

5 0

3 years ago