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kakasveta [241]
3 years ago
13

Factorise 125x^3 -27y^3

Mathematics
1 answer:
telo118 [61]3 years ago
6 0

Answer:

(5x - 3y)(25x² +15xy + 9y²)

Step-by-step explanation:

125x³ - 27y³ is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

Given

125x³ - 27y³

= (5x)³ - (3y)³

= (5x - 3y)((5x)² + (5x)(3y) + (3y)²)

= (5x - 3y)(25x² + 15xy + 9y²)

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Find the arc length of the semicircle. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a d
PSYCHO15rus [73]

Answer:

Step-by-step explanation:

The formula for the length of an arc is s = rФ.

Thus, the arc length of a semicircle is S = rФ/2.

Here the radius is 5 (half the diameter), and so in this case the arc length is

S = (5 units)π/2, or S = (5/2)(3.14) units, or approximately S = 7.85 units

6 0
3 years ago
100 PTS!! PLEASE HELP! OVER DUE
Reika [66]

Answer:

-\frac{1}{2} \vec {c}

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because \frac{4}{4}=1=\frac{-2}{-2}

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that k \vec{c} = \vec {d}, or equivalently, kc_x=d_x and kc_y=d_y.

If kc_x=d_x and kc_y=d_y, we just need to substitute known values and solve for k:

kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}

Double checking that k works for the y-coordinates as well:

kc_y=d_y

(-\frac{1}{2}) (4)    ?    (-2)

-2=-2 \text{ } \checkmark

So, -\frac{1}{2} \vec {c} = \vec {d}

6 0
2 years ago
Please show all work and explanation.<br><img src="https://tex.z-dn.net/?f=6%5Cfrac%7B1%7D%7B4%7D-4%5Cfrac%7B3%7D%7B5%7D" id="Te
Olin [163]

Steps:

6 1/4 - 4 3/15 can also be written as 25/4 - 23/5

The LCD of 4 and 5 is 20.

That gives us 125/20 - 92/20.

Now, just subtract the numerators (leave the denominators the same).

That brings us to 33/20, which can be simplified to 1 13/20

Final Answer:

1\frac{13}{20}

--------------------------------------------------------------------------------------------------------------

<u><em>*Please mark brainliest if that helped!*</em></u>

8 0
3 years ago
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The vertex form of an equation is y = 3(x + 2)2 + 1. What is the standard form of the
Zigmanuir [339]

Answer:

y=3x^2+12x+13

a=3

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c=13

3 0
3 years ago
Use the data set to answer the question.
Liono4ka [1.6K]

Answer:

Yes

Step-by-step explanation:

because if you add that and then you subtract that you get that answer

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2 years ago
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