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Flauer [41]
3 years ago
8

Factor completely 3x4 − 30x3 + 75x2

Mathematics
2 answers:
IgorLugansk [536]3 years ago
6 0

we have

3x^{4}-30 x^{3}+75 x^{2}

Factor the leading coefficient

3x^{2}(x^{2}-10 x+25)

we know that

(x^{2}-10 x+25)=(x-5)^{2}

substitute

3x^{2}(x-5)^{2}=3x^{2}(x-5)(x-5)

therefore

<u>the answer is</u>

3x^{2}(x-5)^{2}


k0ka [10]3 years ago
5 0
3x^2(x^2-10x+25) hope this helps
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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​
-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$\Rightarrow \frac{h}{2}=r

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

  $\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3 (formula)

$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3

$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3

Hence it is true.

Option A, option C and option E are true.

6 0
3 years ago
Read 2 more answers
Someone please help on 43.
Bas_tet [7]

Answer: p=9.7

Step-by-step explanation:

40p+ 10.5p=489.85

50.5p=489.85

9.7=p

6 0
3 years ago
Read 2 more answers
What is the binary number for 17​
matrenka [14]

Answer:

♡ hi there! madeline here. ♡

- your answer is 10001

also, since I answered first, can I get the brainliest?

thank you, have a great day sandra!

✧・゚: *✧・゚:・゚✧*:・゚✧・゚: *✧・゚:・゚✧*:・゚✧

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Find the midpoint of the segment with the given endpoints. (9.-9) and (2.-10)​
kondor19780726 [428]

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{(5.5 \: , \: -  9.5)}}}}}

Step-by-step explanation:

Let the points be A and B

Let A ( 9 , -9 ) be ( x₁ , y₁ ) and B ( 2 , - 10 ) be ( x₂ , y₂ )

<u>Finding</u><u> </u><u>the</u><u> </u><u>midpoi</u><u>nt</u>

\boxed{ \sf{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} }}

\longrightarrow{ \sf{midpoint = ( \frac{9 + 2}{2} , \:  \frac{ - 9  + ( - 10)}{2}}} )

\longrightarrow{ \sf {midpoint = ( \frac{11}{2} \: , \:  \frac{ - 9 - 10}{2}})}

\longrightarrow{  \sf{midpoint = (5.5 \: , \:  \frac{ - 19}{2}}} )

\longrightarrow{ \sf{midpoint = (5.5 \: , - 9.5}})

Hope I helped!

Best regards! :D

5 0
2 years ago
What is an equivalent fraction to 24/72?
crimeas [40]
24/72
Simplify the fraction, by dividing out the GCF: 24
<u>24/24
</u>72/24
1/3
5 0
3 years ago
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