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3 years ago

Greatest common factor of5x²+5x

Mathematics

1 answer:

dusya [7]3 years ago

3 0

Hi there!

$\large\boxed{5x}$

5x² + 5x

Looking at the terms, we can see that both share a common factor of 5x. Therefore:

5x(x + 1)

The GCF of 5x² + 5x is 5x.

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Hi there, hope everyone is well and staying cool :D

gogolik [260]

Answer:

A) By using the Pythagorean Theorem, we will see that $8^2 + 15^2 = 17^2$ . If we simplify it, we will find that the hypotenuse of Δ $ABC = 17$

B) approximately $18.79$

Step-by-step explanation:

A) In all honesty, you don't really need to look at ΔACD at all for this one. Just use the Pythagorean Theorem (like previously stated) and solve!

***Pythagorean Theorem is $leg^2 + leg^2 = hypotenuse^2$

B) Here, you can also use the Pythagorean Theorem! However this time, the equation will be, $8^2 + 17^2 = AD$ .

$8^2 + 17^2 = 64 +289$

$64 + 289 = 385$

$\sqrt{385} \\$ ≈ $18.79$

Hope you do well on the rest of your math problems :D

3 0

3 years ago

Harold uses the binomial theorem to expand the binomial (3x^5 - 1/9y^3)^4

riadik2000 [5.3K]

<h3>The complete question:</h3>

Harold uses the binomial theorem to expand the binomial $(3x^5 -\dfrac{1}{9}y^3)^4$

(a) What is the sum in summation notation that he uses to express the expansion?

(b) Write the simplified terms of the expansion.

Answer:

(a). $(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}( -\dfrac{1}{9}y^3)^k $$$

(b). $(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561}$

Step-by-step explanation:

(a).

The binomial theorem says

$(x+y)^n=$$\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k $$$

For our binomial this gives

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}x^{4-k}y^k $$}$

(b).

We simplify the terms of the expansion and get:

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}y^k $$= \binom{4}{0}(3x^5)^{4-0}(-\dfrac{1}{9}y^3 )^0+\binom{4}{1}(3x^5)^{4-1}(-\dfrac{1}{9}y^3 )^1+\\\\\binom{4}{2}(3x^5)^{4-2}(-\dfrac{1}{9}y^3 )^2+\binom{4}{3}(3x^5)^{4-3}(-\dfrac{1}{9}y^3 )^3+\binom{4}{4}(3x^5)^{4-4}(-\dfrac{1}{9}y^3 )^4$

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}(-\frac{1}{9}y^3 )^k $$= (3x^5)^{4}+4(3x^5)^{3}(-\frac{1}{9}y^3 )+6(3x^5)^{2}(-\frac{1}{9}y^3 )^2+\\\\4(3x^5)(-\frac{1}{9}y^3 )^3+(-\frac{1}{9}y^3 )^4$

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561} }$

3 0

3 years ago

Can someone help me with 9 and 10? I’m really lost— thank you :)

puteri [66]

For 9, do 0.5*6*9.2*5 to get the total area of the visual triangles, add that to 0.5*6*4.1*5 to get the area of the pentagon and you should get 199.5 cm^2for 10, do 0.5*6.9*8*12 to get the total area of the figure and you should get 331.2 cm^2

8 0

4 years ago

Which improper fraction is equal to the mixed number 3 3/8

ikadub [295]

The improper fraction equal to the mixed number 3 3/8 is C. 27/8

6 0

3 years ago

7c^2+5/4a-b if a=1, b= -5 and c=-4

Alexeev081 [22]

Answer:

118.25

Step-by-step explanation:

7c^2+5/4a-b if a=1, b= -5 and c=-4

7(-4)^2 + (5/4)+5

7*16 + 1.25 + 5

112 + 6.25

= 118.25

6 0

3 years ago

Read 2 more answers

Greatest common factor of5x²+5x​

Greatest common factor of5x²+5x