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3 years ago

Use long division to find the quotient below. (2x^3+x2+25)/(2x+5)

Mathematics

1 answer:

Contact [7]3 years ago

3 0

Answer:

x^2 -2x +5

Step-by-step explanation:

x^2 -2x +5

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

2x + 5 / 2x^3 + x^2 + 0x + 25

-(2x^3 + 5x^2)

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

-4x^2 + 0x

-( -4x^2 - 10x )

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

10x + 25

-(10x + 25)

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

The desired quotient is x^2 -2x +5

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3 years ago

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3 years ago

Determine whether the triangles are similar. if so, write a similarity statement and name the postulate ot theorem you used. if

Gekata [30.6K]

Answer: Explained.

Step-by-step explanation: The explanations are as follows :

(7) Since GF is parallel to JK and FK and GJ are tranversals, so we have

∠GFK = ∠JKH,

∠FGK = ∠KJH (pairs of alternate interior angles) and

∠GKF = ∠JHK (vertically opposite angles).

Therefore, both the triangles are similar by AAA similarity rule.

(8) Here,

$\dfrac{AN}{MP}=1,~\dfrac{AD}{PR}=\dfrac{4}{5}.$

Since the ratio of the corresponding sides are not proportional, so the triangles are not similar.

(9) Here,

$\dfrac{PS}{RS}=\dfrac{SQ}{ST}=\dfrac{PR}{QT}=\dfrac{2}{3}.$

So, the triangles are similar by proportionality rule.

(10) Here,

$\dfrac{RQ}{JK}=\dfrac{11}{16},~\dfrac{PR}{KL}=\dfrac{30}{45}=\dfrac{2}{3},~\dfrac{PQ}{JL}=\dfrac{2}{3}.$

Since all the ratios are not equal, so the triangles are not similar.

(11) Here , no angle of one triangle matches with the angle of the other triangle, so the given triangles are not similar.

(12) Here,

$\dfrac{GH}{AC}=\dfrac{GK}{AB}=\dfrac{KH}{BC}=\dfrac{1}{2}.$

So, the triangles are similar by the proportionality rule.

Hence explained.

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3 years ago