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3 years ago

What is the missing term?

Mathematics

1 answer:

Lady_Fox [76]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

The general expansion of (a + b)² is

(a + b)² = a² + 2ab + b²

Applying this to the following expansions

(1)

(x + 2)² = x² + 2(2x) + 2² = x² + 4x + 4 ← missing term is x²

(2)

(2x - 3)² = (2x)² + 2(2x)(- 3) + 3² = 4x² - 12x +9 ← missing term is - 12x

(3)

(3x + 4)² = (3x)² + 2(3x)(4) + 4² = 9x² + 24x + 16 ← missing term is 16

(4)

(x - y)² = x² + 2(x)(- y) + y² = x² - 2xy + y² ← missing term is x²

(5)

(2x + 3y)² = (2x)² + 2(2x)(3y) + (3y)² = 4x² + 12xy + 9y² ← missing term is + 12xy

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Mohamed and Li Jing were asked to find an explicit formula for the sequence -5, -25, -125, -625,....

Nuetrik [128]

Answer:

Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

Step-by-step explanation:

Considering the sequence

$-5,\:-25,\:-125,\:-625,...$

A geometric sequence has a constant ratio r and is defined by

$g_n=g_0\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}$

$\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=5$

So, the sequence is geometric.

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$g_1=-5$

$r=5$

$g_n=g_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$g_n=-5\cdot \:5^{n-1}$

Therefore, Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

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3 years ago

Please Help I dont Know what to do with this question!!!!

Anestetic [448]

Answer:

1. Certain

2. Impossible

3. Likely

4. Unlikely

Step-by-step explanation:

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2 years ago

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zhuklara [117]

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jolli1 [7]

∠G is the shortest

Step-by-step explanation:

Given is a ΔFGH

FG = 8.7

FH = 4.5

GH = 6.1

The triangle will be formed with three angles

F, G and H

"The side opposite to the largest angle of the triangle is the largest"

Similarly, The side opposite to the shortest angle is the shortest.

Converse of this postulate will be:

The interior angle opposite to the shortest side of the triangle is the smallest.

The triangle formed is attached in the form of a picture.

The angle opposite to FH will be the shortest.

Hence,

∠G is the shortest

Keywords: Angles, triangles

Learn more about angles at:

#LearnwithBrainly

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3 years ago

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alekssr [168]

Answer:

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