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mars1129 [50]
4 years ago
6

Which expressions show the prime factorization of 90? Check all that apply. 2 × 3 × 15 22 × 3 × 5 2 × 32 × 5 2 × 5 × 9 2 × 3 × 3

× 5 (please help)
Mathematics
1 answer:
NikAS [45]4 years ago
8 0

Answer:

Prime factors of 90: 2, 3, 3, 5

90 = 2 × 3 × 3 × 5

= 2 × 32 × 5

Factor tree:

90

| \  

45  2

| \  

15  3

| \  

5  3

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Factor out the GCF in the expression below. Put your answer in the box below. <br> `24m^{3}+54m`
d1i1m1o1n [39]

Answer:

Factor of GCF(Greatest common factor) of given expression = [2 × 3 × m]

Step-by-step explanation:

Given expression;

24m³ + 54m

Find:

The factor of GCF(Greatest common factor) of the given expression.

Computation:

24m³ + 54m

Step 1 :

Write in factor form;

[2 × 2 × 2 × 3 × m × m × m] + [2 × 3 × 3 × 3 × m]

Step 2 :

By taking [2 × 3 × m as common]

[2 × 3 × m][(2 × 2 × m × m) + (3 × 3)]

Step 3 :

[2 × 3 × m][(4m²) + (9)]

Factor of GCF(Greatest common factor) of given expression = [2 × 3 × m]

6 0
3 years ago
Show that: |A⃗ + B⃗ |² - |A⃗ - B⃗ |² = 4 A⃗.B⃗ .​
Sladkaya [172]

Answer:

Taking LHS:-

{ | \overrightarrow{A} +  \overrightarrow{B} | }^{2}  - { | \overrightarrow{A}  - \overrightarrow{B} | }^{2}

\boxed{ \mathsf{using \: \overrightarrow{a} .  \overrightarrow{a} =  { |a| }^{2} }}

\implies { | \overrightarrow{A} +  \overrightarrow{B} | }^{2}  = (\overrightarrow{A} +  \overrightarrow{B})(\overrightarrow{A} +  \overrightarrow{B})

\mathsf{using \: distributive \: property \: of \: vector \: multiplication}

<u>eqn 1:-</u>

\implies \mathsf{ \overrightarrow{A} \overrightarrow{A}+\overrightarrow{A} \overrightarrow{B} + \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B}}

same with the other one

\boxed{ \mathsf{using \: \overrightarrow{a} .  \overrightarrow{a} =  { |a| }^{2} }}

{ | \overrightarrow{A}  - \overrightarrow{B} | }^{2} = (\overrightarrow{A}  - \overrightarrow{B})(\overrightarrow{A}  - \overrightarrow{B})

\mathsf{using \: distributive \: property \: of \: vector \: multiplication}

<u>eqn. 2:-</u>

\implies \mathsf{ \overrightarrow{A} \overrightarrow{A} - \overrightarrow{A} \overrightarrow{B}  -  \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B}}

<u>eqn. 1 - eqn. 2 :-</u>

\implies \mathsf{ \overrightarrow{A} \overrightarrow{A}+\overrightarrow{A} \overrightarrow{B} + \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B} -  ( \overrightarrow{A} \overrightarrow{A} - \overrightarrow{A} \overrightarrow{B}  -  \overrightarrow{B}\overrightarrow{A} + \overrightarrow{B}\overrightarrow{B})}

after distributing the minus sign inside the braces AA and BB get canceled, while the other two add up.

\implies \mathsf{2 \overrightarrow{A}\overrightarrow{B} + 2\overrightarrow{B}\overrightarrow{A}}

\boxed{ \mathsf{\overrightarrow{A} \overrightarrow{B}= \overrightarrow{B}\overrightarrow{A}} }

\implies \mathsf{ 4\overrightarrow{A}\overrightarrow{B} }

LHS = RHS

Hence, Proved! =D

5 0
3 years ago
Look at the cups shown below (images are not drawn to scale):
Arisa [49]

Answer: I believe the answer is 28 ft. It'd be more convenient if I knew the area of it...although then you wouldn't need help answering this.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
(Math) Can someone please explain to me how to enlarge a shape?
Zepler [3.9K]
To enlarge a shape use scale factor of three or something like that but dont be mad if im wrong
8 0
4 years ago
The local parts shop buys a machine that costs $500,000. Its value depreciates exponentially each year by 10%. What is the machi
pychu [463]
If you would like to know what is the machine's value after 5 years, you can calculate this using the following steps:

1 year: $500,000 - 10% * $500,000 = 500,000 - 10/100 * 500,000 = $500,000 - $50,000 = $450,000

2 years: $450,000 - 10% * $450,000 = 450,000 - 10/100 * 450,000 = $450,000 - $45,000 = $405,000

3 years: $405,000 - 10% * $405,000 = 405,000 - 10/100 * 405,000 = $405,000 - $40,500 = $364,500

4 years: $364,500 - 10% * $364,500 = 364,500 - 10/100 * 364,500 = $364,500 - $36,450 = $328,050

5 years: $328,050 - 10% * $328,050 = 328,050 - 10/100 * 328,050 = $328,050 - $32,805 = $295,245

The correct result would be $295,000.
7 0
4 years ago
Read 2 more answers
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