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2 years ago

Index notation simplify 4^9 x 4^3

Mathematics

1 answer:

LenKa [72]2 years ago

7 0

Answer:

$4^{12}$

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$ , then

$4^{9}$ × $4^{3}$ = $4^{(9+3)}$ = $4^{12}$

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3 consecutive odd integers such that the sum of twice the first and three times the second is 55 more than twice the third

den301095 [7]

Answer:

Consecutive odd integers are 19 , 21 & 23

Step-by-step explanation:

Let the first 3 consecutive odd intergers be x , (x + 2) and (x + 4).

According to the question,

$2x + 3(x + 2) = 2(x + 4) + 55$

$= > 2x + 3x + 6 = 2x + 8 + 55$

Eliminating 2x from both the sides,

$= > 3x + 6 = 63$

$= > 3x = 63 - 6 = 57$

$= > x = \frac{57}{3} = 19$

So, the consecutive odd integers are = 19 , 21 & 23.

3 0

1 year ago

Find (f-g)(x) if f(x)=3x-5 and g(x)=x2-5x+4

solmaris [256]

Answer:

Step-by-step explanation:

Hello,

$(f-g)(x)=f(x)-g(x)=3x-5-(x^2-5x+4)\\\\=3x-5-x^2+5x-4\\\\=-x^2+8x-9$

Thanks

4 0

2 years ago

If r and s are positive integers, is \small \frac{r}{s} an integer? (1) Every factor of s is also a factor of r. (2) Every prime

Yuri [45]

Answer:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

Step-by-step explanation:

Given two positive integers $r$ and $s$ .

To check whether $\small \frac{r}{s}$ is an integer:

Condition (1):

Every factor of $s$ is also a factor of $r$ .

$r \geq s$

Let us consider an example:

$s = 5^2 \cdot 2\\r = 5^3 \cdot 2^2$

$\dfrac{r}{s} = \dfrac{5^3\cdot2^2}{5^2\cdot2} = 10$

which is an integer.

Actually, in this situation $s$ is a factor of $r$ .

Condition 2:

Every prime factor of s is also a prime factor of r.

(But the powers of prime factors need not be equal as we are not given the conditions related to powers of prime factors.)

Let

$r = 2^2\cdot 5\\s =2^4\cdot 5$

$\dfrac{r}{s} = \dfrac{2^3\cdot5}{2^4\cdot5} = \dfrac{1}{2}$

which is not an integer.

So, the answer is:

If statement(1) holds true, it is correct that $\small \frac{r}{s}$ is an integer.

If statement(2) holds true, it is not necessarily correct that $\small \frac{r}{s}$ is an integer.

8 0

3 years ago

The Caesar Cipher of the sentence "THIS MESSAGE IS TOP SECRET."

vagabundo [1.1K]

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

"THIS MESSAGE IS TOP SECRET."

We need to use the Caesar cipher.

As in general we always take a shift of 3 keys in Caesar cipher.

so, According to shift of 3 keys it becomes,

T→W

H→K

I→L

S→V

M→P

E→H

A→D

G→J

O→R

C→F

R→U

P→S

So, it can be written as

"THIS MESSAGE IS TOP SECRET."

WKLVP HVVDJ HLVWR SVHFU HW.

we make a set of 5 letters in a word after Caesar cypher.

Hence, Option 'a' is correct.

8 0

2 years ago

Explain how algebra tiles represent like terms and zero pairs

Leokris [45]

If there is a negative tile and a positive tile, it creates a zero pair.
Like terms can occur with the same variables (except for terms with exponents)

6 0

2 years ago