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3 years ago

A number increase by three is two more twice the number.find the number.

Mathematics

1 answer:

mixer [17]3 years ago

5 0

Answer:

Step-by-step explanation:

1 increased by 3=1+3=4

Twice of 1=1+1=2

4 is two more than 2.

Therefore, the number=1

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What would be the scale factor?

icang [17]

The scale factor would be 3

7 0

3 years ago

The sum of 5 consecutive integers is 110, what is the fourth number in this sequence?

Xelga [282]

The answer is: " 23 " .

→ The fourth number in the sequence is: " 23 " .

_____________________________________

Explanation:

To solve:

" x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

in which:

"x" = The first number in these sequence;

"(x + 1 )" = the second number in the sequence;

"(x + 2)" = the third number in the sequence;

"(x + 3)" = the fourth number in the sequence;

"(x + 4)" = the fifth number in the sequence;

_____________________________________

Solve for the "fourth number in the sequence" ; or: "(x + 3)" ;

_____________________________________

Given: " x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

↔ " x + x + 1 + x + 2 + x + 3 + x + 4 = 110 " ;

→ Solve for "x" ;

→ then, solve for "(x + 3)" ;

→ which is the fourth number in this sequence;

_____________________________________

→ " x + x + 1 + x + 2 + x + 3 + x + 4= 110 " ;

"5x + 1 + 2 + 3 + 4= 110 " ;

" 5x + 10 = 110 " ;

Solve for "x" :

Subtract "10" from EACH SIDE of the equation; as follows:

" 5x + 10 - 10 = 110 - 10 " ;

to get :

" 5x = 100 " ;

Now, divide EACH SIDE of the equation by "5" ;

to isolate "x" on one side of the equation; & to solve for "x" ; as follows:

5x / 5 = 100 / 5 ;

to get:

" x = 20 " .

_____________________________________

Now, to find the fourth number in the sequence:

→ " (x + 3) " ;

→ Substitute "20" for "x" ;

" x + 3 = 20 + 3 = 23" ;

_____________________________________

The answer is: " 23 " .

The fourth number in the sequence is: " 23 " .

_____________________________________

Let us check our work:

If there are five "5" numbers in the sequence, and "23" is the "fourth number" , then: "24" is the "fifth number" .

As such: "22" is the "third number" ; "21" is the "second number" ; and "20" is the "first number" . Is this consistent with: "x = 20" as the "first number" ? Yes!

Thus, "20 + 21 + 22 + 23 + 25 = ? 110 ? ? ;

→ 20 + 21 = 41 ;

→ 41 + 22 = 63 ;

→ 63 + 23 = 86 ;

→ 86 + 24 = 110 . Yes!

_____________________________________

Hope this answer is helpful!

Best wishes in your academic pursuits—

and within the "Brainly" community!

_____________________________________

5 0

3 years ago

Please help with 15, 17 and 19

Irina-Kira [14]

Given:

15. $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

17. $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

19. $2^{\log_2100}$

To find:

The values of the given logarithms by using the properties of logarithms.

Solution:

15. We have,

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

Using property of logarithms, we get

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$ is 1.

17. We have,

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

Using properties of logarithms, we get

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)$ $[\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}]$

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$ is -1.

19. We have,

$2^{\log_2100}$

Using property of logarithms, we get

$2^{\log_2100}=100$ $[\because a^{\log_ax}=x]$

Therefore, the value of $2^{\log_2100}$ is 100.

6 0

3 years ago

Which of the following expressions is equal to 5^6/5^2

Natali5045456 [20]

Answer:

$\dfrac{5^6}{5^2}$ = $5{\cdot}5{\cdot}5{\cdot}5$

Step-by-step explanation:

The given expression is :

$\dfrac{5^6}{5^2}$

We need to find this expression is equal to what.

$\dfrac{5^6}{5^2}=\dfrac{5^4\times 5^2}{5^2}\\\\=5^4\\\\=5\times 5\times 5\times 5\\\\\text{or}\\\\=5{\cdot}5{\cdot}5{\cdot}5$

Hence, $\dfrac{5^6}{5^2}$ is equal to $5{\cdot}5{\cdot}5{\cdot}5$ . Hence, the correct option is (c).

5 0

3 years ago

Choose the simplified form of the fifth term of 6C4(2x)2(-y2)4.

Katarina [22]

You didn't give us the choices. It doesn't matter. I think you're trying to write

$\displaystyle {6 \choose 4} (2x)^2 (-y^2)^4$

$= \dfrac{6!}{4! 2!} ( 4x^2 y^8)$

$= \dfrac{6(5)}{2} ( 4x^2 y^8)$

$=60x^2 y^8$

Answer: 60 x² y⁸

4 0

3 years ago

A number increase by three is two more twice the number.find the number.​

A number increase by three is two more twice the number.find the number.