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2 years ago

Two times a number plus 3 equals one half of the number plus 30. What is the number please?

Mathematics

1 answer:

Zanzabum2 years ago

7 0

Answer:

Step-by-step explanation:

2*x + 3 = 1/2x + 30 Subtract 3 from both sides

2x = 1/2x + 27 Subtract 1/2 x from both sides

1 1/2 x = 27 change 1 1/2 to 3/2

3/2 x = 27 Multiply by 2/3

2/3 * 3/2x = 27 * 2/3

x = 18

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Is amount off an increase or decrease

Mashutka [201]

Decrease because you taking something off of something

7 0

3 years ago

Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

4 0

3 years ago

Can someone help me p

Serga [27]

Answer:

(3.5, -2)

Step-by-step explanation:

that point is where the edge if the rectangle is

5 0

3 years ago

Select the correct answer. A sound wave enters a new medium where sound travels faster. How does this affect the frequency and w

Ulleksa [173]

Answer:

The correct answer is E. Neither the frequency nor the wavelength is affected. Explanation: The wave frequency does not affect the speed of that wave. An increase in frequency of a wave causes a decrease in wavelength while the wave speed remains the constant. The speed of the waves is significantly higher at higher tensions.

Step-by-step explanation:

5 0

3 years ago

A new Community Sport complex is being built in safe harbor the perimeter of the rectangular playing field is 402 yards the leng

ivanzaharov [21]

Answer:

<h2>length = 159 yards</h2><h2>width = 42 yards</h2>

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 402 yards

The statement

the length of the field is 9 yards less than quadruple the width is written as

l = 4w - 9

Substitute this is expression into the above formula and solve for the width

That's

402 = 2( 4w - 9) + 2w

402 = 8w - 18 + 2w

10w = 402 + 18

10w = 420

Divide both sides by 10

Substitute this value into l = 4w - 9

That's

l = 4(42) - 9

l = 168 - 9

Therefore

length = 159 yards

width = 42 yards

Hope this helps you

3 0

3 years ago