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3 years ago

Explain why 256 + 4 is equivalent to (200 + 4) + (40+4) + (164)

1 answer:

4 0

The expression 256 + 4 is equivalent to (200 + 4) + (40+4) + (16+4) according to distributive and commutative property of addition.

Given the expression 256 + 4. This can be solved using the partial sum expressed as:

256 + 4

= (200 + 40 + 16) + 4

According to the commutative property, A+B = B+A

The arrangement does not affect the result. Hence;

(200 + 40 + 16) + 4 = 4 + (200 + 40 + 16)

Using the distributive law;

4 +(200 + 40 + 16) = (200 + 4) + (40 + 4) + (16 + 4)

Hence the expression 256 + 4 is equivalent to (200 + 4) + (40+4) + (16+4) according to distributive and commutative property of addition.

Learn more on partial sum here: brainly.com/question/6958503

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The sum of three integers is 12

Liula [17]

The three integers are 5,17 and -10

Step-by-step explanation:

Let x, y and z be three integers then

$x+y+z=12 \ \ \Eqn\ 1$

'The sum of the first and second integers exceeds the third by 32'

$x+y=z+32\ \ \ \ Eqn\ 2$

The third integer is 15 less than the first.

$z=x-15\ \ \ \ Eqn\ 3$

From Eqn 2:

$x+y=z + 32\\x+y-z=32$

Subtracting Eqn 1 from eqn 2

$x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20$

Dividing both sides by -2

$\frac{-2z}{-2}=\frac{20}{-2}\\z=-10$

Putting z=-10 in Eqn 3

$z=x-15\\-10=x-15\\x=15-10\\x=5$

Putting x=5 and z=-10 in Eqn 1

$x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17\\$

Hence,

The three integers are 5,17 and -10

Keywords: Linear Equations, Variables

Learn more about linear equations at:

#LearnwithBrainly

3 0

3 years ago

Read 2 more answers

Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and <img src="https://tex

algol13

9514 1404 393

Answer:

a) x = (√5 -1)/2 ≈ 0.618034

b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

<u>Given</u>:

x/(1 -x) = 1/x

<u>Find</u>:

Exactly, and as a decimal approximation, ...

a) x, using the quadratic formula

b) 1/x

<u>Solution</u>:

a) We can multiply the given equation by x(1 -x) to obtain ...

x² = 1 -x

x² +x -1 = 0 . . . . . . add x-1

The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}$

We are only interested in the positive solution, which is ...

$\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}$

b) The quadratic we developed in the first part can be rearranged like this:

x² +x = 1 . . . . . . add 1 to both sides

x(x +1) = 1 . . . . . factor out x

x +1 = 1/x . . . . . .divide by x

Then to find the value of 1/x, we simply need to add 1 to the value of x we have:

$\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}$

5 0

3 years ago

In a school, the number of boys who play

BigorU [14]

Answer:

Step-by-step explanation:

see image for Explanation.

4 0

3 years ago

$300 bases price plus $20 per guest for up to 30 guest

Scilla [17]

Answer:$900

Step-by-step explanation:Because 30 times 20 + 300 equals 900

4 0

3 years ago

Given: m∠MEJ=16°, Measurement of Arc MJ =5 * Measurement of Arc KL, Find: Measurement of Arc KL

Softa [21]

Answer:

The measurement of arc KL is $8\°$

Step-by-step explanation:

Let

x--------> the measure of arc KL

y-------> the measure of arc MJ

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

$m$

we have

$m$

$y=5x$

substitute the given value

$16\°=\frac{1}{2}(5x-x)$

$32\°=(4x)$

$x=8\°$

therefore

The measurement of arc KL is $8\°$

5 0

4 years ago

Explain why 256 + 4 is equivalent to (200 + 4) + (40+4) + (164)​

Explain why 256 + 4 is equivalent to (200 + 4) + (40+4) + (164)