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insens350 [35]
3 years ago
14

This is a popular type of problem that appeared in mathematics textbooks in the 1970s and 1980s. can you find the answer? the su

m of the digits of a two-digit number is 6. if the digits are reversed, the difference between the new number and the original number is 18. find the original number.
Mathematics
1 answer:
kondaur [170]3 years ago
4 0
A digit is a number in one of the places, so for example the number 54 has two digits; a tens place digit (5) and a ones place digit (4).

Say the mystery number is a two digit number = xy
* that's not x times y but two side by side digits.

Info given:
<span>the sum of the digits of a two-digit number is 6
x + y = 6 </span>
<span>if the digits are reversed, yx the difference between the new number and the original number is 18.

**To obtain the number from digits you must multiply by the place and add the digits up. (Example: 54 = 10(5) + 1(4))

Original number = 10x + y
Reversed/New number = 10y + x

Difference:
10y + x - (10x + y) = 18
9y - 9x = 18
9(y - x) = 18
y - x = 18/9
y - x = 2

Now we have two equations in two variables
</span>y - x = 2
<span>x + y = 6

Re-write one in terms of one variable for substitution.
y = 2 + x
sub in to the other equation to combine them.
x + (2 + x) = 6
2x + 2 = 6
2x = 6 - 2
2x = 4
x = 2

That's the tens digit for the original number. Plug this value into either of the equations to obtain y, the ones digit.

2 + y = 6
y = 4

number "xy" = 24

</span>
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Solve for x in the equation.
labwork [276]

Answer:

The solution is \displaystyle x=1\pm \sqrt{47}. Fourth option

Explanation:

Solve for x:

2x^2+3x-7=x^2+5x+39

Move all the terms from the right to the left side of the equation, a zero in the right side:

2x^2+3x-7-x^2-5x-39=0

Join all like terms:

x^2-2x-46=0

The general form of the quadratic equation is:

ax^2+bx+c=0

Solve the quadratic equation by using the formula:

\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

In our equation: a=1, b=-2, c=-46

Substituting into the formula:

\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}

\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}

\displaystyle x=\frac{2\pm \sqrt{188}}{2}

Since 188=4*47

\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}

Take the square root of 4:

\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}

Divide by 2:

\displaystyle x=1\pm \sqrt{47}

First option: Incorrect. The answer does not match

Second option: Incorrect. The answer does not match

Third option: Incorrect. The answer does not match

Fourth option: Correct. The answer matches exactly this option

8 0
3 years ago
Solve the linear system using substitution
levacccp [35]
Hello there!

3x - y = 3
-x + y = 3

We need to solve 3x - y = 3 for y

Let start by adding -3x to both sides

3x - y = 3

3x - 3x - y = 3 - 3x

-y = 3 - 3x
We cannot leave the variable with a negative sign. We must multiply both sides by -1

-y * -1= (3 - 3x)-1

y = 3x - 3

Substitute 3x -3 for y in -x+y=3

-x + y = 3

-x + 3x - 3 = 3

2x - 3 = 3

2x = 3 + 3

2x = 6

x = 6/2

x = 3

Now substitute 3 for x in y=3x -3

y = 3x - 3

y = 3(3) - 3

y= 9 - 3

y= 6

Thus,

The answer is x=3 and y=6

It is always my pleasure to help students like you :)

As always, I am here to help!


7 0
3 years ago
NEED HELP PLZ
skad [1K]

Answer:

look at the picture i sent......

5 0
3 years ago
Read 2 more answers
2 Points
Inga [223]

Answer:

D

Step-by-step explanation:

Given

9 - 7x = (4x - 3)² + 5 ← expand the squared factor

9 - 7x = 16x² - 24x + 9 + 5, that is

9 - 7x = 16x² - 24x + 14 ( subtract 9 - 7x from both sides )

0 = 16x² - 17x + 5, that is

16x² - 17x + 5 = 0 ← in standard form → D

4 0
3 years ago
Which of the following is an irrational number?<br><br>A. π<br>B. -16/3<br>C. 2.6<br>D. 18
victus00 [196]
Which of the following is an irrational number?

A. π
6 0
3 years ago
Read 2 more answers
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