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zepelin [54]
3 years ago
13

In a two-digit number, the units digit is twice the tens digit. If the number is doubled, it will be 9 more than the number reve

rsed. Find the number. :) Thanks!
Mathematics
2 answers:
snow_lady [41]3 years ago
6 0
We know that the ones digit is 2x the tens digit. The number has to be two digits, so this leaves the options of 12, 24, 36, and 48.

Next, we double each number.
12 x 2 is 24
24 x 2 is 48
36 x 2 is 72
48 x 2 is 96

And subtract 9 from each of those. 15, 39, 63, and 87.

63 backwards is 36. The number you are looking for is 36. :)
taurus [48]3 years ago
5 0
10(2x)+x 
21x is the original number

12x is the reversed number
24x is the reversed then doubled number

Set up an equation:
24x=21x+9
3x=9
x=3

The original number is 63 and the reversed number is 36, which then is 72 when doubled.
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How many solutions exist for the following system of equations: 4x + y = 7 and 3x - y = 0 a. no solution b. one solution c. infi
Zanzabum
4x+y=7 \\
\underline{3x-y=0} \\
4x+3x=7+0 \\
7x=7 \ \ \ |\div 7 \\
x=1 \\ \\
3x-y=0 \\
3 \times 1-y=0 \\
3-y=0 \ \ \ |+y \\
y=3 \\ \\
(x,y)=(1,3)

The answer is B. one solution.
6 0
3 years ago
Polynomial expressions with matching​
yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0
3 years ago
Twenty percent of the town's population is over the age of 65. If there are 320 residents over the age of 65, what is the town's
alekssr [168]

Answer:

65

Step-by-step explanation:

I think. hope this hepls

5 0
3 years ago
Read 2 more answers
Supposed Blue spruce was included in the list and the mean decreased to 165 what is the height of the Blue spruce?
postnew [5]
The height of the blue spruce was 45.

We find the mean by adding all of the data points and dividing by the number of data points.  We will add the unknown value x and change the number we're dividing by to 7:

(160+320+100+110+200+220+x)/7 = 165
(1110+x)/7 = 165

Multiply both sides by 7:
1110 + x = 1155

Subtract 1110 from both sides:
x = 45
7 0
3 years ago
Read 2 more answers
Find 3 conservative numbers who's sum is 126
anygoal [31]
The 3 consecutive numbers are 41, 42, and 43 : 41+42+43= 126
6 0
3 years ago
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