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NeTakaya
3 years ago
5

Please solve and show work! Thanks!

Mathematics
1 answer:
Mrac [35]3 years ago
6 0

Answer:

6⅔ minutes

Or, 6 minutes 40 seconds

Step-by-step explanation:

X/10 + X/20 = X/T

(2X+X)/20 = X/T

3X/20 = X/T

3/20 = 1/T

T = 20/3

T = 6⅔ mins

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Using the Extended Euclidean Algorithm, find integers x and y such that 26x + 9y = 1.
Xelga [282]

Answer:

The solution is: x=-1 and y=3.

Step-by-step explanation:

Let's find the solution, but first let's remember the following:

A / B = C + R where:

A=dividend, B=divisor, C=quotient, and R=remainder. This can be express as follows:

A = (C * B) + R, which is the structure we are going to use next.

Using the Euclidian Algorithm we need to find the highst common factor (HCF) between the coefficients from your equation, this means:

The original equation: 26x+9y=1 is in the form Ax+By=C, so A=26, B=9 and C=1.

We need to find the HCF of 'A' and 'B'. Using the Euclidan Algorithm (EA), so we have:

A = (C * B) + R, using our values:

26 = (2 * 9) + 8, look that the divisor (B) is 9 and the remainder (R) is 8.

Now using the (EA) we divide the divisor (B=9) by the obtained remainder (R=8). And we do the same for each obtained result until the las remainder (R) is equal to 0, like this:

A = (C * B) + R

9 = (8 * 1) + 1

using the divisor (B=8) and the remainder (R=1) we obtain:

A = (C * B) + R

8 = (1 * 8) + 0, look that the remainder is now 0, so in summary we can use the method as follows:

26 = (2 * 9) + 8

9 = (8 * 1) + 1

8 = (1 * 8) + 0; and this equations are the ones we are going to use in order to find a solution.

Next step is to use the equation before R=0, so:

9 = (8 * 1) + 1, which is:

9 - (8 * 1) = 1; but if you consider the first obtained equation: 26 = (2 * 9) + 8, we can write:

26 - (2 * 9) = 8, and we can use this expression in the previous one, so:

9 - (8 * 1) = 1, is:

9 - ((26 - (2 * 9)) * 1) = 1, simplifying:

9 - 26 + (2*9) = 1

9 - 26 + (9 + 9) = 1

-26 + (9 + 9 + 9) = 1

-26 + (3 * 9) = 1

26*(-1) + 9*(3) = 1; if you compare the last expression with the original equation, which is: 26x+9y=1, you can see the similarity, where x=-1 and y=3.

So, the solution is: x=-1 and y=3.

8 0
3 years ago
6. Mrs. Martinez graphed the transformation shown below. Which algebraic representation shows the effect of the transformation o
iragen [17]

Answer:

C)

Step-by-step explanation:

3 0
2 years ago
Which quadrant does the coordinate (-8, 12) lie?
marysya [2.9K]
In quadrant 2 is where it lies.
3 0
2 years ago
"isotherms are drawn at regular intervals; on this map, the interval between successive isotherms is ______ fahrenheit degrees."
Marizza181 [45]

An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.

 

Basing from the graph, we can actually see that the interval is:

 

10 <span>Fahrenheit degrees</span>

6 0
3 years ago
The ratio of the measures of the three angles in a tangle 3107. Find the measures of the angles and write them in size order,
N76 [4]

Answer:

27, 90 and 63

Step-by-step explanation:

Given

Ratio of triangle sides

Ratio = 3 : 10 : 7

Required:

The length of each side

Triangles in a triangle add up to 180.

The side with ratio 3 is:

S_1 = \frac{3}{3 + 10 + 7} *180

S_1 = \frac{3 *180}{20}

S_1 = \frac{540}{20}

S_1 = 27

The side with ratio 10 is:

S_2 = \frac{10}{3 + 10 + 7} *180

S_2 = \frac{10 *180}{20}

S_2 = \frac{1800}{20}

S_2 = 90

Lastly:

The side with 7 as its ratio

S_3 = \frac{7}{3 + 10 + 7} *180

S_3 = \frac{7 *180}{20}

S_3 = \frac{1260}{20}

S_3 = 63

Hence, the angles are: 27, 90 and 63

5 0
3 years ago
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