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Gennadij [26K]
3 years ago
11

Rationalise the denominator as per necessary and simplify.​

Mathematics
1 answer:
Minchanka [31]3 years ago
8 0

Answer:

8\sqrt{7}

Step-by-step explanation:

\frac{21}{\sqrt{7}  }  * \frac{\sqrt{7}  }{\sqrt{7}  } = \frac{21\sqrt{7} }{7}

\frac{21\sqrt{7} }{7} = \frac{147\sqrt{7} }{14}

\frac{147\sqrt{7} }{14} - \frac{35\sqrt{7} }{14}

\frac{112\sqrt{7} }{14}

8\sqrt{7}

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Problem PageQuestion Flying against the jetstream, a jet travels 3050 miles in 5 hours. Flying with the jetstream, the same jet
goblinko [34]

Answer: the rate of the jet in still air is 685 mph and the rate of the jetstream is 75 mph

Step-by-step explanation:

Let x represent the rate of the jet in still air.

Let y represent the rate of the jet jetstream.

Distance = speed × time

Flying against the jetstream, a jet travels 3050 miles in 5 hours. This means that the total speed of the jet would be (x - y) mph. Therefore,

3050 = 5(x - y)

3050/5 = x - y

x - y = 610 - - - - - - - - - - - - - -1

Flying with the jetstream, the same jet travels 3800 miles in 4 hours. This means that the total speed of the jet would be (x + y) mph. Therefore,

3800 = 4(x + y)

3800/5 = x + y

x + y = 760 - - - - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

2x = 1370

x = 1370/2 = 685mph

Substituting x = 685 into equation 1, it becomes

685 - y = 610

y = 685 - 610 = 75mph

3 0
3 years ago
The number of patients treated at Dr. McCormick’s dentist office each day was recorded for nine days. These are the data: 13, 16
NARA [144]
First, lets sort the list from smallest to greatest. This will help with median, mode, and range.

4, 6, 10, 12, 12, 13, 16, 16, 16

Next, lets find the mean. Mean is found by adding all numbers up, then dividing them by the number of entries in the data set.

4+6+10+12+12+13+16+16+16 = 105
105 / 9 = 11.7

So the mean is 11.7.

Next, we'll find the median. The median is the value in the center of the list. Because there are 9 values, that means the center of the list is 5 with four numbers on each side of it. The 5th number in the list is 12, so that's our median.

Continuing, the mode is the number or numbers that appears the most often. For this data set, 16 appears 3 times while all other numbers appear 2 times or less. So, the mode is 16.

Lastly, the range is the difference between the largest number and the smallest number.

16 - 4 = 12

So the range is 12.

The second answer in the list matches all of these values, and is the correct solution.
7 0
3 years ago
Read 2 more answers
Fine slope intercept form <br> y = x+7 (2, 3)<br> Help please and thanks
Dimas [21]

Answer:

y=x7 X 5

Step-by-step explanation:

6 0
3 years ago
BRAINLIEST TO WHOEVER HELPS IM DESPERATE PLZ :). Winston is creating a rectangular piece of 8-bit art using squares that are x p
Furkat [3]

Answer:  a(x) = x^2 + 40 x + 384

Step-by-step explanation:

Since, here the length of the rectangle is represented by the function l(x) = x + 24,

While the breadth of the rectangle is represented by the function w(x) = x + 16.

And, we know that the area of the rectangle = length of the rectangle l(x) × breadth of the rectangle.

a(x) = l(x) × w(x)

a(x) = (x + 24) × (x + 16)

a(x) = x^2 + 24 x + 16 x + 24\times 16

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4 0
4 years ago
Read 2 more answers
Find the area of the shaded region.
Ghella [55]
This is a rhombus and in any rhombus, the diagonals intersects in the middle and they are perpendicular:
So all 4 triangles are right triangles and the sides are the hypotenuses.
1st) Calculate the sides: hypotenuse² = 3² + 4² = 25, and hypotenuse = 5

The area of each right triangle is (4 x 3)/2 = 6 units²
And the area of the 4 right triangles = 4 x 6 = 24 init²

4 0
3 years ago
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