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3 years ago

Find the exponential form of 8/27

Mathematics

1 answer:

love history [14]3 years ago

6 0

<h3>Answer: (2/3)^3</h3>

Explanation:

Note how 8 = 2^3 and 27 = 3^3

This means, 8/27 = (2^3)/(3^3) = (2/3)^3

For the last step, I used the rule (a^c)/(b^c) = (a/b)^c

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A triangle has an angle that measures 95°. The other two angles are in a ratio of 3:14. What are the measures of those two angle

Marta_Voda [28]

Answer: 15° and 70°

Step-by-step explanation:

The sum of angles of a triangle is 180.

One of the angle is given to be 95°, this means that the sum of the remaining two angles will be ;

180 - 95 = 85°

The ratio of the two sides is given to be 3 : 14

Calculating the angles of each ,the angle with the ratio 3 will be

3/17 x 85 = 15°

The angle with the ratio 14 will be

14/17 x 85 = 70°

Therefore : the measures of the two angles are : 15° and 70°

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3 years ago

(3x - 15)° 0 + 25) 105° Find the value of a Ox=35 O x 40 O x = 60 * = 65

timurjin [86]

X=40 degree is the correct answer

5 0

3 years ago

The hypotenuse of a right angled triangle is 2√13 cm . If the smaller side is increased by 2 cm and the larger side is increased

White raven [17]

Statement:

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

To find out:

The length of the larger side of the right angled triangle.

Solution:

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = $\frac {(52 - 6y)}{4}$ ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, $\frac {(2704-624y +36y²)}{16}$ + y² = 52

or, $\frac {(2704-624y +36y² + 16y²)}{16}$ = 52

or, 52y²-624y + 2704 = 52 × 16

or, 52y² - 624y + 2704 - 832 = 0

or, 52y² - 624y + 1872 = 0

or, 52(y² - 12y + 36) = 0

or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

Answer:

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0

2 years ago

Convert the following measurements into

Andre45 [30]

Answer:

1) 1076.4ft^2

2). 6561.68ft

3). 2.057kg

4). 1.25×10^-1

5). 6.58×10^1km

6). 278mg

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3 years ago

-4x-10x simplify the expression

n200080 [17]

Answer:

= -14x

Step-by-step explanation:

Since the equation is saying to subtract 10x, we are going to change the minus sign to a addition sign and change positive 10 to negative and continue the rest.

4 0

3 years ago

Read 2 more answers

Find the exponential form of 8/27​

Find the exponential form of 8/27