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3 years ago

Is 61% a rational number

Mathematics

1 answer:

vovikov84 [41]3 years ago

7 0

Answer: No

Step-by-step explanation: It is irrational because 61 is a prime number.

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Simplify.

sertanlavr [38]

Answer:

A=64d B=27d C=24d D=20d

easy Pasy

4 0

2 years ago

Radical functions. please help me!

Sphinxa [80]

These are 8 questions and 8 answers:

1) Quesion 1:

9+√2
---------
4 - √7

Answer: the third option:

36 + 9√7 + 4√2 + √14
-----------------------------
9

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 - √7 = 4 + √7

=>

$\frac{9+ \sqrt{2} }{4- \sqrt{7} } . \frac{4+ \sqrt{7} }{4+ \sqrt{7} } = \frac{(9)(4)+9 \sqrt{7}+4 \sqrt{2} + \sqrt{2} . \sqrt{7} }{(4)^2-( \sqrt{7})^2 } =$

$= \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{16-7}$

2) Question 2: sum

$5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})$

Answer: fourth option

$7x( \sqrt[3]{x^2y} )$

Explanation:

Take x^5 out of the second radical which will result in a like term of the first radical:

$5x( \sqrt[3]{x^2y} )+2( \sqrt[3]{x^5y}) =5x( \sqrt[3]{x^2y} )+2x( \sqrt[3]{x^2y})=7x( \sqrt[3]{x^2y})$

which is the fourth option

3) Question 3. Which expression is equivalent to:

$\frac{ \sqrt{10} }{ \sqrt[4]{8} }$

Answer: the first option

Explanation

$\frac{ \sqrt{10} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{10^2} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{100} }{ \sqrt[4]{8} } . \frac{ \sqrt[4]{8^3} }{ \sqrt[4]{8^3} } = \frac{ \sqrt[4]{(100)(512)} }{8} = \frac{ \sqrt[4]{51200} }{8} = \frac{4 \sqrt[4]{200} }{8} = \frac{ \sqrt[4]{200} }{2}$

4) Question 4 What is the simplest form?

Answer: the second option

Explanation:

$\sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y}$

5) Question 5 Product

Answer: the fourth option:

$104x^4+16x^4 \sqrt{30} [/tex]\\Explanation:\\Use the square of a binomial product: (a + b)^2 = a^2 + 2ab + b^2\\[tex](4x \sqrt{5x^2} )^2+2(4x \sqrt{5x^2})(2x^2 \sqrt{6}) +(2x^2 \sqrt{6} )^2=$

$=16x^2(5x^2)+16x^4( \sqrt{30} )+4x^4(6)=80x^4+16x^4 \sqrt{30} +24x^4=$

$=104x^4+16x^4 \sqrt{30}$

which is the fourth option.

6) Question 6 Product

Answer: fourth option

Explanation:

$\sqrt[3]{16x^7} . \sqrt[3]{12x^9} = \sqrt[3]{2^4.2^2.3x^7x^9} = \sqrt[3]{2^6.3.x^{16}}=2^2 x^5 \sqrt[3]{3x} =4 x^5\sqrt[3]{3x}$

which is the fourth option.

7) Question 7. Simplified form of 2√18 + 3√2 + √162

Answer: 18√2

Explanation:

$2 \sqrt{18}+3 \sqrt{2} + \sqrt{162}=2(3) \sqrt{2} + 3 \sqrt{2} +9 \sqrt{2} =18 \sqrt{2}$

which is the second option.

8) Question 8 which function is undefined for x = 0.

Answer: second option y = √ (x - 2)

Explanation.

The square root function is not defined for negative values.

When x = 0, x - 2 = -2, whose square root is not defined.

Therefore, the square root of x - 2 is not defined for x = 0.

5 0

4 years ago

Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters t

SashulF [63]

Answer:

Cliff is 45 m tall.

Step-by-step explanation:

Given:

Height of Sarah = 1.8 m

Angle of elevation = 60°

Angle of elevation 50 m back = 30°

As shown in the figure we have two right angled triangles SPQ and SPR.

Let the height of the cliff be $h$ meters and $h= h_1+h_s$ .

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ. In ΔSPR.

⇒ $tan(60) = \frac{h_1}{x}$ ...equation (i) ⇒ $tan (30)=\frac{h_1}{x+50}$ ...equation (ii)

Dividing equation (i) and (ii)

⇒ $\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}$

⇒ $3 = \frac{x+50}{x}$

⇒ $3x=x+50$

⇒ $3x-x=50$

⇒ $2x=50$

⇒ $x=\frac{50}{2}$

⇒ $x=25$ meters

To find $h_1$ plugging $x=25$ in equation (i)

⇒ $h_1=x\times tan(60)$

⇒ $h_1=25\times 1.73$

⇒ $h_1=43.25$ meters

The height of the cliff from ground :

⇒ $h= h_1+h_s$

⇒ $h= 43.25+1.8$

⇒ $h=45.05$ meters

The cliff is 45 m tall to the nearest meter.

8 0

4 years ago

13. f(x) = x^4<br> - 9x2 -22x - 24

Anna007 [38]

Answer:

x = 4 or x = -2

Step-by-step explanation:

Solve for x over the real numbers:

x^4 - 9 x^2 - 22 x - 24 = 0

The left hand side factors into a product with three terms:

(x - 4) (x + 2) (x^2 + 2 x + 3) = 0

Split into three equations:

x - 4 = 0 or x + 2 = 0 or x^2 + 2 x + 3 = 0

Add 4 to both sides:

x = 4 or x + 2 = 0 or x^2 + 2 x + 3 = 0

Subtract 2 from both sides:

x = 4 or x = -2 or x^2 + 2 x + 3 = 0

Subtract 3 from both sides:

x = 4 or x = -2 or x^2 + 2 x = -3

Add 1 to both sides:

x = 4 or x = -2 or x^2 + 2 x + 1 = -2

Write the left hand side as a square:

x = 4 or x = -2 or (x + 1)^2 = -2

(x + 1)^2 = -2 has no solution since for all x on the real line, (x + 1)^2 >=0 and -2<0:

Answer: x = 4 or x = -2

3 0

3 years ago

The excavation for a house and the trucks to carry away the material have the dimensions shown. About how many level truck loads

Inessa05 [86]

Answer:

<h3>This means that about 21 level truck loads are necessary to remove all dirts.</h3>

Step-by-step explanation:

To get the number of level truck loads needed to remove all the dirts in the house, first we need to calculate volume of the truck and the house.

Volume of truck = Length * Breadth * Height

If the truck is 5.0 for the length 2.0 for the height 3.0 for the side base;

Volume of the truck = 5*2*3

Volume of truck = 30

For the house;

Volume of house = Length * Breadth * Height

If the house is 4.0 for the height 14.5 for the length and 11.0 for the side base, then

Volume of the house = 4*14.5*11 = 638

Number of level truck loads needed to remove all the dirts = Volume of house/Volume of the truck = 638/30 ≈ 21.3

This means that about 21 level truck loads are necessary to remove all dirts.

8 0

3 years ago

Is 61% a rational number​

Is 61% a rational number