All categories

3 years ago

How do I solve this?

Mathematics

2 answers:

Fed [463]3 years ago

6 0

Hi there! Hopefully this helps!

------------------------------------------------------------------------------------------------------

<h2>Answer: $\boxed{\frac{6\sqrt{5} }{29} = 0.462634754 }$ </h2><h2 /><h2>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</h2>

$\frac{175-172}{\frac{29}{\sqrt{20} } }$

Subtract 172 from 175 to get 3.

$\frac{3}{\frac{29}{\sqrt{20} } }$ ≈ 0.462634754

Factor $20=2^{2} \times 5$ . Rewrite the square root of the product $\sqrt{2^{2} \times 5 }$ ≈ $4.472135955$ as the product of square roots $\sqrt{2^{2} } \sqrt{5}$ ≈ 4.472135955. Take the square root of $2^{2}$ ≈ $4$

$\frac{3}{\frac{29}{2\sqrt{5} } }$

Rationalize the denominator of $\frac{29}{2\sqrt{5} }$ ≈ $6.484597135$ by multiplying numerator and denominator by $\sqrt{5}$ ≈ $2.236067977.$

$\frac{3}{\frac{29\sqrt{5} }{2(\sqrt{5} )^{2} } }$

The square of $\sqrt{5}$ ≈ $2.236067977$ is 5.

$\frac{3}{\frac{29\sqrt{5} }{2 \times 5 } }$ ≈ $0.462634754$

Multiply 2 and 5 to get 10.

$\frac{3}{\frac{29\sqrt{5} }{10 } }$ ≈ $0.462634754$

Divide 3 by $\frac{29\sqrt{5} }{10}$ ≈ 6.484597135 by multiplying 3 by the reciprocal of $\frac{29\sqrt{5} }{10}$ ≈ $6.484597135.$

$\frac{3\times 10}{29\sqrt{5} }$ ≈ $0.462634754$

Rationalize the denominator of $\frac{3\times 10}{29\sqrt{5} }$ ≈ 0.462634754 by multiplying numerator and denominator by $\sqrt{5}$ ≈ $2.236067977.$

$\frac{3\times 10\sqrt{5} }{29(\sqrt{5})^{2} }$ ≈ $0.462634754$

The square of $\sqrt{5}$ ≈ $2.236067977$ is 5.

$\frac{3\times 10\sqrt{5} }{29 \times {5} }$ ≈ $0.462634754$

Multiply 3 and 10 to get 30.

$\frac{30\sqrt{5} }{29 \times {5} }$ ≈ $0.462634754$

Multiply 29 and 5 to get 145.

$\frac{30\sqrt{5} }{145 }$ ≈ $0.462634754$

<h2>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</h2><h2>Divide $30\sqrt{5}$ ≈ $67.082039325$ by 145 to get, you guessed it, $\frac{6}{29}\sqrt{5}$ ≈ $0.462634754.$ </h2>

Jet001 [13]3 years ago

6 0

$\frac{175-172}{\frac{29 }{\sqrt{20} } } = \frac{3}{\frac{29}{\sqrt{20} } } =\frac{3\sqrt{20} }{29}=\boxed{\frac{6\sqrt{5} }{29} } = \boxed{0.463}$

Refer to the attached image for further explanation:

You might be interested in

Question down below thanks

lara [203]

Answer:

-x + 1 > 3, and 4x + 6 < -2

Step-by-step explanation:

The inequality reads x < -2, so the arrow follows any values that are less than -2. So we need to simplify each inequality in the following options to see which match x < -2.

-4x+3> -5 simplifies to x < 2 so it's wrong

-2x + 4 > -4 simplifies to x < 4 so it's wrong

-x + 1 > 3 simplifies to x < -2, so it's right

2x + 5 < -3 simplifies to x < -4, so it's wrong

4x+ 6 < -2 simplifies to x < -2, so it's right

7 0

3 years ago

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or an 8? Round to nea

Viktor [21]

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

$P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}$

$=\dfrac{10}{21}\approx0.476$

Hence, the required probability =0.476

7 0

3 years ago

Is shaman123456 gaysexual

seropon [69]

No. because he just isnt

5 0

3 years ago

A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr

seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

$Perimeter = a\sqrt{2} + b\sqrt{10}$

Required

$a + b$

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$(x_1,y_1) = A(0,1)$

$(x_2,y_2) = B(3,4)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}$

$AB = \sqrt{( - 3)^2 + (-3)^2}$

$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

$AB = \sqrt{9*2}$

$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}$

$BC = \sqrt{(-1)^2 + (1)^2}$

$BC = \sqrt{1 + 1}$

$BC = \sqrt{2}$

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}$

$CD = \sqrt{(1)^2 + (3)^2}$

$CD = \sqrt{1 + 9}$

$CD = \sqrt{10}$

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

$(x_2,y_2) = A (0,1)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}$

$DA = \sqrt{(3)^2 + (- 1)^2}$

$DA = \sqrt{9 + 1}$

$DA = \sqrt{10}$

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

$Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}$

$Perimeter = 4\sqrt{2} + 2\sqrt{10}$

Recall that

$Perimeter = a\sqrt{2} + b\sqrt{10}$

This implies that

$a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}$

By comparison

$a\sqrt{2} = 4\sqrt{2}$

Divide both sides by $\sqrt{2}$

$a = 4$

By comparison

$b\sqrt{10} = 2\sqrt{10}$

Divide both sides by $\sqrt{10}$

$b = 2$

Hence,

a + b = 2 + 10

a + b = 12

3 0

3 years ago

What term refers to common, non-rechargeable batteries?

kiruha [24]

Answer:

Lithium

Explanation:

Lithium batteries features primary cell construction.They are single-use or non rechargeable batteries

6 0

1 year ago