Express 0.16 bar as a rational number

Answer:

Solution given;

Cos (x-[tex]\frac{5}{6}[/tex])=[tex]\frac{\sqrt{2} }{2}[/tex]

Cos (x-[tex]\frac{5}{6}[/tex])=Cos45°

equating corresponding value

(x-[tex]\frac{5}{6}[/tex])=45°

x=45°+5/6

x=45.83°

Answer:

Step-by-step explanation:

Equation of circle: (x - h)² + (y - k)² = r²   where (h,k) is the center.

Center( -4 , 4) and r = 5

(x -[-4])² + (y - 4)²= 5²

(x + 4)² + (y-4)² = 25

x²  + 2*4*x +4²  + y²  - 2*y*4 + 4²  = 25

x²  +8x + 16 + y²  - 8y + 16 = 25

x²  + 8x + y²  - 8y + 16 + 16 -25 = 0

x²  + 8x + y²  - 8y +7 = 0

We have that the an equation of a circle given the center (-4,4) and radius r=5  is mathematically given as

(x-4)^2+(y-4)^2=5^2

Question Parameters:

Given the center (-4,4) and radius r=5

Generally the equation for the Equation of a circle   is mathematically given as

(x-x')^2+(y-y')^2=r^2

Therefore, The resultant equation will be

(x-x')^2+(y-y')^2=r^2

(x-4)^2+(y-4)^2=5^2

Hence,an equation of a circle given the center (-4,4) and radius r=5 is

(x-4)^2+(y-4)^2=5^2

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Answer:

Step-by-step explanation:

None

They are both imaginary or complex. You can check that out by calculating the discriminate. If you get a minus answer, then there are no real roots. Let's try it.

a = - 2

b = - 4

c = - 6

D = sqrt(b^2 - 4*a * c)

D = sqrt( (-4)^2 - 4*(-2)(-6)  )

D = sqrt( 16 - 48)

D = sqrt(-32) which is negative and there are no real roots.

Answer:

Let be a rational complex number of the form [tex]z = \frac{a + i\,b}{c + i\,d}[/tex], we proceed to show the procedure of resolution by algebraic means:

1) [tex]\frac{a + i\,b}{c + i\,d}[/tex]   Given.

2) [tex]\frac{a + i\,b}{c + i\,d} \cdot 1[/tex] Modulative property.

3) [tex]\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)[/tex]   Existence of additive inverse/Definition of division.

4) [tex]\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}[/tex]   [tex]\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}[/tex]  

5) [tex]\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}[/tex]  Distributive and commutative properties.

6) [tex]\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}[/tex] Distributive property.

7) [tex]\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}[/tex] Definition of power/Associative and commutative properties/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction.

8) [tex]\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}[/tex] Definition of imaginary number/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

Step-by-step explanation:

Let be a rational complex number of the form [tex]z = \frac{a + i\,b}{c + i\,d}[/tex], we proceed to show the procedure of resolution by algebraic means:

1) [tex]\frac{a + i\,b}{c + i\,d}[/tex]   Given.

2) [tex]\frac{a + i\,b}{c + i\,d} \cdot 1[/tex] Modulative property.

3) [tex]\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)[/tex]   Existence of additive inverse/Definition of division.

4) [tex]\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}[/tex]   [tex]\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}[/tex]  

5) [tex]\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}[/tex]  Distributive and commutative properties.

6) [tex]\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}[/tex] Distributive property.

7) [tex]\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}[/tex] Definition of power/Associative and commutative properties/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction.

8) [tex]\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}[/tex] Definition of imaginary number/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.

Answer:

It's D:5.3

Step-by-step explanation:

√28 =5.29

Round off therefore is 5.3

Answer:

10,596 cubic inches

Step-by-step explanation:

The shape of the prism with which the sand castle can be modelled = Square prism

The arrangement of the square prism = One on top of the other

The given height of each prism, h = 6 inches

The side length of the base of the bottom prism, s₄ = 30 inches

The side length of the base of the other prism = The side length of the base of the prism below each prism - 7 inches

Therefore;

The side length of a prism = 7 inches + The side length of the prism above it

Given that the side length of the base prism (The fourth prism), s₄ = 30 inches

The side length of the prism, directly above the base prism (The fourth prism), s₃ = (30 - 7) inches = 23 inches

The side length of the prism, directly above the third prism (The second prism), s₃ = (23 - 7) = 16 inches

The side length of the top most prism, s₁ = (16 - 7) inches = 9 inches

The volume of the sand castle, V = h × (s₄² + s₃² + s₂² + s₁²)

∴ V = 6 × (30² + 23² + 16² + 9²) = 10,596

The volume of the sand castle, V = 10,596 in.³

Heyo!

The volume of the sandcastle above is 10,596 cubic inches.

Hope this helps! If so, please lmk! Tysm and good luck guys!

Nice job on getting problem 1 correct.

=================================================

Problem 2

The double stem and leaf plot says we have the following data set for the men's side

Be careful to read the stem first, followed by the leaf (even though the leaf values are listed on the left side of the stem).

Notice how each row is a different stem (in this case, tens digit) to help make things more readable.

If we were to add up all of those values I listed above, then we should get the sum 2707. Divide this over n = 37 to get 2707/n = 2707/37 = 73.162 approximately. This rounds to 73 since your teacher wants you to round to the nearest whole point.

You'll do the same thing for the women's side. That data set is

Again, it's handy to break the scores up by stem or else you'll have a long string of scores to get lost in (or it's easier to get lost in).

Adding up those 37 scores should get you 2824 which then leads to a mean of 2824/n = 2824/37 = 76.324 approximately. This rounds to 76

=================================================

Problem 3

The range for the men is max - min = 98 - 53 = 45

The range for the women is max - min = 100 - 55 = 45

==================================================

Problem 4

It's strongly recommended to use a spreadsheet here. Let's focus on the men's data set.

The idea is to subtract each data value from the mean 73.162, and then square the result. So each term is of the form (x-mu)^2 where mu is the mean.

For example, the data value x = 53 on the men's side will lead to

(x-mu)^2 = (53 - 73.162)^2 = 406.506

We consider this a squared error value.

You'll do this with the remaining 36 other values in the men's data set.

After doing this, you'll add up the 37 items in this new column and you should get roughly 4711.027, and this is the sum of the squared errors (SSE).

Divide this over n = 37 and we get 4711.027/37 = 127.325

Lastly, apply the square root and we arrive at sqrt(127.325) = 11.284 which rounds to 11.28

The steps for the women's standard deviation will be the same. You should get 12.30

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

These are population standard deviation values. If you don't want to use a spreadsheet, a much better option is to use online calculators that specialize in population standard deviation.

1) The men's and women's team each played 37 games.

2) the mean score of men's and women's team is 73 and 76 approximately.

3) the range of men's and women's score is 45.

4)the standard deviation of men and women team 11 and 12 approximately.

Number of observations can be found by counting the observations.

Mean is the average of all observations. It is the sum product of observations divided by the number of observations.

The range of observations is the measure of spread. It is the highest value minus the lowest value.

The standard deviation is another measure of variability. It is the square root of variance, where variance is the sumproduct of observations minus the mean, divided by the number of observations.

The data set is given by:

Men's team

Women's team

1) Number of games each team played :

men's team = 37

women's team = 37

2)mean = [tex]\frac{sum \ of \ observations}{number \ of \ observations}[/tex]

men's team = [tex]\frac{2707}{37}[/tex] =  = 73.162

women's team = [tex]\frac{2824}{37}[/tex]  =  = 76.324

3)range =  highest observation - lowest observation

men's team = 98 - 53 = 45

women's team = 100 - 55 = 45

4)population standard deviation = [tex]\sqrt{ \frac{\sum (x-\bar x)^2}{n}}[/tex]

On using the formula :

men's team = [tex]\sqrt{\frac{4711.027}{37} } = \sqrt{127.325} = 11.284[/tex]

women's team = [tex]\sqrt{151.29}[/tex] = 12.3

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Answer:

(2x - 5)(3x + 1)

Step-by-step explanation:

Brainliest, please! (Almost an Ace)

1. Find the factors of 6x^2. (Either 2x and 3x, or 6x and 1x.)

2. Find the factors of -5. (Either -1 and 5, or 1 and 5.)

3. Set up 4 different pre-FOIL factored expressions.

4. Check and see which one works. It's (2x - 5)(3x + 1)

Answer:

x =10

y = 10 sqrt(3)/ 3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 60 = 5 sqrt(3) / x

x sin 60 = 5 sqrt(3)

x = 5 sqrt(3)/sin 60

x = 5 sqrt(3) / sqrt(3)/2

x = 5*2

x =10

tan theta = opp /adj

tan 60 = x/y

ytan 60 = 10

y = x/ tan 60

y = 10/ sqrt(3)

y = 10/ sqrt(3)  * sqrt(3)/ sqrt(3)

y = 10 sqrt(3)/ 3

There are 30 possible combinations of teachers.

Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:

To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.

Therefore, there are 30 possible combinations of teachers.

Learn more about combinations in https://brainly.com/question/24180105.

Answer:

C

Step-by-step explanation:

Answer:

59.5

Step-by-step explanation:

Half dozen = $4.25

Full Dozen = 2 X (4.25)

= 8.5

7 Dozens price = 7 X 8.5 =

= $59.5

Answered by Gauthmath

Answer:

1st option

1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2

Answered by GAUTHMATH

꙰  Hello there mohammedsaquibali45 ! My Name is ⚝Tobie⚝ and I'm glad you asked! Let me walk you step by step in order to comprehend the question better!   ꙰  

i

{x}^{2}-5x-10x+50

x

2

−5x−10x+50

ii Collect like terms.

{x}^{2}+(-5x-10x)+50

x

2

+(−5x−10x)+50

iii Simplify.

{x}^{2}-15x+50

x

2

−15x+50

(x - 10)(x - 5) = ...

= x^2 + (-10 + (-5))x + (-10•(-5))

= x^2 - 15x + 50

Answer:

the answer will be..

x=-1

x=4

(x+1) (x-4)

but im sorry i dunno what's lesser and greater means

Answer:

x = ¾-a

Step-by-step explanation:

x + a = ¾

Subtract a from each side

x + a -a= ¾-a

x = ¾-a

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]x+a=\dfrac{3}{4}\\\\x=\dfrac{3}{4}-a\\\\x=\dfrac{3-4a}{4}[/tex]

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

x=35/78

Step-by-step explanation:

3/2x-11/5=(7/8)*(64/49)

3/2x-11/5=8/7

3/2x=8/7+11/5

3/2x=117/35

x=(35*3)/(2*117)

x=35/78

Answer: 380.1

Step-by-step explanation:

The area of a circle is pi*r^2. So 11 times 11 is 121. Then multiply by pi. When multiplies by pi you get 380.132711084. rounded to the nearest tenth is 380.1.

Answer:

(-150, 45)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

My best guess from the graph is

(-150, 45)

Answer:

In science, a measurement is quantitative (in terms is which is heavier, lighter, fast, slow and all) or numerical data(numbers like 1m,1cm) that describes a property of an object or event.

Answer:

if the diameter is 11, them the answer is 47.52275cm

Step-by-step explanation:

[tex] \sqrt[6]{5} \times \sqrt[2]{5} [/tex]

[tex] = {5}^{ \frac{1}{6} } \times {5}^{ \frac{1}{2} } [/tex]

[tex] = {5}^{ \frac{1}{6} + \frac{1}{2} } [/tex]

[tex] = {5}^{ \frac{1 + 3}{6} } [/tex]

[tex] = {5}^{ \frac{4}{6} } [/tex]

[tex] = {5}^{ \frac{2}{3} } [/tex]

[tex] = \sqrt[3]{ {5}^{2} } (ans)[/tex]

Answer:

max: -4

Step-by-step explanation:

(x+3)^2 》0 mọi x

<=> -(x+3)^2 《0

<=> -(x+3)^2 -4 《 -4

Step-by-step explanation:

Given that,

We have to find the value of m∠E.

Here, two sides are equal, thus it is an isosceles triangle. As the two sides are equal, so their angles must be equal. So, ∠E and ∠D will be equal. Let us assume the measures of both ∠E and ∠D as x.

→ Sum of all the interior angles of ∆ = 180°

→ ∠E + ∠D + ∠F = 180°

→ 116° + x + x = 180°

→ 2x = 180° – 116°

→ 2x = 64°

→ x = 64° ÷ 2

→ x = 32°

Henceforth,

→ m∠E = x

→ m∠E = 32°

[tex] \\ [/tex]

~

Answer:

Step-by-step explanation:

xa+yb=c

xb+yc=a

xc+ya=b

add

x(a+b+c)+y(a+b+c)=a+b+c

x+y=1 ... (1)

xac+ybc=c²

xab+yac=a²

xbc+yab=b²

add

x(ab+bc+ca)+y(ab+bc+ca)=a²+b²+c²

[tex]x+y=\frac{a^2+b^2+c^2}{ab+bc+ca} \\\frac{a^2+b^2+c^2}{ab+bc+ca} =1\\a^2+b^2+c^2=ab+bc+ca\\a^2+b^2+c^2-ab-bc-ca=0\\a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=(a+b+c)(0)=0\\a^3+b^3+c^3=3abc\\\frac{a^3}{abc} +\frac{b^3}{abc} +\frac{c^3}{abc} =3\\\frac{a^2}{bc} +\frac{b^2}{ca} +\frac{c^2}{ab} =3[/tex]

Answer:

<2 = 34degrees

Step-by-step explanation:

Find the diagram attached below:

First we need to get <1;

<1 + 74 = 180 (angle on a straight line)

<1 = 180 - 74

<1 = 106degrees

Also, <1 + <2 + 40 = 180 (sum of angle in a triangle)

106+<2 + 40 = 180

146 + <2 = 180

<2 = 180-146

<2 = 34degrees

Answer:

34 its the right answer

Step-by-step explanation:

Answer: No solutions

Step-by-step explanation:

[tex]\large \bf \boldsymbol{ \boxed{\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b} }} \\\\\\ \sqrt{25x+75} +3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9x-18} \\\\ \sqrt{25} \cdot \sqrt{x+3}+3\sqrt{x-2} =2+4\sqrt{x-3} +\sqrt{9}\cdot \sqrt{x-2} \\\\5\sqrt{x+3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \ \ =2 +4\sqrt{x-3} +3\sqrt{x-2} \!\!\!\!\!\!\!\!\!\!\bigg{/} \\\\(5\sqrt{x+3})^2 =(2+4\sqrt{x-3} )^2 \\\\ \ \ \ let \ \ t=x+3 \ \ ; \ \ \ t-6=x-3 \\\\ \big(5\sqrt{t} \ \big)^2=(2+\sqrt{t-6} )^2 \\\\[/tex]                                   [tex]\large \boldsymbol{} \bf 25t=4+16\sqrt{t-6} +16(t-6) \\\\(9t+92)^2=(16\sqrt{t-6} )^2 \\\\81t^2+1656t+8464=256(t-6)\\\\81t^2+1400t+10000=0 \\\\ D=1400^2-324000=-128000=> \\\\D<0 \ \ no \ \ solutions[/tex]

Answer: 14

Step-by-step explanation:

If they hit the ball 4/8 times, that equals 1/2, so we just multiply 1/2 (or 0.5) by 28 and you get 14 :)

Answer:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]