If the point (x,square root 3/2) is on the unit circle, what. is x?

Answer: 83 degrees

Step-by-step explanation:

In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:

[tex]cos(x)=\frac{2}{16} =\frac{1}{8}[/tex]

[tex]arccos(cos(x))=arccos(\frac{1}{8} )=x[/tex]

Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:

[tex]x=arccos(\frac{1}{8} )[/tex]

[tex]x=83[/tex]

The expression of the unit rate was defined with all parameters rightly inputed the Molly's unit rate is 2.5 pages per minutes

Given Data

The speed/ rate is defined as the number of pages read per minutes passed

Hence the expression for the unit rate is given as

Unit Rate = Number of pages/Time Taken

Substituting our given Parameters

Unit Rate = 75/30

Unit Rate = 2.5 pages per minutes

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A function is a relation where there is only one output for every input. In other words for every x value, there is only one y value.

Example : Multiply by 3 is a very simple function.

Input : 0 Output : 0

Input : 1 Output : 3

Input : 2 Output : 6

Input : 3 Output :9

And so on!

Hope this helps!

Answer:

B.

Step-by-step explanation:

Using it's concept, it is found that there is a There is a 0.1667 = 16.67% probability that the sum is less than 8 if the pink die shows a number less than 4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the possible outcomes for the pair of dice are given by:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

We want to find the probability that the sum is less than 8 if the first die(the pink one) shows a number less than 4.

There are 18 total outcomes in which the pink die is less than 4, and in 3, the sum is less than 4, hence:

p = 3/18 = 1/6 = 0.1667.

There is a 0.1667 = 16.67% probability that the sum is less than 8 if the pink die shows a number less than 4.

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Answer:

1st option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{4}{5}[/tex] , then

y = - [tex]\frac{4}{5}[/tex] x + c

to find c substitute (5, 1 ) into the equation

1 = - 4 + c ⇒ c = 1 + 4 = 5

y = - [tex]\frac{4}{5}[/tex] x + 5 ( multiply through by 5 to clear the fraction )

5y = - 4x + 25 ( add 4x to both sides )

4x + 5y = 25 ← in standard form

- 6/17 = (-6) / 17 (2nde solution)

         = - (6/17) (4th solution)

         = 6/(-17) (last solution)

The expression that represents the volume of the prism, in cubic centimetres is [tex]28.476(2x+1) \: \rm cm^3[/tex] approx

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross section is same as its base, then its volume is:

[tex]V = B \times h[/tex]
where h is the height of that prism and B is the area of the base of that prism.

For this case, we are provided a prism which has pentagon as its cross sections, and its height is [tex]2x + 1[/tex] units.

Let B be the area of those pentagons, then:
Volume of the prism = [tex]B(2x + 1) \: \rm cm^3[/tex]

It is provided that the apothem of the pentagon is 2.8 cm.

An n sided regular polygon has internal angles' sum as 180(n-2)°

Thus, each internal angle would be of  180(n-2)/n°

For n = 5, this comes as 108°

Since the line AO is bisecting the internal angle, the angle OAB is o of 108/2 = 54°

Using the tangent ratio, we get:

[tex]\tan(54^\circ) = \dfrac{|OD|}{|AD|}\\\\|AD| = \dfrac{2.8}{\tan(54^\circ)} \approx 2.034 \: \rm cm[/tex]

Thus, area of the triangle AOD = [tex]\dfrac{1}{2} \times |AD| \times |OD| \approx \dfrac{1}{2} \times 2.034\times 2.8 = 2.8476 \: \rm cm^2[/tex]

There are 10 such triangles, all congruent, thus:

Area of pentagon = [tex]B \approx 10 \times 2.8476= 28.476 \: \rm cm^2[/tex]

Thus, volume of the pentagonal prism is:

[tex]V = B \times h \approx 28.476(2x+1) cm^3[/tex]

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Answer:

14x^2+7x

B

Step-by-step explanation:

I did the test.

Answer:

To find the volume of this figure, we must find the base area(pentagon) and multiply it by the figure's height.

Formula for area of a pentagon:-

A = 1/2 x p x a

Where 'p' represents the perimeter, and 'a' represents the apothem.

First, let's figure out the perimeter of the base pentagon.

One side of this pentagon is 10cm, and there are 5 side lengths of 10cm to this pentagon. So it'll result in (5 x 10) = 50cm altogether.

The apothem is given, 6.9cm.

So, we plug these into our formula:-

A = 1/2 x p x a

A = 1/2 x 50 x 6.9

A = 50/2 x 6.9

A = 25 x 6.9

A = 172.5cm, is the area of the pentagon.

Now we find the height of this figure and multiply it by the base area we've found(pentagon).

Our height is 17cm.

172.5(17)

= 2,932.5 cubic centimetres, is our volume.

Sales tax amount:-

Price:-

Answer:

$17,280

Step-by-step explanation:

Given

Solving :

For zeroes i.e for value(s) of q and s, the given equations must be equal to 0, so let's start with first equation and then 2nd equation ;

[tex]{:\implies \quad \sf 6q^{2}-17q+12=0}[/tex]

[tex]{:\implies \quad \sf 6q^{2}-9q-8q+12=0}[/tex]

[tex]{:\implies \quad \sf 3q(2q-3)-4(2q-3)=0}[/tex]

[tex]{:\implies \quad \sf (3q-4)(2q-3)=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:3q-4=0\:\:\:or\:\:\: 2q-3=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:3q=4\:\:\:or\:\:\:2q=3}[/tex]

[tex]{:\implies \quad \bf q=\dfrac{3}{2},\dfrac43}[/tex]

Now, turning to the second equation ;

[tex]{:\implies \quad \sf 8s^{2}+2s-15=0}[/tex]

[tex]{:\implies \quad \sf 8s^{2}+12s-10s-15=0}[/tex]

[tex]{:\implies \quad \sf 4s(2s+3)-5(2s+3)=0}[/tex]

[tex]{:\implies \quad \sf (4s-5)(2s+3)=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:4s-5=0\:\:\:or\:\:\: 2s+3=0}[/tex]

[tex]{:\implies \quad \sf Either\:\:4s=5\:\:\:or\:\:\:2s=-3}[/tex]

[tex]{:\implies \quad \bf s=\dfrac{5}{4},-\dfrac32}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

I am assuming you want to factor these expressions.

6q^2 - 17q + 12

We need 2 numbers whose product is (6*12) = 72 and whose sum is -17.

Theses are -9 and -8 so we write:

= 6q^2 - 9q - 8q + 12

= 3q(2q - 3) - 4(2q - 3)

= (3q - 4)(2q - 3)

If you want the solution of this expression = zero they are q = 4/3, 3/2.

8s^2 + 2s - 15

8 * -15 = -120.   -120 = -2 * 2 * 2 * 3 * 5 = +12 * -10 ( to give the +2s)

= 8s^2 + 12s - 10s - 15

= 4s(2s + 3) - 5(2s + 3)

= (4s - 5)(2s + 3)

If you want the solution of this expression = zero they are s = 5/4, -3/2.

Answer:

Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.

So he does 1/20 of the job per minute.

.

Rob can do the job in 30 min. His rate is 1/30 of the job per minute.

.

Working together how does it take?

.

1/20*x + 1/30*x = 1 job done

, where x = minutes.

.

Step-by-step explanation:

Answer:

Statements #1:  <L (congruent sign) <I

Statements #2: <H (congruent sign) <K

Statements #3: GH (congruent sign) MK

Reasons #2: given

Reasons #3: given

Reasons #4: angle angle side

The largest exponent is the degree.

this only has one exponent so the degree would be 3

Answer:

G

Step-by-step explanation:

The answer is statement G

Answer: 42.0

Step-by-step explanation:

Answer:

the answer is 1/2 the first one

Step-by-step explanation:

Because a dice has 6 sides, 3 of the numbers are odd so 3/6 and that is equal to 1/2 when simplified.

Answer:

gradient = 2

Step-by-step explanation:

calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 3) ← 2 points on the line

m = [tex]\frac{3-(-1)}{2-0}[/tex] = [tex]\frac{3+1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

1.) you're going to subtract 4 from 46

46-4= 42

7x=42

Then you divide 7 from 42 and get 6..........x=6

2.) you're going to do the same thing for this one

17-9=8

4x=8

8÷4=2

x=2

3.) you're going to do the same thing

1-1=0

2x=0

0÷2=0

x=0

Step-by-step explanation:

Hope this helps:)....if not then sorry for wasting your time and may God bless you:)

Answer:

35.4

Step-by-step explanation:

divide 72.8 by 6.5 to get the other two sides. Then you will have all four sides. From there you can add all four sides. 6.5 + 6.5 + 11.2 + 11.2 = 35.4. Hope that helps!

Answer:

(2, -1)

Step-by-step explanation:

x = 2, y = −1

Answer:

4.2

Step-by-step explanation:

The square root of 18 is 4.24

So, on this number line, it should go about 1 cm away from 4 to indicate that it is not 4, but 4.2.

Put the dot where you think it would be appropriate to be labled as 4.2.

Also if you didnt know the x axis is the one on the bottom.

Answer:

5a - 4b

Step-by-step explanation:

= 8a - 6b - 3a +2b

= 8a - 3a - 6b + 2b

= 5a - 4b

Hope it helps :)

Answer:

5a - 4b

Step-by-step explanation:

Answer:

y = m x + b     is the standard form of a straight line

m = (y2 - y1) / (x2 - x1) = (10 - (-8)) / (-3 - 0) = 18 / -3 = -6

When x = 0 y = b from the equation for a line

y = - 8

So our equation is  

y = -6 x - 8

As a check let x = -2 then

y = (-6 * -2) - 8 = 12 - 8 = 4

Check on the graph to verify that this equation holds

The distance between the two buildings is 844.23 feet apart, we go this answer by simply applying the SOH CAH TOA method

Given Data

Applying the SOH CAH TOA Approach we have

Tan  θ = Opp/Adj

Substituting our given data we have

Tan 35 = 400/x

0.4738 = 400/x

make x subject of the formula we have

x = 400/0.4738

x = 844.23 feet

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Answer:

Radius = 8 in

Area = πr2 = 3.14 x (8)2= 3.14 x (64)

Area = 201.1429 in²

Step-by-step explanation:

hope this helps if not please let me now

Answer:

a bit more than 48°

Step-by-step explanation:

We use the law of cosines for this.

The theorem is an extension of pythagoras' theorem, working for all triangles. In our case

[tex]\overline{BC}^2=\overline{AB}^2+\overline{AC}^2-2\overline{AB}\cdot\overline{AC}cos \hat A[/tex]

Let's replace all the values we have and find whatever is left.

[tex]10^2=11^2+13^2-2(11)(13)cos \hat A\\-286cos\hat A = -190\\cos \hat A\approx 0.6643 \rightarrow \hat A \approx 48\°[/tex]

A dot plot or for chart is a statistical plot consisting of data points that are plotted on a scale using dots.

Your information is incomplete. Therefore, an overview of a dot plot will be given. A dot plot is a data visualization where the day points are plotted as dots on the graph.

Dot plots are used for relatively small data sets. It uses the dots to show where the data values in the distribution are.

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Hope this helps!! :)