If a randomly thrown dart hits the board below, what is the probability it will hit the shaded region?​

Answer:

x = √3

Step-by-step explanation:

Find the diagram attached

Given

Opposite = √3

Adjacent = x

Acute angle theta = 45degrees

According to SOH CAH TOA;

tan theta = opp/adj

tan 45 = √3/x

x = √3/tan45

x = 1

x = √3

Hence the value of x in its simplest radical form is √3

Answer:

[tex]x=\frac{1+\sqrt{41}}{5},\\x=\frac{1-\sqrt{41}}{5}[/tex]

Step-by-step explanation:

The quadratic formula states that the solutions for a quadratic is standard form [tex]ax^2+bx+c[/tex] are equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

In [tex]5x^2-2x-8=0[/tex], we can assign the values:

Thus, we have:

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(5)(-8)}}{2(5)},\\x=\frac{2\pm \sqrt{164}}{10},\\\begin{cases}x=\frac{2+ \sqrt{164}}{10}, x=\frac{1}{5}+\frac{\sqrt{41}}{5}=\frac{1+\sqrt{41}}{5}\\x=\frac{2- \sqrt{164}}{10}, x=\frac{1}{5}-\frac{\sqrt{41}}{5}=\frac{1-\sqrt{41}}{5}\end{cases}[/tex]

Answer:

(1+√41)/5, (1-√41)/5

Step-by-step explanation:

quadratic formula is (-b±√(b^2-4ac))/2a

in this equation,

a = 5

b = -2

c = -8

plug in the values

(2±√(4 - 4(5)(-8))/10

(2±√(4 + 160)/10

(2±√(164)/10

(2±2√(41))/10

1. (2+2√41)/10

(1+√41)/5

2. (2-2√41)/10

(1-√41)/5

Answer:

60

Step-by-step explanation:

Note that angle ZXY is the bisected angle which was split into angle 1 and 2

Also note that bisectors split angles into to separate congruent angles ( So if angle ZXY was bisected into angle 1 and angle 2 then angle 1 = angle 2 )

If angle 2 = 30 then angle 1 also = 30

Like stated multiple times angle ZXY is made up of angle 1 and 2

Hence, Angle ZXY = Angle 1 + Angle 2

Angle ZXY = 30 + 30 = 60

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { C) \:7 + 4 \sqrt{3}}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {( - 2 - \sqrt{3} )}^{2} [/tex]

[tex] = ({ - 2})^{2} - 2.( - 2). \sqrt{3} + { (\sqrt{3}) }^{2} [/tex]

[tex] = 4 + 4 \sqrt{3} + 3[/tex]

[tex] = 7 + 4 \sqrt{3} [/tex]

[tex] ({a - b})^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]

[tex] \sqrt{a} \times \sqrt{a} = a[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

5/36

Step-by-step explanation:

There are 12 tiles

P( blue) = blue /total = 5/12

We put the first tile back so there are still 12 tiles in the bag

P(yellow) = yellow/total = 4/12 = 1/3

P( blue, yellow) = 5/12 * 1/3 = 5/36

You Have Passed Thy Test!!! BADAAAA (\•o•/)

Answer:

b

Step-by-step explanation:

it's right cause I took the quix

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

Work Shown:

Rise = -3

Run = 2

Slope = rise/run = -3/2 = -1.5

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

Notes:

Answer:

m = - 3 / 2

Rise : -3

Run : 2

Step-by-step explanation:

According to the picture,

first coordinate : ( 2 , 1 )

second coordinate : ( 4 , - 2 )

Formulae : m=(y2-y1)/(x2-x1)

Substituting,

m = ( - 2 - 1 ) / ( 4 - 2 )

m = - 3 / 2

If this helps you, please mark brainliest!

Answer:

angle x= 60

so it is in the ratio 1:2:√3

√3x=3

ie.x=√3/3

adjacent side=x=√3/4

Step-by-step explanation:

everything can be found in the picture

Answer:

answer to the question is 10 units..

Answer:

10 units

Step-by-step explanation:

(0 , 6) = (x1 , y1)

(8 , 0) = (x2 , y2)

distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

=[tex]\sqrt{(8 - 0)^2 + (0 - 6)^2}[/tex]

=[tex]\sqrt{8^2 + (-6)^2}[/tex]

=[tex]\sqrt{64 + 36}[/tex]

=[tex]\sqrt{100}[/tex]

=10 units

Answer:

Domain { -13,12,20 }

Step-by-step explanation:

The domain is the input values

Domain { -13,12,20 }

We list them in order from smallest to largest and do not list repeats

Answer:

D

Step-by-step explanation:     Time Stamp (6  9  10  32)

Easiest way is to graph both equation and look for the intersections  see attached sreen shot

or  solve by substitution

y = 2x

y = x²- 8

2x = x²- 8                  solve for x

0  = x² - 2x - 8          factor

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

0 = 0   when x = 4 and -2      

calculate the y values

y = 2x      x = 4

y = 8                              (4, 8)

y = 2x      x = -2

y = -4                            (-2, -4)

The base is 5 units and the height is 4 units.

Hope this helps! :)

Answer:

Step-by-step explanation:

Tangent from the point outside the circle are equal

WX  = XY

7x - 29 = 2x + 16 {Add 29 to both sides}

7x  = 2x + 16 +29

7x = 2x + 45 {Subtract 2x from both sides}

7x - 2x = 45

5x = 45     {Divide both sides by 5}

x = 45/5

x = 9

WX = 7x - 29

       = 7*9 - 29

        = 63 - 29

WX = 34

Answer:

y = [tex]\sqrt{x-5}[/tex]

This is the correct answer because I got it right.

Answer:

three trillion four hundred and sixty eight million, seven hundred and twenty nine thousand and one hundred sixty five

Step-by-step explanation:

Answer:

7.61 miles

Step-by-step explanation:

Given that,

Haley hikes 3 miles north and 7 miles east.

We need to find the shortest distance from the campground to the waterfall. Let the distance is D.

It can be calculated as follows :

[tex]D=\sqrt{3^2+7^2}\\D=7.61\ miles[/tex]

So, the shortest distance from the campground to the waterfall is 7.61 miles.

Answer:

The author sold a total of 30240 books following this trend.

Step-by-step explanation:

Let's find 5% of 14400 first;

14400 * 5%

14400 * 5/100

144 * 5

720 (So now we know that they are decreasing by 720 each month; therefore thats the constant)

=> aₙ = a₁ + r(n - 1)

=> a₂₃ = 14400 + 720(23 - 1)

=> a₂₃ = 14400 + 720(22)

=> a₂₃ = 14400 + 15840

=> a₂₃ = 30240

Hope this helps!

The author sold a total of 30240 books following this trend.

Let's find 5% of 14400 first;

[tex]14400 * 5\%\\14400 * 5/100\\144 * 5=720[/tex]

A, is a type of numerical sequence studied by Mathematics, where each term or element counting from the second is equal to the sum of the previous term with a constant.

So using the arithmetic progression we have:

[tex]a_n = a_1 + r(n - 1)\\a_{23} = 14400 + 720(23 - 1)\\ a_{23} = 14400 + 720(22)\\ a_{23} = 14400 + 15840\\a_{23} = 30240[/tex]

See more about arithmetic progression at brainly.com/question/20385181

Median is the middle value.

Writing the values from smallest to largest you have :

1/8, 1/8, 2/8, 2/8, 2/8, 3,8, 3/8, 4/8, 5/8

There are 9 values. The middle value ( median) would be the 5th number ( this would give you 4 numbers below it and 4 numbers above it.

The Median is 2/8

Answer:

2/8 is the median. In decimal, it is 0.25.

Happy learning!

--Applepi101

Answer:

w equal to 9z

or z equals to w/9

Answer:

50  ft²

Step-by-step explanation:

ΔABC ≅ ADC; therefore the area of ΔADC is 25 sq feet also

2(25) = 50 sq feet

Answer:

B. ) 36-48-60

Step-by-step explanation:

From Pythagoras theorem, we can determine the sides of the triangle by testing the options

a^2 + b^2 = c^2

Then test the options

B. ) 36-48-60

36^2 + 48^2 = 60^2

3600 + 2304 = 3600

3600= 3600

Since both sides have equal values, then OPTIONS B express a correct sides of the triangle

C.) 6-10-14

6^2 + 10^2 = 14^2

36+ 100= 196

136= 196( it doesn't make an equality then it's not the answer

Answer:

Kiera has a lower ratio of raisins to nuts. (2:5)

Step-by-step explanation:

To find this, you would have to make the number of nuts the same in each to accurately compare them.

It starts with Kiera's 2 cups of raisins and 5 cups of nuts. So it will be 2:5 (raisins first then nuts.)

Desmond will be 3:6 (have to make it the same order, raisins and then nuts.)

So I multiplied both the 2 and the 5 in 2:5 by 6 first.

Then multiply both the 3 and 6 in 3:6 by 5 to make the number of nuts the same in both.

So Kiera will have 12:30 and Desmond will have 15:30.

Then you can conclude that Kiera has the lower ratio.

Answer:

4

Step-by-step explanation:

Answer:

There are several different means:

Arithmetic: 4 (This is most likely your answer.)

Geometric: 3.0862

Harmonic: 2.3736

Hope that this helps!

Ratio remains same

[tex]\\ \rm\rightarrowtail \dfrac{6}{3}=\dfrac{x}{24}[/tex]

[tex]\\ \rm\rightarrowtail 2=x/24[/tex]

[tex]\\ \rm\rightarrowtail x=48[/tex]