Find the area of a regular hexagon if given a side length of 1.9 to the square root of 3.

Answer:

[tex]sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}[/tex]

Step-by-step explanation:

[tex]\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\[/tex]

[tex]sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}[/tex]

Answer:

[tex]-\frac{9}{14}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}*-\frac{6}{7}\\\\\frac{3}{2} *\frac{3}{7} \leftarrow \text{Cross Cancel Common Factor}\\\\ -\frac{3*3}{2*7}\\\\-\frac{9}{14}[/tex]

Answer:

negative 9/14

Step-by-step explanation:

Answer:

x = -6 and x = 7

Step-by-step explanation:

x² - x - 42 = 0

find two number which

a + b = -1

a*b = -42

a = -7

b = 6

x² - x - 42 = 0

(x-7)(x+6) = 0

x-7 = 0

x = 7

x +6 = 0

x = -6

Answer:-6 or 7

Step-by-step explanation:

Answer:

⇒ x = 3.4975

Step-by-step explanation:

Assume cost of each figure = x

Given:

32x + 2.32 = 114.24

Find:

Value of x

Computation:

⇒ 32x + 2.32 = 114.24

⇒ 32x = 114.24 - 2.32

⇒ 32x = 111.92

⇒ x = 111.92 / 32

⇒ x = 3.4975

Answer:

Bentley got $20 for her allowance.

Step-by-step explanation:

Answer:

The correct option is;

DE/PQ = 3/2 which is StartFraction DE Over PQ Endfraction = three-halves

Step-by-step explanation:

The information given bout the triangles are;

DF/PR = FE/RQ = 3/2

Therefore since the given sides of triangle DEF are 3/2 times the sides of triangle PQR, the given sides of triangle DEF have been scaled 3/2 times to get the given sides of triangle PQR

Therefore, to prove that ΔDEF ~ ΔPQR, the ratio of the third side of triangle DEF, that is DE, to the third side of triangle PQR, which is PQ must be three-halves.

Answer:

The answer is  DE/PQ = 3/2 or D.

Step-by-step explanation:

Just did it on edge. hope you do good :)

Answer: 11.3

Step-by-step explanation:

To find the distance, we will need the distance formula.

[tex]D=\sqrt{(x_{2}-x_{1} ) ^2+(y_{2}-y_{1})^2 }[/tex]

Since we know our x and y, we can plug them into this equation.

[tex]D=\sqrt{(5-(-3))^2+(1-9)^2}[/tex]

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

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

[tex]D=\sqrt{128}[/tex]

[tex]D=11.3[/tex]

The distance between the points is 11.3.

Answer:

x=5/3log(3) -1

x=2.949317

Step-by-step explanation:

reorder terms

3log(3)x(x+1)+5

distribute 3log(3)

3log(3)x+3(log)=5

Move constant to the right

3log(3)x=5-3log(3)

Divide both sides by 3log(3)

x=5/3log(3) -1

Solve 3log(3)

3log(3)= 3.949317

3.949317-1=2.949317

Answer:

Reduce every dimension except thickness by 20%.

The requried new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.

To find the dimensions of the new candy bar after reducing the volume by 20%, we need to determine the reduction in length and width.

Let's start by calculating the original volume of the candy bar using the formula: volume = length × width × thickness.

Original volume = 13 cm × 7 cm × 2 cm = 182 cm³

Since the management wants to reduce the volume by 20%, we need to find 20% of the original volume and subtract it from the original volume.

20% of 182 cm³ = 0.2 × 182 cm³ = 36.4 cm³

Reduced volume = 182 cm³ - 36.4 cm³ = 145.6 cm³

Now, we need to determine the new dimensions while maintaining the 2 cm thickness.

Let's assume the reduction in length and width is x cm for both dimensions.

The new volume can be calculated using the formula:
volume = (length - x) × (width - x) × thickness.

Setting this equal to the reduced volume, we have:

(13 - x) × (7 - x) × 2 = 145.6

Simplifying and rearranging the equation, we get:

(91 - 20x + x²) = 72.8

x² - 20x + 18.2 = 0

Using the quadratic formula, we can solve for x:

[tex]x = \dfrac{-(-20)\pm \sqrt{(-20)^2- 4(1)(18.2)}} {2(1)}\\x = \dfrac{20 \pm \sqrt{400 - 72.8}} {2}\\x =\dfrac {20 \pm \sqrt{327.2}} {2}[/tex]

x ≈ (20 ± 18.09) / 2

Taking the positive value, we have:

x ≈ (20 + 18.09) / 2

x ≈ 19.045 / 2

x ≈ 9.5225

Since the dimensions cannot be negative, we discard the negative value.

Therefore, the reduction in length and width is approximately 9.5225 cm.

To find the new dimensions, we subtract this value from the original length and width:

New length = 13 cm - 9.5225 cm ≈ 3.4775 cm

New width = 7 cm - 9.5225 cm ≈ -2.5225 cm (discard as it is negative)

Therefore, the new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.

Learn more about dimensions here:

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Answer:

solution,

Let the points be A and B

A(-3,4)---->(X1,y1)

B(5,4)----->(x2,y2)

now,

Distance:

[tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {(5 - ( - 3))}^{2} + (4 - 4) ^{2} } \\ = \sqrt{ {(5 + 3)}^{2} + {(0)}^{2} } \\ = \sqrt{ {(8)}^{2} + 0} \\ = \sqrt{64} \\ = \sqrt{ {(8)}^{2} } \\ = 8 \: units[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

the one with 12, 18, 22

Step-by-step explanation:

in the first one, 9-3=6 and 6-3=3 so -3 is the constant of the proportionality

in the second one 3-1=2, 2-1=1 so here the constant of proprtionality is -1

in the third one 16+2=18, 18+2=20 so the constant of proportionality is 2

fourth one 4 + 0.5= 4.5 and 4.5+0.5= 5, constant of proportionality is 0.5

fifth one 12+6=18, but 18+6=24

and the rest are all proportional

Answer:

12, 18, 22

Step-by-step explanation:

Answer:

C) 105

Step-by-step explanation:

The box plot suggests that about 50% of hight schools in orange county have more than 105 band members.

This can be inferred from the boxplotvprovided in the attachment. 50% refers to the median of the distribution which is denoted by the vertical line dividing the box into two. Tracing the vertical line to the horizontal label marked from 70 to 150, the vertical line falls on the 105 mark. Hence the value of the median or 50th percentile

The sell price is the wholesale price plus 20%

Divide the sell price by 1.2 ( 100% + 20%)

145 / 1.2 = 120.83

The wholesale price is $120.83

Answer:

The wholesale price is $120.83

Answer:

Range { 2,4,9,16}

Step-by-step explanation:

The range of the function is the output of the system

Range { 2,4,9,16}

Answer:

Step-by-step explanation:

Range is ll the y-points the outputs {2,4,9,16}

Answer:

second and third choice

Step-by-step explanation:

supplamentary = add up to be 180

Answer:

3 is not in the domain of [tex]f\circ g[/tex].

Step-by-step explanation:

The given functions are

[tex]f(x)=\sqrt{x+5}[/tex]

[tex]g(x)=-4x+4[/tex]

We need to check whether 3 is in the domain of [tex]f\circ g[/tex] or not.

[tex]f\circ g=f(g(x))[/tex]

[tex]f\circ g=f(-4x+4)[/tex]     [tex][\because g(x)=-4x+4][/tex]

[tex]f\circ g=\sqrt{(-4x+4)+5}[/tex]     [tex][\because f(x)=\sqrt{x+5}][/tex]

[tex]f\circ g=\sqrt{-4x+9}[/tex]

This function is defined if

[tex]-4x+9\geq 0[/tex]

[tex]9\geq 4x[/tex]

[tex]\dfrac{9}{4}\geq x[/tex]

It means domain of the function [tex]f\circ g[/tex] is [tex](-\infty,\dfrac{9}{4}][/tex].

[tex]3\notin (-\infty,\dfrac{9}{4}][/tex]

Therefore, 3 is not in the domain of [tex]f\circ g[/tex].

Answer:

x=65

Step-by-step explanation:

x/5 - 2 = 11

x/5= 11+2

x/5=13

x=13×5

x=65

Answer:

Step-by-step explanation:

Question = x/5 - 2 = 11

1. Isolate the variable

x/5 - 2 = 11

    + 2   + 2

x/5 = 11

2. Remove the fraction

x/5 = 11

*5      *5

3. Simplify

x = 55

The answer is x = 55.

Hope this helped,

Kavitha

Answer & Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The option (A) (1/2)mQRS = ∠T is correct because the measure of an inscribed angle is one-half the measure of its intercepted arc.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have:

Rahim is constructing a proof to show that the opposite angles of a quadrilateral inscribed in a circle are supplementary.

From the central angle theorem:

(1/2)mQRS = ∠T because the measure of an inscribed angle is one-half the measure of its intercepted arc.

Thus, the option (A) (1/2)mQRS = ∠T is correct because the measure of an inscribed angle is one-half the measure of its intercepted arc.

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Answer:

3 boys may be answer of this question

Answer:

19/44

Step-by-step explanation:

19 boys

25 girls

19+25=44 (red hair)

19/44

Answer: y=1/2x−2

Step-by-step explanation:

Answer:

solution,

[tex](2 + 3 \times 2 + {3}^{2} ) - {4}^{2} \\ = (2 + 6 + 9) - 16 \\ = 17 - 16 \\ = 1[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

1

Step-by-step explanation:

Multiply  

3  by  2 . 2 + 6 + 3 2 − 4 2 Raise  3  to the power of  2 . 2 + 6 + 9 − 4 2 Raise  4 to the power of  2 . 2 + 6 + 9 − 1 ⋅ 16 Multiply  − 1  by  16 . 2 + 6 + 9 − 16

Simplify by adding and subtracting.

Add  2  and  6 . 8 + 9 − 16 Add  8  and  9 . 17 − 16  Subtract  16  from  17 .

1

Answer:

( -3, 1)

........

Answer:

(-3, 1)

Step-by-step explanation:

The point lies on the line x = -3.

The point lies on the line y = 1.

Where both lines intersect, that is the coordinate.

(x, y)

(-3, 1)

Answer:

-i^5=-i

Step-by-step explanation:

rewrite the equation ;

i^4=1

I^4 *-i = 1*-i=-i

Answer:

3.625 is ans

Step-by-step explanation:

4.5+0.25_+1.125=3.625

Step-by-step explanation:

this is your answer sis ...

Answer:

BD=7

ED=5

BE=7

AD=10

AE=5

Step-by-step explanation:

given CD = 7 you use that to find BD and BE because CD´s line length is the same as BD and BE

given BC = 5 you use that to find ED and AE and AD because BC is the same length as ED (they create the same triangle) and than given AE also equals 5 you add ED and AE to get AD

hope this helps

Answer:

a) 1/3

b) 7/9

Step-by-step explanation:

The first part asks for the probability that Matt takes the red counter.

There are 6 red counters out of total 6+4+8 = 18 counters.

6/18

Simplify the fraction.

= 1/3

The second part asks for the probability that the counter is not blue.

The counters that are blue are 4. Not blue becomes 18-4 = 14. 14 red or green counters out of total 18.

14/18

= 7/9

Answer:

Total outcome =  6 + 4 + 8 = 18

a) Probablity that the counter is red = 6/18 = 1/3

b) Probablity that the counter is blue = 14/18 = 7/9

Answer: A

Step-by-step explanation:

it's easy

Answer:

14cm² is the area of the shaded region

Step-by-step explanation:

recognize that those two small triangles plus that arc area is equal to 1/4 of the area of the circle.

56 / 4 = 14cm

Answer:

See below.

Step-by-step explanation:

46.

Theorem:

The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.

The 100-deg angle is an exterior angle whose remote interior angles are angles E and F.

m<E + m<F = 110

5x + 6x = 110

11x = 110

x = 10

m<E = m<FEG = 5x = 5 * 10 deg = 50 deg

Answer: C. 50 deg

47.

A is not true since we know that 5x + 6x must equal 110, not 70.

Answer:

<FEG=50

A. is wrong

Step-by-step explanation:

For the first question, we know <F &<E are remote interior angles which add up to 110 (exterior angle)

so:

[tex]5x+6x+110\\11x=110\\x=10[/tex]

so:

[tex]5x= 5(10)\\FEG=50[/tex]

Now using what we know, we can determine that A. is wrong since 5x+6x is 110° not 70°

Hope this helps!