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The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)[/tex]

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3  and c = 36 inches.

Put the value, in the cosine law, the measure of angle A.

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\[/tex]

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

[tex]\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}[/tex]

Use the following formula to find area of ΔABC.,

[tex]A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2[/tex]

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

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Answer:

Tom sits in the middle and he is 18

Step-by-step explanation:

On the table you will first mark off Tom from being in the rear, as well as being 19

You will mark off Tom and Roy from the 1st, which places Davis as 1st, you also know that Tom is neither 1st nor last, so he is in the middle.

Now you see that Roy is neither in the 1st nor middle, so he is last.

Last is also the 20 yr old, so Roy is 20yrs and last seat.

Tom is neither 19 or 20.

So Tom is in the middle and 18yrs old

Answer:

Trigonometry Examples

Since π3 is in the first quadrant, the reference angle is π3 .

Since π3 is in the first quadrant, the reference angle is 60 degrees

Step-by-step explanation:

HOPE THIS WILL HELP YOU

Answer:

1: 3

Step-by-step explanation:

2 triangles : 6 circles

Divide each side by 2

2/2 : 6/2

1 :3

1 triangle : 3 circles

Considering the given linear equation, it is found that the correct statement is given by:

B. The graph of this equation is a vertical line.

It is:

Ax + By = C

Considering that A ≠ 0 and B = 0, the expression is represented by:

Ax = C

x = C/A.

Which means that the graph is a vertical line, hence option B is correct.

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Answer:

All of the rugs are the same size after making the cuts. The vertical line goes down the center of the rectangle, making two congruent parts. The diagonal line also splits the rectangle into two congruent parts because the area of a right triangle is exactly half the area of the rectangle.

Step-by-step explanation:

Answer:

3,052.08

Step-by-step explanation:

Formula for sphere: (4/3)(pi)(r^3)

Filled in: (4/3)(3.14)(729)

Calculated: 3,052.08

Answer:

root 7

Step-by-step explanation:

apply tan60=p/b=root 21/ x

Answer:

x^14 y^9

Step-by-step explanation:

Add the exponent of the x's

(x^5) + (x^9) = x^14

Add the exponent of the y's

(y^7) + (y^2) = y^9

You can't combine different varibles so your answer will be x^14 y^9

The error in Courtney claims that Option 2 would result in the class using 270 gallons is that he multiplied rather than dividing.

From the information given, it should be noted that Courtney claims that Option 2 would result in the class using 270 gallons of water during 180 minutes of showering is incorrect because she should have divided and not multiplied. This will be:

= 270 / (3/2)

= 180 × 2/3

= 120

Therefore, 120 gallons will be used.

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Answer:

[tex] \dfrac{1}{9^6} [/tex]

Step-by-step explanation:

[tex] \dfrac{9^3}{9^9} = 9^{3 - 9} = 9^{-6} = \dfrac{1}{9^6} [/tex]

Answer:

1) 108 A+    2) 98 B+

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ M(\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 0}{2}~~~ ,~~~ \cfrac{ y + 8}{2} \right)~~ = ~~\stackrel{\textit{\Large Q}}{(4~~,~~10)}\implies \begin{cases} \cfrac{x+0}{2}=4\\[1em] \boxed{x=8}\\[-0.5em] \hrulefill\\ \cfrac{y+8}{2}=10\\[1em] y+8=20\\ \boxed{y=12} \end{cases}[/tex]

Answer:

m<ABC = 90 degrees  m<ABD = 57 degrees

Step-by-step explanation:

OMG this is soooooo easy I love geometry.

Answer:

9.16

Step-by-step explanation:

350 = 12 (x + 20)

350 = 12x +240

350 = 12x +240

-240           -240

110 = 12x

_______

     12

9.16 or 9.17 = x

Find the volume of a cylinder with a radius of 4 meters and a height of 13 meters. Use * 3.14.

radius of the cylinder = 4 m

height of the cylinder = 13 m

To find: The volume of the cylinder (where pi = 3.14)

We know that volume of cylinder

[tex] \pi {r}^{2} h[/tex]

Now by using the formula = 3.14 × (4) × (4) × 13

= 3.14 × 208

= 653.12 m³

Answer:

d

Step-by-step explanation:

Answer:

$114.19

Step-by-step explanation:

7.25*15 = 108.75

108.75*1.05 = 114.1875

You can't have less than a cent, so it is $114.19

Answer: $114.19

Step-by-step explanation:

Answer:

25 years

Step-by-step explanation:

Answer:

126 square units

Step-by-step explanation:

Area of section 1 is 8 square units which is triangle and,

Area of triangle is =  [tex]\frac{1}{2}\times b\times h[/tex]

b= 2 units and height =8 units

So,

Area of section 1  =  [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]

Same Area is of section 2 which is also a triangle and has same base and height.

So,

Area of Section 2 = [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]

Now the Area of section 3 which is square with side of 10 units

So,

Area of section 3 =  [tex]a^{2} =10\times10=100\quad \text{square units}[/tex]

Total Area of Trapezoid = [tex]8+8+100=126 \quad \text{square units}[/tex]

A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.

A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.

The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,

[tex](2x-5)=0\\\\2x=5\\\\x=\dfrac52[/tex]

[tex]x-5=0\\\\x=5[/tex]

Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.

[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0[/tex]

Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.

[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}[/tex]

Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.

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Answer:

39 units

Since two side lengths and a right angle are given, we can use pythogoras theorem to determine the missing side (c) of the triangle. It should be noted that pythgoras theorem can only be used if the triangle is a right triangle.

Pythogoras theorem formula:

[tex](\text{Side}_{1} })^{2} + (\text{Side}_{2} )^{2} = (\text{Hyptenuse})^{2}[/tex]

Substitute the legs of the triangle and the hyptenuse

[tex]\implies (36)^{2} + (15 )^{2} = (c)^{2}[/tex]

Simplify both sides of the equation

[tex]\implies 1296 + 225 = (c)^{2}\\[/tex]

[tex]\implies 1521 = (c)^{2}\\[/tex]

Take square root both sides

[tex]\implies \sqrt[2]{1521 } = \sqrt[2]{c^{2} }[/tex]

Solve for "c" by simplifying the roots

[tex]\implies \sqrt[2]{39 \times 39 } = \sqrt[2]{c \times c }[/tex]

[tex]\implies \boxed{39 = c}[/tex]

Thus, the measure of the missing side length (c) is 39 units.

Answer:

A, g(x) = -f(x)+5

Step-by-step explanation:

The probability of getting exactly 8 hits in his next 20 at-bats is 0.153 (Round off to the nearest thousandth.).

The correct option is (c)

Binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.

Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]

where, n= number of trial,

r= number of success desire,

p= probability of success,

q= probability of Failure

probability of success = 0.34

To find the probability of winning exactly 8 hits in next 20 at-bats we find

dbinom (8, 20, 0.34)

Since p= 0.34

q= 1-p

 = 1-0.34

 = 0.66

n= 20, r=8

Using Binomial Distribution, we get

Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]

                 =[tex]\frac{n!}{r!(n-r)!} p^{r}\; q^{(n-r)}[/tex]

                 = [tex]\frac{20!}{8!(20-8)!} (0.34)^{8}\; (0.66)^{(20-8)}[/tex]

                = 125970 x 0.0001785794 x 0.00683168

                = 0.1536830

                ≈ 0.153 (Round off to the nearest thousandth.)

Hence, the probability of getting exactly 8 hits in his next 20 at-bats is 0.153.

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Answer:

√250 + 2 = 5√10 + 2

Step-by-step explanation:

1. refer to image attached

2. split the area into a rectangle and triangle (see red line)

3. find the area of the triangle

a. find the base (2)

b. find the height (2)

area = base * height / 2 = 2 * 2 / 2 = 2

4. find the area of the rectangle

a. find the width

the width can be found from the right triangle at the top right. the height is 2 and the bottom leg is 1, so using the pythagorean theorem, the hypotenuse, which is the width of the triangle, equals

√(2²+1²)  = √5 as our width

b. find the length

given the top right triangle, we have a height of 5 and another leg length of 5, so the length = √(5²+5²) = √50

the area of the rectangle is thus √50 * √5 = √250

4. the area is thus the two areas added up, or √250 + 2

3n+19

Explanation:

(1/2)(6n + 38)

Since it had the lowest mean absolute deviation, his scores were closest together in Math.

Hence, lower values of the mean absolute deviation means that the scores are closer, and thus his scores were closest together in Math.

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