20 POINTS

Layla and Cayden are racing at the playground. The playground is rectangular and has a length of 82 meters and a width of 50 meters. Cayden will run around the entire perimeter of the rectangular playground while Layla will run diagonally across the playground twice. (She will end where she started). Cayden runs 3 meters per second and Layla runs 2 meters per second.
A: Who will finish first?

B: How much faster will that person's finish time be?


HELP PLEASEEEEEEEEEEEEEEEEEEEEEEE
FOR THE SECOND TIME I ASKED THIS QUESTION ;-;

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

Read more about distance from angle of elevation at: https://brainly.com/question/25748640

#SPJ1

Answer:

3.167

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

(7*5) + 42 - (23/4)

35 +42 - 5.75

71.25

Could you have meant to write the problem differently

(7*5 + 42 - 23) / 4

54 /4

13.5

Im sorry, but None of those options (with the current way its written is posible, Is the problem written exactly like that? or a way that im missing

--Gage Millar, Algebra 1/2 tutor

answer

the answer is 49 i did the test to if you what to know the rest hear they are 160/(1+32)+53-102=11  and 12.(1/4 + 1/3)+2/3=4 3/4, 0.33/0.9.20+6.4/0.2= 32.6  (14-32+1)1/3.1/4=432 hope this helps ✨

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

146.82 yards is the distance from tee to hole.

Step-by-step explanation:

Let A is the position of tee and where the golfer is standing.

C is the position of hole.

CB is the vertical distance between greens and tee.

Angle of elevation,

To find: side AC.

Using trigonometric functions, we know that value of sine is:

\(sin\theta=\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\)

Here \(\theta=\angle BAC=15^\circ\)

Perpendicular is side CB.

Hypotenuse is side AC.

\(\text{sin}12^\circ=\dfrac{\text{CB}}{\text{AC}}\)

\(\implies\text{CB}=\dfrac{38}{\text{sin}15^\circ}\)

\(\implies\text{CB}=146.82\)

Hence, 146.82 yards is the distance from tee to hole.

Answer:

4y

Step-by-step explanation:

y - (-3y)

y + 3y

4y

When you see two negatives they basically become an addition symbol. In this case you then add the like terms which are y and 3y to get 4y. Hope this helps!!

Answer: 11/12

Step-by-step explanation:

it is a rise over run so the slope would be 11/12

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

For more such questions on line segment

https://brainly.com/question/30756145

#SPJ8

Answer:

\(x\neq 0\)

Step-by-step explanation:

Dividing by 0 is undefined, hence not allowed.

The denominator of the first term contains x^2.

Hence 0 is not allowed.

The value of the tax for the meal is $1.05.

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.

Depending on the regulations in that country, a business may be responsible for sales taxes in that jurisdiction if it has a presence there, which can be a physical site, an employee, or an associate.

Given the  cost of the meal = $15.00

and rate of tax = 7%

converting the rate of tax into decimal form,

rate of tax = 7% = 7/100

rate of tax = 0.07

amount of tax = cost x rate of tax

amount of tax = 15 x 0.07

amount of tax = $1.05

Hence the amount of tax is $1.05.

Learn more about sales tax;

https://brainly.com/question/29442509

#SPJ1

Reason:

Negative even integers aren't mentioned, but they are less than 10.

For example, something like -14 is less than 10 and is even.

If the question said "the set of all positive even integers less than 10" then {0,2,4,6,8} would be the correct full solution set, and the statement would be true.

Answer:

$300

Step-by-step explanation:

Let \(x\) be the original price.

\(x \times (1-0.04)=288\)

\(0.96x=288\)

\(x=\frac{288}{0.96}\)

\(x=300\)

Answer:

$300

Step-by-step explanation:

If it was a 4% reduction then we get:

\(x*0.96=288\\\)

Divide both sides by 0.96

\(x=300\)

The original suit price was $300

Perimeter of computer chip = 14.428 * ( \(10^{-7}\) ) meters .

Given : length = 7.18×10⁻⁷ meters

            breadth = 3.4×10⁻⁹ meters    

To find = perimeter of computer chip

Formula for perimeter of a rectangle :      

Perimeter = 2 ( length + breadth )

Calculations :

Perimeter = 2 [ (  7.18×10⁻⁷ ) + ( 3.4×10⁻⁹ ) ]

On simplifying ,

                = 2 [ \(10^{-7}\) ( 7.18 + 0.034 )

            = 2 [  \(10^{-7}\) ( 7.214 ) ]

              = 14.428 * ( \(10^{-7}\) ) meters

Hence , perimeter = 14.428 * ( \(10^{-7}\) ) meters .

To learn more on perimeter follow link :

https://brainly.com/question/19819849

#SPJ9

Answer:

Area of a triangle

Step-by-step explanation:

1/2bh is used to find the area for a triangle

The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.

To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

Scale factor = Length of corresponding side in D' / Length of corresponding side in D

For the corresponding sides, we have:

Scale factor = 6/18 = 1/3

Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.

For more such questions on  corresponding side

https://brainly.com/question/29071853

#SPJ8

Answer:

E[T] = 10

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the expected value of the uniform distribution is given by:

\(E = \frac{a+b}{2}\)

Uniformly distributed between 0 and 20 minutes.

This means that \(a = 0, b = 20\)

Let T be the number of minutes you wait until you board a bus. Find E[T].

This is

\(E[T] = \frac{a + b}{2} = \frac{0 + 20}{2} = 10\)

E[T] = 10

The value of angle x in the triangle is 15°

Given: the triangle ABC with equal sides of 9 units.

Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).

Thus, <A = <B = < C =  4x°

Since the sum of angles in a triangle is 180°. We have:

<A + <B + < C = 180°

4x + 4x + 4x = 180°

12x = 180

x = 180/12

x = 15°

Therefore, the value of x is 15°

Learn more about angles in a triangle on:

https://brainly.com/question/7620723

#SPJ1

The required area of the given figure is  19.68 in².

Given that,

length of first diagonal = p = 16.4 in.

length of 2nd diagonal = q = 2.4 in.

Since, the given figure is nothing but rhombus,

And a parallelogram is a particular instance of a rhombus and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus

And we know that area  of a rhombus = (p q)/2

Where p and q are diagonals of the given rhombus

Therefore,

Area = 16.4 x 2.4/2

        =  19.68 in²

So the area of given rhombus is 19.68 in².

To learn more about rhombus visit:

https://brainly.com/question/10008134

#SPJ1

Answer:

2856 I'm thinking

Step-by-step explanation:

hope this helped

Answer: 674 ft

Step-by-step explanation:

\(\tan 12^{\circ}=\frac{y}{1315} \\ \\ 1315\tan 12^{\circ}=y\)

\(\tan 8^{\circ}=\frac{y}{x+1315} \\ \\ (x+1315)\tan 8^{\circ}=y \\ \\ (x+1315)\tan 8^{\circ}=1315 \tan12^{\circ} \\ \\ x \tan 8^{\circ}+1315 \tan 8^{\circ}=1315 \tan 12^{\circ} \\ \\ x \tan 8^{\circ}=1315 \tan 12^{\circ}-1315 \tan 8^{\circ} \\ \\ x=\frac{1315 \tan 12^{\circ}-1315 \tan 8^{\circ}}{\tan 8^{\circ}} \approx \boxed{674 \text{ ft}}\)

Answer:

16 year old

step by step explanation

Answer:

hey bro ur correct

Step-by-step explanation:

cus (1) , (4) and (6) and not possible

The correct statements regarding the given figure are -

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

Given is a parallelogram as shown in the image.

The correct statements are -

Therefore, the correct statements regarding the given figure are -

To solve more questions on parallelogram, visit the link -

brainly.com/question/30098550

#SPJ1

Answer: the present age of son is 15 years, and the present age of father is 45 years.

Step-by-step explanation:

Let the age of son be 'x' and that of his father be 'y'.

So according to the question, the 1st equation that can be formed will be:

y = 3(x) ->(1)

[as father's age is 3 times the age of son]

Now after 5 years:

Age of son = (x+5)

Age of father = (y+5)

So according to the question, the 2nd equation that can be formed will be:

(y+5) = 2.5×(x+5) ->(2)

[as father is now two and half times old as his son]

Substituting the value of equation (1) in (2), we get:

(3x+5) = 2.5×(x+5)

=> 3x + 5 = 2.5x + 12.5

=> 3x - 2.5x = 12.5 - 5

=> 0.5x = 7.5

=> x = 7.5/0.5 = 15

Thus, the present age of son is 15 years.

Note : we can calculate the age of father by putting the value of x in equation (1) or (2):

y = 3(x) = 3 × 15 = 45 (putting x in equation 1)

Thus, the present age of father is 45 years.

The correct answer is 45.5 km

Explanation:

The total distance from the locksmith to the hotel, located in the east of the graph is not directly given; however, this distance can be calculated by considering the partial distances given. This includes the distance from the locksmith to the furniture store (18.3 km), and the distance between the furniture and the hotel (27.2) as the total distance = distance from the locksmith to the furniture store + distance from the furniture store to the hotel. Thus, the total distance is 18.3 km + 27.2 km which is equal to 45.5 km.

Answer:
T = 320

Step-by-step explanation:
64+ (960-144) ÷ 4 = 64+ (816) ÷ 4 = 64+ 204 = 320

1. The Cost of debt financing for CGT is 5.74%

2. CGT's capital structure consists of 42.4% debt and 57.6% equity.

3. CGT's weighted average cost of capital is 9.12%.

a. The cost of debt financing can be calculated using the formula:

Cost of debt = Yield to maturity x (1 - Tax rate)

where Yield to maturity is the return investors require on the company's debt.

Given that the noncallable $1,000 par value, 20-year, 7.25% bonds with semiannual payments are selling for $875.00, the current yield to maturity can be calculated as:

Yield to maturity = (Annual coupon payment + Annual capital gain) / Current bond price

Annual coupon payment = $1,000 × 7.25% = $72.50

Annual capital gain = ($1,000 - $875) / 20 = $6.25

Yield to maturity = ($72.50 + $6.25) / $875.00 = 9.57%

Therefore, the cost of debt financing for CGT is:

Cost of debt = 9.57% x (1 - 0.40) = 5.74%

b. The cost of equity financing can be calculated using the Capital Asset Pricing Model (CAPM):

Cost of equity = Risk-free rate + Beta * (Market return - Risk-free rate)

where the risk-free rate is the yield on a 6-month Treasury bill, the beta is 1.25, and the market return is the required return on the stock market.

Given that the yield on a 6-month Treasury bill is 3.50%, and the required return on the stock market is 11.50%, the cost of equity financing for CGT is:

Cost of equity = 3.50% + 1.25 * (11.50% - 3.50%) = 13.00%

c. The firm's capital structure can be calculated as follows:

Debt ratio = Total debt / Total assets

Equity ratio = Total equity / Total assets

Debt ratio = $59,000,000 / $139,000,000 = 0.424

Equity ratio = $80,000,000 / $139,000,000 = 0.576

Therefore, CGT's capital structure consists of 42.4% debt and 57.6% equity.

d. The weighted average cost of capital (WACC) can be calculated as:

WACC = Weight of debt x Cost of debt + Weight of equity x Cost of equity

where the weights of debt and equity are the proportions of total capital represented by each component.

Given that the weights of debt and equity are 0.424 and 0.576, respectively, the WACC for CGT is:

WACC = 0.424 x 5.74% + 0.576 x 13.00% = 9.12%

Learn more about Debt and Equity here:

https://brainly.com/question/17286021

#SPJ1