The front of the stage, side C, is 50 feet long. A 40-foot rope runs along the side of square B. A 30-foot rope runs along the side of square A. Is the roped off area, triangle ABC, a right triangle? Explain. (2 points)
e) The diagonal of square A, marked off by the red stars, is where the concession stand is located. A local high school band is performing at the outdoor theater on a summer evening. The band has a school banner that is 40-feet long, and band members would like to hang it across the concession stand to let people know they are performing. Estimate the length of the concession stand to determine if the school banner can fit across the length of the concession stand. Show your work and explain your reasoning. (2 points)

The Front Of The Stage, Side C, Is 50 Feet Long. A 40-foot Rope Runs Along The Side Of Square B. A 30-foot

Answers

Answer 1

Answer:

ΔABC is a right triangle

length of the concession stand = 42.4 ft (nearest tenth)

Step-by-step explanation:

Given:

Side length of square A = 30 ftSide length of square B = 40 ftSide length of square C = 50 ft

We can use Pythagoras' Theorem to prove if ΔABC is a right triangle.

Pythagoras' Theorem: a² + b² = c²  (where a and b are the legs, and c is the hypotenuse of a right triangle)

Given:

a = side length of square A = 30b = side length of square B = 40c = side length of square C = 50

⇒ a² + b² = c²

⇒ 30² + 40² = 50²

⇒ 900 + 1600 = 2500

⇒ 2500 = 2500

Therefore, ΔABC is a right triangle

To find the diagonal of square A, use Pythagoras' Theorem:

Given:

a = side length of square A = 30b = side length of square A = 30c = diagonal of square A

⇒ a² + b² = c²

⇒ 30² + 30² = c²

⇒ 900 + 900 = c²

⇒ c² = 1800

⇒ c = √(1800)

⇒ c = 42.42640687

Therefore, the length of the concession stand (diagonal of square A) is 42.4 ft (nearest tenth)


Related Questions

Solve this question:
[tex]5 \times \frac{5}{10} \times 10 = [/tex]
Thanks :)​

Answers

Answer:

25

Step-by-step explanation:

Answer:

25

Step by step explanation:

Hey

Find the area of the semicircle. Round your answer to the nearest hundredth.

Answers

I have no idea I’m sorry I need the points for my homework 18
6.2832. Is the closest decimal I can figure out.

Wayne uses 4 inches of ribbon for each bow he makes. How many bows can he make with 3 yards of ribbon?

Answers

Answer:

27

Step-by-step explanation:

1 yard is 3 feet, so 3 yards is 9 feet.

9 feet is 108 inches, so Wayne has 108 inches of ribbon to work with.

Divide 108 by 4, because Wayne needs 4 inches of ribbon to make 1 bow, and we get 27.

Hopefully, this helps with whatever you need to do!

Listing broker Bob gets a 6 .5% commission on a $280,000 sale . He pays 3% to the selling broker and splits his share evenly with the listing agent . How much does the listing agent receive?

Answers

Answer:

4900 to listing agent

Step-by-step explanation:

SO Bob gets 6.5 -3 = 3.5 %   and then splits it ==>1.75% to Bob and to listing agent

1.75% = .0175

.0175 * 280000 = 4900

Ben wants to try a new honey-glazed salmon recipe. He starts with 1
2
3
cups of honey. He uses
1
5
of it to make the glaze. How much honey does Ben have left?

Answers

What you have to do is 1. Work for it yourslef. 2. use ur brain.

Divide. 8,375 ÷ 45 number and remainder

Answers

Answer: 186 with a remainder of 5.

Method One:

      See attached for my work, I used long divison.

Method Two:

     We will use a calculator to find the value, then multiply the value (without the decimals) by the divisor. Lastly, we will subtract. This makes more sense with the work:

8,375 ÷ 45 = 186.11111111

186 * 45 = 8,370

8,375 - 8,370 = 5

The number of Smart TVs owned by residents in Picayune increased by 25% this year. Assuming that the 824 Smart
TVs owned last year are still being viewed, what is the total number of Smart TVs in Picayune this year?
A)
206
B)
618
942
D)
1,030

Answers

Answer:

25% of 824

25/100 × 824

206

New prices of the TV is

824+206= 1030

Just please help me!!!!!

Answers

Answer:

n= 5/3 or 1.67

Step-by-step explanation:

9n^2 -9 =16

9n^2 = 16 + 9

9n^2 = 25

n^2 =25/9

n^2 =25/9

[tex]\sqrt{n^2} = \sqrt{\frac{25}{9} }[/tex]

n= 5/3 or 1.67

[tex]~~~~~~9n^2 -9 = 16\\\\\implies 9(n^2 -1) = 16\\\\\implies n^2 -1 = \dfrac{16}9\\\\\implies n^2 = \dfrac{16}{9}+1\\\\\implies n^2 = \dfrac{25}{9}\\\\\implies n=\pm\sqrt{\dfrac{25}{9}}\\\\\implies n= \pm\dfrac 53\\\\\implies n = \pm1.67[/tex]

Find the probability of the event.

A class has seven students. What is the probability that exactly four of the students were
born on a weekday (Monday through Friday)? (round to the nearest thousandths when
needed)

Answers

The answer is 21% I hope this helps

can anyone help me find the area pls ty

Answers

Since its a square we put one of the side lengths to the power of 2 3 to the power of 2 equals 9 so the area is 9

QUESTION 21 ✓ Round 5 1/3 to the nearest whole number?

Answers

Answer:

5

Step-by-step explanation:

1/3 is only 0.33 and 0.33 isnt higher than 0.50, so you cant round anything. 5 is the answer.

Answer: Justice.

Step-by-step explanation:The Answers Justice.

Which of the following is the sum of 1/2 and -2/3

Answers

-1/6

hope it helps...!!!

The angle of elevation to a nearby tree from a point on the ground is measured to be 74^{\circ} ∘ . How tall is the tree if the point on the ground is 54 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.

Answers

The height of the tree whose angle of elevation is [tex]74^{0}[/tex] and 54 feet tall is 188 foot.

Height of the tree= 188 foot (rounding off nearest tenth)

What is angle of elevation?

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

We know by trigonometric ratios,

[tex]tan \; \theta = \frac{P}{B}[/tex]

[tex]tan \; 74^0 \;[/tex] = [tex]\frac{P}{54}[/tex]

3.48 = [tex]\frac{P}{54}[/tex]

P= 3.48 x 54

 = 187.92 feet

 ≈ 188 foot (rounding off nearest tenth)

The height of the tree whose angle of elevation is  and 54 feet tall is 188 foot.

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Answer: 188.3 feet tall*

Step-by-step explanation:

thats the questin i need halp with

Answers

Answer:

40% increase

Step-by-step explanation:

7-5=2

plug in:

2/5=x/100

x=40

40% increse

The sandwhich increased by 2 dollars. The amount of change must be divided by the original. 7-5 is 2, which means we must divide 2 by 5. 2/5 is .40. Which translates to 40% or 40/100. This means that the price of the sandwhich increased 40%.

Hope this helped you <3!

Eight meters is equal to how many centimeters

Answers

Answer:

800 Cm

Step-by-step explanation:

bro typa question is that its common sense that 100 cm = 1 meter

8 meters is equal to 800 centimeters

Jason earns $4,024 dollars in 20 days. He does not go to work for 7 days. Calculate his mean daily earnings

Answers

Answer:

309.54

Step-by-step explanation:

he makes about $309.54 in one day

Surface area and volume of cone

Answers

The surface area and the volume of the cone is 816.4 km² and 7536 km³ respectively.

What is volume?

Volume is the capacity of an object.

To calculate the surface area and volume of the cone shown above, we use equation 1 and equation 2 respectively.

Formula:

S = πr√(r²+h²)............. Equation 1V = πr²h.................. Equation 2

Where:

S = Surface area of the coneV = Volume of the coner = Radius of the base of thye coneh = Vertical height of the cone.

From the diagram,

Given:

r = 10 kmh = 24 kmπ = 3.14

Substitute these values into equation 1 and equation 2 respectively.

S = 3.14×10[√(24²+10²)S = 31.4(√676)S = 31.4×26S = 816.4 km²

Also for the volume of tyhe cone

V = 3.14×10²×24V = 7536 km³

Hence, The surface area and the volume of the cone is 816.4 km² and 7536 km³ respectively.

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Carlos wrote the number 52,700,000 in scientific notation. Which number did he write?

Answers

Answer:

5.27 × 10⁷ is the scientific notation for 52,700,000.

Suppose the McCall family wants to rent a truck for a day. They have a choice of two truck rental companies. After how many miles are the cost at the two companies equal?
if explanation is given with steps I will give brainliest

Company A: $20 per day plus $ .70 per mile
Company B: $45 per day plus $ .25 per mile

Answers

Answer:

the trip is 10 miles long

Step-by-step explanation:

im sorry i dont know the steps

Lucas has 2 chocolate bars more than Caidon. Together they have 30 chocolate bars. How
many chocolate bars does Lucas have? (hint: use only one variable)
Help me

Answers

Answer:

Lucas has 16 chocolate bars

Step-by-step explanation:

Let x = number of chocolate bars Lucas has

⇒ x - 2 = number of chocolate bars Caidon has

If they have 30 chocolate bars altogether then:

⇒ x + x - 2 = 30

⇒ 2x - 2 = 30

⇒ 2x = 32

⇒ x = 16

Therefore, Lucas has 16 chocolate bars (and Caidon has 14 chocolate bars).

How many two-digit, positive integers can be formed from the digits 1, 3, 5, and 9, if no digit is repeated?
24
16
12

Answers

Answer:

12

Step-by-step explanation:

Using Permutation Formula :

⁴P₂4! / 2!4 x 3 x 2! / 2!4 x 312

Given that y is inversely proportional to x y =0.25 when x =4, find the value of y when x =5

Answers

Answer: y=0.2

Step-by-step explanation:

y∝(1/x)

this implies that

y=k/x    eq(*)

when y =0.25 when x =4

0.25=k/4

k=1

for y when x=5

y=k/x

y=1/5

y=0.2

Cathleen Brooks obtained an 18 month loan of $3,200. The interest rate is 15% Her monthly payment is $199.68. The balance of the loan after 6 payments
is $2,341.45.

a. What is the interest for the first payment?


b. What is the interest for the seventh payment?


Answers

a. The interest for the first payment is $40.

b. The interest for the seventh payment is $29.27.

What is interest?

In financial accounting and management, interest refers to the finance charge for obtaining or giving a loan or credit.

The interest payment or revenue is based on the interest rate applied to the principal or loan balance.

Data and Calculations:

Loan = $3,200

Monthly payment = $199.68

Interest rate = 15%

Loan balance after 6 payments = $2,341.45

Interest for the first payment = $40 ($3,200 x 15% x 1/12)

Interest for the seventh payment = $29.27 ($2,341.45 x 15% x 1/12)

Thus, while the interest for the first payment is $40, the interest for the seventh payment is $29.27.

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Carol's last credit card statement said that she had an account balance of -$118. Which of the following account balances represents a debt greater than Carol's?

A: -157

B: $157

C: $79

D: -$79

Answers

I think it would be b im pretty sure.

Answer: A. -$157

Step-by-step explanation:

This is would be much more in debt for his credit card statement, it would take him longer to pay off.

2 Latoya has 60 CDs in her collection.
• 40 are Pop
. 12 are Country
• 6 are Rock
• 2 are Jazz
.
If she randomly selects a CD from her collection, what is the probability that she will NOT select a Country CD?

Answers

60 cds - 12 country = 48 cds are not country.


probability of picking one that is not country = total of non country/ total cds


probability = 48/60 which reduces to 4/5


answer: 4/5

An airplane is flying at an altitude of 36,000 feet when it begins it's descent for landing. Twelve minutes into its descent, it's at 29,400 feet. Find the rate of change in altitude.​

Answers

36000 divided by 29,400 get the answer then divide by 12

if each polygon has 12 sides and each side length was 20 cm what is the area

Answers

Answer: approximately 4478.46096908264 square cm.

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

Explanation:

I'm assuming this is a regular 12-sided polygon

The area formula for regular polygons is

[tex]A = 0.25n*s^2*\cot(180/n)[/tex]

where in this case we have n = 12 sides and each side is of length s = 20

So,

[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*12*(20)^2*\cot(180/12)\\\\A = 0.25*12*(20)^2*\cot(15)\\\\A = 0.25*12*(20)^2*\frac{1}{\tan(15)}\\\\A \approx 4478.46096908264\\\\[/tex]

The area of this regular polygon is approximately 4478.46096908264 square cm.

Make sure your calculator is in degree mode when computing that value of cot(15) or 1/tan(15).

Area is measured in square units. This means that if we divide the shape into squares that are equal in size and count them up, the area is the total number of squares. Square units are always one unit of length long and one unit of length wide. In the song, the unit of length we use is feet. So each square unit is one foot long and one foot wide, or one square foot. Since there are 72 of these units in total, we say the area is 72 square feet. Square units can use other units of length, like inches or miles. Make sure you know what unit of length you’re using.

Jason is finding the area of a rectangle that is 7 inches long and 4 inches wide. Jason says the area of the rectangle is 28 inches. Is Jason correct or incorrect?

A: Jason is correct because 7 x 4 = 28.
B: Jason is incorrect because the area is 28 square inches.
C: Jason is incorrect because 7 + 4 = 11.
D: Jason is incorrect because the area is 28 square feet.

Answers

Answer:

B

Step-by-step explanation:

Area is always squared; area of a rectangle is length x width so 7*4= 24in^2

If this answer helped you I would greatly appreciate brainliest :D.

( marking right as brainliest and 5.0 star! ) Seaira measures and records the lengths, in feet, of 9 lizards. The line plot below shows the information she records, based on the line plot what is the difference between the lengths in feet, of the longest lizards and the shortest lizards?

Answers

Answer:

5/8

Step-by-step explanation:

The longest lizard there is, is 3/4 feet. The shortest lizard is 1/8. The equation to solve this is 3/4 - 1/8. The answer to this is 5/8. I hope this helps :)

Maths problem in simultaneous equations

Answers

Answer:

Question 6: The cost of a chocolate bar is $1.20 and the cost of a box of gum is $0.75

Question 7:  There were 7 students

Step-by-step explanation:

Question 6:

We will be using system of equations which a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations intersect.

Our Variables:

- chocolate bar which will be represent as b in the equation

- box of gum which will be represent as g in the equation

Forming the equations:

Sally -

bought 2 chocolate bars (b)

bought 1 box of gum (g)

to a total of $3.15

so 2b + 1g = $3.15

Evans -

bought 1 chocolate bars (b)

bought 2 box of gum (1)

to a total of $2.70

so 1b + 2g = $2.70

Solving using substation:

2b + 1g = $3.15              we want to isolate b to input into the other equation

1b + 2g = $2.70                  

2b + 1g = $3.15             subtract 1g from both sides, divided both sides by 2

2b / 2 + 1g - 1g = $3.15 - 1g / 2

b = $3.15 - 1g / 2

Now substation b into the second equation

1b + 2g = $2.70 becomes 1($3.15 - 1g / 2) + 2g = $2.70

simplify,

$3.15 + 3g / 2 = $2.70                isolate g

$3.15 + 3g / 2 x 2 = $2.70 x 2   multiply both sides by 2

$3.15 + 3g = $5.40                     subtract $3.15, divided by 3 from both sides

$3.15 - $3.15 + 3g / 3 = $5.40 - $3.15 / 3

g = $5.40 - $3.15 / 3

g = $2.25 / 3

g = $0.75

Now plug in g to get b into any equation:

If Sally equation is used

2b + 1g = $3.15

2b + 1(0.75) = $3.15    →    2b + 0.75 = $3.15

2b + 0.75 - 0.75 = $3.15 - 0.75

2b = $2.40    →    2b / 2 = $2.40 / 2

b = $1.20

If Evans equation is used

1b + 2g = $2.70

1b + 2(0.75) = $2.70     →    1b + 1.50 = $2.70

1b + 1.50 - 1.50 = $2.70 - 1.50

1b / 1 = $1.20 / 1

b = $1.20

Question 7:

Our Variables:

- adult which will be represent as A in the equation

- student which will be represent as S in the equation  

Forming the equations:

- sample size: group of 30

- Adult cost $5        (A)

- Student cost $2    (S)

- Five members are free

to a total cost is $104

so A + S = 30 - 5

this is how many of each variable from the total group and we subtract 5 as 5 members were free

so 5A + 2S = $104

Solving using substation:

A + S = 25                     we want to isolate a to input into the other equation

5A + 2S = $104

a = 18

s =7

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