A garden has the form of a right triangle. One leg of the triangle is formed by a 2000-ft long sea wall. The hypotenuse of the triangle is 400 ft longer than the other leg. What are the dimensions of the garden?

Answers

Answer 1

Answer:

[tex]H = 5200[/tex] - Hypotenuse

[tex]S_1 = 2000[/tex] - Leg 1

[tex]S_2 = 4800[/tex] - Leg 2

Step-by-step explanation:

Represent the dimensions as:

[tex]H = Hypotenuse[/tex]

[tex]Other\ Legs = \{S_1,S_2\}[/tex]

So, we have:

[tex]S_1 = 2000[/tex]

[tex]H = 400 + S_2[/tex]

Required

Determine the dimensions

Apply Pythagoras theorem

[tex]H^2 = S_1^2 + S_2^2[/tex]

This gives:

[tex](400 + S_2)^2 = 2000^2 + S_2^2[/tex]

Open bracket

[tex]160000 + 800S_2 + S_2^2 = 4000000 + S_2^2[/tex]

[tex]160000 + 800S_2 = 4000000[/tex]

Collect Like Terms

[tex]800S_2 = 4000000 - 160000[/tex]

[tex]800S_2 = 3840000[/tex]

Solve for S2

[tex]S_2 = \frac{3840000}{800}[/tex]

[tex]S_2 = 4800[/tex]

Recall that:

[tex]H = 400 + S_2[/tex]

[tex]H = 400 + 4800[/tex]

[tex]H = 5200[/tex]

Hence, the dimensions are:

[tex]H = 5200[/tex]

[tex]S_1 = 2000[/tex]

[tex]S_2 = 4800[/tex]


Related Questions

What is the equation of the line in slope-intercept form? ​

Answers

Answer:

y=1/2x-2

Step-by-step explanation:

RIse / run

find a point then go up one and right two to the next point which gives you 1/2

the y intercept is -2 because thats where the line is interceting

Last month, a car dealership sold 80 cars. Of all the cars sold, 15% of them were red. How many cars that were sold were red?

Answers

Answer:

12 red cars

Step-by-step explanation:

15% is 0.15

So, you do 80 × 0.15, which is 12.

283838383838382828 + 838383838

Answers

Answer:2.8383838e+17

Step-by-step explanation:

Answer:

2.8383838e+17

Step-by-step explanation:

283838383838382828 + 838383838=2.8383838e+17

which expression is equavalent to -3(2m-1)-n
A 6m-n-3
B 6m-n+3
C -6m-n-3
D -6m-n+3

Answers

Answer:

D.) -6m - n + 3

Step-by-step explanation:

-3 (2m - 1) - n

-6m + 3 - n

-6m - n + 3

If I helped, please mark me the Brainliest!?!

Please help lol and thank u

Answers

Step-by-step explanation:

The picture shows us that the shape is a square.

To find the area of a square you would use the formula s^2

s= 8ft

8ft^2 = 64ft^2

with area you would need to use the unit ft^2

I hope this helps!!!

Answer: DDDDDDD

Step-by-step explanation: The formula is width x height, so we can use the expression 8 x 8 assuming this is perfectly square. 8 x 8 is 64 square units

write as a rate
4 shirts for every 3 pairs of pants

A:3/4
b:4 shirts/3 pairs of pants
c:3 pairs of pants/4 shirts
d:4/3​

Answers

Letter b is your answer

pwease help me and i will mark u brainliest

Answers

Answer:

19/15

Step-by-step explanation:

We need to find the difference, so subtraction. But first we should make them improper fractions:

(18/5)-(7/3)

Lets make the common denominator 15:

(54/15)-(35/15)

54-35= 19

19/15

What is the probability of the following.
(a) An event A that is certain to occur?
(b) An event B that is impossible?
Enter an exact number

Answers

Answer:

(a) The probability of an event A that is certain to occur is 1.

(b) The probability of an event B that is impossible is 0.

Step-by-step explanation:

The probability of an event can be described as the chance that the event will occur.

The probability that an event will occur is between 0 and 1.

Based on the above, we can answer as follows:

(a) What is the probability of an event A that is certain to occur?

The probability of an event A that is certain to occur is 1.

(b) What is the probability of an event B that is impossible?

The probability of an event B that is impossible is 0.

Which terms in the expression
5c + 8 + 12c are like terms ​

Answers

Answer:

Step-by-step explanation:

like terms are 5c and 12c because both have the same variable, c

Answer:

The terms 5c and 12c are like terms. They can both be added.

Step-by-step explanation:

It could be any number the variable has to stay the same and if there is none, it can’t be paired. Also watch out for problems like 12c + 5c^2. THey don’t have the same variable due to th ^2

Can someone please help me

Answers

Answer:

3/4

Step-by-step explanation:

While your image is blurry so it hard to, we know to find a slope we do rise (up)/run(Left) at section where they cross the dot. So i did this

A water well drilling rig has dug to a height of -15 feet in three hours. If the rig has been running constantly and is currently at a height of -192.5 feet, for how long has the rig been running?



22.25 hours

97.4 hours

38.5 hours

12.8 hours

Answers

A. 22.25 i think it’s a because it you do your math correctly it was give you A

I NEED HELP NOWWW WIRNSJJAJJDJDJMAMA

Answers

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation: 9 cm and 18cm

Evaluate 0 with a 4 on top

Answers

9514 1404 393

Answer:

  0

Step-by-step explanation:

0 to any positive power is 0.

  0^4 = 0×0×0×0 = 0

Find the domain of the graphed function.
10
-104
A. -4sxs8
B. -4 sxs 9
C. xis all real numbers.
D. X2-4

Answers

Answer:

Answer would be B.

Step-by-step explanation:

there are two dors located at x= -4 and x=9

500 Bhadgaule caps bought for Rs. 200000 in Nepali market are sold in Britain after paying
5% export tax then 150% profit was made. Find the selling price of each Cap in Pound Sterling.
[£ 1 = Rs. 155.63]​

Answers

Answer:

Selling price of each cap = £6.75 (Approx.)

Step-by-step explanation:

Given:

Number of caps = 500

Cost of caps = Rs. 200,000

Export tax = 5%

Profit = 150%

£ 1 = Rs. 155.63

Find:

Selling price of each cap

Computation:

Cost of 1 cap = 200,000 / 500

Cost of 1 cap = Rs 400

After Add export tax = 400 + 400(5%)

After Add export tax = Rs 420

After profit = 420 + 420(150%)

After profit = Rs 1050

Selling price of each cap = 1,050 / 155.63

Selling price of each cap = £6.75 (Approx.)

A bricklayer's apprentice takes 10 hours longer than the bricklayer to make a fireplace. The apprentice worked alone on a fireplace for 5 hours, after which the bricklayer began to help. It took 2 more hours for them to finish the fireplace. How long would it take the apprentice to make the fireplace on his own?

Answers

Answer:

It would take the apprentice 14 hours to make the fireplace on his own.

Step-by-step explanation:

Let x represent the hours it takes the bricklayer to make a fireplace on his own and x + 10 represent the hours it takes the bricklayer's apprentice to make a fireplace on his own.

7/(x + 10) + 2/x = 1

7/(x+10) represents the fraction of the fireplace the bricklayer's apprentice made (total amount of time the bricklayer's apprentice worked on the fireplace/time it takes the bricklayer's apprentice to make a fire place on his own) while 2/x represents the fraction of the fireplace the bricklayer made (total amount of time the bricklayer worked on the fireplace/time it takes the bricklayer to make a fire place on his own). The 1 on the right side of the equation represents the number of fireplaces they made in that time.

Multiply both sides of the equation by x(x + 10) to get rid of the denominators:

x(x + 10)[7/(x + 10) + 2/x] = x(x + 10)1

x(x + 10)[7/(x + 10)] + x(x + 10)(2/x) = x(x + 10)

7x + 2(x + 10) = x² + 10x

7x + 2x + 20 = x² + 10x

Gather all the terms to one side of the equation:

x² + 10x - 7x - 2x - 20 = 0

x² + x - 20 = 0

Factoring the simplified equation:

(x + 5)(x - 4) = 0

Solving for each factor:

When x + 5 = 0,

x = -5

When x - 4 = 0,

x = 4

Since a negative solution wouldn't make sense for this question, it would take the bricklayer 4 hours to complete the fireplace on his own.

Substituting x = 4 into x + 10 to find out how long it would take the apprentice to make the fireplace on his own:

x + 10 = 4 + 10 = 14

Therefore, it would take the apprentice 14 hours to make the fireplace on his own.

answer quickly please Which number is the BASE?
2 = 8

Answers

Answer:

The base of the number is 8

Leslie and her friend eat lunch at a restaurant.
To determine how much money to leave as a tip, she multiplies the bill by 0.18.
How much money should she leave as a tip if the bill is $25?

A. $6.25
B. $5.00
C. $4.50
D. $3.70

Answers

Problem:

Leslie and her friend eat lunch at a restaurant.

To determine how much money to leave as a tip, she multiplies the bill by 0.18.

How much money should she leave as a tip if the bill is $25?

A. $6.25

B. $5.00

C. $4.50

D. $3.70

Solution:

[tex]25 \times 0.18[/tex]

[tex] = 4.5[/tex]

Answer:

C. $4.50

#CarryOnLearning

#AnswerForTrees

#BrainlyBookSmart

A variable needs to be eliminated to solve the system of equations below. Choose the
correct first step.
7x +y = 33
-7x + 6y = -47

Answers

Answer:

x=5 and y=-2

Step-by-step explanation:

The given system of equations are :

7x +y = 33  ....(1)

-7x + 6y = -47 ....(2)

We need to find the solution of the given equations.

Adding equation (1) and (2) we get :

7x +y + (-7x) +6y = 33+(-47)

7y = -14

y = -2

Put the value of y in equation (1).

7x +(-2) = 33

7x-2=33

7x=33+2

7x = 35

x = 5

Hence, the solution of the above equations are x=5 and y=-2

Crew owes his mom $23 and James owes his mom $8. Which amount has the greatest magnitude?

Answers

Crew because 23>8 23 is larger than 8

Magnitude=A great size, or extent of something

the diameter of a cylinder is 8 inches. the height is 12 inches. what is the surface area of the cylinder?

Answers

Answer:

[tex]\boxed{\boxed{\pink{\tt \leadsto The \ Surface\ Area \ is \ 402.28\ in.^3. }}}[/tex]

Step-by-step explanation:

Given that the the diameter of a cylinder is 8 inches. the height is 12 inches. And we need to find its surface area .

Hence here ,

Height = 12 inches Diameter of base = 8 inches

Figure :-

[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4\ in.}}\put(9,17.5){\sf{12\ in.}}\end{picture}[/tex]

[tex]\bf\implies TSA_{Cylinder}= 2\pi r ( r + h) \\\\\bf\implies TSA_{Cylinder} = 2\pi \dfrac{8\ in.}{2} \bigg( \dfrac{8\ in.}{2} + 12 in.\bigg)\\\\\bf\implies TSA_{Cylinder} = 2\pi \times 4 ( 4 \ in.+ 12 \ in.) \\\\\bf\implies TSA_{Cylinder}= 8 \times \dfrac{22}{7}\times 16 in.^3 \\\\\bf\implies\boxed{\red{\bf TSA_{cylinder}= 402.28 in.^3}}[/tex]

Hence the Surface area of the Cylinder is 402.28 in.³ .

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The surface area of the cylinder is 402.124 inches².

What is a cylinder?

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

The surface area of a cylinder is the sum of the area of the base and the lateral area of the curved cylinder.

Given that the diameter of the cylinder is 8 inches, while the height of the cylinder is 12 inches. Since the radius is half the length of the diameter. Therefore, the radius of the given cylinder is 4 inches.

Now, the surface area of the cylinder is,

Surface area of the cylinder = Area of the bases + Area of the curved surface

= 2(πr²) + 2πrh

= 2(π × 4²) + (2 × π × 4 × 12)

= 2(50.265) + 301.5928

= 100.5309 + 301.5928

= 402.124 inches²

Hence, the surface area of the cylinder is 402.124 inches².

Learn more about Cylinder here:

https://brainly.com/question/12248187

#SPJ2

Triangle V P M. Angle V is 52 degrees, angle P is 78 degrees, angle M is x degrees. What is the measure of AngleM?

Answers

Answer:

The answer is 50

Step-by-step explanation:

Got it right on edge

Answer:

50 the guy under me got it right on edge 2021

Step-by-step explanation:

Hopes this helps!!! ^^

order dessert
no dessert
split the check
one person pays

Answers

I don't understand, what's the question?

A large rock (mass = 4.0 kg) moving at a velocity of 2.0 m/s has a momentum of _______ kg*m/s

Answers

Step-by-step explanation:

❁ [tex] \underline{ \underline{ \text{Given} }}: [/tex]

Mass of a large rock ( m ) = 4.0 kgVelocity ( v ) = 2.0 m/s

❁ [tex] \underline{ \underline{ \text{ \: To \: find}}}: [/tex]

Momentum ( p )

✑ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]

[tex] \boxed{ \underline{ \sf{Momentum \: = \: mass \: \times \: velocity}}}[/tex]

plug the known values :

⟹ [tex] \sf{Momentum = 4.0 \: kg \: \times \: 2.0 \:m/s } [/tex]

⟹ [tex] \sf{Momentum = 8 \: kg \: m/s}[/tex]

[tex] \red{ \boxed{ \boxed{ \tt{⟿ \: Our \: final \: answer : \bold{ \underline{8} }\: kg*m/s}}}}[/tex]

⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆

✑ [tex] \underline{ \underline{ \text{Learn \: more about \: momentum}}}: [/tex]

Imagine that a car and a truck both have the same speed on the road. Which one can stop easily ? Of course , it is hard to stop the truck relative to the car. The reason is that the car and the truck have the same speed bit different masses. Thus , we can say that to stop a heavier body is harder than to stop a lighter one even both of them have the same speed.

If two tennis balls are hit towards you in different velocities , it is not equally easier to stop them. The ball in more velocity is difficult to stop relatively. Thus , we can say that to stop a body in more velocity is harder than to stop a body with less velocity , eventhough they have the same speed.

The physical quantity that describes the quantity of motion of a body is called momentum. The momentum of a moving body or linear momentum is defined as the product of mass & velocity of a moving body.

Mathematically ,

Momentum = mass × velocity

i.e p = m × v

The SI unit of momentum is kg • m/s. Since velocity is a vector quantity and multiplied with mass ( scalar quantity) , momentum becomes a vector quantity. Direction of momentum is the same as velocity.

Hope I helped ! ♡

Have a wonderful day / night ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

h = 4x and x= 3t write h in terms of t

Answers

Answer:

h = 12t

Step-by-step explanation:

Its given that x = 3t.

Also its given that h = 4x

Substituting the value of x gives =

h = 4(3t) = 4 × 3t = 12t


Write an equation for the nth term of
the arithmetic sequence:
15,28,41 ....

Answers

Answer:

The equation for the nth term of  the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]

Step-by-step explanation:

We need to write an equation for the nth term of  the arithmetic sequence:

15,28,41 ....

The equation for arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]

Where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is first term and d is common difference

In the given sequence we have:

a₁ = 15

a₂ = 28

We can find common difference using the formula:

[tex]a_n=a_1+(n-1)d\\Put\: n=2, a_2=28\: and\: a_1=15\\a_2=a_1+(2-1)d\\28=15+d\\d=28-15\\d=13[/tex]

So, the common difference d is 13

Now, equation for nth term will be:

[tex]a_n=a_1+(n-1)d\\Put\:a_1=15, d=13\\a_n=15+(n-1)13\\Solving:\\a_n=15+13n-13\\a_n=13n+2[/tex]

So, the equation for the nth term of  the given arithmetic sequence is: [tex]\mathbf{a_n=13n+22}[/tex]

where n=1,2,3..

HELP PLEASEE ANYBODY

Answers

Answer:

you didn’t provide a question

Step-by-step explanation:

Find domain of the function
F(x)=7x+4

Answers

Answer:

all real numbers or infinity

Step-by-step explanation:

this function is linear and linear functions always have an infinite domain and range

help now plsssss!!!!!!!

Answers

The answer is 5, all you have to do is multiply one of the denominations and if you multiply 6 by 10 it = 60 and if you multiply 10 by 6 you get 60 there for you simplify that which equals to 5

Can anyone help me with this?

Answers

Answer:

D. -6m²n² + 10m²n + 8mn² - 10mn

Step-by-step explanation:

(-7mn + 8mn² - 8m²n²) + (10m²n + 2m²n² - 3mn)

Apply the distributive property to remove the parentheses

-7mn + 8mn² - 8m²n² + 10m²n + 2m²n² - 3mn

Combine like terms together and arrange in standard form

-7mn + 8mn² - 8m²n² + 10m²n + 2m²n² - 3mn

-8m²n² + 2m²n² + 10m²n + 8mn² - 7mn - 3mn

-6m²n² + 10m²n + 8mn² - 10mn

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