the hypotenuse of a right triangle is 24ft long. The length of one leg is 20ft more than the other. Find the length of the legs.

Answers

Answer 1
By the Pythagorean Theorem, the hypotenuse squared is equal to the sum of the sides squared...

h^2=x^2+y^2  

We are told that y=x+20 and h=24 so

x^2+(x+20)^2=24^2

x^2+x^2+40x+400=576

2x^2+40x+400=576

2x^2+40x=176

x^2+20x=88

x^2+20x+100=188

(x+10)^2=188

x+10=±√188

x=-10±√188, x>0 so

x=-10+√188 ft

y=10+√188 ft

If you want approximations...

x≈3.71 ft

y≈23.71 ft
Answer 2
Final answer:

We can find the lengths of the legs of the right triangle using the Pythagorean theorem. One leg is x and the other leg is x+20. A quadratic equation can be solved to find x.

Explanation:

The problem involves a right triangle, and we are given the length of the hypotenuse and a relationship between the lengths of the legs. We can solve it using the Pythagorean theorem, which for a right triangle with legs of lengths 'a' and 'b' and hypotenuse 'c' is stated as a² + b² = c².

Let's assign 'x' to the shorter leg. Given that the other leg is 20ft longer, it would be 'x + 20'. The hypotenuse is given as 24, hence the equation becomes: x² + (x + 20)² = 24².

By solving this equation, we find two potential values for 'x', but since a length can't be negative, we exclude the negative value. Hence, the length of the shorter leg is 'x' and of the longer leg is 'x + 20'.

Learn more about Pythagorean theorem here:

https://brainly.com/question/28361847

#SPJ2


Related Questions

A total of 634 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 fewer students tickets sold than adult tickets. Him many adult tickets were sold?

Answers

x= student tickets
y= adult tickets 

x+y=634
y=x-66

x+y=634 x-y=66   2x=700 x=350 

350+y=634  y=284
 A total of 634 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 fewer student tickets sold than adult tickets. How many adult tickets were sold?
So say adult sold would be x, then student sold would be x-66
add them

x+x-66=634 solve for x
2x=700 divide each side by 2
x=350
so 350 adult and 350-66=284 student

18000 decrease by 15% every year for 3 years

Answers

1st year= 18000 x 0.85 = 15300
2nd year= 15300 x 0.85 = 13005
3rd year= 13005 x 0.85= 11054.25

How to factor 4(x+5)^3(x-1)^2-(x+5)^4 • 2 (x-1) by grouping?

Answers

[tex]\bf 4(x+5)^3(x-1)^2-(x+5)^4\cdot 2(x-1) \\\\\\ 4(x+5)^3(x-1)^2-2(x-1)(x+5)^4 \\\\\\ \underline{2}\cdot 2\underline{(x+5)^3}(x-1)\underline{(x-1)}~-~\underline{2}\underline{(x-1)}(x+5)\underline{(x+5)^3}\leftarrow \begin{array}{llll} notice~the\\ common\\ \underline{factors} \end{array} \\\\\\ 2(x+5)^3(x-1)~[~2(x-1)-(x+5)~] \\\\\\ 2(x+5)^3(x-1)~[2x-2-x-5]\implies 2(x+5)^3(x-1)(x-7)[/tex]

Look at the quadratic equation below. x2 - 10x + 16 = -5 What is this quadratic equation written in standard form? A.5x2 + 10x - 16 = 0 B.5x2 - 10x + 16 = 0 C.x2 - 10x + 11 = 0 D.x2 - 10x + 21 = 0

Answers

ax^2+bx+c=0 is the standard form, so we add 5 to both sides to get 

1*x^2+(-10)x+21=0

Reducing the original price of an item is often called

Answers

Should be markdown, but if you have other options let me know and I'll tell you which it is.  But if markdown is one of your choices, or if this is fill-in, it's markdown.

Answer:

Price reduction.

Step-by-step explanation:

The act of reducing the selling price of products in order to attract costumers is called Price Reduction. This comprehends a marketing strategy.

24x2+25x−47=(−8x−3)(ax−2)−53

Answers

hello : 
the question is : find : a 
24x²+25x−47=(−8x−3)(ax−2)−53
                      = -8ax²+16x-3ax +6-53
                       =  -8ax²+16x-3ax  - 47

24x²+25x−47= -8ax² + (16-3a)x -47
so : -8a = 24
       16-3a =25
a = 24/-8 = -3
16-3(-3) =25...right
conclusion : a = = -3

Traveling at 65 miles/hour, how many feet can you travel in 22 minutes? How do you know?

Answers

65 miles per hour


feet in a mile: 5,280 ft


65 divided by 60= 1.08 miles per minute

22 x 1.08 = 23.76 miles

23.76 mi x 5,280 ft = 125,452.8 ft in 22 minutes
keeping in mind that there are 5280 feet in 1 mile, and 60 minutes in 1 hour.

[tex]\bf \cfrac{65~\underline{miles}}{\underline{hr}}\cdot \cfrac{5280~ft}{\underline{miles}}\cdot \cfrac{\underline{hr}}{60~min}\implies \cfrac{65\cdot 5280~ft}{60~min}\implies \cfrac{343200~ft}{60~min} \\\\\\ 5720\frac{ft}{min}[/tex]

now, if you can do 5720 feet in 1 minute, how many can you travel in 22 minutes?

well, just 22 * 5720.

this figure is a regular 12 sided polygon and measure of a angle is 4

Answers

Well, a 12 sided polygon is called a dodecagon. I hope this helps!

car rental in Thailand cost $35 per day when booked in advance. If rented locally you would be charged 1800 bahts per day. If the exchange rate is 40 bahts equals $1 how much cheaper is it to book in advance

Answers

40 bahts = $ 1.....so 1800 bahts = 1800/40 = $ 45

book in advance = $ 35

so it is (45 - 35) = $ 10 bucks cheaper to book in advance

Answer:

advance booking is cheaper by 400 bahts or $10.

Step-by-step explanation:

Car rental cost in advanced booking = $35 per day

and

when the rented locally it is charged = 1800 bahts per day

it is given that,

$1 is equal to 40 bahts.

now,

Car rental cost in advanced booking =  35  × 40

                                                              = 1400 bahts

hence, when booking is done advance

  the cost is cheaper  by  1800 - 1400 = 400 bahts

hence, advance booking is cheaper by 400 bahts or $10.

Use the direct variation equation y=x/4 to solve for x when y =60

Answers

We have to solve for x when the equation is y = x / 4 and y = 60. We will charge y = 60 into the function:
60 = x / 4
or:
60 = x : 4
x = 60 * 4
Answer:  x = 240

Add or subtract the following mixed numbers using the first method. Be sure your answers are in mixed number format and reduced to lowest terms. 3 3/8 + 2 1/6 =

Answers

we have the number here are 3 3/8 and 2 1/6
by using the first method,
multiplying 3/8 with 3/3 and 1/6 with 4/4 we get 9/24 and 4/24 so,
3 9/24 + 2 4/24 = (3+2) and (9/24 + 4/24)
when adding 3 and 2 we get 5 and adding 9/24 and 4/24 we get 13/24
so the answer is 5 and 13/24

jane drinks 3 1/2 pints of milk a day. how much is this in cups?

Answers

Hey there!

So what we need to know first is how many cups are in a pint...

1 pint = 2 cups 

So now we can set this up as a ratio or a fraction... then give the value of cups a variable (x)

1:2 = 3.5:x
x = 7 cups      <----- That's your answer!  

I hope this helps! :D

Please vote me for Brainliest if there is a second answer! ^__^

A salesperson earns a base salary of $36,000 plus 2 1/2% commission on sales. His total sales for one year was $500,000. Find the salesperson's total pay for that year.

Answers

The answer would be 48,500. 
Final answer:

To calculate the salesperson's total annual pay, we add the commission earned from the total sales to the base salary. The commission is $12,500, and the base salary is $36,000, resulting in a total pay of $48,500.

Explanation:

The question asks us to determine the total pay for a salesperson with a base salary and a commission percentage on total sales. To find the salesperson's total pay for a year, we calculate the commission earned from total sales and add it to the base salary. The salesperson's commission is 2 1/2% of $500,000, which can also be written as 0.025. We calculate the commission by multiplying 0.025 by $500,000, which equals $12,500. Therefore, the total pay for the salesperson for that year is the sum of the base salary of $36,000 plus the commission of $12,500, which gives us $48,500.

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time/4347395/f56da09a?utm_source=registration

Answers

The current grading rate is
(30 minute)/(5 papers) = 6 minutes/paper.

She has 3 hours (or 180 minutes) to grade 35 papers.
She now has 180 - 30 = 150 minutes left, and she has  35- 5 = 30 papers left.

The remaining grading rate is
(150 minutes)/(30 papers) = 5 minutes/paper

Therefore she must work at 1 minute/paper faster to complete grading 35 papers in 3 hours.

Answer: She should work faster at an increased rate of  1 minute per paper.

You place a cup of 200 degrees F coffee on a table in a room that is 67 degrees F, and 10 minutes later, it is 195 degrees F. Approximately how long will it be before the coffee is 180 degrees F? Use Newton's law of cooling: T(t)=T[a]+(T[o]-T[a])e^-kt A. 40 minutes B. 15 minutes C. 1 hour D. 35 minutes

Answers

195=67+(200-67)e^(-10k)

195=67+133e^(-10k)

128=133e^(-10k)

128/133=e^(-10k)

ln(128/133)=-10k

k=-ln(128/133)/10

T(t)=67+133e^(tln(128/133)/10), if T(t)=180

180=67+133e^(tln(128/133)/10)

113=133e^(tln(128/133)/10)

113/133=e^(tln(128/133)/10)

ln(113/133)=tln(128/133)/10

10ln(113/133)=tln(128/133)

t=10ln(113/133)/ln(128/133)

t≈42.5 minutes...

t≈40 minutes (to nearest 5 minutes? :P)


43 mins to keep it
short but other than that same as the the other guy

find the sum
5^71+5^72+5^73=?

Answers

OK: 1312901068244165525555899876053445041179656982421875
What is the purpose??

Which of the following nonlinear inequalities is graphed below? Picture included below!! PLEASE HELP ASAP!

Answers

I think it is A, cause the horizontal axis is 4 (x), and the vertical axis is 8 (y)
and then the <= means that it is inside the ellipse

Answer:

The correct option is A.

Step-by-step explanation:

The general form of an ellipse is

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where, (0,0) is the center of ellipse, (±a,0) are x-intercepts and (0,±b) are y-intercepts.

From the given graph it is clear that the center of ellipse is (0,0), (±2,0) are x-intercepts and (0,±4) are y-intercepts. So, the equation of ellipse is

[tex]\frac{x^2}{(2)^2}+\frac{y^2}{(4)^2}=1[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{16}=1[/tex]

The shaded region is inside the ellipse, (0,0) lie in the solution set and the points lie on the ellipse are included in the solution set, therefore the sign of inequality is ≤.

[tex]\frac{(0)^2}{4}+\frac{(0)^2}{16}\leq 1[/tex]

[tex]0\leq 1[/tex]

This statement is true. The required inequality is

[tex]\frac{x^2}{4}+\frac{y^2}{16}\leq 1[/tex]

Therefore, the correct option is A.

4^2(2^3-3)^1+8(2-1)^10

Answers

Hello Brainly User.

You must use PEMDAS 
4^2(2^3-3)^1+8(2-1)^10
4^2(5)^1+8(1)^10
16(5)+8(1) 
80+8
88

Feel free to contact me with your questions. I am more than happy to help. :)

Find the area of the shaded segment. Round your answer to the nearest square centimeter. Will make brainliest answer if correct :)

Answers

First find the area of the circle using A=pi*r^2
pi*36
Then divide this by 4 because the shaded region is 1/4 of the circle
(36*pi)/4=9*pi
Final answer: B

Draw a quadrilateral with the given description

A rhombus with 6-centimeter sides and two 80 degree angles

Answers

By definition, a quadrilateral is a general term for a parallelogram and a rhombus. They are both 4-sided two-dimensional shapes with two sets of parallel sides. However, a rhombus is a special case. It has equal sides. Consequently, all its angles are equal. Therefore, the resultant drawing is alike to what's in the attached picture. But technically, all its sides are equal to 6 cm and all its angles are equal to 80°.

Answer:

Step-by-step explanation:

By definition, a quadrilateral is a general term for a parallelogram and a rhombus. They are both 4-sided two-dimensional shapes with two sets of parallel sides. However, a rhombus is a special case. It has equal sides. Consequently, all its angles are equal. Therefore, the resultant drawing is alike to what's in the attached picture. But technically, all its sides are equal to 6 cm and all its angles are equal to 80°.

Which system is equivalent to
y= 9x^2
x+y=5
?

Answers

Answer : Option A

Explanation:

we can clearly see that from x+ y=5 we can substitute  y = 5-x in y = 9x^2

Option B is clearly incorrect  x can not be y -5

Option C  is incorrect because y can not be 5 +x

Option D is incorrect because  its y = 9x^2 not y^2 =9x^2 so y can not be 3x

if its y^2 = 9x^2 then  only  implies y =  3x

Answer:

Option 1st is correct

[tex]5-x= 9x^2[/tex]

[tex]y = 5-x[/tex]

Step-by-step explanation:

Given the equations:

[tex]y = 9x^2[/tex]      .....[1]

[tex]x+y = 5[/tex]         .....[2]

We can write equation [2] as:

[tex]y = 5-x[/tex]

Now, substitute this y value in [1] we have;

[tex]5-x= 9x^2[/tex]

Therefore, the system which is equivalent to the given system equation is,

[tex]5-x= 9x^2[/tex]

[tex]y = 5-x[/tex]

For his long long distance phone service Chris pays a $6 monthly fee plus 8 cents per minute. Last month, Chris's long distance bill was $11.52. For how many minutes was Chris billed

Answers

total bill would be X=6.00 +0.08m

where m = minutes

X = total bill

so 11.52 = 6.00+0.08m

subtract 6 from each side

5.52 = 0.08m

 now divide both sides by 0.08

5.52/0.08 = 69

 he was billed for 69 minutes.

In a study of blood donors, 200 were classified as group O and 250 had a classification other than group O. What is the probability that a person will have group O blood? (Enter your answer as a fraction.)

Answers

Probability of O = (number with O)/(Total number of cases)

It always works like this.

P(O) = 200/450 = 4/9

Find the quotient of 3 1/8 and 1 2/7 .

Answers

The answer is 2 because you have to 3 1/8 and 1 2/7


Identify each statement as true or false, show how you would rewrite it to make it a statement.

Answers

1. false= 3•2+3•4
2. true
3. false= 7•20+7•8
4. false= 4•5+4•10
5. true

Identify the domain of the exponential function shown in the following graph: (2 points) Exponential graph starting at point 0, 30000 and approaching the x axis as it moves left to right. Select one: a. all real numbers b. x ≥ 0 c. 0 ≤ x ≤ 30,000 d. 7 ≤ x ≤ 30,000

Answers

b. x>=0
You don't say it terminates but goes to infinity, therefore all values of x>=0 is the domain

Answer: b. [tex]x\geq 0[/tex] , where x is the positive real numbers.

Step-by-step explanation:

We Know that, The Set of all Possible values of independent variable is called Domain of the function.

Since, Exponential graph starting at point (0, 30000),

Thus, the initial value of value of independent variable is 0.

Also,  The given exponential function is approaching the x axis as it moves left to right.

Therefore, The Domain must contain the all positive real numbers.

Thus, the Domain of the given function is [tex]x\geq 0[/tex] , where x is the positive real numbers.

Therefore, Option b is correct.

Sixty dash fivesixty-five percent of households say they would feel secure if they had? $50,000 in savings. you randomly select 88 households and ask them if they would feel secure if they had? $50,000 in savings. find the probability that the number that say they would feel secure is? (a) exactly? five, (b) more than? five, and? (c) at most five.

Answers

 To solve the following problems, we use the binomial probability equation:

P (r) = [n!/(n-r)! r!] p^r q^(n-r)

where,

n = total number of households = 8

r = number of sample

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

 

A. r = 5

P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

P (r=5) = 0.28

 

B. r >5

P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

P (r=6) = 0.26

P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

P (r=7) = 0.14

P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

P (r=8) = 0.03

Therefore total is:

P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

 

C. r ≤ 5

P (r ≤ 5) = 1 - P (r>5)

P (r ≤ 5) = 1 – 0.43

P (r ≤ 5) = 0.57

 

 

if 3×1=34 2×3=65 6×1=67 5×4=209 then 6×3=

Answers

189.

3*1=34 --> split this into two parts. 3*1 is 3 and 3+1 is 4 so put them together and you get 34.

Answer:

189 is the answer

Step-by-step explanation:

What are the domain and range of f(x)=1/5x

Answers

Domain: -∞<x<∞
Range: -∞<y<∞

(-) stands for negative

You have $36,948.61 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until your account totals $280,000. you expect to earn 11% annually on the account. how many years will it take to reach your goal? round your answer to two decimal places at the end of the calculations.

Answers

Current amount in account
P=36948.61

Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n

Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11

We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000

We can solve this by trial and error.


The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000.  It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.

So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.

So it takes 15.00 years to reach the goal of 280000 years.
Other Questions
3. Your teacher wants to make sure everyone has a pencil for class. She has 104 students in all of her classes. The office gave her 4 boxes of pencils. How many pencils were in each box if each of her students receives 1 pencil? Question 3 options: A 26 B 25 C 100 D 50 Candle stubs can be remoulded to form new candles. 6 stubs are required for each new candle. If there are 301 candle stubs, how many new candles can possibly be made IN TOTAL? Vactin corp., a construction company, buys ten truckloads of cement for its new construction project. given this information, the cement bought is an example of a(n) _____. Estella is afraid of cats. to help her overcome her fear, her mother calmly pets and strokes a cat while estella is watching. her mother encourages her to imitate her behavior. estella's mother is using ________. (1 point) Which term refers to careful and deliberate word choice in speaking or writing? Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has. ten less than twice a number is the same as 7 times the number. find the number Which sentence presents a faulty either/or argument? Perhaps more teachers would continue to teach, rather than leave the field, if their salaries were higher. If we value education as much as we claim, we should put our money where our mouth is and raise teachers salaries. Increasing teacher salaries might attract more competent individuals to the profession. If we dont double teachers salaries, then the public education system in this country will fail. An activity book has 21 pages of crossword puzzles, 18 pages of cryptograms, and 12 pages of mazes. bianca randomly selects a page, completes the activity, and then randomly selects another page to complete. what is the probability that bianca first completes a maze and then completes a crossword puzzle? HELP PLEASE!!!!The amount of people in the city of Blonton is increasing due to children being born and because people are moving to the area.~The population is increasing due to births by 13% each year and about 2300 people move to the area in any given year.~The increase due to people moving to the area is represented by the function M(t) = 2300t.~The population at any time when taking into account new births is found by P(t) = 375,000(1.013)t where 375000 was the initial population and t stands for the number of years after 1990.If we added these functions together, what would the sum represent? Jasmin belongs to the chess club on her campus. she prefers to associate with other members of the chess club while avoiding people that do not belong to this group. jasmin has a(n) ________ bias. What is the dividend on an 8 percent preferred stock that currently sells for $45 and has a face value of $50 per share? Read the sentence:If the poem is about going mad when love is lost, what would happen if love didnt die? Identify the independent clause.ANSWERS:1. If the poem is about going mad when love is lost2. if love didnt die3. what would happen4. when love is lostWill give brainliest! Please answer as soon as possible... 44^4 = 22^4 * ? find the missing factor in exponential form. How would you solve this? If the price of an item is $34 and the sales tax on it is $1.36, what is the sales-tax rate? summarize the events and forces that shaped human evolution Which of the following is NOT a workplace right? Overtime pay for hourly workers who work more than 40 hours in one week equal pay for two people doing the same job with the same set of skills 12 weeks of paid leave for the birth of a child or illness children under 18 cannot work in hazardous conditions an architect designs a rectangular flower garden such that the width is exactly two thirds of the length if 320 ft of the antique picket fencing are to be used to enclose the garden find the dimensions of the garden Four is no less than the quotient of a number x and 2.1 Labor rate = $7.50 per hour Labor time = 6.5 hours Retail price of parts = $0 Total job cost = $82.00 Overhead rate? Steam Workshop Downloader