The length of the longer leg of a right triangle is 3 m more than three times the length of the shorter leg. The length of the hypotenuse is 4 m more than three times the length of the shorter leg. Find the side lengths of the triangle. Length of the shorter leg: ​

Answers

Answer 1

Answer:

  7 m, 24 m, 25 m

Step-by-step explanation:

This problem can be solved by writing an equation expressing the given relationships and the Pythagorean theorem. Or, it can be solved by reference to common Pythagorean triples. Here, we're interested in a triple that has a difference of 1 between the hypotenuse and the longer leg. Such triples include:

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}, {11, 60, 61}, ...

We note that for the triple {7, 24, 25}, the longer leg is 3 more than 3 times the shorter leg: 3 +3(7) = 24.

The side lengths are:

shorter leg: 7 mlonger leg: 24 mhypotenuse: 25 m

__

In case you're unfamiliar with Pythagorean triples, or you want to write the equation, you can let s represent the length of the shorter side. Then the longer side is (3s+3) and the hypotenuse is (3s+4). The Pythagorean theorem tells you the relation is ...

  (3s +4)² = (3s +3)² +s²

  9s² +24s +16 = 9s² +18s +9 +s²

  s² -6s -7 = 0 . . . . . subtract the left side and put in standard form

  (s -7)(s +1) = 0 . . . . factor

  s = 7  or  -1 . . . . . . solutions to the equation

The side length must be positive, so the shorter leg is 7 meters long. Then the other two legs are ...

  3s +3 = 3(7) +3 = 24 . . . . meters

  3s +4 = 3(7) +4 = 25 . . . . meters

The side lengths are 7 m, 24 m, and 25 m.


Related Questions

A basket contains 4 pears, 1 pineapple, 5 bananas, 3 oranges, and 2 limes.
vin randomly selects one piece of fruit from the basket. What is the
robability that he selects an orange from the basket?

Answers

Answer:

3/15

Step-by-step explanation:

there is 15 kinds of fruit totally

4 + 1 + 5 + 3 + 2 = 5 + 5 + 3 + 2 = 10 + 3 + 2 = 13 + 2 = 15

there are 3 oranges; therefore the bility that an orange will be picked is 3 out of 15

The radius of a circle is 61 centimeters.
Enter the circumference of the circle, in centimeters. Round your answer to the nearest hundredth.

Answers

Answer:

Circumference of the circle=383.32cm

Step-by-step explanation:

r= 61cm π = 3.142

Formula for the circumference of a circle=2πr

Therefore;

Circumference=2×3.142×61 = 383.32cm.

I need HELP with this question!

Answers

Answer:

It will be C

Step-by-step explanation:

Because it says least to greatest and C says 1/2 3/8 5/16 7/16 9/32 15/32 and that is least to greatest there you go

If x and y vary inversely, and x = 8 when y = 1/4, what is y when x = -4?

Answers

[tex]y \propto \dfrac 1x\\\\\implies y = \dfrac kx \\\\\implies \dfrac 14 = \dfrac k{8}\\\\\implies k=2\\\\\text{When}~ x =-4\\\\y = \dfrac{k}{x} = \dfrac{2}{-4}= -\dfrac 12[/tex]

Solve for p.

3(p + 4) = 48
A. 13

B. 12

C. 14

D. 19

Answers

Step-by-step explanation:

3 ( p + 4 ) = 48

3p + 12 = 48

3p = 48 - 12

3p = 36

p = 36 ÷ 3

p = 12...

Suppose we want to choose 6 letters, without replacement, from 10 distinct letters.

Answers

Answer:

Step-by-step explanation:

If order matters (much like forming... a 4 digit number-maybe for a safe?), you will be computing "permutations".  The  formula for "r" items chosen from  "n" items, where order matters is   Npermutations = nPr  =  n!/ (n-r)!

Npermutations = 10P6 =  10!/(10-6)= 10*9*8*7*6*5 = 151200

When order doesn't matter (such as in dealing a poker hand, its the cards you end up with that matter not the order in which they are dealt into your hand) you will be computing combinations.   The formula for the number of combinations of  "r "items from "n" choices is  Ncombinations =  nCr = n!/((n-r)!r!)

Ncombinations = 10C6 =  10!/((10-6)!6!) =  (10*9*8*7)/(4*3*2*1) = 210

Notice how there are far fewer combinations than permutations.  This makes sense because if you think about how 6 colors  {red, blue, green, white, black, yellow} can be arranged, there are 6!=720 ways to arrange these 6 colors if order matters.  If order doesn't matter, this set of 6 colors counts only once.
Same thing with numbers :)

Hope this helped, brainliest is always appreciated! :)

Have a nice day CX
~Mitsuna

Each marble bag sold by Lashonda's Marble Company contains 8 orange marbles for every 5 red marbles. If a bag has 45 red marbles, how many orange marbles does the bag contain?

Answers

Answer:

72 orange marbles

Step-by-step explanation:

First, divide 45 by 5 to determine how many red units there are. Then, use that number (9) to multiply with 8 to get the number of orange marbles, which is 72.

Hopefully this helps- let me know if you have any questions!

Solve
4x957+8465x563+834
please help i need an answer for my homework

Answers

Answer:

the answer should be 477,0457 if x means multiply but if not you are not putting the equation in a correct way

Answer:

4770457

you just need to calculate them

Which is the better choice: $1000 deposited for a year at a rate of 4.8% compounded semiannually 19) or at a rate of 4.7% compounded quarterly?

Answers

[tex]~~~~~~ \stackrel{\textit{\Large 4.8\% semiannually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &1 \end{cases}[/tex]

[tex]A=1000\left(1+\frac{0.048}{2}\right)^{2\cdot 1}\implies \boxed{A\approx 1048.58}~~\textit{\Large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\Large 4.7\% quarterly}}{\textit{Compound Interest Earned Amount}}[/tex]

[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.7\%\to \frac{4.7}{100}\dotfill &0.047\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &1 \end{cases} \\\\\\ A=1000\left(1+\frac{0.047}{4}\right)^{4\cdot 1}\implies \boxed{A\approx 1047.83}[/tex]

Write an explicit formula for an; the nth
term of the sequence 6, 12, 18, ....

Answers

Answer:

F(n) = 6n

Step-by-step explanation:

An explicit sequence goes by the pattern: A0 + (n-1)d, where A0 is the starting term, n is the nth term in the sequence, and d is the common difference. The explicit formula for this sequence is F(n) = 6 + 6(n-1), or 6n

The answer your looking for is 6n, it starts with six and goes up by six each time.


Which function is shown on the graph?
U
T
30
2
2
O f(x) = sino
-14
O f(x) = jcos
OS I
2

O f(x) = -cos
COS
O f(x)=- sin

Answers

Answer:

Read the explanation

Step-by-step explanation:

look at the photo

The ratio of men to women working for a company is 4 to7. If there are 198 employees total, how many men work for the company

Answers

Answer:

                                                         

Step-by-step explanation:

What inverse operation will be used to undo the volume of Julie's jewelry box to find its edge lengths?

Volume formula for a cube is: volume = edge ^ 3

Answers

Answer:

Cubed root

Step-by-step explanation:

Do the inverse of cubed, cubed root

Sam buys a tent priced at $50 if the sales tax is 5% how much tax will Sam pay

Answers

tax will be = 50 x 5% = $2.5

Find the missing factor.______ x 7 = 2,800
A) 4
B) 40
C) 400
D) 4,000

Answers

Answer:

400

Step-by-step explanation:

[tex] \huge\mathbb\orange{ANSWER} [/tex]

[tex] \mathsf \purple{c) \: 400}[/tex]

A container holds 4 gallons of lemonade. How much is this in pints

Answers

Answer:

i think I'd be / the answer is 46

Solve for x.

x−8=−518

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answers

The value of x in the equation, as a mixed number in simplest form is solved as: x = 2 2/9.

How to Solve an Equation?

To solve for a variable, say x, in an equation, it means to find the value of x that will make the equation true. Do this by isolating x in the equation.

Given the equation:

x/−8 = −5/18

Cross multiply

18x = (-5)(-8)

18x = 40

Divide both sides by 18

x = 40/18

x = 2 2/9.

Therefore, the value of x in the equation, as a mixed number in simplest form is solved as: x = 2 2/9.

Learn more about equation on:

https://brainly.com/question/1214333

A cone has a hight of 18 meters and a radius of 10 meters what is its volume use 3.14

Answers

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=10\\ h=18 \end{cases}\implies V=\cfrac{\pi (10)^2(18)}{3}\implies \stackrel{using~\pi =3.14}{V=1884}[/tex]

Suppose you budgeted $2800 for fuel expenses for the year. How many miles could you drive if gas were $2.70 per gallon and your vehicle averaged 28 mi/gal?

Answers

Answer:

29037.036 miles

Step-by-step explanation

There are two possible ways to solve this problem.

The first option starts with the $2800 dollars for the years. You first want to divide this by $2.70, because it will give you the amount of gallons of gas you can buy with that money.

2800/2.70 = 1037.037

This means you can buy 1037.037 gallons of gas in the year. Now you need to convert this to miles by multiplying by the amount of miles per gallon.

1037.037 x 28 = 29037.036 gallons

The second way to look at this is dimensional analysis. If you have learned this, then continue on reading this, but if you haven't I might only confuse you. I only suggest this because it can make it a little easier.

For the dimensional analysis, you need to start with what you are given and move to what you need to know, so you will start with the $2800 dollars and move to gallons. $2.70 per gallon and 28 miles per gallon are your conversion factors.

Set it up like this:

[tex]2800 dollars * \frac{1 gallon}{2.70 dollars} * \frac{28 miles}{1 gallon} = 29037.036 miles[/tex]

This allows the equation to be more organized, and you can check your work by canceling the units.

Hope this helps.

Answer the following math questions thank you math experts

Answers

Answer:

1) the connection between 2 or more meausures

2) when the r value is closer to 1 or -1 it is a stronger correlation

3) positive correlation would be height and weight. Taller people tend to be heavier. A negative correlation is a relationship between two variables in which an increase in one variable is associated with a decrease in the other

Step-by-step explanation:

choose me as brainlyest:)

The answer to this math question is?

Answers

Answer:

58 seconds

Step-by-step explanation:

Very very easy, no formulas or +,- required here.

You can see that the swim times go till 44 on the line, that is the lowest, that means the FASTEST swim time. But we need the slowest swim time. That we can find by finding where does the line end in the right side. We can see it ends between 56 and 60, and if we calculate, then we can find out that the bar in the middle represents 58, so hence, her slowest timing for her swim time is 58 seconds.

So hence, your answer is 58 seconds!

-------------------------------------------------------------------------------------------------------------

If you see someone without a smile, give them one of yours!

Thanks!

~MiniMeteorologist~

Have a great day!

:D

784x44=? Step by step.

Answers

Answer:

34496

Step-by-step explanation:

i dont know how 2 explain this but you have to do the traditional way of multiplying PLS MARK BRAINLIEST

find the equation of the line that passes through point a and b

Answers

Answer:

y=2x-1

Step-by-step explanation:

How many quarts are in 9 gallons?

Answers

Answer:

1 gallon = 4 quarts

4 × 9 = 36

36 quarts are in 9 gallons

Find the area enclosed by the figure
Fastttttt plsssss​

Answers

Answer:

Explanation:

So you want to start by finding the area of the big square.

We know the width of the big square is 60cm. The length of the big square is

19

+

24

+

13

=

56

Big square

A

r

e

a

=

L

W

=

56

60

=

3360

Now let’s find the little square inside the bigger square. We see from the picture that the width is 34 and the length is 24cm. Using the same formula, we can find the area of the little square.

Little square

A

r

e

a

=

L

W

=

24

34

=

816

The area enclosed in the area of the big square minus the area of the little square.

3360

816

=

2544

So the area enclosed is

2544

c

m

2

Step-by-step explanation:

Multiply 6−√5 by its conjugate and simplify

Answers

[tex]6 - \sqrt{5} \times \frac{6 + \sqrt{5} }{6 + \sqrt{5} } [/tex]

[tex] \frac{(6 - \sqrt[]{5})(6 + \sqrt{5} ) }{6 + \sqrt{5} } = \frac{36 - 5}{6 + \sqrt{5} } = \frac{31}{6 + \sqrt{5} } [/tex]

Mrs. Woods wants to give each of her 25 students a pencil on the first day
of school. The pencils come in boxes of 12. How many boxes will she need
to purchase?

Answers

Answer

3 boxes

Step-by-step explanation:

So she needs to give 25 pencils to each student.

1 box = 12

number of boxes = 25/12

                                  =2.08

round it to 3

Therefore she need 3 boxes

Help picture below please

Answers

Answer:

B. NRS

Step-by-step explanation:

You have to put the letters left to right.

Jackson bought cupcakes for his sister's birthday party. 72 out of the 96 cupcakes had sprinkles on top. What percentage of the cupcakes had sprinkles?

Write your answer using a percent sign (%).

Answers

We divide 72/96 which the answer is 0.75 or 75%

Which symbol < > = will make the comparison true 4/6 and 4/8

Answers

Answer:

4/6 > 4/8

Step-by-step explanation:

To see if the following is true:

We can cross multiply:

[tex]\frac{4}{6}\neq \frac{4}{8}[/tex]        {4* 8 = 32}      {4*6=24}

Thus,

[tex]\frac{4}{6}=32[/tex]

[tex]\frac{4}{8}=24[/tex]

Hence, [tex]\frac{4}{6} > \frac{4}{8}[/tex]

We can also turn them into decimal:

[tex]\frac{4}6=0.6667[/tex]

[tex]\frac{4}{8}=0.5[/tex]

0.5 is NOT greater than 0.6667 which also means that 4/8 is NOT greater than 4/6.

~lenvy~

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