The hypotenuse of a right triangle is one inch longer than the longer leg. The shorter leg is seven inches shorter than the longer leg. Find the length of the hypotenuse.

Answers

Answer 1

Answer:

Length of hypotenuse is 13 unit or 5 unit

Step-by-step explanation:

Find;

Length of hypotenuse

Computation;

Assume;

Length of hypotenuse = h

Length of longer leg = h - 1

Length of shorter leg = h - 1 - 7

Using Pythagorean theorem

hypotenuse² = longer leg² + shorter leg²  

h² = (h - 1)² + (h - 1 - 7)²  

h² = (h - 1)² + (h - 8)²  

h² = h² - 2h + 1 + h² - 16h + 64  

h² = 2h² - 18h + 65

h² - 18h + 65 = 0

h² - 13h - 5h + 65 = 0

h(h - 13) -5(h - 13)

(h - 13)(h - 5)

So,

Length of hypotenuse is 13 unit or 5 unit


Related Questions

hey! i’ll give brainliest please help

Answers

Answer:

subject

Step-by-step explanation:

subject is a noun (person, place or thing)

verb is doing something *example: running

object is a thing *example: apple

conjunction is a word used to connect sentences *example: but

The underline answer is the subject.

Verb: hit
Object: home run.
No conjunction present in that sentence

The difference of two numbers is 45. Their sum is 55. What are the two numbers?The difference of two numbers is 45. Their sum is 55. What are the two numbers?

Answers

Answer:

50, 5

Step-by-step explanation:

X=number 1

x-45=number 2

x+(x-45)=55

2x=100

x=50 number 1

x-45 is number 2

50-45=5 number 2

The system of linear equations Negative 2 x + y = 8 and Negative 3 x minus y = 7 is graphed below.

On a coordinate plane, 2 lines intersect at (negative 3, 2).

What is the solution to the system of equations?

Answers

Answer:

x= -3

y= 2

Hope it helps :D

Answer:

its A

Step-by-step explanation:

on edge  2021

2x2 = 4 4x 10 = 40 x 32 = ?

Answers

Answer:

1280

Hope this helped :D

hey! i’ll give brainliest please help

Answers

Answer:

A subject and a predicate

Step-by-step explanation:

Have a good day :)

Someone please help <3
How many solutions does the equation 6n − 6n − 12 = 14 − 2 have?
Thank you!!

Answers

Answer:

i think there's zero solutions

calculate the compound interest on an investment of R6500 at 7,5% per annum invested for 3 years​

Answers

Answer:

Compound interest = Rs 1,575 (Approx.)

Step-by-step explanation:

Given:

Amount invested = R.s 6,500

Rate of interest = 7.5% per annum

Number of year = 3 year

Find:

Amount of compound interest

Computation:

Compound interest = P[(1+r)ⁿ - 1]

Compound interest = 6500[(1+7.5%)³ - 1]

Compound interest = 6500[(1+0.075)³ - 1]

Compound interest = 6500[(1.075)³ - 1]

Compound interest = 6500[1.2423 - 1]

Compound interest = 6500[0.2423]

Compound interest = 1574.95

Compound interest = Rs 1,575 (Approx.)

Find the number of moles of Argon in 97.37 grams.

Answers

Answer:

n = 2.43 moles

Step-by-step explanation:

Given mass, m = 97.37 grams

The mass of Argon is, M = 39.948 g/mol

We know that,

No. of moles = given mass/molar mass

[tex]n=\dfrac{97.37}{39.948}\\\\n=2.43\ moles[/tex]

Hence, there are 2.43 moles of Argon.

can somebody help me please and thank you, this is due today. No links please!​

Answers

Answer:

Yes

Step-by-step explanation:

Y=9x2

Y=18

So you put a dot on 18 on the vertical axis and draw a line which is horizontal.

Suma masurilor a doua unghiuri este egala cu 180(de grade). Determinati masura fiecarui unghi stiind ca unul dintre unghiuri are masura egala cu 20% din masura celuilalt unghi

Answers

Answer:

150 grados

30 grados

Step-by-step explanation:

Sea x la medida del primer ángulo

Sea la medida del segundo ángulo y

Según la pregunta;

x + y = 180 -------- (1)

De la segunda oración;

x = 0,2 años -------- (2)

Sustituyendo (2) en (1)

0,2 años + y = 180

1,2 años = 180

y = 180 / 1,2

y = 150 grados

Pero;

x = 0,2 años

Entonces

x = 0,2 (150)

x = 30 grados

Por eso;

y = 150 grados

x = 30 grados

If f(x)=7(x-1)+8f(x)=7(x−1)+8 , what is the value of f(1)f(1) ?

Answers

Answer:

8

Step-by-step explanation:

All you have to do is plug in 1 for the x value, which leaves you with the equation 7(1-1) + 8, then you simplify it to be 7(0) + 8

7 times 0 is 0, so you are left with 8 as your answer

Edward has a box of following Skittles: 5 red, 4 green, 6 orange, 3 purple, and 7 yellow. He wants to know what the probability of choosing a red Skittle, eating it, and then choosing a yellow Skittle is. Which expression below shows Edward how to correctly find the probability of this situation? Skittles Original O 7/25 x 4/25 5/25 x 7/25 5/25 x 7/24 05/24 x 7/24​

Answers

Answer:

Let's add the total skittles to get our outcome:

25 in total.

5(red skittles)/25(total skittles in all)

7(yellow skittles)/24(total skittles in all NOW since you took a red skittle)

So therefore your expression is:

5/25 x 7/24



A certain television is advertised as a 59-inch TV (the diagonal length). If the width of

the TV is 49 inches, how tall is the TV? Round to the nearest tenth of an inch.

Answers

Answer:

32.9 inches

Step-by-step explanation:

this can be solved using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base = 49

c =  hypotenuse = diagonal = 59

l² + 49² = 59²

l² = 59² - 49²

3481 - 2401 = 1080

find the square root

32.9 in

What is the range of 10, 20, 5, 6, 7, 8, 15, 17

Answers

Answer: 15

Step-by-step explanation: Line them up from smallest to largest. 5, 6, 7, 8, 10, 15, 17, 20. Then do the largest number minus the smallest number. In this case, its 20 - 5. That equals 15, so thats your answer

PLEASE HELPPP, ITS DUE IN 1 HOUR!! I WILL GIVE BRAINLIEST!! LINKS=REPORT

PLEASE SOLVE FOR THE CHART AND GRAPH. PLEASE SHOW ON GRAPH

Answers

Answer:

It's the first graph

Step-by-step explanation:

I don’t not know how to do this and I’m struggling,please help.

Answers

Answer:

The answer is option c) 56.5 ft²

Step-by-step explanation:

Area of shaded region =

Area of Big Circle - ( Area of 1st small circle+ Area of 2nd small circle )

Area of 1st small circle:

π x r²

r = 3ft

Area =  3.14 x 3 x 3 => 28.26 ft²

Area of 2st small circle:

π x r²

r = 3ft

Area =  3.14 x 3 x 3 => 28.26 ft²

Area of big circle:

π x r²

r = 6ft ( ∵ Diameter of 1st small circle = 6 and since 2 small circles have equal area, their diameter should be the radius of big circle )

Area =  3.14 x 6 x  6 => 113.04 ft²

Area of shaded region => 113.04 - (28.26 + 28.26 )

=> 113.04 - 56.52

=> 56.52 ft²

find the value of x........................

Answers

Answers: x = 4 and y = 3

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

Explanation:

Triangle UBD is congruent to triangle RAN

Note the order of the lettering as it's important.

BD and AN are the last two letters of UBD and RAN in that order. Therefore, these sides correspond and BD = AN. From that, we know,

BD = AN

2y+5 = 3y+2

5-2 = 3y-2y

3 = 1y

y = 3

-----------

Using similar logic, UD and RN are the first and last letters of UBD and RAN respectively. So,

UD = RN

15 = 2x+7

2x+7 = 15

2x = 15-7

2x = 8

x = 8/2

x = 4

Ahmad and 19 of his friends won a competition.they shared the prize money of $70,000 equally.ahmad saved $2500 of his share and donated the rest.How much did ahmad donate? ​

Answers

Answer:   1000 dollars

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

Explanation:

There are 1+19 = 20 people total. The prize money $70,000 is divided among those 20 people equally to get (70,000)/20 = 3500 dollars per person.

Ahmad saves $2500 of his $3500 prize, leaving 3500-2500 = 1000 dollars leftover. This is the amount he donates.

1000 I agree and I’ve solved this as well

Easy 6th Grade Math. Help me out for 100 points <3

Answers

Answer:

the answer is 33

Step-by-step explanation:

for every 2 Illustrations there are 3 texts meaning if there is 22 Illustrations there would be 33 texts

Answer:

33 text

Step-by-step explanation:

Text : illustrations

3                 2

For every 3 text, there are 2 illustrations

We have 22 illustrations so we need to multiply by 11

Text : illustrations

3*11            2*11

33                  22

We need 33 text

Simplify the expression. Write your answer as a power.5^8/5^5​

Answers

Answer:

5^3

Step-by-step explanation:

First, find 5 to the 8th power:

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 390, 625

Then, find 5 to the 5th power:

5 x 5 x 5 x 5 x 5 = 3,125.

Finally, divided the two numbers:

390, 625/3,125 = 125

Now, right this as a power:

5^3

Can some one help me answer all ten questions they are due at 10:00 I will give out brainly. Part 3 Bonus question

Answers

Answer:

226

Step-by-step explanation:

Area of rectangle:

x+6=17

x=11

11+6=17

11+3=14

17×14=238

Area of triangle:

[tex] \frac{1}{2} \times b \times h[/tex]

Use phytagoras theorem to find the base of the triangle:

c²=a²+b²

5²=4²+b²

25=16+b²

b²=25-16

b²=9

b=√9

b=3 (only the half)

b=6 (the whole base)

[tex] \frac{1}{2} \times 6 \times 4[/tex]

3×4

12

Shades region:

238-12

=226

a recipe for pancakes requires 1 3/4 cups of milk. how much milk is needed to get twice as many pancakes

Answers

Answer:

7/2 cups of milk.

Step-by-step explanation:

1 3/4=7/4

2(7/4)=14/4=7/2

Answer:

7/2 cups of milk.

Step-by-step explanation:

If you want double the pancakes You must double the amount of milk:

First change it into an improper fraction:

1 3/4=7/4

then multiply it by two and simplify:

2(7/4)=14/4=7/2

Allison measured her rectangular deck and found that it has dimensions of
yards by 8 yards. Both the length and the width may have a measurement error of up to
%
What is the maximum possible area of Allison's deck, rounded to the nearest thousandth of a square yard?

Answers

Answer:

Step-by-step explanation:

Shannon won $200 dollars playing Bingo last week. This week she won
$450. What is the percent of change in her winnings?

55.5% increase

125% decrease

55.5% decrease

125% increase

Answers

Answer: 125% increase

Step-by-step explanation: She won 200 dollars last week and now she won 450. If more, less divides. So 450 is more than 200.

This would give you 450/200. You're trying to find percentage so you multiply by a hundred. 450/200 * 100. This will give you 125%

Write a inequality for the graph below

Answers

Answer:

X ≥ -6

Step-by-step explanation:

since the arrow is pointing towards the right side i.e tending towards x

7 - 2x - x4
b) How many terms are there?
c) What is the leading coefficient?
d) What is the constant term?
e) What is the degree of the expression?

Answers

Answer:

b)  three terms

c)  -1

d)  7

e) 4

Step-by-step explanation:

put the expression in decreasing exponent order with the constant at the end

-x⁴ - 2x + 7

With this format it is easy to find the leading coefficient which is the coefficient of the term with the highest exponent; in this case you only see a negative sign but every variable, if no other coefficient is present, has an invisible '1'

I have no idea what I’m doing

Answers

Answer:

15.2 cm, 130 m

Step-by-step explanation:

1. The sine of angle Z is XY/17.4; (opposite/hypotenuse);

sin(61) = XY/17.4; multiply both sides by 17.4 to find XY

17.4sin(61) = 15.2 cm

2.

This triangle is made by the anchor of the balloon to the ground, the balloon, and the area on the ground directly below the balloon.

The hypotenuse of the triangle is the 170 m string.

The angle of inclination is 50 degrees.

The height of the triangle will be opposite of the angle of inclination.

Therefore,

sin(50) = height/170 (opposite/hypotenuse)

170sin(50) = 130.2 meters

the answer would be C, lol we all don’t pay attention in class sometimes haha

Mrs. Genebe worked all year
and earned $23,400. How
much did she earn per week?

Answers

Answer:

$450

Step-by-step explanation:

that's the right answer

need help on this please

Answers

Answer:

5.7

Step-by-step explanation:

7^2- 4^2= 33

[tex]\sqrt{33}[/tex]= 5.7

5.7 is the main answer which is correct

Solve for x: 3(x - 2) = -9
1. 1
2. -1
3. - 7/3
4. 3/7

Answers

Answer:

2) -1

Step-by-step explanation:

Answer:

the answer is 2. -1...............

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