The hypotenuse of a right triangle is 10 inches long. The longer leg is 2 inches longer than the shorter leg. Find the side lengths of the triangle.

Answers

Answer 1

Answer: Shorter leg = 6 inches

Longer leg = 6+2 = 8 inches

Step-by-step explanation:

Let the shorter leg bw represented by x.

Therefore, the longer leg will be x+2.

The hypothenuse is 10inches

We should note that in Pythagoras theorem, the square of the longer and shorter side equals the square of the hypothenuse. This will be:

x² + (x+2)² = 10²

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4

2x² + 4x = 96

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

x² + 8x - 6x - 48 = 0

x(x + 8) -6(x + 8) = 0

x - 6 = 0

x = 0+6.

x = 6

Shorter leg = 6 inches

Longer leg = 6+2 = 8 inches


Related Questions

1 2/5
rename the mixed number as an improper faction
a. 3/5
b, 12/5
c, 2/6
d, 7/5

Answers

Answer:

the answer is b

Step-by-step explanation:

i don't know I just do lol

A bag contains 18 balls. There are 6 red balls, 6 yellow balls, and 6 green balls. A ball is drawn at random and returned. Then another ball is drawn at random. Select ALL statements that are true.

A. The expected probability of drawing a green ball first is the same as the expected probability of drawing a green ball second.

B.There are six possible outcomes.

C.The probability of drawing a red ball first is the same as not drawing a red ball second.

D.The expected probability of drawing a red ball and then a yellow ball is 19.

Answers

Answer:

There are 18 balls in the bag:

6 are red

6 are yellow

6 are green.

A ball is drawn at random and then returned.

Then another ball is drawn.

Now, let's analyze each option and let's see if it is true or not.

A) The probability of drawing at random a green ball is equal to the quotient between the number of green balls and the total number of balls.

Then for the first draw, the probability is 6/18

Because the drawn ball is returned, for the second draw we still have 6 green balls and 18 balls in total, then the probability still is 6/18

Statement A is true

B) if we define the notation:

YR

as:

Yellow in the first draw, red in the second draw.

The possible outcomes are:

YR

YG

YY

RR

RG

RY

GR

GG

GY

So we have a total of 9 outcomes, we also can calculate this in the following way:

For the first event (first draw) we have 3 possible outcomes (Y, G, and R)

For the second event (second draw) we have again 3 possible outcomes.

The total number of outcomes is the product between the possible outcomes for each event, this is:

3*3 = 9

Then statement B is false.

C) The probability of drawing a red ball first is:

p = 6/18

The probability of NOT drawing a red ball second, is equal to the probability of drawing a yellow or green ball second (we have 12 balls that are green or yellow, and 18 total balls) then this probability is:

q = 12/18

The probabilities are different, then we can conclude that statement C is false.

fD) The expected probabilty of drawing a red ball and then a yellow ball is the product of the individual probabilities, this is:

prob of drawing a red ball first = 6/18

prob of drawing a yellow ball second = 6/18

Joint probability:

P = (6/18)*(6/18) = (1/3)*(1/3) = 1/9

So statement D is true.  (it says 19, i suppose that there is a mistake in this sentence and it actually should say 1/9)

What are the steps to solving this?

Answers

Answer:

m = 6[tex]\sqrt{3}[/tex] , n = 6

Step-by-step explanation:

Using the sine and cosine ratios in the right triangle and exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{m}{12}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2m = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

m = 6[tex]\sqrt{3}[/tex]

and

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{n}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2n = 12 ( divide both sides by 2 )

n = 6

HELPP! E(f + g) =




Help

Answers

What! You need more information if you want people to help you.

What is the volume of this square pyramid?

Answers

Answer:

400m^3

Step-by-step explanation:

Answer: [tex]400m^{2}[/tex]

Step-by-step explanation:

In order to solve this square pyramid's volume, we use the formula:

V = 1/3(B)(h)

Now, we plug in what we know. Since it has a square base, the sides of the base are all the same:

1/3(10*10)(12)

Now we solve:

1/3(100)(12)

1/3(1200)

400

Help fast as you can worth 7 points

Answers

Answer:

d

Step-by-step explanation:

Answer: B

Step-by-step explanation: you have to multiply the 4 and 2

helpppppppppppppppppppp​

Answers

Answer:

6:5:4

Step-by-step explanation:

6 + 5 + 4 = 15

3000/15 = 200

200 x 6 = 1200 = eldest

200 x 5 = 1000 = 2nd eldest

1200 + 1000 = 2200

3000 - 2200 = 800

200 x 4 = 800 = youngest

Answer 6 : 5 : 4

Step-by-step explanation:

Its simply because

1200 ÷ 6 is 200 which is a whole number... If you divide for example 1200 by 7 it wont give you a whole... And also the first number of the ratio should be the greatest since the first child got the most money and the last the least which means the least should be the smallest number.

Given that y varies inversely with x, if y=-5 when x=-6, find x when y=-2.5.

Answers

15

Explanation:

If y varies inversely as x, the two variables can be represented in an equation in the form

y

=

k

x

where

k

is some constant.

We are given that

y

=

5

when

x

=

6

. We can plug this into the above equation to find what

k

is:

5

=

k

6

30

=

k

Based on this we can create our equation:

y

=

30

x

And then find

x

when

y

=

2

:

2

=

30

x

2

x

=

30

x

=

15

pleaseeee help me, i dont have much time to finish

Answers

Answer:

[tex]\sqrt{80} \\OR \\ 5\sqrt{4}[/tex]

Step-by-step explanation:

pythagorean theorm

and then simplify with a factor tree or leave it as is.

BRAINLIEST PLEASE IF RIGHT

Use the diagram to answer, given that line LM is a common tangent to circle P and circle Q. Leave answers in simplified radical when necessary. (Please let me know if the first blank is correct and answer the second one.)

Answers

Answer:

PL = 9

PN = 5√5

Step-by-step explanation:

8/12 = 6/PL

8PL = 72

PL = 9

PN² = 10² + 5² = 100 + 25 = 125

PN = √125 = 5√5

plz help with everything in the pic

Answers

HERE I TOOK PICTURES

i only understand number 11

The product of 6x5/3 will be (less than, greater than, equal to) 6 because the fraction 5/3 is (less than, greater than, equal to) 1

Answers

Answer:

The product of 6x5/3 will be greater than 6 because the fraction 5/3 is greater than 1.

Step-by-step explanation:

Note: If any fraction which the numerator and denominator have the same number , for example 6/6 it will equal to 1. If the numerator overpasses the denominator, it will be more than 1.

During April, he charges $387.92 to the card, and at the end of April, he makes a payment of $400.00. What will be the new balance on his card?

Answers

he would have no money because he used it

A single card is drawn from a standard 52 card deck.
Work out the probability of choosing the "5 of diamonds".
Give your answer

Answers

Answer:

1/52

Explanation:

Solve using substitution x=-6 6x+10y=14

Answers

Answer:

(-6 , 5)

Step-by-step explanation:

6x + 10y = 14

6(-6) + 10y = 14

-36 + 10y = 14

10y = 50

y = 5

A sequence defined by the rule f(n)=4f(n-1)+2.if f(1)=3 then find f(4)=?

Answers

Answer:

f(4) = 6

Step-by-step explanation:

Given the rule f(n) = 4f (n - 1) + 2 where f(1) = 3, f(n) is just a fancy way to name the variable y. As you've seen before, there are equations that are usually y equals x and something. For example:

y = mx + b

is the same thing as

f(n) = y = mn + b.

It might be that you have multiple of the same equation where f(n) and f(x) have two different outcomes.

The f(n) part (bolded) is the "x variable" in this equation. So in f(1), n = 1.

f(n) = 4f (n - 1) + 2

f(n) = (4fn - 4f) + 2

f(n) = (n) + 2

f(1) = 1 +2

3 = 3

Now do the same thing for f(4):

f(n) = 4f (n - 1) + 2

f(n) = (4fn - 4f) + 2

f(n) = (n) + 2

f(4) = 4 + 2

f(4) = 6

3) What is 3x +15y=-16 in slope intercept form?

Answers

Answer:

y=-1/5x-16/15

Step-by-step explanation:

slope intercept form y=mx+b

3x+15y=-16

15y=-3x-16 divide both sides by 15

y=-3/15x-16/15   simplify -3/15 to -1/5

y=-1/5x-16/15

can someone pls help me with this question

Answers

Answer:

6

Step-by-step explanation:

The x intercept is the value of x when y equals zero. The table tells us that when x goes up by one, y goes down by two.

Knowing this, all we have to do is increase x by 1 and decrease y by two until y is zero, and we can look and see what x is.

I also made a visual in the file below if this is confusing

Ramsay cuts out a piece from a circular cardboard for a school project. The radius of the cardboard is 10 inches and the measure of the central angle is 54 degrees, as shown.

What is the length of the curved boundary of the piece of the cardboard Ramsay cuts out?
Leave in terms of π.

Answers

Answer:

34 inches

Step-by-step explanation :

54/360 X 20

pls help, The graph shown below shows the relationship between average heart rate (in beats per minute) of several
mammal species and their life expectancy (in years)

Answers

Answer:

The answer is Nonlinear Association

Hi There Answer Nonlinear Association

Step-by-step explanation:

Complete the table below to classify the triangles as scalene or isosceles.
Triangle
Classification
2
2
3
5
10
9
<
3

Answers

Answer:

1) Isosceles

2) Scalene

3) Scalene

Step-by-step explanation:

The 1st choice is isosceles because 2 side lengths are equal.

The 2nd and 3rd choice are scalene because none of the sides equal the other sides.

H E L P
what is the slope??

Answers

1/3 is the slope
X= 12-6=6
Y= 4-2=2
I got the slope 1/3 I used the points (6,2), (12.4)

Maurice fills a ball in the shape of a sphere with air. The diameter of the ball when it is filled is 24 inches. How much air, in cubic inches, is in the ball when it is filled? Solve in terms of π like the example above.


PLEASE HELP ME

Answers

Answer:

2304pi inches³

Step-by-step explanation:

volume of ball = 4/3pi r³

=4/3 x pi x 12³=2304 pi inches³

If a fair coin is tossed 6 times, what is the probability, to the nearest
thousandth, of getting exactly o heads?

Answers

Answer:

0

Step-by-step explanation:

the probability of getting 0 heads is not possible as either 1 side has to be a head or a tail

It cannot be none

Therefore...Probability is 0 of getting 0 heads

plz mark as brainliest

thanks

Decrease £16855.21 by 13.5%

Answers

Answer:

£14579.76

Step-by-step explanation:

First do 16855.21 * .135 =  2275.45335 now do 16855.21 - 2275.45335 to get 14579.75665 round this to get 14579.76

2 students want pancakes and 9 students want waffles. What is the ratio of the number of
students who want pancakes to the number of students who want waffles?

Answers

Answer:

2:9

Step-by-step explanation:

To create the ratio, put the number of students that want pancakes to the number that wants waffles.

Since 2 want pancakes and 9 want waffles, the ratio will be 2:9

So, the answer is 2:9

Answer:

2:9

Step-by-step explanation:

beacause if every 2 students want pancakes and 9 want waffles

A rectangular piece of fabric was used to make a banner. It measured 12 feet long and had an area of 24 square feet. What is its perimeter?

Answers

Answer:

the perimeter is 28

Step-by-step explanation:

2+2=4

12+12=24

24+4=28

Answer:

Perimeter = 28 feet

Step-by-step explanation:

The formula to find the area of a rectangle is Length * width and we already have one dimension here, so we simply plug it in and make an equation to the find the unknown measurement

12 * d = 24

d = 24/12

 d = 2

So the missing dimension is 2 feet

Now we simply find the perimeter of the rectangle  using the formula

   2 ( length + width)

 = 2 (12 + 2 )

           = 2 ( 14 )

           = 28 feet

 

GAHHHHHHHHHHHHHHHHHHHHHHHHH
HELP PLEASE

Answers

P.PENEEEEEEEE,TE GUSTAA∞[tex]\pi \sqrt{x} x^{2} \neq \alpha \sqrt[n]{x} \sqrt[n]{x}[/tex]

Simplify: 6^6/6^−3 Leave your answer in exponential form

Answers

Answer:

6⁹

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Exponential Rule [Multiplying]:                                                                        [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Exponential Rule [Dividing]:                                                                             [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{6^6}{6^{-3}}[/tex]

Step 2: Simplify

Exponential Rule [Dividing]:                                                                              [tex]\displaystyle 6^{6 - -3}[/tex]Rewrite:                                                                                                             [tex]\displaystyle 6^{6 + 3}[/tex]Add:                                                                                                                   [tex]\displaystyle 6^{9}[/tex]

hi please help i’ll give brainliest

Answers

Answer:

The answer is B

Step-by-step explanation:

IT SHOWS THAT A SOLAR ECLIPSE OCCURS WHEN THE MOON CASTS A SHADOW OVER EARTH.

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