A right triangle with a hypotenuse of square root of 61 has an area of 15 square inches. Find the lengths of the other two sides.



Answers

Answer 1

The lengths of the other two sides are 6 inches and 5 inches

Let b represent the base of the right triangle, h represent the height of the right triangle and x represent the hypotenuse.

Since the area of the triangle is 15 in², hence:

Area(A) = (1/2) * base * height

15 = (1/2)bh

bh = 30  

b = 30/h         (1)

Applying Pythagoras theorem also:

x² = b² + h²

(√61)² = b² + h²

61 = (30/h)² + h²

61 = 900/h² + h²

61h² = 900 + h⁴

h⁴ - 61h² + 900 = 0

h = -6, -5, 5, 6

Since the length cant be negative, hence h = 5 or h = 6

When h = 5; b = 30/5 = 6

When h = 6; b = 30/6 = 5

Therefore the lengths of the other two sides are 6 inches and 5 inches

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Related Questions

What property is illustrated by the statement? 5(- 7 10 )=(- 7 10 )5 A) Commutative Property of Multiplication B) Commutative Property of Addition C) Associative Property of Multiplication D) Associative Property of Addition

Answers

Answer:

commutative property of multiplication

Step-by-step explanation:

Name the property used: commutative property of multiplication

Answer: commutative property of multiplication

thanks in advance big boys​

Answers

Answer:

The answer is sides are congruent by the reflexive property

Step-by-step explanation:

The answer is sides are congruent by the reflexive property because the two red lines on the triangles represnt that they are congruent. The reason teh fourth one can be a correct answer, but it is not, is because the angles are not vertical. The angles would hav eto be in teh middle of the triangle and congruent, to be right. So it is a reflexive property.

Sorry for any gramatical or spelling mistakes!

Lewis is rolling a 10-sided die 250 times. Each side of the die is labeled with a number 1 – 10. Based on the theoretical probability, how many times would Lewis be expected to roll a multiple of 3?

A. 25
B. 30
C. 75
D. 83

Answers

Answer: So the multiplies of 3 on a ten sided die are 3, 6, and 9. theoretically each side should be rolled 25 times (250/10=25). Lewis would be expected to roll a multiple of three 75 times

Step-by-step explanation: Please mark brainliest

Answer:

75 -- i think

Step-by-step explanation:

let me know if im right.

Of 90 gallons of water the average person uses each day, 30% is used outdoors. Mason wants to know how much water is used outdoors. How much water is used outdoors.

Answers

Answer:

The Awnser is 27 for both I did that I-ready before

Step-by-step explanation:

Answer:

27 for both blanks

Step-by-step explanation:

I just did it on iready and I got it correct

Joleen and Pablo want to fertilize a rectangular garden
with an area of A square feet. They know that 5 cups of
fertilizer will cover an area of 240 square feet. They each
write an equation to represent the relationship between
the area, A, and the number of cups of fertilizer, c.
Joleen's equation: A = 480
Pablo's equation: c = 45
:

Which of the equations is correct? Explain how you know.

Answers

Answer: A

Step-by-step explanation:

Because 489 + 45

Determine the probability of selecting a two-child family with one boy and one girl assuming boys and girls are equally likely

Answers

Using the binomial distribution, it is found that there is a 0.5 = 50% probability of selecting a two-child family with one boy and one girl.

For each child, there are only two possible outcomes, either it is a boy, or it is a girl. The probability of a child being a boy or being a girl is independent of any other child, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.

In this problem:

Two children, hence [tex]n = 2[/tex].Equally as likely to be a boy or a girl, hence [tex]p = 0.5[/tex].

The probability of one of each is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{2,1}.(0.5)^{1}.(0.5)^{1} = 0.5[/tex]

0.5 = 50% probability of selecting a two-child family with one boy and one girl.

A similar problem is given at https://brainly.com/question/24863377

Write the prime factorization of 26.​

Answers

Answer:

The factors of 26 are 1,2,13,26 The prime factors of 26 are 2 and 13.

Step-by-step explanation:

Answer:

2 and 13

Step-by-step explanation:

First, we can see that the last digit of

26

is even, and thus

26

is divisible by

2

. If we divide by

2

, we find

26

2

=

13

. As

13

is a prime number, there are no further prime factors of

26

, and so the prime factorization of

26

is

2

×

13

.

here's my question. ​

Answers

Answer:

30 Chocolates

Step-by-step explanation:

The box was new and therefore full, so it had 5/5 of chocolates left.

When Bob ate 18, 2/5 were left, so he must have eaten 5/5 - 2/5 or 3/5 of the chocolates:

5/5 - 2/5 = 3/5

You know that 3/5 of the chocolates are 18, as he ate 18 chocolates. Divide 18 by 3 to get 6:

18 / 3 = 6

This is 1/5 of the chocolates. Multiply this by 5 to get 30:

6 * 5 = 30

This is 5/5 of the chocolates and therefore the total is 30 chocolates.

Two air ducts together remove 525 cubic feet of air per minute. The larger duct removes 45 cubic feet of air less than twice the amount of air removed by the smaller duct. How many cubic feet of air per minute are removed by each duct?

Answers

Answer:

I don't know

Step-by-step explanation:

The smaller duct removes 190 cubic feet of air per minute and the larger duct removes 335 cubic feet of air per minute.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Let's assume that the smaller duct removes 'x' cubic feet of air per minute.

So, The larger duct removes (2x - 45) cubic feet of air per minute.

x + (2x - 45) = 525.

3x = 525 + 45.

3x = 570.

x = 190.

So, the smaller duct removes 190 cubic feet of air per minute and the larger duct removes (2(190) - 45) = 335 cubic feet of air per minute.

learn more about linear equations here :

https://brainly.com/question/11897796

#SPJ2

Brainiest fastest answer no link or bot or I report you I report you if you report me

Answers

38.793053.63904.782544.69226.19402.121072.331526.8128.73113.13801.33268.082094.475.494.2537.71884.962065.2419861.71385.44287.984.193619.11113.150.27

I did this really quick so I hope all the answers are right, and double check them if you have time just in case

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 30 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 360 books. Graphically solve a system of equations in order to determine the number of small boxes sent, x, and the number of large boxes sent, y.

Answers

Answer:

altogether can hold 360 books. Graphically solve a system of equations in order to determine the number of small boxes sent, x, and the number of large boxes sent, y.

Step-by-step explanation:

Answer:

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 30 books (30x), each large box can hold 45 books (45y)and altogether can hold a total of 360 books, we can write the following equation to represent this:

30x+45y=360

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation:

y=8-2x/3

Brainliest plz

A moving company charges $450 plus $12 per hour. Another moving company charges $21 per hour. How long is the job that costs the same no matter which moving company is used?

Answers

Answer:

50 hours

Step-by-step explanation:

685,327 round to the nearest thousand

Answers

Answer:

685,000

Step-by-step explanation:

Answer:

685327.000

 

Step-by-step explanation:

The triangle is to be reduced by a ratio of 1:2.
a

Answers

Answer:

where is the triangle?

Step-by-step explanation:

Help me with questions please​

Answers

Answer:

530.93 OR 530.9

Step-by-step explanation:

Since we know what the radius is 13 we replace R with 13 in the formula form area of a circle. area = [tex]\pi 13^{2}[/tex]

So now we multiply 13 squared or 13 x 13 which equals 169

Now we multiply pi and 169 which gives us 530.929 depending on what number you should round to give  us our answer.

530.93

530.9

CALCULATE THE AVERAGE RATE OF CHANGE OF THIS POLYNOMIAL ON THE
INTERVAL (-1.1)

Answers

Answer:

  -1

Step-by-step explanation:

The average rate of change of function f(x) on the interval [a, b] is ...

  m = (f(b) -f(a))/(b -a)

We have ...

  f(-1) = (-1)^5 -2(-1) +3 = -1 +2 +3 = 4

  f(1) = (1)^5 -2(1) +3 = 1 -2 +3 = 2

Then the average rate of change is ...

  m = (2 -4)/(1 -(-1)) = -2/2 = -1

The average rate of change on the given interval is -1.

when randy started his job he earned $8.00 per hour now he makes $450 for working a 40-hour week how much more does he earn per hour than he did when he started

Answers

Answer:

3.25?

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

He now earns:

450/40 = 11.25 dollars per hour.

So he gets 11.25 - 8

= 3.25 dollars more.

all graphs range from -10 through 10 ;)​

Answers

Answer:B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

First, we want to find out what is X.

               3x = -6 --->  x = -2

X is -2 so we want the graph point to start at -2 and from there go down to -10.

hello I need help please help me​

Answers

Answer:

1) equation

2) equation

3) expression

4) expression

Step-by-step explanation:

An equation has a result, or something that equals to .

Numbers 1 and 2 have the word "is" which means equaled to, so they are equations. 3 and 4 don't, so they are only expressions.

Hope that helped :)

Step-by-step explanation:

Examples:

[tex]a+4;\ 3b;\ \dfrac{x}{4}-\text{these are the expressions}\\\\x=5;\ c+5=3c;\ p=q-\text{these are the equations}[/tex]

[tex]1.\ n+4=12-\bold{the\ equation}\\\\2.\ 5\cdot n=50-\bold{the\ equation}\\\\3.\ C\cdot 7-\bold{the\ expression}\\\\4.\ 6\cdot(12+t)-\bold{the\ expression}[/tex]

The scatterplot shows the heights and arm spans of 12 girls on a basketball
team. The line of best fit for the scatterplot is y = x + 2. What is the predicted
arm span for a girl who is 61 inches tall?
72
70
68
Arm span (inches)
66
60
60 62 64 66 68 70 72
Height (inches)

Answers

Answer:63

Step-by-step explanation:

Took the test

Using the equation for the line of best fit of the scatterplot, the predicted arm span is: 63 inches.

What is the Line of Best Fit?

The line of best fit for a scatter plot is modelled as y = mx = 2, where m is the slope and b is the initial value.

Given the equation of the line of best fit as, y = x + 2, to find the predicted arm span, y, for a girl who is 61 in. tall (x), substitute x = 61 into y = x = 2.

y = 61 + 2

y = 63

Therefore, using the equation for the line of best fit of the scatterplot, the predicted arm span is: 63 inches.

Learn more about line of best fit on:

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i need help on this math problem

Answers

Answer:

[tex]\sqrt{81}[/tex] = 9

[tex]\sqrt{169}[/tex] = 13

Step-by-step explanation:

Calculate the average of these values: 38, 48, 58, 68?​

Answers

Answer:

53 is the average value.

Step-by-step explanation:

To find the average, or mean of multiple values you first add them all up:

38+48+58+68=212

Then you count how many different numbers there are, (there are 4 numbers here, if there are 2 of the same numbers you still count them both, just so you understand).

Then you need to divide the total you got, 212, by the total amount of numbers, 4, to get the average amount, 53.

I hope that my answer has helped you, have a great day, ask any questions you have below.

I need help for these 5 questions​

Answers

Answer:

1. 6²=36

2. 289[tex]\frac{1}{2}[/tex] = 17

3. [tex]14^{-2}[/tex] = [tex]\frac{1}{196}[/tex]

4. 10³=1000

5. [tex]5^{4}[/tex]=625

Step-by-step explanation:

Answer:

1. 6² = 36

2. 289^1/2 = 17

3. 14^-2 = 1/196

4. 10³ = 1000

5. 5⁴ = 625

Step-by-step explanation:

I just used the rule that logₓy = n means that xⁿ = y and a logarithm without a base, has a base of 10 (called a "common logarithm").

If an amount of $25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $28,500? The function describing your balance is M(n) =25,000(1+0.04/2)^2n, where n is time in years. Round up your answer to the next period.

Answers

It will take 3 years and 4 months to accumulate $ 28,500.

To determine, if an amount of $ 25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $ 28,500, the following calculation must be performed:

25,000 x (1 + 0.04 / 2) ^ (2X) = 28500 25000 x 1.02 ^ 2X = 28500 1.02 ^ 2X = 28500/25000 1.02 ^ 2X = 1.14 1.02 ^ 6.62 = 1.14 6.62 / 2 = X 3.33 = X

Therefore, it will take 3 years and 4 months to accumulate $ 28,500.

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What is the probability that a point chosen at random in the rectangle is also in the blue triangle?

A triangle inside of a rectangle. The triangle is shaded and has a base of 5 inches and height of 4 inches. The rectangle is not shaded and has a height of 4 inches and length of 5 inches.
One-half
Four-fifths
1
2Simplify:

Answers

Answer:

1/2

Step-by-step explanation:

I did the quiz on Edge 2021 and got it right with 100%.

Please give me brainliest!

Lillian misses 10% of the free throws she attempts in a season. How many total free
throws did she attempt if she missed 51
help fast

Answers

Answer:

510

Step-by-step explanation:

10/100 = 51

10*10/100 = 51*10

100/100 = 510

Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6.

The equation is y−

Answers

Answer:

Step-by-step explanation:

Okay, so the point-slope form is  

(y - y1) = m(x - x1)  

Where m = the slope of the line

and where (x1, y1) is a point on the line

So, if the slope is 6, then m = 6

Now, you plug that and the point (4, -9) into the equation above.

(y -(-9)) = 6(x - 4)

y + 9 = 6(x - 4)

This is the point slope form of the line

Kevin Went for a drive in his new car. He drove at a speed of 56 miles per hour for 358.4 miles. for how many hours did he drive?​

Answers

Answer:

Kevin Drove For 6 Hours and 40 Minutes

Step-by-step explanation:

56 times 6.4 Equals 358.4

Convert it into miles 56MI X 6.4(HR) = 358.4MI

Find the equation of the line with slope 43 and y-intercept (0,−1)

Answers

Answer:

y = 43x -1

Step-by-step explanation:

Using slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = 43x -1

please help!

15 - (-20)

Answers

I think it should be 35
35, the two negatives cancel out if they are next to each other, making it a plus sign instead, so its 15 + 20 = 35
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