△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has length 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.

Answers

Answer 1

Given:

In △ABC is a right angle triangle.

AC is 6 units longer than side BC.

[tex]Hypotenuse=2\sqrt{17}[/tex]

To find:

The length of AC.

Solution:

Let the length of BC be x.

So, Length of AC = x+6

According to the Pythagoras theorem, in a right angle triangle

[tex]Hypotenuse^2=Base^2+Perpendicualar^2[/tex]

△ABC is a right angle triangle and AC is hypotenuse, so

[tex](2\sqrt{17})^2=(x)^2+(x+6)^2[/tex]

[tex]68=x^2+x^2+12x+36[/tex]            [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]

Subtract 68 from both sides.

[tex]0=2x^2+12x+36-68[/tex]

[tex]0=2x^2+12x-32[/tex]

[tex]0=2(x^2+6x-16)[/tex]

Divide both sides by 2.

[tex]x^2+6x-16=0[/tex]

Splitting the middle term, we get

[tex]x^2+8x-2x-16=0[/tex]

[tex]x(x+8)-2(x+8)=0[/tex]

[tex](x+8)(x-2)=0[/tex]

[tex]x=-8,2[/tex]

Side cannot be negative, so x=2 only.

Now,

[tex]AC=x+6[/tex]

[tex]AC=2+6[/tex]

[tex]AC=8[/tex]

Therefore, the length of AC is 8 units.


Related Questions

An item that cost $220 has been marked up by 15% since last year. However, a person can buy the item for a 25%
employee discount. How much will the employee pay?

Answers

Answer:189.75

Step-by-step explanation: 220 * 0.15 = 33

220 + 33 = 253

253 * 0.25 = 63.25

253 - 63.25 = 189.75

i need help pls i cant understand my math hw​

Answers

Answer:

Ok

Step-by-step explanation:

So what are we magically supposed to know what the equation is

Answer:

uh

Step-by-step explanation:

for us to help please write the question you are stuck on

when a pendulum swings, at which point is potential energy highest?

Answers

The bottom. Mark Brainliest

Simplify.
7√10+2√10-√10

Answers

7√10+2√10-√10

Every square root has the same radicand, which is 10. So, simply combine terms.

7 + 2 - 1 = 9 - 1 = 8

Answer: 8√10

Use these methods to normalize the following group of data:
200, 300, 400, 600, 1000
a) min-max normalization by setting min = 0 and max = 1
b) z-score normalization
c) normalization by decimal scaling

Answers

Step-by-step explanation:

b is the answer , z-score normalization

Normalization is applied to data values in other to ensure that the data scales well, such that data values conforms to a certain range. The output of the various normalization techniques are given below ;

Given the data:

200, 300, 400, 600, 1000

1.)

Min - Max normalization :

[tex]\frac{value - min}{max - min} [/tex]

Min = minimum = 200

Max = maximum = 1000

Value = 200 :

[tex]\frac{200 - 200}{1000 - 200} = 0[/tex]

Value = 300 :

[tex]\frac{300 - 200}{1000 - 200} = 0.125[/tex]

Value = 400 :

[tex]\frac{400 - 200}{1000 - 200} = 0.25[/tex]

Value = 600 :

[tex]\frac{600 - 200}{1000 - 200} = 0.5[/tex]

Value = 1000 :

[tex]\frac{1000 - 200}{1000 - 200} = 1[/tex]

Normalized values = (0, 0.125, 0.25, 0.5, 1)

2.)

Zscore normalization :

[tex]\frac{value - μ}{σ} [/tex]

Using a calculator :

Mean, μ = 500Standard deviation = 316.227

Value = 200 :

[tex]\frac{200 - 500}{316.227} = -0.949[/tex]

Value = 300 :

[tex]\frac{300 - 500}{316.227} = -0.632[/tex]

Value = 400 :

[tex]\frac{400 - 500}{316.227} = -0.316[/tex]

Value = 600 :

[tex]\frac{600 - 500}{316.227} = 0.316[/tex]

Value = 1000 :

[tex]\frac{1000 - 500}{316.227} = 1.581[/tex]

Normalized values = (-0.949, -0.632, -0.316, 0.316, 1.581)

3.)

Decimal Scaling :

Maximum value = 1000

Hence, we can divide our values by 10000

200 / 10000 = 0.02

300/1000 = 0.03

400/1000 = 0.04

600/1000 = 0.06

1000/1000 = 0.1

Hence, the Normalized values (0.02, 0.03, 0.04, 0.06, 0.1)

Learn more : https://brainly.com/question/19132215

Store A sells 3 candy bars for $3.45.
Store B charges $5.45 for 5 candy bars.
Store C sells 7 candy bars for $7.56.
Which store offers the best value?

Answers

Answer:

store C

Step-by-step explanation:

if you divide 7.56 by 7 it'll be $1.08 per candy bar.

A builder is designing a rectangular patio that has a length of 12 units. Find the total number of square units the patio will cover if the width is 4

Answers

Answer:

48 square units

Step-by-step explanation:

Use the area formula, A = lw, where l is the length and w is the width

Plug in the length and width:

A = lw

A = (12)(4)

A = 48

So, the patio will cover 48 units²

48 square units .. hopes this helps ;)

An electric company charges each of its customers a monthly fee of $19 to maintain the account and nine cents per kilowatt hour what is an equation that relates the monthly cost c in dollars of power consumed P in kilowatt hours 

Answers

Answer:

c = 19 + 0.09P

Step-by-step explanation:

The total cost is the $19 monthly fee plus the amount per hour.

c = 19 + 0.09P

Forty-seven thousand people ride the city bus every day. On
average, about how many people ride the bus each hour?

Answers

1,958 I think hope this helps

16x^2+25 factor completely

Answers

Answer:

You can't factor further

Hope this helps!

-413.4=-15.9n please help

Answers

Answer:

[tex]\boxed {n = 26}[/tex]

Step-by-step explanation:

Solve for [tex]n[/tex]:

[tex]-413.4 = -15.9n[/tex]

-Switch sides:

[tex]-15.9n = -413.4[/tex]

-Divide both sides by [tex]15.9[/tex] and expand by multiplying both numerator and denominator by [tex]10[/tex]:

[tex]\frac{-15.9n}{-15.9} = \frac{-413.4}{-15.9}[/tex]

[tex]n = \frac{-4134}{-159}[/tex]

-Divide [tex]-4134[/tex] and [tex]-159[/tex]:

[tex]n = \frac{-4134}{-159}[/tex]

[tex]\boxed {n = 26}[/tex]

Therefore, the value of [tex]n[/tex] is [tex]26[/tex].

In the figure shown, What is the value of x? a. 57° b. 123° c. 33° d. 147°

Answers

Answer:
d. 147 degrees

Explanation:
Please check the picture attached after reading the explanation :)

Assuming that l1 and l2 are parallel, we can identify that the angle at the intersection point of l3 and l2 is the alternate exterior angle of the angle that measures 57 degrees.

This means that that angle also measures 57 degrees.

We can see that l2, l4 and l3 form this little triangle at the corner and we now know that one of its angles measure 90 degrees and the other measures 57 degrees.

In a triangle, the sum of all its interior angles is equal to 180 degrees so we can find the last angle of the triangle by subtracting 90 and 57 from 180.

180-57-90
=33 degrees

A straight lines has an angle measure of 180 degrees as well, so we can find angle x by subtracting 33 from 180.

180-33
=147

Therefore, the measure of angle x is 147 degrees.

I hope this helps!

Can someone Help me ASAP plss!!

Answers

A, it will increase

what is the correct standard form for 30+2+0.1+0.005

Answers

Answer:

32.105

Step-by-step explanation:

30

2

+ 0.1

0.005

32.105 so answer is 32.105

At Mr. McNeely's farm, there were 75 sheep and 60 cows. What is the ratio of the number of cows to the number of sheep at Mr. McNeely's farm?

Answers

Answer:

4:5

Step-by-step explanation:

The ratio will be 60 : 75

When simplified becomes 4:5

Simplify the fraction 36/8

Answers

Answer:

4 4/8

Step-by-step explanation:

36 can go into 8, 4 times. With 4 left over so the answer is 4 4/8.

Answer:

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

Step-by-step explanation:

determine the slope of the line that passes through each pair of points (3,8) and (1,5)

Answers

Answer:

3/2

Step-by-step explanation:

Will mark as brainless if you answer correctly

Answers

Answer:

ans=10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

10(4-7) /   -(4 - 1)

10(-3)  /    -(3)

-30    /    -3 =

10

A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph. What was the average speed of the car for the entire journey? \

Answers

Answer:

19.2 mph

Step-by-step explanation:

just trust me

PLZZZZZZZZZZZZZZZZZZZZZZ HELP!

-3x+4=-2 show your work!!!

Answers

Answer:

x=2

Step-by-step explanation:

as for $65 each and included a 60% mark
+

Answers

Answer:

revenue: $104 profit: $39

Step-by-step explanation:

rationalise the denominator 1/√20

Answers

Answer:

1/10

Step-by-step explanation:

uf no me dij hi g go be h in go i

Step-by-step explanation:

Given:

1/√20

The denominator = 20

We know that

The rationalising factor of a is a. To rationalise the denominator of 1/√20, we multiply this by √20/√20.

1/√20

→ (1/√20) * (√20/√20)

→ [1(√20)]/[(√20)(√20)]

→ (√20)/√(20×20)

→ √20/20 Ans.

You have 1 pounds of egg whites
You need 8 oz to make one serving of meringue
How many servings can you make?

Answers

Answer:

2 servings

Step-by-step explanation:

1 pound is 16 ounces

2 servings because 16oz is 1 pound

The ratio of boys to girls is 1:1.
If there are 250 boys, how many
girls are there?

Answers

250 for every 1 boy there is 1 girl simple

a plane takes off from an airport and travels at a steady speed of 350 miles per hour. which of these graphs best represents the distance the plane is from the airport, y, after traveling for x hours?

Answers

Answer:

what do the graphs look like, it would have a slope of 350

Step-by-step explanation:


3z2 - 2z + 8
-
(10z2 +7z - 12)

Answers

Answer: 7z²-9z+20

Step-by-step explanation:

PEMDAS - Please Excuse My Dear Aunt Sally - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

David has available 40 yards of fencing and wishes to enclose a rectangular area.

Answers

Answer:

5 units will be your width and 15 will be your length so it would look like side#1=5 side #2=15 side number3 is 5 and side number 4 is 15 assuming that side 1 and 3 are parallel.

Step-by-step explanation:

yes

18. Which product is greater. (-4)-(-6) or
(-7).(-8)? Explain.

Answers

Answer:

So when u do (-4)-(-6) it equals 2.

But when u do (-7)*(-8) it equals 56

Therefore saying that (-7)*(-8)=56 is the greatest product.

Step-by-step explanation:

What is 20 divided by 740 with remainder

Answers

Answer:

37 R0

Step-by-step explanation:

740/20=37, so there is no remainder.

I hope this helps you! Have a great day c:

Dividing 20 by 740 gives us remainder 20 and quotient 0.

To find the result of 20 divided by 740 with a remainder,

Perform the division and take note of the quotient and remainder.

20 ÷ 740 = 0 with a remainder of 20.

Division is a mathematical operation that involves splitting a number (the dividend) into equal parts,

with a divisor indicating how many parts we want to split it into.

The quotient is the number of equal parts, and the remainder is what's left after have split the dividend into as many equal parts as possible.

20 divided by 740, we are trying to find out how many times 740 can fit into 20.

Since 740 is much larger than 20, it cannot fit even once.

So, the quotient is 0, indicating that 0 whole units of 740 can fit into 20.

However, there is a remainder of 20.

The remainder represents the portion of 20 that cannot be evenly divided by 740.

It is what remains after we have divided the dividend by the divisor as many times as possible.

Therefore, 20 divided by 740 is 0 with a remainder of 20.

learn more about remainder here

brainly.com/question/29019179

#SPJ2

Find all whole numbers m such that m and 5m+1 are prime numbers.

Answers

Answer:

2 only

Step-by-step explanation:

Only even PRIME number is 2.

Why do we need EVEN PRIME numbers?

Say we do 11*5 we get 55 but when we add one we get 56

Meaning: An odd number multiplied by an odd number plus an odd number equals EVEN number which isn't PRIME. 2 being the ONLY even prime is therefore the only number we can choose.

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