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Artist 52 [7]
4 years ago
5

55 POINTS!!! The hypotenuse of a right triangle is 5cm more than 4 times the length of the shortest leg. The longer leg and the

hypotenuse are consecutive integers. Find all lengths. ​
Mathematics
1 answer:
max2010maxim [7]4 years ago
7 0

Answer:

Short leg is 9.

Hypotenuse is  41.

Long leg is 40.

Step-by-step explanation:

Shortest leg  is x.

Hypotenuse is (4x + 5).

Longer leg is shorter than hypotenuse, and they are consecutive numbers,

so longer leg is (4x + 5 - 1) = (4x + 4).

Using Pythagorean theorem

x² + (4x + 4)² = (4x + 5)²

x² + 16x² + 2*4x*4 + 4² = 16x² + 2*4x*5 + 5²

x² + 32x + 16 = 40x + 25

(x - 4)² = 5²

x - 4 = 5 or  x - 4 = - 5

x = 9 , or x = - 1

Leg cannot be negative.

So, short leg is 9.

Hypotenuse (4x+5) = (4*9 + 5) = 41

Long leg is 41 - 1 = 40

Check:

9² + 40² = 41²

1681 = 1681 True

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storchak [24]

Answer:

1

Step-by-step explanation:

(−4)−(−2)–{(−5)–[(−7)+(−3)–(−8)]}

PEMDAS

Work from the inside out

Change subtracting negatives to adding

(−4)+2–{(−5)–[(−7)+(−3)+8)]}

(−4)+2–{(−5)–[(-2)]}

(−4)+2–{-5+2}

(−4)+2–(−3)

Changing to adding

(−4)+2+3

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8 0
3 years ago
Read 2 more answers
What is the measure of the angles
finlep [7]
They are vertical angles and would be the same so set them to equal each other and solve:

3x-4 = 2x+9

add 4 to both sides:

3x = 2x +13

subtract 2x from each side:

x = 13

now replace x with 13 in the original equations:

3x-4 = 3(13) -4 = 39-4 = 35
2x+9 = 2(13)+9 = 26+9 = 35

the angles = 35 degrees


7 0
3 years ago
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What is value of <br> 6x6x6x6x6x6x6=6x
pychu [463]

Answer:

46656

Step-by-step explanation:

6x6x6x6x6x6x6 can be written in its index form as 6⁷

6x = 6⁷

6x = 279936

Applying change of subject formula, divide both sides of the equation by 6

6x/6 = 279936/6

x = 46656

8 0
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ANTONII [103]
The answer is 13/20

The number (n) halfway between x and y is:
n = (x + y) : 2

The number (n) halfway between 3/5 and 7/10 is:
n = (3/5 + 7/10) : 2
n = (6/10 + 7/10) : 2
n = 13/10 : 2
n = 13/10 : 2/1
n = 13/10 * 1/2
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4 0
4 years ago
2. ABC: You eat at your favorite restaurant, and your bill is $52.60. On top of that, you need to pay 8% sales tax, and leave a
OLga [1]

Answer:

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Step-by-step explanation:

52.60 x 8%  = 52.60 x 0.08 = 4.21

52.60 x 20% = 52.60 x 0.20 = 10.44

52.60 + 4.21 + 10.44 = 67.25

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3 years ago
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