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Yuliya22 [10]
3 years ago
12

A right triangle has an area of 50 square inches. If the triangle is an isosceles triangle, what are the lengths of the legs of

the triangle? If the triangle is not an isosceles triangle, what are all the possible lengths of the legs?
Mathematics
1 answer:
Fed [463]3 years ago
4 0
<span>If this is an isosceles triangle, then it has two 45 degree angles corresponding to two legs of equal length.  Orient the base of this triangle so that it's horizontal, and represent its length by b.  Let h represent the height of the triangle.  Then the area of this right triangle is 50 square inches = (1/2)(b)(h), or A = (b/2)h = 50 in^2.   

Due to the 45 degree angles, the height of this triangle is equal to half the base, or h = b/2.  Thus, (b/2)h = 50 becomes (b/2)(b/2) = 50, or b^2=200. Thus, b = 10sqrt(2), and h=(1/2)(10 sqrt(2)), or h = 5sqrt(2).

The length of one of the legs is the sqrt of  [5sqrt(2)]^2+[5sqrt(2)]^2, or

sqrt(25(2)+25(2)) = sqrt(100) = 10.



</span>
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find the length of DE if D is between points C and E, CD = 6.5 centimeters, and CE = 13.8 centimeters.
grin007 [14]

Answer:

DE = 7.3 cm

Step-by-step explanation:

All you have to do is take the length of the full line (13.8 cm) and subtract it by the first part (6.5 cm). Doing this gets you the final length of DE with is 7.3 cm.

5 0
2 years ago
I need help on these questions please! Quickly too
ale4655 [162]
By definition, a rational number is a precise number: or in other terms, we know its exact value. Irrational numbers are number that has endless digits on the right of the decimal points: in other terms, we can't know its exact value.

First question:
√2.5 = 1.58113.... It's endless, so irrational.
-√64 = -8 it's a whole number, so rational.
4√5 = 8.94427.... Endless, so irrational.
√14.4 = 3.7947... Endless so irrational.

So -√64 is the rational number.

Second:
7.885 is rational because has a defined number of digits after the decimal points.
π² = 9.8696.... Endless, so irrational.
√0.144 = 0.3794.... Endless, so irrational
√91 = 9.5393.... Endless, so irrational

So 7.885 is the rational number.

Third:
-7.8 bar: You can notice the line over the 8, this means that there's an infinite number of 8 after the decimal points. So it's 7.88888888888.... Endless, so irrational.
√25 = 5, whole number so rational
25.8125 Has a definite number of digits after the decimal point, so is rational.
√0.025 = 0.1581... Endless, so irrational.

So -7.8 bar and √0.025 are irrational.

Fourth:
π= 3.1415... Endless, so irrational.
1.425 has a definite number of digits after the decimal point, so rational.
√50 = 7.0710.... Endless, so irrational
√-4 Doesn't exist. Finding the square root of a negative number is mathematically impossible.

So 1.425 is the rational number.

Fifth:
√10 = 3.1622..... Endless, so irrational.
√100 = 10, a whole number so rational.
√1000 = 31.6227..... Endless, so irrational
√100000 = 316.2277...... Endless, so irrational.

√100 is the rational number.

Hope this helps!! :D And I hope you understood the lesson a bit more xD
5 0
3 years ago
If correct ill give brainly
Rina8888 [55]

Answer:

Hello! answer: x = 16

Step-by-step explanation:

16 × 16 = 256

12 × 12 = 144

256 + 144 = 400

√400 = 20 therefore x = 16 hope that helps!

6 0
3 years ago
Read 2 more answers
Set of integers x such that x - 5 ​
My name is Ann [436]

The set of integers that satisfy the inequality is x ∈ (-∞, 30) where x is an integer.

<h3>What is inequality?</h3>

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The question is incomplete.

The complete question is:

Set of integers x such that x - 5 is less than 25​.

We have an inequality:

x - 5 < 25

Adding 5 both sides:

x - 5 + 5 < 25 + 5

x < 30

x ∈ (-∞, 30) where x is an integer.

Thus, the set of integers that satisfy the inequality is x ∈ (-∞, 30) where x is an integer.

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ1

3 0
2 years ago
Ava deposited $3,500 in an account that earned 4.375% interest
Bumek [7]

Answer:

4335.61

Step-by-step explanation:

Using the equation A = P (1 + r/n)^nt

lets fill  in the variables,

P (principal) is 3500.00

r (rate) is .04375  - we do this in decimal form

n (number of times interest is doubled) here it is annually, could be monthly or daily too, but we are told annually, so we use 1

t (time) is 5 years

So:   3500(1+.04375/1) ^ 1(5)

pemdas

parenthesis first 1 +.04375/1 = 1.04375

exponents next 1 x 5 = 5

so now we have 3500 (1.04375) ^5

take 1.04375 to the power of 5 (pemdas) then multiplication

= 3500(1.2387465058)  or

A = 4335.61

This is the same result as calculating simple interest for 5 years but each year calculating off the new Principal amount that includes interest.

3500 x  .04375 = 153.125  or 3653.125   *(year one)

159.82 = 3812.95  

166.82 = 3979.77

174.11 = 4153.88  

181.73 = 4335.61

5 0
3 years ago
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