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Zarrin [17]
3 years ago
12

Find the length of side x in the simplest radical form with a rational denominator.

Mathematics
1 answer:
krok68 [10]3 years ago
7 0

Answer:

\sqrt{2}

Step-by-step explanation:

We can use either angle, but I'm going to use the one on the bottom. So, in order to find x, we need to use tangent. One side we know is the adjacent, and the side we don't know is the opposite, therefore we need tangent. Here's the equation:

tan(45)=\frac{x}{\sqrt{2}}

Obviously, we can't have a root in our denominator, so we need to get rid of it somehow. Here's how:

We multiply the denominator of the fraction by \sqrt{2}. \sqrt{2} multiplied by itself is simply 2. Try it! We also want to multiply the numerator by \sqrt{2}, but there isn't really a number we can use with that, so we'll just add it to the side. The equation you have now is:

tan(45)=\frac{x\sqrt{2} }{2}

Let's try to work this out now. Since the denominator is 2, we have to multiply both sides by it to find x.

\frac{x\sqrt{2} }{2*2} =x\sqrt{2}

tan(45)*2=2

We can plug 2 in for the x in the numerator now:

\frac{2\sqrt{2} }{2}

2 and 2 cancel out, so you get 1 in both the numerator and denominator. That's how we get our answer of x=\sqrt{2}

Also, because this is a 45-45-90 triangle, you don't really have to do all that work. If it's a 45-45-90 triangle, both legs should be the same length. :)

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4≤n−4. a little help?
saveliy_v [14]

Answer:

Just isolate the variable by performing inverse operations. Its like solving an equation but the sign is different.

Step-by-step explanation:

Well add 4 to both sides

8≤n

Thats basically it

5 0
3 years ago
Read 2 more answers
Calculate the length of AB if A is the point (2,3) and B is the point (-2,0)
d1i1m1o1n [39]

Answer:

Formular for coordinate length:

length =  \sqrt{ {(x_{1}  - x _{2} )}^{2}  +  {(y_{1}  - y_{2})}^{2} }

In considerance of coordinates given of A and B

x _{1} \: \:  is \:  \: 2 \\ x_{2} \:  \: is \:  \:  - 2 \\ y_{1}  \: \: is \:  \: 3 \\ y_{2} \:  \: is \: \:  0

therefore substitute:

length =  \sqrt{ { \{2 - ( - 2) \}}^{2}  +  {(3 - 0)}^{2} }  \\  \\  =  \sqrt{ {(2 + 2)}^{2} +  {3}^{2}  }  \\  =  \sqrt{ {4}^{2} +  {3}^{2}  }  \\  =  \sqrt{16 + 9}  \\  =  \sqrt{25}  \\  \\ { \boxed{ \boxed{length  \:  \: is \:  \: 5 \: units}}}

5 0
3 years ago
Read 2 more answers
The areas of two square fields are respectively 256 and 625 sq.m. find the ratio of their sides
Arlecino [84]
We know that
area of the square=b²-------> b=√area
where
b is the side length of the square

for the smaller square
area=256 m²
b=√256-------> b=16 m

for the larger square
area=625 m²
b=√625-----> b=25 m

<span>the ratio of their sides is 16/25</span>

4 0
3 years ago
1. Susan’s art class is 9 hours long. How long is her class in minutes?
erastova [34]
1. 9(60) = 540 minutes.

2. There is 0.5 pints = 1 cup, so three cups. :)

3. 4(2) = 8 pints.

4. 1,00 millimeters = 1 meter, so 9 meters. 
Hope it helps! :)
4 0
3 years ago
The business department at a university has 18 faculty members. Of them, 11 are in favor of the proposition that all MBA student
drek231 [11]

Answer:

0.225

Step-by-step explanation:

Total outcomes of choosing 5 out of 18 members = 18C5

Outcomes of choosing 2 out 11 favourers, 3 out of 7 members  =          11C2 & 7C3

Probability = Favourable outcomes / Total outcomes

= ( 11C2 x 7C3 ) / 18C5

<u>[ { 11 ! / 2! 9! } {7 ! / 3! 4! } ] </u>

       [ 18 ! / 5! 13! ]

( 55 x 35 ) /  8568

1925 / 8568

= 0.2246 ≈ 0.225

8 0
3 years ago
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