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Tomtit [17]
3 years ago
11

The perimeter of a​ standard-sized rectangular rug is 40 ft. The length is 2 ft longer than the width. Find the dimensions.

Mathematics
1 answer:
charle [14.2K]3 years ago
3 0
The length is 11ft the width is 9ft
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Convert the complex number z = 4 - 10i from rectangular form to polar form.​
mrs_skeptik [129]

ANSWER

r = 2 \sqrt{29} ( \cos(292 \degree)  + \sin(292 \degree))

EXPLANATION

The polar form of a complex number ,

z = x + yi

is given by:

z = r( \cos( \theta)  + i \sin( \theta) )

where

r =  \sqrt{ {x}^{2} +  {y}^{2}  }

The given complex number is:

z = 4 - 10i

r =  \sqrt{ {4}^{2}  +  {( - 10)}^{2} }

r =  \sqrt{16  + 100}

r =  \sqrt{116}  = 2 \sqrt{29}

And

\theta=  \tan^{ - 1}(\frac{ y}{x} )

\theta=  \tan^{ - 1}(\frac{  - 10}{4} )

\theta=  292 \degree

Hence the polar form is :

r = 2 \sqrt{29} ( \cos(292 \degree)  + \sin(292 \degree))

6 0
3 years ago
0.25(8)+0.15x=0.35(20+x)
IRINA_888 [86]
X=-25 is the answer.
3 0
3 years ago
You can walk 1.75 miles in 30 minutes. What is your average speed?
Varvara68 [4.7K]

Answer:

The answer is 3.5 mph

Step-by-step explanation:

30 x 2 = 60 minutes = 1 hour

1.75 x 2 = 3.5 miles

So 3.5 miles in 1 hour

3.5 mph

3 0
3 years ago
Find AB<br> Round to the nearest tenth.
lianna [129]

Answer:4.1

Step-by-step explanation:

c=AB

C=26°

B=122°

b=8

Using sine rule

c/sinC = b/sinB

c/sin26=8/sin122

Sin26=0.4384

Sin122=0.8480

c/0.4384=8/0.8480

Cross multiply

c x 0.8480=8 x 0.4384

c x 0.8480=3.5072

Divide both sides by 0.8480

(c x 0.8480)/0.8480=3.5072/0.8480

c=4.1

7 0
3 years ago
Cos^2 2x−cos^2 6x=sin4x sin8x<br> please help me prove it
Olin [163]
Cos² 2x = (1+cos 4x )/2
cos² 6x  = (1+cos 12x)/2
subtract to get  1/2 (cos 4x - cos 12x )   
=  1/2 (2 sin  4x sin 8x )       as cos A - cos B =  2 [ sin (A+B)/2  sin (A-B)/2 ]
so the answer
4 0
3 years ago
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