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3 years ago

Find each of these values.

1 answer:

4 0

$192=4\cdot41+28\iff192\equiv28\pmod{41}$
$28=3\cdot9+1\iff28\equiv1\pmod9$

$323=24\cdot13+11\iff323\equiv11\pmod{13}$
$11^2\equiv0\pmod{11}$

$73=3\cdot23+4\iff73\equiv4\pmod{23}$
$4^2\equiv16\pmod{31}$

$212=14\cdot15+2\iff212\equiv2\pmod{15}$
$2^3\equiv8\pmod{22}$

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On a scale drawing inch = 1 foot. What are the dimensions on the scale for a room that is 27 feet by 20 feet?

Rufina [12.5K]

If 1 inch = 1 foot then 1 foot = 1 inch.
With this, you can make a ratio of 1 foot:1 inch, or 1:1.
Starting with the first dimension, 27 feet, just change the 1 to 27 in the ratio.
27:?
To find how many inches this is in the scale drawing, find how much 1 had to be multiplied by to get to 27. This is 27, since anything times 1 is itself.
Just multiply the other side by 27 as well to get the answer for the first dimension.
1 • 27 = 27
So 27 feet = 27 inches in the scale drawing.
Now do the same for the second dimension.
1:1
20:?
1 • 20 = 20
20:20
The answer is that the scale drawing has dimensions of 27 inches by 20 inches if 1 inch = 1 foot is the scale

7 0

3 years ago

5 0 = - in = in quadrant II Given cos = Find sin 3

____ [38]

Answer:

sinΘ = $\frac{2}{3}$

Step-by-step explanation:

using the identity

sin²x + cos²x = 1 ( subtract cos²x from both sides )

sin²x = 1 - cos²x ( take square root of both sides )

sinx = ± $\sqrt{1-cos^2x}$

given

cosΘ = - $\frac{\sqrt{5} }{3}$ , then

sinΘ = ± $\sqrt{1-(-\frac{\sqrt{5} }{3})^2 }$

= ± $\sqrt{1-\frac{5}{9} }$

= ± $\sqrt{\frac{4}{9} }$

= ± $\frac{2}{3}$

since Θ is in quadrant II where sinΘ > 0 , then

sinΘ = $\frac{2}{3}$

7 0

2 years ago

Factorise the following: a) x + 3x - 4 b) x - 2x - 3 c) x + 2x - 8

Komok [63]

Are they supposed to be quadratic equations? Is it x^2 +3x -4 etc?

8 0

3 years ago

I need help solving this trig problem w/ identites.

Charra [1.4K]

$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)}
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3 0

3 years ago

What is the value of the expression 2^2 + 4^2 ÷ 2^2?

Dennis_Churaev [7]

Answer:

The answer is C.

Hope this helped!!

6 0

3 years ago