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We know that the angles of the triangle are in the ratio 3:5:10, and we know that the sum of the three interior angles of a triangle is 180°, so we can do:

\(3x + 5x + 10x = 180°\)

\(18x=180°\)

\(x=10°\)

We can now multiply 3, the smallest interior angle, by x.

\(3\cdot 10\)

\(30°\)

Answer: 30°

The denominator cannot  = 0

Therefore, every real number except x = 7  is in the domain

So

(-inf, 7) U ( 7 , inf)

The exterior angles sum to  360°

360 -  120  -  75   =    165°

Basically, we're trying to find the distance between (1, 0) (0, 0) x the distance between (2, 1) (0, 0) x the distance between (3, 0) (0, 0) x the distance between (0, 1) (0, 0)

By using the distance formula, we can find

distance between (1, 0) (0, 0) = 1

distance between (2, 1) (0, 0) = √3

distance between (3, 0) (0, 0) = √5

distance between (0, 1) (0, 0) = 1

$|1| |2i| |3| |i|$ = 1 x √3 x √5 x 1 = √3 x √5 = √15

Simplify  as

6x^2 + ( k - 12)x + 9  = 0

We have non-real roots when the discriminant > 0

So

(k  -12)^2  - 4(6)(9) < 0

(k -12)^2  -  216 <  0

(k -12)^2  < 216    take both roots

k - 12 < sqrt (216)                and        k - 12 >  -sqrt (216)

k < 12 + 6sqrt (6)                                 k > 12 - 6 sqrt (6) 

k  on this interval →  ( 12 -6sqrt(6)  , 12 + 6sqrt (6) )                                     

x+y = 10     =====>  y = 10 -x       sub this definition of y into the second equation

x^2 + (10-x)^2  - 2 x(10-x) -32 = 0      now solve for the value(s) of x 

x^2 + x^2 - 20x + 100  - 20x + 2x^2 -32 = 0 

4 x^2 -40x + 68 = 0            Quadratic Formula shows x =  7.828    and    2.172 

using these values in the line equation shows            y =   2.172     and  7.828

-b =  (4 + 2i)  + (-5 + 8i)  =  -1 + 10i

b = (1 -10i)

c = (4 + 2i) (-5 + 8i)  =   -20 -10i + 32i + 16i^2  =  -36 +22i

b + c  =  (-1 + 10i)  + ( -36 + 22i)  =   -37 + 32i

3^(2c + 1)  = 28 *3^c  + 4*3^c -25 - 9

3* 3^(2c)  = 32*3^c  - 34

3* (3^c)^2  -  32*3^c  + 34  = 0          let  3^c  = x     so  that  (3^c)^2  = x^2

So we have

3x^2  - 32x +  34 =  0

Using the Quadratic Formula

x =    [ 32 + sqrt [ 32^2 - 4 * 3 *34] ]  / 6    =    [ 32 + sqrt (616) ] / 6  = 

[32 +2sqrt (154) ] / 6  =  [16 + sqrt (154) ] / 3

And x = the conjugate  =  [ 16 -sqrt (154) ] / 3

So

3^c  = [ 16 - sqrt (154) ] / 3       take the log of  both  sides

log 3^c  = log ( [16 - sqrt (154)] / 3)

c log 3  = log ( [ 16 - sqrt (154)]/3)

c = log ( [16 -sqrt (154)]/3) / log 3 ≈ .163         and   

c  =  log ([16 + sqrt (154) ] / 3) / log 3  ≈  2.046

Something like this ( Not to Scale)

 By the property of medians  ON = (1/3)QN = (1/3)(1) = 1/3

And  since N is  a midpoint of PR then  NR = (1/2)PR =  1/2

And QN perp to PR  so   triangle RNO is right with angle RNO  =  90

By the Pythagorean Theorem

OR = sqrt (ON^2  + NR^2)   = sqrt [ (1/3)^2  + (1/2)^2 ] =  sqrt [ 1/9 + 1/4]  = sqrt  [ 13 / 36 ]  = 

sqrt (13) / 6  ≈  0.6

I tried simplifying the equation and then maybe putting all the \(c\) 's on one side, but I don't know what to do after or if i'm in the right direction.

\(3^{2c+1} = 28\cdot 3^c - 9 + 4 \cdot 3^c - 25\)

\(3^{2c+1} = 32\cdot 3^c-34\)

\(3^{2c+1}+34 = 32\cdot 3^c \)

\(3^{c+1}+\frac{34}{3^c} = 32\)

\(3^{c+1}+34\cdot3^{-c} = 32\)

I don't know 😒

We need to know BC

Simplify these as

(1/2)x - 2y =  -12      (1)

12x + 7y =  97         (2) 

Multiply (1) through by 2

x  - 4y  = -24   →  x =  4y - 24    (3)

Sub (3)  into (2) for x

12 (4y -24) + 7y  = 97

48y - 288 +7y   = 97

55y  = 385

y = 385/ 55  =   7

x = 4(7) - 24  =  4

(x, y)  = (4, 7)

Simplify as

(2/5)x - 1 = -3x + 7

2x - 5  = -15x + 35

17x  = 40

x = 40 / 17  = r

Since r >  1, this  series does not converge to any value

\(\frac{a + 2}{a + 1} = \frac{b}{8} \)

Rewrite  as

8(a + 2)  / (a + 1)  =  b

As a approaches  -infinity and  + infinity,  b  approaches 8

a         b

0       16

1       12

3       10

7        9

-2       0

-3       4

-5       6

-9       7

Well, the probability that the mean will be between 121 and 133 pounds is 0.9836, so the probability that the mean will be more than 133 pounds or less than 121 pounds is 1 - 0.9836 = 0.0164

Answer: 0.0164

1. A tree diagram can be:
 

                                                                                                         VISHY

                                                         1st game                                                                            2nd game

                                    W   W   W   W   W   D   D   D   L   L                                     W   W   W   W   W   D   D   D   L   L

2. The probability that Vishi will win both games is \(\frac{5}{10}\cdot\frac{5}{10}\), which is \(\frac{25}{100}\), which simplifies to \(\frac{1}{4}\)

Answer: 1/4

The compound interest formula is  \(P=C(1+r/n)\)^\(nt\), where P is the final value, C is the initial deposit, r is the interest rate, n is how frequently interest is paid, and t is how many years the money is invested.

We know that \(C=3200, r=0.13, t=8, \) and \(n=1\), so we can now solve for P, the final value.

Plugging in the values, we get:

\(P=3200(1+0.13)^8\)

\(P=3200(1.13)^8\)

\(P=3200\cdot2.6584441929064321\)

\(P=7975.3325787192963\)

\(P=$7975.33\)

The final value is \($7975.33\)

Answer: $7975.33

\(2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.\)

We can calculate that \(2 \cdot 2^2 \)is 8, and that \( 3 \cdot 2^3 \) is 24, and because 8 + 24 is 32, then n is 3, and the equation \(2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32\) is \(2 \cdot 2^2 + 3 \cdot 2^3 =32\)

Answer: 3

To find the ordered triple (p,q,r), we can use substitution:

First equation: \(2q=-p\) ---> \(q=-p/2\)

Second equation: \(-p/2-2r=0\) ---> \(-p/2=2r\) ---> \(p=-4r\)

Third equation: \(-4r+ r=5\) ---> \(-3r=5\) ---> \(r=-5/3 \)

Plugging in -5/3 for r: \(q+10/3=0\) ---> \(q=-10/3\)

Plugging in -10/3 for q: \(p-20/3=0\) ---> \(p=20/3\)

the ordered triple (p,q,r) is ( 20/3 , -10/3 , -5/3 )

Answer: ( 20/3 , -10/3 , -5/3 )

Again, STOP COPYING MY USERNAME

We can solve using substitution, but first, let's simplify the second equation:

\(-2x=2y+5\)

Now let's isolate the variable x:

\(x=-y-2.5\)

Substituting, we get:

\(-2y-5+y=-7\) ---> \(-y=-2\) ---> \(y=2\)

Plugging in 2 for y, we get:

\(2x+2=-7\) ---> \(2x=-9\) ---> \(x=-4.5\)

The ordered pair (x,y) is ( -4.5 , 2 )

Answer: ( -4.5 , 2 )

First , simplify the system to 

2x + y = -7 

4x - 2y = 5         Multiply the first equation by two then add them together to get 

8x = -9 

x =  - 9/8          sub this in one of the equations to find y =  -4 3/4