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\(\text{I think I'd just use the quadratic formula and see what comes out }\\ r_{1,2} = \dfrac{19 \pm \sqrt{19^2 + 4\cdot 63\cdot 30}}{126} = \dfrac{19\pm 89}{126} \\ r_{1,2} = \dfrac 6 7,~-\dfrac{5}{9} \)

\(\text{so }63x^2-19x-30 = \\ 63 \left(x - \dfrac 6 7\right)\left(x + \dfrac 5 9\right) = \\ (7x-6)(9x+5)\)

(x) 1 over 5 times (x) 4 over 3?

\(\large {x^1 \over 5 \times {x^4 \over 3}}=\frac{3}{5x^3}\)   ??

  !

this is a simple ratios and proportions question

since 1 us dollar= 120 isk, all you need to do is to divide these two numbers because you are trying to find U.S dollars

so 2370 isk/120isk = 19.75

$19.75 where a = 1, b= 9, c= 7, and d=5

(144) (3/2)  =

(144/2) * 3 =

72 * 3 =

216

144 + 3/2  =

144 + 1.5 =

145.5

You literally have this

(0)^9  + (1)^6 +  [  (2^3)^4  ÷ (2)^3  ]

0 + 1  +   [ 2^12 ÷ 2^3 ]  =

1 + 2^9  =

513

However.... you may have meant

[ (0)^9  + (1)^6 +    (2^3)^4 ]  ÷ (2)^3      =

[ 1 + 2^12] / 2^3 =

[4097 ] / 8

          A

 B                 C

Angle BAT = 30°

And....by the Law of Sines

AB / sin ATB =  AT / sin ABC

AB / sin 105 =  24 / sin 45

AB = 24 sin (105)  / sin 45  =

24 sin (60 + 45) / sin 45   =

24 [  sin (60)oos(45) /  sin (45)   +  sin (45)cos (60) /sin (45) ]  =

24 [ sin (60) +  cos (60)  ]  =

24 [ sqrt (3) /2 + 1/2 ]  =

12 [ sqrt (3) + 1 ]

And using the Law of Sines again

AB / sin ACB  = BC / sin BAC

12 [ sqrt (3) + 1 ] / sin (75)  = BC / sin (60)

12 [ sqrt (3) + 1 ] =  BC sin (75) /sin (60)

12 [sqrt (3) + 1 ] * sin (60)   =  BC [ sin(30)cos (45) + sin (45)cos(30) ]

6 [ sqrt (3) + 1] * sqrt (3)   = BC  [ (1/2)(sqrt (2) / 2  + (sqrt (2) /2) sqrt (3) /2 ]

6 [ sqrt (3) + 1 ] * sqrt (3)  =  BC [ sqrt (2) + sqrt (6) ] / 4

 [ 24 [ sqrt (3) + 1] *sqrt (3) ]  / [ sqrt (2) + sqrt (6) ]  =  BC

[ 24 (3 + sqrt (3) ] / [ sqrt (2) + sqrt (6) ]  = BC

[ 24 (sqrt (3) + 3 ] [ sqrt (6) - sqrt (2) ] / 4 = BC

[ 24 (sqrt (18) + 3sqrt (6) - sqrt(6) - 3sqrt (2) ] = BC

 6  [ ( 3sqrt (2) + 2sqrt (6) - 3sqrt (2) ]   = BC

12 sqrt (6) = BC

So...the area of ABC =

(1/2)AB * BC * sin (45) =

(1/2) [ 12 (sqrt (3) + 1) ] [ 12 sqrt (6) ] sqrt (2) / 2  = 

(1/4) (144) (sqrt (3) + 1) (sqrt (12) )  =

36 [ sqrt (36) + 2sqrt(3) ]    =

36 [ 6 + 2sqrt (3) ] =

36 (2 * 3 + 2 sqrt (3) ]  =

72 [ 3 + sqrt (3) ]  units^2  ≈  340.7 units^2

nice answer

thanks

you do aops classes? cool i used to 

also keyboard not typing happens with me sometimes when i play minecraft, im trying to move and it stops, what i do is wait a bit

How do you take a set of numbers you want to add up and show that in Riemann Sum?

^{[First, you may want to review the use of relative pronouns in English composition. See: www. learnmehowtowrightegudder.org]}

^{If you don’t want to do that, you should preface your questions and comments with a bold-face “Ummm...”}

Riemann Sums are used to find the area under a curve.

\(\LARGE \int _a^b \large f(x)dx = \lim _{n \to \infty} \LARGE \sum \limits_{i=0}^{n-1} \large f(x_{i}) \Delta x. \)

Here’s a well-explained introduction for this concept:

thanks for helping my dumbass :')

Thank you

                             A

   E                        B                       C

                            D

Angle AEB = Angle BAC

Angle ABE = Angle ABC

Thus, by AA congruency, triangle EBA is similar to triangle ABC

Angle CAB = Angle BCD

Angle CBA = Angle CBD

Again, by AA congruency, triangle ABC is similar to triangle CBD

So..by transivity......triangle EBA is similar to triangle CBD

So

EB / BA  = CB / BD

So

EB * BD = BA * CB        which is the same as.....

EB * BD =   AB * BC

maybe 1001 base n.

hint: draw a venn diagram

The perimeter is   2*18 +  3*34   =  138 yds

10  and 3

what does 1001_n mean?

Part b)

When x=-1/2. the denominator of the first expression becomes undefined. When x=-1/2, the second expression's third term becomes undefined too. Therefore, they are not equal because the first expression is entirely undefined while the second expression has only one term undefined.

Thanks!

The length of the side of the large square = 5  units

The length of the side of the small square = √7   units

The length of the shorter side of a rectangle =   [ 5 - √7] / 2

The length of the longer side of the rectangle =  5 - [ 5 - √7 ] / 2   =  [ 5 +  √7]/ 2

So.....the squared length of the rectangle's diagonal  =

(  [ 5 - √7] / 2 )^2   +  ( [ 5 + √7] / 2 )^2  =

[ 25 - 10√7 + 7 ] / 4   +  [ 25 + 10√7 + 7 ] / 4  =

[ 64 / 4 ]   =

16

So......the diagonal length =  √16  =   4 units

you're right!

my method is messed up.  Thanks

The sum is actually just

\(\sum \limits_{i=1}^\infty \dfrac{1}{5^i} = \dfrac{1}{1-\dfrac 1 5}-1=\dfrac 5 4 - 1 = \dfrac 1 4\)

Here's part (c)

2x^2  + 3   +   [ 4 ] / (2x + 1)     can be simplified as

[ (2x^2 + 3)(2x + 1)  + 4 ] / [ 2x + 1] =

  [ 4x^3 + 2x^2 + 6x + 7 ]  / [ 2x + 1] 

Which is equal to the first function

With this in mind....(a)  must be true