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For each fraction, put parenthesees around the numerator divided by the denominator. Then just multiply them together.

Like this:

one half would be (1/2)

three fourths would be (3/4)

one half times three fourths would be (1/2)*(3/4)

You can't determine the radius if you only know where the center is located. That's like asking how long a piece of string is if you can only see one end of it.

Did you mean what is the radius of a circle where the center is at the origin (0,0) and (19/2,9) is a point on the circle?

This forms a rectangle

AB  =  √ [  (4 - 0 )^2 + ( - 1 - 3)^2]  = √[4^2 + (-4)^2 ] = √[16 + 16] = √ 32 = 4√2

BD  =  √ [  (4 - 2 )^2 + ( - 3 - - 1)^2]  = √[2^2 + (-2)^2 ] = √[4 + 4] = √ 8 = 2√2

So...the area  =   4√2  * 2√2 =   8 * 2  = 16  sq units

You have 4, if you eat number 2 ;)

sqrt (7+3^2) =   4

sqrt 25  = 5   so you are left with

(4-2)/2   x  5  )  ^(10) +5

5^10  + 5 = 9765630

2x-3y = 8 

4x+3y = -2       add these  giving

6x = 6      divide by 6

x = 1

And use either equation to find  y

4(1) + 3y = - 2

4 + 3y  = - 2      subtract 4 from each side

3y  = -6        divide by 3

y = - 6/3  = - 2

5 u idoit

a)   sqrt(50) / 5 = sqrt(2)

√50/ 5  = √ [2 * 25] / 5  =  [ √2 *√25] / 5  = [√2 * 5] / 5  = √2 * [5/5]  = √2 * 1  = √2

b)   (sqrt(24) - sqrt(6))^2 = 6

[√24 - √6] [√24 -√6]  =

24 -  2*√24*√6  +  6  =

30 - 2√144  =

30 - 2 (12)  =

30 - 24  =   6

c)   sqrt(27) - sqrt(12) + sqrt(75) - sqrt(18) x sqrt(6) = 0

[The key here is to wrtie  each using a similar sqrt]

√ 27 - √12 +√75 - [√18 * √6]

√[9 * 3] - √[4 *3] + √[25 * 3] - √108

√9* √3 - √4 *√3 + √25 *√3  - √36*√3

3√3 - 2√3 + 5√3 - 6√3      ......   factor out √3  ......

√3  [ 3 - 2 + 5 - 6]

√3 [ 1 + 5 - 6]

√3 [6 - 6 ]

√3 [0]  =   

0

d)   (sqrt(2) - sqrt(3)) x (sqrt(2) + sqrt(3)) = -1

[ √2 -√3 ] [√2 + √3 ]

√2*√2 -√3*√2 +√2*√3 -√3*√3

2 - √6   + √6  - 3

2 - 3  =  

- 1

y=-2;x=1

a) Solve:   logx^3 + 2logx^2 - 14 = 0

3log x + 4 log x  = 14

7 log x  = 14      divide by 7

log x  = 2    means  that      10^2  = x   →  x  = 100

b) Solve:   (log x)^2 - log x - 6 = 0      Factor

[ log x - 3 ] [ log x + 2]  = 0         set each factor to 0

log x - 3  = 0   →   log x  = 3     →  10^3  = x  = 1000   .... and........

log x + 2  = 0  →   log x = - 2  →   10^-2 = x  =  1 / 100

0 and 10 are the roots....and the verex is at  x = 5

So...the point   (5, -100) is on the graph

The x coordinate of the vertex  = -b/[ 2a]  = 5  →  b = -10a

And the product of the roots  = c/a.....so    0 * 10  = 0 =   c/a →  c = 0

And we know that

a(5)^2 - 10a(5)  = -100

25a - 50a  = - 100

-25a  = - 100      divide by -25 

a = 4

And b  = -10(4)  = - 40

So....the function is :

y = 4x^2 - 40x

Here's a graph :

https://www.desmos.com/calculator/lt3x4r8nt7

Lemons do not make raisins; grapes do

n=1 is 5

n=2 is 11

n=3 is 21

n=4 is 35

n=5 is 53

Same person (as above)

would n=1 be 5, n=2 be 10, n=3 be 24, n=4 be 38 and n=5 be 56??

Tim has 10 corn husks, because since the number of apples Jane and Michael have is limited, it seems as if the month is winter, since apples are most scarce in winter. Corn is also easiest to come by in fall like apples, and corn husks are generally grown in larger numbers than apples at a rate of 1 apple to 1.27 corn husks. Therefore, Tim most likely has 10.16 corn husks (rounded down to 10 whole husks).

9+10 is obviously 19

Ab outlier is a piece of data which is not within the "normal" boundries of a data set.

For Example: 

1(a) log x^3 +2logx^2-14=0   

Use the fact that log x^n = nlogx,   so logx^3 = 3logx   and 2logx^2=2(2logx)=4logx   to give

3logx +4logx -14=0

7logx                  =14       logx =2

1(b)   (logx)^2-logx-6=0    This is a quadratic equation.Can write like X^2-X-6=0  where X = logx

Factorise to get (X+2)(X-3)=0

So (logx  +2)(logx -3) +0           logx=-2   and logx =3

2. Understand that sqrt(ab)= sqrt(a)   X  sqrt(b) ;that is what these questions are testing.

sqrt(50) = sqrt(25x2)  =sqrt(25) X sqrt(2)   = 5 sqrt2 so sqrt (50)/5=5(sqrt2)/5 =sqrt2.

All the other examples here are similar,now that you have seen the one I just did,you should have the idea to try the rest

what?

pretty sure it's because the image is 48 x 48 pixels

100-30 < 100-29 (or any number smaller than 29)

Another method (see diagram)

Law of sines  :   13.413/sin 165.8  =  x/sin6.1      x = 5.8103 m

then   sin 8.1 = H/5.8103          H = .81867 m

So with 200 grams of liquid, you have 40% juice and 60% water.

200 * 40% = 200 * .4 = 80 grams of juice

200 * 60% = 200 * .6 = 120 grams of water

Now we add 200 more grams of water.

120 + 200 = 320 grams of water

More importantly...

200 + 200 = 400 grams of liquid

Now we need the percent of juice in the new mix. Note that now there is 400 grams of liquid, as we started with 200 grams and added another 200 grams.

80 / 400 = 0.2 = 20%

For a quick reality check, you can see this answer makes sense. You are doubling the amount of overall liquid, but the amount of juice stays the same. The % juice is halved from 40% to 20%, so the answer makes sense.

Find out the 'unit cost ' per student then multiply by (9+4more)

unit cost =  202.50/9 = 22.5 /student

22.5/student x (9+4)students = 292.50   total cost

I am not sure i 'get' your question !

    16

x     2

-------------

   32                 2 times the 6 is 12     write down the '2' and carry the '1'     then

                              2 x 1 = 2   and you have to add the carried '1' to get '3' ...then write that down  2 x 16 = 32  !