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Call Wilma's speed,  W

So when Wilma runs 100m, Betty runs 100 - 10 = 90m

So...Betty's speed is 9/10 of Wilma's =  (9/10)W

Note that Wilma rums 110 m  and her rate  = W

Call the distance that  Betty runs, D,   and her rate is  (9/10)W

So ...D /R  = Time

so....equating times, we have

110 / W  =  D / [(9/10)W]         multiply both sides by [ (9/10)W ]

110 (9/10)W / W  =  D

110 (9/10)  = D

[(110/ 10) * 9]   =  D

11 * 9     = D

99  = D

So....Betty  runs 99m  in the same time that Betty runs 110m....so....Betty is 1  m   from the finish line when Wilma finishes the 110m

B + D   =  180    ....so...

[ 2x + 3 ]   +  [ 4x + 3  ] =  180

6x + 6  =  180

6x  =  174      divide both sides by 6

x  = 29

So 

C  =  2(29)  + 1   =   59°

We can use this

sin 60  =  x  / 4

√3 /2  =  x  / 4     multiply both sides by 4

4√3 / 2  =  x

2√3 m =  x

I agree with CPhill

Well, are they talking about 1 year saving or over the lifetime of the mortgage? For one year savings, they have already listed for you in the bottom left-hand side as $5,977.36. If they are talking about the lifetime of the mortgage over 30 years, then the total interest paid would be about $410,390.19. And if you are in 30% tax bracket, then you save: $410,390.19 x 30% =$123,117.06 over 30 years. This would have the same effect as reducing your interest rate from 8% compounded monthly to about 5.96% compounded monthly. So, obviously the mortgage would be less expensive.

Not sure if this answers your question.

We have this

m XYZ  =  (1/2) (m XSZ  - m XZ )  =  (1/2) ( 220 -  140 )  = (1/2) (80)  = 40°

Hopefully it's easier to read my question now thanks!

I don't see any figure.....

Mass  / Volume   =  Density

So....multiply both sides by  Volume

Mass  =  Density * Volume

Mass  =  4.5g / cm^3   * 0.4 cm^3

The cm^3  cancels....and we're left with

Mass  =   4.5 g  *  0.4   =   1.8 g

What is the question that you don't understand?

Thank you guys sooo much! That really helped!

10000x^2  - 64   =  0       factor as a difference of squares

(100x - 8) (100x + 8)  = 0

Set both factors to 0  and solve for x

100x  - 8   =  0                    100x  + 8  = 0              

100x  = 8                             100x  =  - 8

x  = 8/100  =  2/25                x  =  -8/100  =  -2/25

9x^2  - 8  =  -34        rearrange  as

9x^2 + 34x - 8  =  0    factor

(9x - 2) (x + 4)  =  0

Set both factors to 0  and solve for   x

9x - 2  = 0                 x  +  4  =  0

9x  =  2                      x =  - 4          

x  = 2/9

2x^2 - 4x + 7  = 0     us the quadratic formula

x  =    4 ± √ [ 4^2 - 4*2* 7 ]           4  ± √ [-40]           4  ± 2 i√ 10

         ________________   =     __________   =    _________  =

              2 (2)                                    4                            4

2  ± i√10

_______

    2

3.2x + 0.2x^2 - 5  = 0      rearrange

0.2x^2 + 3.2x - 5  =  0     multiply through by 10

2x^2 + 32x - 50  = 0        divide through by 2

x^2 + 16x - 25  =  0       complete the square on x

x^2 + 16x + 64  =  25 + 64

(x + 8)^2  =  89         take both rots

x + 8   =   ± √89

x  =   ± √89  - 8

1. We can move 64 to the other side to get 10,000\(x^2\)=64. We then divide both sides by 10,000 to get 64/10000=\(x^2\)

we can then square root both sides to get 8/100=2/25. 

2. We move 34x to the right side to get 9x^2+34x-8=0 you can then use the quadratic formula(or factor, I was just too lazy) to get x=-4, 2/9

3. You can also use the quadratic formula to get imaginary solutions. There are no real solutions to this one. 

4. You can also use the quadratic formula to get -3.2 plus minus \( \sqrt{14.24}\) all over 4. 

13  Construct an altitude to Hypotenuse c  and label it CD

14  I answered this one, here :

https://web2.0calc.com/questions/help-please_34288#r2

Since Jordan's position is set.......the total possible arrangements are

3  ways to pick the runner in the first position

2  ways to oick the runner for the second position

1 way to select the rnner for the third position

So...3 * 2 * 1  =    6 different orders

First one...we can use the Law of Sines

sin R / 30  =  sin 69 / 35       multiply both sides by 30

sin R  = 30 sin (69) / 35

Use the arcsin to find R

arcsin [ 30 sin (69) / 35 ]  =  R  ≈   53.15°  =  53°

Second one.....

Note that angle F  =  180  - 87  - 40  =  53°

So...we can use the Law of Sines, again

x / sin 87  = 13 / sin 53     multiply both sides by sin 87

x  =  13 * sin 87  / sin 53     ≈ 16.25 cm   =  16 cm  (rounded)

Thank you!

20/1 divided by 1/5=

20*5/ 1*1=

100

The answer is 100.

sin (40)  = cos (3x)

These angles will sum to 90°  since they are co-functions....so...

40  + 3x  =  90      subtract  40  from both sides

3x  =   50     divide both sides by 3

x  = 50 / 3

Thank you!

OK...look  at the following  :

So...the total number of students  is   8 + 5 + 13   =  26

Thank you!!!

8^x  = 69

log₈ 69  =  x

Call the total number in the bag, N

Call the number  of red marbles, R

Call the number white, W

Call the number blue, B

Call the number green, G

4 reds are chosen has  the same probability as  1 blue  and 3 reds

R  *  (R-1) * (R - 2) *   (R - 3)             B      R          R- 1     R - 2

__   ____       _____   ______  =     ___   _____    _____  ____

 N    N - 1      N - 2        N - 3             N     N - 1      N  - 2   N - 3

Note that the denominators in each case will be the same  in all cases...so...we can ignore these

So...this simplifies to  R - 3  =  B     (1)

4 reds   has the same probability  as  1  white , 1  blue  and 2 reds

So....subbing (1)  in for B

R (R-1) (R - 2) (R - 3)   =  W (R - 3)  R (R -1)

This simplifies to

R - 2  =   W      (2)

4 reds  has the same probability  as one of each color

Subbing  (1) and (2)  in for B, W   we have

R (R - 1) (R - 2) (R - 3)   =  R (R - 2) (R -3) G

This simplifies to

R - 1   =  G

Since there has to be at least one of each color....let the number of Red  = 4

Let the number of Green  = R - 1  =  3

Let the number of White  = R  - 2  =  2

Let the number of Blue  = R - 3  =  1

So.....the fewest number possible is 10