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See https://web2.0calc.com/questions/geometry_59373

The ANSWER WIl be 10 yards.

first down is 1st and 10. lost 5 on play

second down is 2nd and 15. lost 9 on play

third down is 3rd and 24. gained 12

fourth down 4th and 12. lost 8

so the team lost a total of 10yds

Seven years ago, Grogg's dad was 6 times as old as Grogg, and 4 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?  

Call Grogg's age now "G" and his dad's age now "D"  

Seven years ago                           (D – 7)  =  6 * (G – 7)  

Four years ago                              (D – 4)  =  4 * (G – 4)  

Multiply them out                            D – 7  =  6G – 42          (eq 1)  

                                                       D – 4  =  4G – 16          (eq 2)  

Subtract (eq 2) from (eq 1)                – 3  =  2G – 26  

                                                           23  =  2G  

                                                             G  =  11.5  

Find D by

plugging G back into (eq 1)               D – 7  =  (6)(11.5) – 42 

                                                        D – 7  =  69 – 42  

                                                              D  =  27 + 7  

                                                              D  =  34  

Check answer by

plugging G back into (eq 2)                D – 4  =  (4)(11.5) – 16  

                                                         D – 4  =  46 – 16 

                                                               D  =  30 + 4  

                                                               D  =  34 

_.

The probability that Alpha wins two games out of three is (6/10)^2 + 6/10*4/10 = 3/5, so the probability that Beta wins is 1 - 3/5 = 2/5.

The distance is 11.7.

k = 3, m = -8.

1. Find the area of triangle ABC if AB = 6, BC = 8, and angle ABC = 90 degrees.

Since it's a right triangle, either leg (but not the hypotenuse) can be considered the base. 

The area is half the base times the height,and so (1/2)(6)(8) =  24 sq units  

2. If angle ABC = 135 degrees, and angle ACB = 30 degrees, what is angle BAC?

For this I'm assuming we're talking about a triangle, which was not specified.  

The sum of all three angles of a triangle is 180^o so 180^o – (135^o + 30^o)  =  15^o  

edited to add about #1 ~  Actually, the hypotenuse can be used as the base, but  

you get all mixed up with sine or tangent or Pythagoras, so it's easier to use a leg.  

_.

Real numbers a and b satisfy

a + ab = 250

a - ab = -240

Enter all possible values of a, separated by commas.  

If you add the two equations together                a + ab  =   250  

                                                                           a – ab  = –240  

                                                                          ————————  

you get                                                              2a         =  10  

from which                                                                  a  =  5  

find b by substituting  

a back into a + ab = 250                                       5 + 5b  =  250  

                                                                                5b  =  245  

                                                                                  b  =  49  

check b by substituting  

a back into a – ab = –240                                  5 – 5b  =  –240  

                                                                              –5b  =  –245  

                                                                                   b  =  49  

_.

typo 

Subtract (eq 2) from (eq 2)  should have been  Subtract (eq 2) from (eq 1)  

I like that approach, but I don't think it is entirely correct. In this problem, \(|z-1|=|x+yi-1|=|(x-1)+yi|=\sqrt{(x-1)^2+y^2}\), because \(|x+yi|\) signifies the magnitude of the number, which is \(\sqrt{x^2+y^2}.\) I think that you interpreted it as absolute value.

Thanks!

Makes so much sense now. Thank you!

BULL. 

Don't believe the trolls who just post some random number.  

Two cubes contain a total of 54 cubic centimeters.

One cube contains half the total... i.e., 27 cm³  

The cube root of 27 is 3 cm.  

_.

That is because your "solution" is:

2^25 = 2 x  2^24 - and that is "no solution" to Beal's Conjecture!

>>   Copy the link then paste it in to the URL field   <<  

If you're on a computer you can just select the whole link then right click it.  

...equal to 21*4 times the largest...  

I've seen this problem before, many times, but

it never said 21*4 so I think there's a typo here.