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Since the large vertical line is 4 times the small vertical line,

then the large diagonal line is 4 times the small diagonal line. 

Large diagonal line is 4 x 26 = 104  

?  = 104 – 26  =  78   

The picture is not to scale.

A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.  

Call the first number X and call the second number Y. 

                                                                        X + 2Y  =  14      (eq 1)  

                                                                        2X + Y  =  10      (eq 2)  

Multiply both sides of equation 1 by 2              2X + 4Y  =  28    (eq 3)

Subtract equation 2 from equation 3                        3Y  =  18  

Divide both sides by 3                                                 Y  =  6    

Substitute 6 for the Y in equation 2                   2X  +  6  =  10    

Subtract 6 from both sides                                        2X  =  4   

Divide both sides by 2                                                 X  =  2    

_.

The remainder is 4x^2 - 7.

X is 25/4, and y is 35/4

Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?  

Observe that "catch the first" car means "reach the same distance". 

Distance equals velocity x time.  S = v • t   

1st car will travel this distance:                  S  =  40 mph • H hours    

2nd car will travel this distance                  S  =  60 mph • (H – 3) hours  

Since the 2nd car catches up with the 1st and that's the same as saying they've traveled the same distance, then set the distances equal. 

                                                                  40 mi/hr • H hr  =  60 mi/hr • (H – 3) hr 

Drop the units for ease                              40H  =  60H – 180 

Subtract 60H from both sides                     –20H  =  –180  

Divide both sides by –20                                  H  =  9

Since we were talking about time, 

then the applicable units is Hours                    The 2nd car catches the 1st car after 9 hours  

Check answer                                                  Does 40 • 9  =  60 • 6 ?   Yes, it does. 

_,

Let the time taken by the first car =T

Distance =Time x speed

40T = 60*(T - 3)

40T =60T - 180

60T - 40T = 180

T = 9 hours for the first car, or:

9 - 3 = 6 hours for the second car - when it catches up with the first car.

Check: 40 mph x 9 hours =60 mph x 6 hours =360 miles covered.

Sorry, it's incorrect

The question is in the Title. 

_.

Assuming that they have all the limbs they are supposed to have,

5.

If there are 5 horses and 10-5=5 clowns, there would be 20 horse legs and 10 clown legs. Adding these values and we get 30 legs in total.

Let the number of gallons of 30% solution =G

Then, the number of gallons of 80% solution =14 - G

[0.3G + 0.8(14 - G) ] =0.4 x 14, solve for G

G =56/5 =11.2 gallons of 30% solution

14 - 11.2  =2.8 gallons of 80% soltution.

The point is (2/3)(-6,19) + (1/3)(15,-5) = (1,11).

Reflection matrix for y = 1/2*x + 5 applied to (6,2):

\(\begin{pmatrix} 3/5 & 4/5 \\ 4/5 & -3/5 \end{pmatrix} \begin{pmatrix} 6 \\ 2 \end{pmatrix} = \begin{pmatrix} 26/5 \\ 18/5 \end{pmatrix}\)

So the relfection is B = (26/5,18/5).

You can track the probabilities using different case, i.e. Anty gets to 0 after 1 steps, 2 steps, 3 steps, and so on.  This gives us e = 1/2*1 + 1/4*2 + 1/8*3 + 1/16*4 + ... By arithmetico-geometric series, e = 2.  Similarly, f = 1/2*2 + 1/4*3 + 1/8*4 + 1/16*5 + ... = 3, so (e,f) = (2,3).

1. By long division, the remainder is x^2 + 4x - 3.

2. By long division, the remainder is 7x - 2.

I set up a system of equations as such: 1.5x+4y=746 and x+y = 289. From there, I just solved it normally and got that 164 children and 125 adults went to the park.

This is not my homework as I am on summer vacation.

Well it tells you how much 80% solution u need. It's ____. As for the 30%, just guess. That's the best way! (-:

Thank you very much for giving us your homework!

None bec the park went broke.

He solves 112 problems the day he drinks coffee

(3p+7)(t-4) = 2tp
===> .
Since both t and p are positive integers,  can only take on the values 0, 1, or 2. (Why?)
 does not yield any value of p.

 ===> p = 7.
 ===> p = 0, which is not acceptable.
Therefore, p = 7,
===> ,
and the mathematician solved (3*7 + 7)(8-4) = 28*4 = 112 problems

What was the question???

Idk :o

If I understand the question correctly, the answer is n!   

n! means n factorial, which is (1)(2)(3) • • • (n)