geno3141

-24/7 is a rational number, which also makes it a real number and a complex number.

-5/6 is a rational number, which also makes it a real number and a complex number.

sqrt(196) = 14 is a counting number (also called a natural number), which also makes it a whole number, an integer, a rational number, a real number, and a complex number.

sqrt(29) is an irrational number, which also makes it a real number and a complex number.

To find the x-intercept, subustitue 0 for the y-term, and solve for x:

-2x + (1/2)y  =  18     --->     -2x + (1/2)(0)  =  18     --->     -2x  + 0  =  18     --->     -2x  =  18     --->     x = -9

The -intercept is the point (-9, 0)

For these problems, find the difference between the incorrect answer and the correct answer (subtract, if the answer is negative, ignore the negative sign); divide this difference by the correct answer, and multiply by 100.

Board:  13.2 - 12.0  =  1.2     --->     1.2/12  =  0.10     --->     0.10 x 100  =  10%

Dog food:  11.5 - 10  =  1.5     --->     1.5/10  =  0.15     --->     0.15 x 100  =  15%

Can you do the other two?

-111 + 51p  =  -35(12p + 57)

Using the distributive property:

-111 + 51p  =  -420p - 1995

Adding 420p to both sides:

-111 + 471p  =  -1995

Adding 111 to both sides:

471p  =  -1884

Dividing both sides by 471

p  =  -4

First, subtract the wrapping fee (because tax wasn't paid on the wrapping):  122.36 - 35.00  =  87.36

The equation now is:  (Price) + (7% of the Price)  =  87.36

                                       P + 0.07P =  87.36

                                             1.07P  =  87.36

--->  P  =  81.64

(Actually a total of 87.36 is impossible; if the original amount is 81.64, the tax will be 5.71, for a total of 87.35.

If the original amount is 81.65, the tax will be 5.72, for a total of 87.37.)

What is the problem?

One way of looking at this problem;

If you can mow 3/8ths of an acre in 45 minutes, she can mow 1/3rd of that amount in 15 minutes.

1/3 of 3/8  =  1/3 x 3/8  =  1/8th of an acre in 15 minutes.

Since 15 minutes is 1/4th of an hour, multiply what can be done in 15 minutes by 4:  1/8 x 4  =  4/8  or  1/2 of an acre.

This is an impossible situation:  -x + -x + x + x  =  0  and 0 doesn't equal 53!

The 7th term is 6 steps away from the first term. Going 6 steps from the original number, you will need to subtract 6 8's from 200:  200 - 6(8)  =  200 - 48  =  152

This is a right triangle, Pythagorean Theorem, problem.

If you start at Point A and walk 34 meters south to point C and from this point walk 41 meters east to Point B, you have walked the two legs, AC and CB, of right triangle ACB (with the angle at corner C the right angle). To find the straight line distance from A to B, use the Pythagorean Theorem:  AC² + CB² = AB²   --->   41² + 34²  =  AB²

--->   2837 =  AB²   --->   AB =  53.3

Walking from A to C to B =  41 + 34 = 75 meters.

Walking from A to B will save you 75 - 53.3 = 21.7 meters.