Solve: 8|2-9p|-2=14

8|2-9p|-2=14
8|2-9p|-2+2=14+2
8|2-9p|=16
8/8|2-9p|=16/8
|2-9p|=2 

case 1)
2-9p=2
-9p=0
p=0 

case 2)
2-9p=-2
-9p=-4
p=4/9

Explain why solving an equation containing one absolute value expression does not apply to the expression | x - 5 | = -3?

One useful and naturally intuitive definition is that the absolute value of an number is it's distance from 0 on the number line. If we use this definition then we require that the absolute value of a real valued quantity be greater than or equal to zero. We also know that both sides of any equation must have the same sign to have a solution- therefore this equation is a contradiction.

Solve: 3 = x-2√x

leads to
 or 
but only  is viable and it leads to

Hi. Can someone please help me solve this question? Given the simultaneous equations: {3x+4y=-3, 5x=2y+19} (a) Write the equations in the form AX=B, where, A, X andB are matrices. (b) Determine A-1 (that's inverse; -1). (c) Calculate A-1<-- (inverse) B (d) Hence, solve for x and y.

Use matrices to solve the system of equation. { 3x-2y+4z=4, x+y+z=3, 6x-2y-3z=10}

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.

Find the values of the constants C and b so that the curve y = Cb^(x) contains the points (4 , 3) and (5 , 6) .

for the point (4,3) we can write 
for the point (5,6) we can write 

then taking the quotient of these two equations leads to


s we see that



Now we can use either point (we'll go with (4,3)) and b directly to write





so,

Use matrices to solve the system of equation. {x+2y=-4, 2x+y=1}

solution: (2,-3)

The tenth term of an arithmetic sequence is 42 more than the seventh term.If the first term is -14.Find the second term of the sequence?

Now

Solve |x-6|<= 7

means


After adding 6 to both sides we get

Solve |7-4x|>= |3|

so


has the same solution

Removing the absolute values leaves us with

1) 

or

2) 

1)


or
2)

The sum of two numbers is 41, and their difference is 11. What are the two numbers?

1) n+m=14
2) n-m=11
adding 1) and 2)...
2n=25
n=25/2

m=14-25/2=3/2

A cup of skim milk has 10 more than half the calories of a cup of whole milk. a cup of whole milk has 40 more calories than a glass of apple juice. If someone consumed a cup of each of the three, they would have 370 calories. how many calories must be in each?

1) s= w/2+10
2) w=a+40 (or a=w-40)
3) a+s+w=370

rewriting 3)...






then we find the others:

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bailey's mean score on 5 assessments is 73. what does she need to make on her next 2 assessments for her average to be at least a 78?

This is a weighted average.






Her two scores must add to 181

A number is divided by three. The result is divided by seven, for a final result of eight. What was the original number?

 


 

how many even 5 digit numbers are there?

clearly half of the 5 digit integers are even so 45000, but let's show it another way...



using arithmetic sequences