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1.

-9  <  4x + 3  ≤  27

                                     We can decrease each part by  3  and still keep the inequality true.

-12  <  4x  ≤  24

                                     Now we can divide through by  4 .

-3  <  x  ≤  6

2.

7x − 9  <  12                Add  9  to both sides.

7x  <  21                      Divide both sides by  7 .

x  <  3

                            or

1/4x + 8  >  11             Add  8  to both sides.

1/4x  >  19                   Multiply both sides by  4 .

x  >  76

So...     x < 3    or    x > 76

3.

She wants at least 4 times as many yellow rosebushes as red rosebushes.  So...

the number of red bushes is greater than or equal to 4 times the number of yellow bushes.

y  ≥  4x

She can spend no more than $125.  So...

the total cost of the yellow bushes + the total cost of the red bushes is less than or equal to $125.

7.50x + 4.75y  ≤  125

Also...she can't buy a negative number of bushes....and she must have each type....so

x  >  0   and

y  >  0

log x   - log y  = a

log y  - log z  =  15

log z   - log x   =   -7

Add  the first two equations and we get that

log x  - log z   =  a  + 15

Multiplying the third equation by  -1 on both sides we have that

log x  -  log z  =  7

This implies that

a + 15  =  7         subtract 15 from both sides

a  = - 8

log x - log y   =   a        so        x/y  =  10^a

log y - log z   =   15      so        y/z  =  10^15

log z - log x   =   -7       so        z/x  =  10^-7        so        z  =  x * 10^-7

y/(x * 10^-7)  =  10^15

y/x * 10^7  =  10^15

y/x   =   10^8

x/y   =   10^-8

10^-8  =  10^a

a  =  -8

x^(1/2)  +  x^(1/4)   = 30        subtract 30 from both sides

x^(1/2)   +  x^(1/4)  - 30    =  0     we can factor this directly as

[  x^(1/4 )  +  6  ]    [ x^(1/4)  - 5  ]   =  0

Settting both of these factors to 0  and solving for x, the first produces no solution

For the second, we have that

x^(1/4)  - 5  = 0     add 5 to both sides

x^(1/4)  = 5           take both sides to the 4th power

x  = 5^4   =    625

The denominators that you have indicate that this is probably  with replacement

The number of possible sums  without replacement are  12 * 11   =  132

Sums of 10  =

1   9

9   1

2   8

8   2

7   3

3   7

4   6

6   4

So.......the probability that the numbers sum to 10  without replacement is just    8  / 132   =  2 / 33

However.....with replacement we have    12  * 12   =  144 possible sums

1   9

9   1

2   8

8   2

7   3

3   7

4   6

6   4

5   5

So....the probability  that we have a sum of 10 with replacement is just   9  / 144   =  1  / 16

Pefectly fine, hectictar.....!!!!

We want to find all ordered pairs such that  y  = x

This cannot happen with the first function whose only ordered pair is (1, 3)

With the second function we have that

y  =  7-x       .....so.....

x  = 7 - x       add x to both sides

2x  =  7        divide both sides by 2

x   = 7/2  and this is in the domain of this function...so the ordered pair that make f(x)  = x   for this function is  (7/2, 7/2)

For the third function, we have that

y  = 10-2x      ......so....

x  = 10-2x        add 2x to both sides

3x  = 10   divide both sides by 3

x  = 10/3   and this is in the domain of this function.....so the ordered pair that make f(x)  = x for this function is (10,3, 10,3)

Finally

y  = 10- x     ......so....

x  = 10 - x   add x to both sides

2x  = 10    divide both sides by 2

x  = 5  and this is in the domain  of this function....so the ordered pair that make f(x)  = x  for this function is  (5,5)

So.....the ansers are:      (7/2, 7/2), (10/3, 10/ 3) , (5,5)

1.

-8x - 7y  =  96      multiply this equation through by  5  to get      -40x - 35y  =  480

-3x + 5y  =  -25    multiply this equation through by  7  to get      -21x + 35y  =  -175

(-40x - 35y) + (-21x + 35y)   =   480 + -175

-61x  =  305

x  =  -5              Use this value for  x  in the second given equation to find  y  .

-3(-5) + 5y  =  -25

15 + 5y  =  -25

5y  =  -40

y  =  -8

2.    Let Marty's age be  " m " ,  and let Warren's age be  " w " . The problem tells us that...

m  =  6w - 3

                              and

m + w  >  11

Plug in   6w - 3   for   m   into the inequality.

6w - 3  + w  >  11      Add  3  to both sides and combine like terms.

7w  >  14

w  >  2        Warren has to be older than  2  .

So if his age has to be a whole number, the youngest he can be is  3 .

3.    (−∞, 3]  or  (7, ∞)

I don't know if this is the way you are supposed to do it, but here I made a table with all the different possible combinations, and highlighted each unique sum once:

I count  19  .  

any answer pleaaase !!!

THANK YOU

anyone, please ???

thanks!

THANK YOU! THANK YOU! THANK YOU! THANK YOU SO MUCH!!!!

-18x^10 z^4 + 6x^6 z^3

Go to Mathway.com and put ur question in and it will give it to you simplified...

AH!!!!....this site does NOT LIKE the use of  too many "<"  signs....I don't know why, but it cut off my answer....!!!!!

The answer is  

angle FEK  = angle HGK

angle EFK  = angle GHK

Sorry...."Ghosts in the machine "

EF¯¯¯¯¯ ∥ HG¯¯¯¯¯¯    =  Definition of a parallelogram

? = When two parallel lines are cut by a transversal, alternate interior angles are congruent.

EF¯¯¯¯  ≅ HG¯¯¯¯ = The opposite sides of a parallelogram are congruent.

△EKF≅△GKH = ASA Congruence Postulate

EK¯¯¯¯  ≅ GK¯¯¯¯       =CPCTC

FK¯¯¯¯  ≅ HK¯¯¯¯

EG¯¯¯¯ bisects HF¯¯¯¯ nad HF¯¯¯¯ bisects EG¯¯¯¯ = Def. of bisector

Where the REASON says: When two parallel lines are cut by a transversal, alternate interior angles are congruent. 

Which STATEMENT would it be?: 

(A) ∠EKF  ≅ ∠HKF

(B) ∠FEK  ≅ ∠HGK

      ∠EFK  ≅ ∠GHK

                                                                        Definition of a Parallelogram

EF  = HG

EK  = GK

FK  = HK

                                                                    Definition of  bisector

Note :

PM / YP  = BE / WB      ....so.....

32 / 15  = BE / 21   multiply both sides by 21

(21/15)* 32  =  BE  =   (7/5)*32  =  44.8 

Correct  !!!!

Here's  2

There were 65000 people in the stadium when the trend began

The number of people in the stadium decreased by 4% for each 10 minute period since the trend began

Point P is the midpoint of  AA

AA  is perpendicular to XY

1:

log₄(20x - 10) - 2log₄(3)  =  log₄(4x + 10)

log₄(20x - 10) - log₄(3²)  =  log₄(4x + 10)       by the Power Property of Logarithms

log₄( \(\frac{20x-10}{9}\) )  =  log₄(4x + 10)       by the Quotient Property of Logs. (They also changed  3²  to  9)

\(\frac{20x-10}{9}\)   =   4x + 10      by the Equality Property of Logarithms

Hey!! That handwriting looks pretty familiar......  👀

[    1/x^2  + 2/y  ]   /  [ 5/x  -  6/y^2]

Multiply numerator/ denominator by x^2y^2

[ y^2  + 2x^2y ]  / [ 5xy^2 - 6x^2]