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The vertex is (4, -5).

If you substitute 4 for x into each of the possibilities, only (d) gives a y-value of -5; so, choose (d).

Generally speaking, if the vertex occurs at (h,k), the formula will be:  y  =  a(x - h)² + k.

The term a is an "expansion factor". 

Call the fraction  x/y.

To increase x by 10% :  x + 10%x  =  x + 0.10x  =  1.00x + 0.10x  =  1.10x.

To decrease y by 50%:  y - 50%y  =  y - 0.50y  =  1.00y - 0.50y  =  0.50y.

The new fraction is now  (1.10x) / (0.50y)  =  (1.10/0.50)(x/y)  =  (1.1/.5)(x/y  =  (11/5)(x/y).

11/5  =  2.2   --->   The new fraction is now  2.2 times the old fraction (x/y).

So the new fraction is 2.2 times as large as the old fraction.

2.2 times is 220%; however, to calculate the percentage of increase, you must subtract the original (which is 100%) from this 220% (which represents the original plus the increase); giving an increase of 120%. 

100/100=90/50=1.9 -1=.80 X 100=80% increase in the fraction

Solve for x:
4 x^2-24 x+31 = 0

Divide both sides by 4:
x^2-6 x+31/4 = 0

Subtract 31/4 from both sides:
x^2-6 x = -31/4

Add 9 to both sides:
x^2-6 x+9 = 5/4

Write the left hand side as a square:
(x-3)^2 = 5/4

Take the square root of both sides:
x-3 = sqrt(5)/2 or x-3 = -sqrt(5)/2

Add 3 to both sides:
x = 3+sqrt(5)/2 or x-3 = -sqrt(5)/2

Add 3 to both sides:
Answer: | x = 3+sqrt(5)/2      or         x = 3-sqrt(5)/2

y= e^x sinx

Remember, Yura_chan.....we are using the Product Rule, here.....

y '  = e^xsinx + e^xcosx  =  e^x(sinx + cosx)

Use the Product and Chain Rules to find y "

y "   = e^x(sinx + cosx)   + e^x(sinx + cosx)^0 * ( cosx - sinx)   =

e^x(sinx + cosx) + e^x (cosx - sinx)  =

e^x [ sinx + cosx + cosx - sinx]  =

e^x [2 cosx] =

2e^xcosx

Nothing's wrong with it. It is 100% correct. 

Try writing this: (-1*4)*(-1*6)=24

(-4)*(-6)=24

24=24

by circling in*

negative times negative= positive   

The easy part is the answer, im struggling with the calculation

That makes no sense you aready did it

(OP) 

Yeah i know the correct answer i'm looking for the calculation.

-Fgt

Yes you are correct

-Casey

8.5 = 17/2 and 26/e^(0.8 x) = 26 e^(-4 x/5):
17/2 = 26/e^((4 x)/5)

17/2 = 26/e^((4 x)/5) is equivalent to 26/e^((4 x)/5) = 17/2:
26/e^((4 x)/5) = 17/2

Divide both sides by 26:
e^(-(4 x)/5) = 17/52

Take reciporicals of both sides:
e^((4 x)/5) = 52/17

Take the natural logarithm of both sides:
(4 x)/5 = log(52/17)

Multiply both sides by 5/4:
Answer: | x = 5/4 log(52/17)=1.3975........etc.

sqrt(225)/5*sqrt(245) = 46.9574275274955836, so I'd believe irrational.

Solve for x:
12 x-7 x^2 = 10

Divide both sides by -7:
x^2-(12 x)/7 = -10/7

Add 36/49 to both sides:
x^2-(12 x)/7+36/49 = -34/49

Write the left hand side as a square:
(x-6/7)^2 = -34/49

Take the square root of both sides:
x-6/7 = (i sqrt(34))/7 or x-6/7 = 1/7 (-i) sqrt(34)

Add 6/7 to both sides:
x = 6/7+(i sqrt(34))/7 or x-6/7 = 1/7 (-i) sqrt(34)

Add 6/7 to both sides:
Answer: | x = 6/7+(i sqrt(34))/7      or        x = 6/7-(i sqrt(34))/7

Wonderful job!

Hold on, I've done my math(s) incorrect. Melody is right.

NEVER MIND I FIGURED IT OUT GUYS x = about 19 

Its amazing

1/3 + 1/9 = 4/9

but what's the calculation

Same with 1/2 - 2/5 = 1/10 

calculations please

Simplify the following:
1/3+1/9

Put 1/3+1/9 over the common denominator 9. 1/3+1/9  =  3/9+1/9:
3/9+1/9

3/9+1/9  =  (3+1)/9:
(3+1)/9

3+1 = 4:
Answer: |  4/9

Simplify the following:
1/2-2/5

Put 1/2-2/5 over the common denominator 10. 1/2-2/5  =  5/10+(2 (-2))/10:
5/10+(2 (-2))/10

2 (-2)  =  -4:
5/10+-4/10

5/10-(4)/10  =  (5-4)/10:
(5-4)/10

5-4 = 1:
Answer: |  1/10

Cont. That means that the sine(x = n/3n right? Is there any way to find out x as an exact measure?

1        1       4

---  +  --- =  ---

3        9        9

You have to make sure the denominator match. You can easily make 3 into 9 by multiplying it by 3, but what you do to the bottom you have to do the top.

1*3        1       4

---  +  --- =  ---

3*3        9        9

Then your equation would be:

3        1       4

---  +  --- =  ---

9        9        9

The by solving that you get 4/9.

Did you ask your teacher "why?".

Add them all up and divide their sum by the number of terms: Example: 1, 2, 3, 4, 5. Add them all up and you get=15. Then divide 15/5(number of terms)=3 is the "mean".