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If x2 is \(x^2\) then use the quadratic formula.

 \(x^2+9x+16=0\)

\(x = {-9 \pm \sqrt{9^2-4 \cdot 1 \cdot 16} \over 2 \cdot 1}\)

\(x = {-9 \pm \sqrt{81-64} \over 2}\)

\(x = {-9 \pm \sqrt{17} \over 2}\)

Since this is irrational, the expression cannot be factored.

The three diagonals define APB to be a 45-45-90 triangle, so x=\(\sqrt{2}\).

I'm glad you could give me this answer. Thanks!

Could someone show me a detailed way to solve this problem so I can use it elsewhere?

Given that the temperature rose 1 1/2 degrees every 3/5 of an hour, we can convert the given information into a rate per hour.

Let's calculate the change in temperature per hour:

First, we'll find the change in temperature for 1 hour.

Since 3/5 of an hour is equal to 1, we can say that in 1 hour, the temperature will rise by 1 1/2 degrees.

Therefore, the rate at which the temperature rose is 1 1/2 degrees per hour, which can also be written as a mixed number: 1 1/2.

The only number that will satisfy the stipulation that it  

be a multiple of 6 and a multiple of 4 is the number 12.  

It could land on one of 14 areas,  

but only one is the desired area, 

then the probability is 1 in 14.  

_.

          12 is a multiple of 6 and a multiple of 4   

Kaylee conducted a scientific experiment. For a certain time, the temperature of a compound rose 1 1/2​ degrees every 3/5 of an hour. What was the rate, in degrees per hour, that the temperature of the compound rose? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.  

Sometimes we aren't certain whether to multiply or divide.  

Tip:  In math, "per" means "divided by" so  

"degrees per hour" means divide the degrees by the hours  

                                                               3 / 2  degrees  

                                                             –––––––––––––  

                                                               3 / 5  hour    

To divide by a fraction,   

invert the divisor and  

multiply.   

                                                                3         5  

                                                               –––  *  –––   deg/hr  

                                                                 2         3  

The 3's cancel, leaving  

                                                                5  

                                                               –––   deg/hr  

                                                                 2  

Which probably the simplist form is  2-1/2 deg/hr  (two and a half degrees per hour)  

_.

The answer is 21/2.

The smallest n that works is 100.

... 9

6 gallons

Let's assign a variable for the total capacity: t

1/2t - 1/6t = 1/3t

1/3t = 2

2 * 3 = 6

So the total capacity of the tank is 6 gallons

Oh thanks, but what does the "C" stand for? Thanks so much for the help!!

Oh, thank you so much! I understand now!

The focus is at (-3,6).

10 + 1/2 = 10.5. 10 * 2 = 20, 20 + 1 = 21. 21/2 is 10.5 as a fraction 

Solved by computer:

for (n = 3..2019) {

   x = x + cscdeg(2^n);

}

output(x);

output = 1.002441898

This is equal to \(\sec 4^\circ\), so n = 4.

Add equations together to get 15(a+b+c+d+e)=215.

Divide to get a+b+c+d+e=43/3.

Now take equation 1, subtract it from equation 2.

a+b+c+d-4e=-26. Subtract the two equations shown to get 5e=121/3, so e=121/15.

See if you can use this same method to determine a, b, c, and d.

(3, 5, 43) ,(3, 7, 41) ,(3, 11, 37) ,(3, 17, 31) ,(3, 19, 29) ,(5, 5, 41) ,(5, 17, 29) ,(5, 23, 23) ,(7, 7, 37) ,(7, 13, 31) ,(11, 11, 29) ,(11, 17, 23) ,(13, 19, 19) ,(17, 17, 17) ,>>Total =  14 such triplets of prime numbers.

x = 81.

yeah absolutly!!!!

yes perfect

5+3+7=9

3 cookys

5 cookies cuz 2+3=5