The statement suppose <span>that r varies directly with s and inversely with t is best represented as:
r </span>α s/t
To make it into equality, we insert a proportionality constant, k:
r = ks/t
Using the initial conditions, we solve for k.
r = ks/t
<span>r = 2 when s = 3 and t = 12
2 = k(3)/12
k = 8
Thus, when </span><span>s = 5 and t = 4,
</span>
r = 8(5)/4
r = 10 -----> OPTION C
Answer: x=5 or x=−13
Step-by-step explanation:
8x−65=−x2
8x−65−(−x2)=−x2−(−x2)
x2+8x−65=0
(x−5)(x+13)=0
x−5=0 or x+13=0
x=5 or x=−13
The correct answer is Choice A.
This is an example of an exponential equation, so we need the formula

.
The a value is the starting value of 100. The b value must be a decimal lower than 1 because it is decreases.
If you substitute in 8 for x, you will see that the output is about 50 (half of 100).
Answer:
3
Step-by-step explanation:
g(x) = x² + 2x+4
h(x) = -3x+2
(g*h)(1) is the same as
g(h(1)) , next solve for h(1) first by substituting in h(x), x with 1
g( h( x= 1)) = g( -3*1 +2) = g( -1) so substitute in g(x) , x with -1
g(x= -1) = (-1)² +2(-1) +4 =1-2+4 =3
Answer:

Step-by-step explanation:
Given: 
Let's changed that mixed number to an improper fraction. Now we get:

Let's find out least common denominator. This one is easy, the LCD is 8. Now that we know the LCD, let's convert both our fractions:

We can use
because it is equal to
. Now, all we need to do is subtract the numerators:
