The 2 small black lines through the sides of the triangle indicate that the 2 sides are the same length.
Because the 2 sides are the same the 2 bottom angles are also the same.
This means that 9x +3 = 84
Now we can solve for x:
9x +3 = 84
Subtract 3 from each side:
9x = 91
Divide both sides by 9:
x = 81 / 9
x = 9
Answer:
c.4
Step-by-step explanation:
hope it helps ............
Answer:
1.6 with the bar on top of the 6
Step-by-step explanation:
Selection C is appropriate.
_____
Whenever you solve for something, consider what operations are done to that something. Undo them in reverse order.
Here, "a" is
• multiplied by 2
• has -b^2 added
The last operation is adding -b^2, so we undo that first. We undo it by adding its opposite, b^2.
.. x +b^2 = 2a -b^2 +b^2
.. x +b^2 = 2a . . . . . . . . . . . the point is to cancel the -b^2 term on the right.
The operation before that is multiplying "a" by "2". We undo that by multiplying by the reciprocal of 2, which is 1/2.
.. (1/2)*(x +b^2) = (1/2)*2a
.. (x +b^2)/2 = a . . . . . . . . . the point is to cancel the multiplication by 2 on the right.
You will note this matches answer selection C.
Answer:
a. C(t)=205*(1-0.08)^t
b. t=log_0.92(C(t)/205)=(log_10(C(t)/205))/(log_10(0.92))
c. 16.92 hours
Step-by-step explanation:
Let's say that C(t) is the expression of the amount of caffeine remaining in Darrin's system after t time, hours in this particular case.
a. Then for the first hour the expression would be:
C(t)=205*(1-0.08)
For the second hour:
C(t)=205*(1-0.08)-205*(1-0.08)*(1-0.08)
For the third
C(t)=205*(1-0.08)-205*(1-0.08)*(1-0.08)-205*(1-0.08)*(1-0.08)*(1-0.08)
And so on, for that reason the best way to fit the expression is:
C(t)=205*(1-0.08)^t
2. To find the correct expression for time, we must solve for t the equation recently written above:
Considering that log_b(a)=c and log_b(a)=log_c(a)/log_c(b), then:
t=log_0.92(C(t)/205)
t= (log_10(C(t)/205))/(log_10(0.92))
3. Finally we replace the given value of C(t) into the equation for t:
t= (log_10(50/205))/(log_10(0.92))=16.92
t= 16.92 hours
