Answer:
x≈6.4
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }24900
a=starting value = 24900
r=\text{rate = }6.75\% = 0.0675
r=rate = 6.75%=0.0675
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.0675=0.9325
b=1−r=1−0.0675=0.9325
\text{Write Exponential Function:}
Write Exponential Function:
y=24900(0.9325)^x
y=24900(0.9325)
x
Put it all together
\text{Plug in y-value:}
Plug in y-value:
15900=24900(0.9325)^x
15900=24900(0.9325)
x
\frac{15900}{24900}=\frac{24900(0.9325)^x}{24900}
24900
15900
=
24900
24900(0.9325)
x
Divide both sides by 24900
0.638554=0.9325^x
0.638554=0.9325
x
\log 0.638554=\log 0.9325^x
log0.638554=log0.9325
x
Take the log of both sides
\log 0.638554=x\log 0.9325
log0.638554=xlog0.9325
use power rule to bring x to the front
\frac{\log 0.638554}{\log 0.9325}=\frac{x\log 0.9325}{\log 0.9325}
log0.9325
log0.638554
=
log0.9325
xlog0.9325
Divide both sides by log(0.9325)
6.418279=x
6.418279=x
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Answer:
<h2>x ≥ 2</h2>
Step-by-step explanation:
our expression is defined when x ≥ 1 ,
because , when x ≥ 1
x - 1 ≥ 0
x + 2√(x - 1) ≥ 0
x - 2√(x - 1) ≥ 0
According to case 1 and 2 the solution set for this equality is {x real number where x ≥ 2 }.
Answer:
Step-by-step explanation:
GIVEN: Emma started biking to the coffee shop traveling , after some time the bike got a flat so Emma walked the rest of the way, traveling If the total trip to the coffee shop took and it was away.
TO FIND: how long did Emma travel at each speed.
SOLUTION:
Let the distance traveled by Emma through bike is
Total time taken when traveled by bike
Distance traveled through feet
Total time taken when traveled by feet
Now,
Total time taken
Distance traveled through feet
Hence distance traveled using bike is and by feet is
Triangle QST is an isosceles triangle. You can tell because two of the legs are congruent. Thus angle T is also an x-variable.
Add all of the degrees together, set them equal to 180 and solve for x.
x + x + 74 = 180
2x + 74 = 180
2x = 180 - 74
2x = 106
x = 53
This rules out options C and D.
Now we have to find angle PQS:
The measurements of triangle PQR are congruent to each other so 180 / 3 = 60 they are all 60 degrees.
Angles PQR, PQS, and SQT are in line with each other so they add up to 180.
60 + PQS + 74 = 180
134 + PQS = 180
PQS = 180 - 134
PQS = 46
Triangle PQS is another isosceles triangle. Thus, the two base angles are the same. We are going to add them together plus y and set it all equal to 180 to solve.
46 + 46 + y = 180
92 + y = 180
y = 180 - 92
y = 88
x = 53, y = 88. Your answer is option B