Answer:
<em>In the next year, Anthony worked 2,084 hours</em>
Step-by-step explanation:
Anthony worked 1,697 hours in 2010.
We also know Anthony worked 22.8% more hours than in 2010.
The problem requires to calculate how much did Anthony work in the next year.
It can be calculated as follows:
Take 22.8% of 1,697:
Now calculate by adding it to the original number of hours:
1,697 + 387 = 2,084 hours
In the next year, Anthony worked 2,084 hours
5 obtuse no acute and no right
<span>This is the equation made from the problem where x=mystery number
</span><span>2x+3(x+1)=4(x-1)</span><span>
</span><span>Now let's solve for x!
</span><span>
</span><span>We start by distributing 3 into (X+1)
</span><span>
</span><span>3(x)=3x and 3(1)=3
</span><span>
</span><span>Now our equation is 2x+3x+3=4(x-1)
</span><span>
</span><span>Let's combine both x values on the left side of the equation: 2x + 3x=5x
</span><span>
</span><span>We now have 5x+3=4(x-1)
</span><span>
</span><span>Let's distribute 4 into (x-1)
</span><span>
</span><span>4(x)=4x and 4(-1)=-4
</span><span>
</span><span>Now our equation is 5x+3=4x-4
</span><span>
</span><span>subtract 3 form both sides
</span><span>
</span><span>5x=4x-7
</span><span>
</span><span>subtract 4x from both sides
</span><span>
</span><span>x=-7
</span><span>
</span><span>Yay! So the number she is thinking of is -7!</span><span>
</span>
The standard equation of a circle is:
where (h,k) is the center and r is the radius.
We need to make an equation of a circle, whose center is (11,-5) with any radius. Therefore, substitute the value.
The bolded part is your answer. Since the radius is not given, we can put any value.
Answer:
P(t) = 12e^1.3863k
Step-by-step explanation:
The general exponential equation is represented as;
P(t) = P0e^kt
P(t) is the population of the mice after t years
k is the constant
P0 is the initial population of the mice
t is the time in months
If after one month there are 48 population, then;
P(1) = P0e^k(1)
48 = P0e^k ...... 1
Also if after 2 months there are "192" mice, then;
192 = P0e^2k.... 2
Divide equation 2 by 1;
192/48 = P0e^2k/P0e^k
4 = e^2k-k
4 = e^k
Apply ln to both sides
ln4 = lne^k
k = ln4
k = 1.3863
Substitute e^k into equation 1 to get P0
From 1, 48 = P0e^k
48 = 4P0
P0 = 48/4
P0 = 12
Get the required equation by substituting k = 1.3863 and P0 = 12 into equation 1, we have;
P(t) = 12e^1.3863k
This gives the equation representing the scenario
