Answer:
(g+f)(x)=(2^x+x-3)^(1/2)
Step-by-step explanation:
Given
f(x)= 2^(x/2)
And
g(x)= √(x-3)
We have to find (g+f)(x)
In order to find (g+f)(x), both the functions are added and simplified.
So,
(g+f)(x)= √(x-3)+2^(x/2)
The power x/2 can be written as a product of x*(1/2)
(g+f)(x)= √(x-3)+(2)^(1/2*x)
We also know that square root dissolves into power ½
(g+f)(x)=(x-3)^(1/2)+(2)^(1/2*x)
We can see that power ½ is common in both functions so taking it out
(g+f)(x)=(x-3+2^x)^(1/2)
Arranging the terms
(g+f)(x)=(2^x+x-3)^(1/2) ..
Answer:
A. 6
B. 143
C. The words "less than", "equal to", and "no more than"
Step-by-step explanation:
For a, we would want to first make an equation to represent the problem. It appears you've already figured that out though, so lets solve it!
Subtract 56 on both sides.
-6m=-36
Now divide -36 by -6 to isolate m.
m=6
It will take her 6 minutes.
For B, we need to make another equation.
2.95b<450-28
First, we can subtract 28 from the total, because she has already spent $28.
Now our equation is 2.95b<422
Lastly, just divide both sides by 2.95 to isolate b.
Our solution is 143. So she can buy 143 batteries.
Lastly, for 13, we can say that the words "less than", "equal to" and "no more than" can indicate an inequality in a real word problem.
Hope this helps!
Answer:
6,226 tiles of 9 in are needed to cover an area of 400 square feet
Step-by-step explanation:
Let
A -----> an area in square feet
t(A) ---> the total number of 9 in. tiles needed
we have
For A=400 ft^2
substitute in the equation and solve for t
That means -----> 6,226 tiles of 9 in are needed to cover an area of 400 square feet
The division is using extra zeros.
2 * 16 = 32, but 3200 was placed below 3426.
Now 1 * 16 = 16, so 160 goes below 226.
The number that goes in the box is 160.
(1+x^2)^8
=(1+8x^2+8*7/(1*2)x^4+8*7*6/(1*2*3)x^6+8*7*6*5/(1*2*3*4)x^8+....)
=1+8x^2+28x^4+56x^6+70x^8+....)
For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.
1.01=(1+0.1^2) => x=0.1 in the above expansion
(1.01)^8
=1+8(0.1^2)+28(0.1^4)+56(0.1^6) [ limited to four terms, as requested]
=1+0.08+0.0028+0.000056 (+0.00000070)
=1.082856 (approximately)
