Step-by-step explanation:
let no. of hours be x.
45x - 12 ≥ 117
45x ≥ 129
x ≥ 2.8667 (5sf)
therefore, 3 hours (round up to next whole number).
Topic: inequalities
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Yes they are equivalent because when you multiply by 10, you move the decimal place one spot to the right.
There are 5 solutions for this system.
x^2 + 4y^2 = 100 ____1
4y - x^2 = -20 ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80 (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y : y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
When finding the domain of a square root, you have to know that it is impossible to get the square root of 0 or any negative number. since domain is possible x values this means that x cannot be 0 or any number less than 0. However, you can find the square root of the smallest most infinitely small number greater than 0. since an infinitely small number close to zero can not be written out, we must must say that the domain starts at 0 exclusive. exclusive is represented by an open or close parenthesis so in this case the domain starts with:
(0,
we can get the square root of any number larger than 0 up to infinity but infinity can never be reached so it is also exclusive. So so the ending of our domain would be:
,infinity)
So the answer if the square root is only over the x the answer is
(0, infinity)
But if the square root is over the x- 5 then this would brIng a smaller amount of possible x values. since anything under the square root sign has to be greater than 0, you can say that:
(x - 5) > 0
x > 5
Therefore the domain would start at 5 and the answer would be:
(5, infinity)
Answer:
B
Step-by-step explanation:
As x tends to infinity and - infinity, the function will tend to +infinity for both
