Answer:
(-1,4)
Step-by-step explanation:
Using elimination, add the two equations to get rid of the y variable.
17x = 43 - 15y
+8x = -68 + 15y
=25x = -25
<u>x = -1</u>
Now plug in -1 for x in any of the equations.
17(-1) = 43 - 15y
-17 = 43 - 15y
-60 = -15y
<u>y = 4</u>
Answer:
ABD = CDB
AB is parallel to DC
Step-by-step explanation:
angle a and c are right angles so they are equal and angle b and d are equal because they have a line that touch both letters
AB and DC are parellel because they are the same looking lines just on oppisite sides
The composition of a function and its inverse is x. So an easy approach to solve this question is to find the composition of a function with itself. If the composition results in an answer "x", then this will mean that function and its inverse are the same.
Finding the composition for 1st option:
Since the composition of the function with itself is not x, the function and its inverse are not the same.
Similarly, we can find the compositions of next 3 functions with themselves. The results of compositions are listed below:
(gog)(x)=g(g(x)) = x
(hoh)(x)=h(h(x))=
(kok)(x)=k(k(x))= x
Thus the option 2 and 4 are the correct answers i.e. these functions are the same as their inverse functions.
Answer:
the first choice
Step-by-step explanation:
-0.8 is the smallest number considering it is negative.
-1/3 is negative too, but it is not as much at -0.8 since when reduced to a decimal, it's would be -0.3334 (rounding up).
2/3 is not as much as 1 since it is not a whole number.
1 is the biggest number in the graph.
Answer:
The farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
Step-by-step explanation:
The question tests the applications of differential calculus. We are informed that the farmer will use the wall of his barn as one side of the enclosure implying that the 144 feet of fencing will only be used to form the three remaining sides of the rectangular enclosure.
If we let x denote the width of this rectangular enclosure to be formed, then its length will be 144-2x since we shall be having two sides each measuring x and the total length of the fencing is 144. 2x will be used on the width leaving 144-2x for the length since one side of the length is formed by the wall.
If we let A denote the area of the rectangular enclosure, then;
A = x(144 - 2x)
since the area of a rectangle is simply the product of the length and the width. We open the brackets;
A = 144x - 2x^2
Clearly, the Area is a function of the width that is A is the dependent variable while x is the independent one.
At the maximum area, the slope of the tangent to the curve 144x - 2x^2 is 0. Therefore, we differentiate the given function of x with respect to x then set the resulting expression to 0 to determine x that will maximize A;
dA/dx = 144 - 4x
We set this expression to 0 and solve for x;
144 - 4x = 0
144 = 4x
x = 36
Therefore, the farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
