Choose the statement which is equivalent to sin(x)+cos(x)=0
1 answer:
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Answer:
1. (a) A function is a mapping where there should be different values of y for different x.
So, given ordered pairs:
(3,7), (3,8) ,(3,-2) ,(3,4) ,(3,1)
It is not a function because there are multiple y values for single x-value.
Option 2 is correct.
(b) We need to find range of the function f(x)= -4x +1
So, we have given the domain which means the value of x we will put thses given values of x to find y
Values of y is the range in a function
So, given domain is: {-5,-1,0,2,10}
When
When
when
when
when
So, Range is: {-39,-7,1,5,21}
Option 1 is correct.
(c) We have given a function
Where c is the number of cup jug of milk which is 16.
Put c=16 in given function
So, c=16, v(c)=1568 is reasonable domain and range of the function.
Option 1 is correct.
(d) We need to find the inverse of given ordered pairs (1,2) (3,4) ,(6,8)
So, the inverse means values of x and y interchange.
So, the required inverse is: (2,1) ,(4,3) ,(8,6)
Option 3rd is correct.
2. We need to find the inverse of given scatter plot in which we have to find the inverse
So, given scatter plot represents (-4,-2) ,(1,-1) ,(2,1) ,(3,2)
So, in inverse values of x and y interchange
So, inverse scatter plot should represent (-2,-4) ,(-1,1) ,(1,2), (2,3)
Attached is the scatter plot inverse
Graph 1 is correct.
3.We have been given a function:
So, f(x)=y
That is
We will find x from above equation we get
Now, interchange x and y
is the required inverse
Therefore, option 3rd is correct.
Answer: 44 hours.
Step-by-step explanation:
Marisol is being paid $792.
We know that the job took her 8 hours more than she expected, so if we define T as the time she expected, this job took her:
T + 8 hours.
The amount of money per hour that she expected is calculated as:
$792/T = X
And for those 8 extra hours, she won $4 less per hour, then we have:
$792/(T + 8hs) = X - $4
Then we have a system of equations:
$792/T = X
$792/(T + 8hs) = X - $4
To solve this, we can notice that in the first equation X is isolated, then we could replace that in the second equation to get:
$792/(T + 8hs) = $792/T - $4
Now we can solve this for T.
$792 = ($792/T - $4)*(T + 8hs) = $792 + $792*(8hs/T) - $4*T + $32*hs
0 = $792*(8hs/T) - $4*T + $32*hs
Let´s multiply this both sides by T
0*T = ($792*(8hs/T) - $4*T + $32*hs)*T
0 = $792*8hs - $4*T^2 +$32*T*hs
This is a quadratic equation, where i will write this witout units so it is easier to read and follow:
0 = -4*T^2 + 32*T + 792*8
The solutions cab be found by using the Bhaskara´s formula, these are:
Then the solutions are:
T = (-32 + 320)/-8 = -36 hours (This is a negative time, and it does not really have a meaning in this problem, so we can discard this option)
The other solution is:
T = (-32 - 320)/-8 = 44 hours.
Then we can conclude that she expected the job would take 44 hours in total.