Answer:
27 Chickens
Step-by-step explanation:
<em>Represent the chicken with A and the cows with B</em>
Given
A has 2 legs and B has 4; So:
Required
Determine A and B
Make B the subject of formula in the first equation
Substitute 30 - A for B in the second equation
Open the bracket
Collect Like Terms
Divide through by -2
<em>Hence, the farmer has 27 chickens</em>
Answer:
The x-coordinate gives the solution of the original equation.
Step-by-step explanation:
Let us assume that the original equation is 2x = x + 5 ........... (1) and the solution that this equation has will be x = 5.
But, if we solve the equation by graphing each side as a separate line i.e. y = 2x and y = x + 5, then solving those two equations we get the solution x = 5 and y = 10.
Therefore, the x-coordinate i.e. x = 5 gives the solution of the original equation (1). (Answer)
Answer:
21.69% decrease.
Step-by-step explanation:
So we want to find the percentage change from 16.6 to 13.
First, since 13 is smaller than 16.6, we know that this is decrease.
The formula for percentage change is given by:
The new value is 13. The old value is 16.6. Put these into the equation:
Simplify the numerator. 13-16.6 is -3.6. Thus:
Multiply both the numerator and denominator by 10:
Reduce the fraction:
Use a calculator. Approximate:
We ignore the negative because the negative simply tells us that it's decreasing (on a side note, if the answer is positive, it's a percent increase). So, the percent change is an approximate 21.69% decrease.
Answer:
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Step-by-step explanation:
For part a: you just need to find how far the vertex has been moved from the origin, or the point (0,0). As the vertex is at the point (2,-3), it has been translated right 2 horizontally and down 3 vertically.
For part b: you use the info found in part a to create the equation in the form of y=A(x-h)^2+k. In this case, A =1, so you can ignore it. The h value is the horizontal distance the vertex has been moved. Since it has been moved right 2, this part of the equation would be (x-2). I know it seems like it should be plus 2, but values in parentheses come out opposite. For the k value, find the vertical shift, which is down3, or -3.
Now that you have h and k, substitute them back into the equation.
Your final answer for part b is: y=(x-2)^2 -3.