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3 years ago

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Mathematics

2 answers:

mihalych1998 [28]3 years ago

8 0

The equation, y=4x+15 represents the relationship shown in the graph.

Finger [1]3 years ago

4 0

Answer:

4. $-4x+y=15$

Step-by-step explanation:

We have been given a graph of a linear function and we are asked to find the correct equation representing the relationship shown in the graph.

Since we know that the standard form of an equation is in form: $Ax+By=C$ , where A, B and C are integers.

First of all we will find the slope of our line and write equation of line in slope-intercept form. Then we will change it into standard form.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{23-15}{2-0}$

$m=\frac{8}{2}=4$

Slope of our line is 4. We can see that y-intercept (b) is 15. Now let us write equation of our line in slope-intercept form.

$y=mx+b$

$y=4x+15$

Now we will change our given equation into standard form by subtracting 4x from both sides of our equation.

$-4x+y=4x+15-4x$

$-4x+y=15$

Therefore, the equation $-4x+y=15$ represents the relationship shown in the graph in standard form and 4th option is the correct choice.

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Sharon is conducting research on two species of birds at a bird sanctuary. The number of birds of species A is represented by th

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Answer: After 7 years the number of birds of species A and B are same. and the number of birds during that year will be 140.

Step-by-step explanation:

Given: Sharon is conducting research on two species of birds at a bird sanctuary.

The number of birds of species A is represented by the equation below,where S represents the number of birds, x years after beginning her research.

$S=2^x+12$

The number of birds of species B is represented by the equation below,where S represents the number of birds, x years after beginning her research.

$S=15x+35$

To plot the above function, first find points by which they are passing.

For species A, At x=0 , $S=1+12=13$

At x=2 , $S=2+12=14$

Similarly find more points and plot curve on graph.

For species A, At x=0 , $S=0+35=35$

At x=2 , $S=15+35=50$

Plot a line with the help of these two points.

Now, from the graph the intersection of curve (for A) and line (for B) is at (7,140) which tells that After 7 years the number of birds of species A and B are same. and the number of birds during that year will be 140.

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Step-by-step explanation:

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