Pherris is graphing the function f(x) = 2(3). He begins with the point (1,6). Which could be the next point on his graph?

Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine

NikAS [45]

Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is $A=\frac12bh$ . One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in $x=0$ .

Which gives you this when you plug it into both equations:

$-y=1\\y=-1\\y=8$

So the y-intercepts for the graphs are $(0,-1)\\$ , and $(0,8)$ respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

$x-y=1\\2x+y=8\\3x=9\\x=3$

Now to solve for the y component substitute:

$2(3)+y=8\\y=2$

Therefore, the graphs intersect at the following:

$(3,2)$

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

$b=8-(-1)\\b=9$

The height must also be accounted for which is the following:

$h=3$

Now the formula can be used:

$A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2$

7 0

3 years ago

Read 2 more answers

The equation y=x is a function. True or False?

Margaret [11]

Answer:

false

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

Find the distance between the points (6,5√5) and (4,3√2). 2, 2√2, 2√3

FromTheMoon [43]

Answer:

D= $\sqrt{(147-30\sqrt{10}}$

Step-by-step explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here we are given two coordinates as

$(6,5\sqrt{5} ) , (4,3\sqrt{2} )$

Substituting these values in the Distance formula given above we get

$D=\sqrt{(6-4)^2+(5\sqrt{5} -3\sqrt{2}) ^2}$

$D=\sqrt{(2)^2+(5\sqrt{5})^2+(3\sqrt{2})^2-2*5\sqrt{5}*3\sqrt{2}}\\$

$D=\sqrt{4+125+18-2*15\sqrt{10}}\\D=\sqrt{147-30\sqrt{10}}\\$

Hence this is our answer

6 0

3 years ago

Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x3 - 5x2 - 9x - 2

olchik [2.2K]

Polynomials in the fourth degree are called quartic equations. In solving the roots of polynomials, there are techniques available. For quadratic equations, you use the quadratic formula. For cubic equations, you use the scientific calculator. But for quartic equations and higher, it is very complex. The method is very lengthy and can get very messy because you introduce a lot variables. So, I suggest you do the easiest method to estimate the roots.

Graph the equation by plotting arbitrary points. The graph looks like that in the figure. The points at which the curve passes the x-axis are the solution which are encircled in red.In approximation, the rational roots or zero's are -3.73, -1, -0.28 and 2.

3 0

3 years ago

Abe is going to plant 5454 oak trees and 2727 pine trees. Abe would like to plant the trees in rows that all have the same numbe

xxTIMURxx [149]

You would need to find the GCF of 54 and 27.

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Factors of 27: 1, 3, 9, 27

so, the GCF is 27

6 0

3 years ago