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4 years ago

Omar wants to graph the system of equations below log6x=log2(x+4) which system of equations should Omar use

2 answers:

7 0

The equation can be split into two equations:
y = log 6x
y = log 2(x + 4)

which is the system of equations that Omar can use to graph the single equation. The equations are logarithmic equations. They can be plotted directly into the coordinate system, use a logarithmic scale coordinate system, or linearize the equations before plotting.

Maurinko [17]4 years ago

5 0

The answer to this question is the last one.

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3) Determine if the ordered pairs represent a function.

erastovalidia [21]

No, it does not represent a function

3 0

3 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

1 year ago

A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the

Vitek1552 [10]

Answer:

Last one

t = 1.5; it takes 1.5 seconds to reach the maximum height of 36 meters.

Step-by-step explanation:

h(t) = −16t² + 48t

h(t) = -16(t² - 3t)

h(t) = -16(t² - 2(t)(1.5) + 1.5² - 1.5²)

h(t) = -16(t - 1.5)² + 36

Axis of symmetry:

t = 1.5

Max height = 36

7 0

3 years ago

A rectangle has a length of 5 yards and a width of 3 yards what is the perimeter

faltersainse [42]

Answer:

Step-by-step explanation:

Perimeter equation: 2W + 2L

Width: 3 yards

Length: 5 yards

So, 2(3) + 2(5) = perimeter

The perimeter is 16 yards.

3 0

3 years ago

Read 2 more answers

I NEED HELP WITH ALL OF THESE PLEASE! I HAVE A TEST AND I NEED HELP ASAP

Studentka2010 [4]

So what you do for distributive property is take #1 for example: 3(2x + 10) = 54. When there’s a parenthesis, you take the outside number which is the 3 times the numbers inside the parenthesis. So after doing that first step you should get 6x + 30 = 54. Now you want to get rid of the 30 so you do 30-30=0 but you have to do it on the other side as well. So subtracting 30 on both sides you should have 6x = 24. Now you want to get x by itself. The opposite of multiplying is dividing so you divide 6 from 6x. So the same on the other side. You get your answer x=4 if you did everything correct

4 0

3 years ago