Step-by-step explanation:
<u>Step 1: Determine the axis of symmetry</u>
The axis of symmetry is middle of the parabola. In this equation we see that at x = -1 we have the vertex and also the middle of the parabola. So our axis of symmetry is x = -1.
<u>Step 2: Determine the vertex</u>
The vertex is the minimum or maximum of a parabola and is bent in a crest form. In this example the vertex is at (-1, -3) because we are using the tip of the graph.
<u>Step 3: Determine the y-intercept</u>
The y-intercept is where the graph intersects with the y-axis. In this example we intersect the y-axis at -4 so that means that our point would be (0, -4) meaning that we intersect x = 0 at -4.
<u>Step 4: Determine if the vertex is a min or max</u>
Looking at the graph we can see that the rest of the red line is beneath the vertex point which means that the vertex is a max.
<u>Step 5: Determine the domain</u>
The domain is the x-values that we are going to be using and we know that we are reaching toward positive and negative inifity which means that we are using all real numbers.
<u>Step 6: Determine the range</u>
The range is the y axis and what y values we are able to reach using the graph. In this example we can see that all y-values above -3 are not being used therefore the range is 
Answer:
Step-by-step explanation:
Nice summary problem.
<AEC
- AEC = 360 - 243.5 = 116.5
- The number of degrees in 1 rotation of a circle = 360o. You have accounted for 243.5 degrees. What is left over is the answer.
<EAD and <ECD
Both of these are tangents to a circle. Tangents meet radii at 90 degree angles.
<EAD = <ECD = 90 degrees
<ABC
<ABC is 1/2 the central angle. The Central angle is <AEC
- < AEC = 116.5
- <ABC = 1/2 * 116.5
- <ABC = 58.25
<ADC
There are 2 ways of doing this. You should know both of them.
<em><u>One</u></em>
All quadrilaterals = 360 degrees. You know three of the angles. You should be able to find ADC
- <ADC + 90 + 90 + 116.5 = 360 Add the four angles together.
- <ADC + 296.5 = 360 Combine terms on the left
- <ADC = 360 - 296.5 Subtract 238.25 from both sides
- <ADC = 63.5 Answer
<em><u>Method Two</u></em>
<ADC = 1/2 (major Arc - Minor Arc) This formula is fundamental to circle / tangent properties. The Major arc is the larger of the two parts of the circumference of a circle. The Minor arc is the smaller.
- <ADC = 1/2(243.5 - 116.5)
- <ADC = 1/2(127)
- <ADC = 63.5
-3.8 - 0.5m <== ur expression
the variable (m) represents number of minutes
First, Jane must know the volume of the box.
Volume = l * w * h
Volume = 1 * 0.5 * 0.5
Volume = 0.25 yard^3
1 yard^3 = $25
So,
1 : 25 = 0.25 : x
x = 25 * 0.25
x = $6.25
So she need to spend $6.25
when x = -14
f(-1) = 4^-1 = 1 / 4^1 = 1/4
Answer
1/4 or 0.25
