When David first got a job, his annual income was $20,000. He worked hard and got more experience. After 8 years, he realized th
at his average increase in pay was about $4,000 every year. Which scatter plot represents this situation?
1 answer:
Answer:
The equation would be:
y= 4,000(x-1)+20,000
y= annual income
x= number of years
With this you can find the points for the scatter plot:
x=1 y= 20,000
x=2 y= 24,000
x=3 y= 28,000
x=4 y= 32,000
x=5 y= 36,000
x=6 y= 40,000
x=7 y= 44,000
x=8 y= 48,000
The scatter plot that represents this situation is attached.
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Answer:
Harry buys 6 apples and 5 oranges at the store.
Step-by-step explanation:
Given:
Cost of each apples = $0.8
Cost of each oranges = $0.95
Total money spend =$9.55
Number of fruits bought= 11
We need to find the number of apples bought and number of oranges were bought.
Solution:
Let the number of apples bought be 'a'.
Let the number of oranges were bought be 'o'.
Number of fruits bought= 11
So we can say that;
Number of fruits bought is equal to sum number of apples bought and number of oranges were bought.
framing in equation form we get;
⇒ equation 1
Now we can say that;
Total money spend is equal to number of apples bought multiplied by Cost of each apples plus number of oranges were bought multiplied by Cost of each oranges.
framing in equation form we get;
⇒ equation 2
Now Multiplying equation 1 by 0.8 we get;
⇒ equation 3
Subtracting equation 3 from equation 2 we get;
Dividing both side by 0.15 we get;
Substituting the value of o in equation 1 we get;
Hence Harry buys 6 apples and 5 oranges at the store.
1. Determine y-intercept.
<em>The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.</em>
2. Determine the zeros.
<em>Factor the polynomials first. </em> <em>This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2</em>
3. Determine the Axis of Symmetry
<em>We can solve this by using the formula of </em> <em>However, I'll be solving the Axis of Symmetry with Calculus instead.</em>
<em /><em />
<em>Then let f'(x) = 0 to find the Axis of Symmetry.</em>
<em /><em />
<em>Therefore, the Axis of Symmetry is -1/2</em>
4. Determine the vertex.
<em>Substitute the value of Axis of Symmetry in f(x).</em>
<em /><em />
<em>Therefore the vertex is at (-1/2, -4)</em>
5. Does the vertex representing max-pont or min-point?
<em>The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE. </em>
7. Graph f(x)
<em>Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).</em>
<em>--------------------------- </em>End of Part 1 --------------------------------
2. Write the general form of Quadratic Function in standard form.
<em>The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is. </em>
<em>For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.</em>
3. Write in Factored Form
<em>These are factored forms with different types of operators.</em>
<em>The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)</em>
4. Write in Vertex Form.
<em>The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.</em>
<em>The vertex is at (h,k) and the axis of symmetry is at x = h.</em>
<em>For example, </em><em />
<em>The vertex would be at (2,3) and the axis of symmetry is x = 2.</em>