Here are the answers based on the questions and statements you've provided:
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Select the statement that is true for the equation \( y=−(x+2)^2−6 \)
True Statement: Statement #1: The parabola opens down, has an axis of symmetry at \( x=−2 \), and a vertex at \( (−2,−6) \). -
Use the graph to write the equation in vertex form of the quadratic function.
If the vertex form is \( y = a(x - h)^2 + k \), you may need to fill in specific values based on the image you refer to but the standard vertex form based on the original equation is:
\( y = - (x + 2)^2 - 6 \) -
Identify the y-value of the y-intercept of \( y=4x^2−3x+2 \).
To find the y-intercept, set \( x=0 \):
\( y = 4(0)^2 - 3(0) + 2 = 2 \).
Y-Intercept: 2. -
When writing the equation of the quadratic function on the graph in standard form \( y=ax^2+bx+c \), what is the a-value?
This will depend on the graph you are referring to. If you are talking about \( y = 4x^2 - 3x + 2 \), the a-value would be 4. -
If \( y=4.25(6)^x \) and \( x=4 \), what is the corresponding y-value?
Calculate by substituting \( x = 4 \).
\( y = 4.25(6^4) \).
Calculate \( 6^4 = 1296 \), then \( y = 4.25 \times 1296 = 5508 \).
Y-Value: 5508. -
Given the graph of the exponential equation that goes through the points (0, 3) and (1, 4), which option is the correct exponential equation for the graph?
A suitable option would be Option #2: \( y=3(3^4)x \), but you will have to verify it. -
Compare the functions \( f(x) \) and \( g(x) \). When is \( g(x) \) greater than \( f(x) \)?
From the given data, it seems \( g(x) \) is greater than \( f(x) \) when \( x < -1 \). -
Which of the following tables correctly shows the order of operations that transforms \( f(x)=x^2 \) to \( f(−2x)+3 \)?
The correct order of operations appears to be Option #1. -
Place the transformations in the order in which they occurred to transform \( f(x)=x^2 \) to \( f(−x+4)+3 \):
- First Transformation: 1 (translate left 4 units)
- Second Transformation: 3 (reflect over the x-axis)
- Third Transformation: 2 (translate up 3 units)
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The function is a dilation of the original function \( y=2^x \).
Based on the options, the transformation would be best described by Use the coordinates to show that each point has been dilated using the rule \( y = k(2^x) \), where \( k = 4 \). -
Create a table of values that models the function in the graph reflected over the x-axis.
The correct response to reflect over the x-axis would be:
\( x, y \)
-2, -9
-1, -3
0, -1
1, -3
2, -9 -
Using the linear model \( y=34x+2 \), what prediction can be drawn?
An option like A car can go over 500 miles on 15 gallons of gas seems plausible. You can validate using \( y = 34(15) + 2 \). -
Find the slope and an equation that represents the scenario.
The slope is about \( 65 \) feet per hour and the equation can be expressed as:
65; \( y−360=65(x−5) \). -
Creating an exponential model for the rhinoceros population that declines at a rate of 6% per year with 82 currently remaining.
The option that correctly models the problem is Option #4: \( f(x)=82(0.94)^x \). -
Estimate the amount of sunlight visible at a depth of 50 meters.
According to the options, it could be around 5% if you have a noticeable drop-off at that depth. -
The two numbers whose sum is 22 and product is 120 are:
\( 10 \) and \( 12 \). -
The missing values in the two-way frequency table:
The missing values depend on accurate data, so solving the equation set based on rows and columns is necessary. -
There is an association between completing a rough draft and earning an A on the final essay.
Thus, the correct statement is Option #2. -
Distinguish whether the scatterplot represents a linear or nonlinear relationship.
The correct choice seems to be The graph represents a nonlinear relationship because the points form a curve. -
For Michael's x and y values, if the y-intercept is \( (0, 31.06) \), the accurate interpretation of the y-intercept is:
When Michael started training, he was running 5 kilometers in approximately 31 minutes. -
Again using the car line of best fit model, the previous prediction suffices.
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Can Maria conclude that missing homework causes low test scores?
Answer Type 2 for No. -
Which type of function best models the data in the table?
You can go with linear or check if the values fit better with other options. -
For the weak positive linear association in the provided table:
The possible correlation coefficient could be Option #2: 0.60.
Make sure to verify values with the actual data/image where applicable.