Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
( x, y ) → ( x-3, y+4 )
A ( 1, 1) → A' (1-3, 1+4) A' (-2, 5)
<span><span>I think the answers are:
Statement Reason</span><span><span><span>
<span>12=<span>13</span>x+5 </span></span>Given</span><span><span>
<span>7=<span>13</span>x </span></span>Subtraction Property of Equality</span><span><span>
21 = x </span>Multiplication Property of Equality</span><span><span>
x = 21 </span><span>Symmetric Property of Equality
By the way, I'm doing the same exam for Geometry as well. There's a lot of proof questions on there which I'm not good at doing for the reasoning part. If you finish the exam before I do, maybe you can message me what the answers are for some of the questions on there so I know if my answers for the questions are incorrect or not.
Besides that, hope the answer above is correct for you.
<em>~ ShadowXReaper069</em></span></span></span></span>
Answer:
The 90% confidence interval for the mean test score is between 77.29 and 85.71.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 2.064
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 81.5 - 4.21 = 77.29
The upper end of the interval is the sample mean added to M. So it is 81.5 + 4.21 = 85.71.
The 90% confidence interval for the mean test score is between 77.29 and 85.71.
A triangle do it out on paper
