Can someone check my answers which ones form right triangles
1 answer:
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Part 1)
we have that
F(x) =(x+3)²<span>−1
using a graph tool
see the attached figure N 1
we know that
t</span><span>he x-intercepts of the graph is when y=0
the points are (-4,0) and (-2,0)
</span><span>the y-intercepts of the graph is when x=0
the point is (0,8)
the graph is a vertical parabola that opens up
so
the vertex of the parabola is a minimum
the vertex is the point (-3,-1)
Part 2) </span>Write the function g(x) in the form y=a(x−h)²<span>+k . Write the equation for the line of symmetry for the graph of g(x)
</span>
we have that
G(x) =−2x²<span>+8x+3
</span><span>Group terms that contain the same variable
</span>G(x) =(−2x²+8x)+3
Factor the leading coefficient
G(x) =-2*(x²-4x)+3
<span>Complete the square. Remember to balance the equation
</span>G(x) =-2*(x²-4x+4-4)+3
G(x) =-2*(x²-4x+4)+3 +8
G(x) =-2*(x²-4x+4)+11
the vertex is the point (2,11)
so
the equation for the line of symmetry is x=2
Part 3) we have that
H (t) =−16t²<span>+28t
see the attached figure N 3
</span><span>the total length of time, in seconds, it took the dolphin to complete one jump is the difference for t=0 sec and t=1.75 sec
(1.75-0)=1.75 sec
the answer Part 3) is 1.75 sec</span>
we have that
F(x) =(x+3)²<span>−1
using a graph tool
see the attached figure N 1
we know that
t</span><span>he x-intercepts of the graph is when y=0
the points are (-4,0) and (-2,0)
</span><span>the y-intercepts of the graph is when x=0
the point is (0,8)
the graph is a vertical parabola that opens up
so
the vertex of the parabola is a minimum
the vertex is the point (-3,-1)
Part 2) </span>Write the function g(x) in the form y=a(x−h)²<span>+k . Write the equation for the line of symmetry for the graph of g(x)
</span>
we have that
G(x) =−2x²<span>+8x+3
</span><span>Group terms that contain the same variable
</span>G(x) =(−2x²+8x)+3
Factor the leading coefficient
G(x) =-2*(x²-4x)+3
<span>Complete the square. Remember to balance the equation
</span>G(x) =-2*(x²-4x+4-4)+3
G(x) =-2*(x²-4x+4)+3 +8
G(x) =-2*(x²-4x+4)+11
Rewrite as perfect squares
G(x) =-2*(x-2)²+11
the answer Part 2) is
G(x) =-2*(x-2)²+11
see the attached figure N 2
the vertex is the point (2,11)
so
the equation for the line of symmetry is x=2
Part 3) we have that
H (t) =−16t²<span>+28t
see the attached figure N 3
</span><span>the total length of time, in seconds, it took the dolphin to complete one jump is the difference for t=0 sec and t=1.75 sec
(1.75-0)=1.75 sec
the answer Part 3) is 1.75 sec</span>
Answer:
Null hypothesis:
Alternative hypothesis:
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
Step-by-step explanation:
For this case they are trying two proof if there is a significant difference between two states in the percents of high school students who order yearbooks, and we chan check this with the difference of proportions.
Lets say that are the two proportions of interest and we want to check the following hypothesis:
We have the following info given:
proportion of students that had ordered a yearbook from one state
proportion of students that had ordered a yearbook from another state
sample size from one state
sample size from another state
Null hypothesis:
Alternative hypothesis:
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.