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 
Hey, It looks like you're in Algebra and I'm here to give the best solution I can!
To write the equation, you are going to use the Standard Form. Standard Form is one way of solving this problem, and it is used to find the x,and y-intercepts of a problem.
Standard Form can be written using the equation <span>ax+by=c
</span>In your problem, you will write the equation like so, with 'x' representing T-Shirts, and 'y' representing pants:
<span>
8x+5y=220</span>
Now, in order to find the x-intercept you need to substitute a 0 for the 'y' variable and solve the new equation, 8x=220.
I'm sure you know you need to divide both sides by 8 which will give you the answer x=27.5.
Now, in order to find 'y' you would substitute a 0 for the 'x' variable which will give you an equation that should look like 5y=220.
Then, divided both sides by 5 to get your y-intercept.
y=44
Finally,you know that each T-Shirt (x) is $27.50, and each pair of pants(y)costs $44
-I hope this helped you, Sincerely, Auhrevo!
Answer:
(3, -3) is correct
Step-by-step explanation:
-4 × 3 = -12. -12 + 9 = -3
Answer:
The slope is 2
Step-by-step explanation:
Pick two points and plug into this equation: y2-y1/x2-x1
(-3,2) and (-1,6)
2-6/-3-(-1)=-4/-2= 2
Answer:
H0 : μ = 0.5
H0 : μ > 0.5
Kindly check explanation
Step-by-step explanation:
H0 : μ = 0.5
H0 : μ > 0.5
We perform a right tailed test :
Sample proportion :
Number of games won, x = 142
Number of games, n = 250
phat = x / n = 142 / 250 = 0.568 = 56.8%
Yes, it is consistent
Test statistic :
(phat - p) * √Phat(1-Phat)/n
1 -Phat = 1 -0.568 = 0.432
(0.568 - 0.5) /√(0.568*0.432)/250
0.068 / 0.0313289
= 2.17
The Pvalue using the z test statistic :
Pvalue = 0.015
α = 0.03
Since ;
Pvalue < α ; We reject the null and conclude that teams tend to win more often when they play at home.
