Answer:
- (1,3) is inside the triangle
Step-by-step explanation:
Orthocenter is the intersection of altitudes.
We'll calculate the slopes of the two sides and their altitudes ad find the intersection.
<h3>Side QR</h3>
- m = (3 - 5)/(4 - (-1)) = -2/5
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through S(-1, -2):</u>
- y - (-2) = 5/2(x - (-1)) ⇒ y = 5/2x + 1/2
<h3>Side RS</h3>
- m = (-2 - 3)/(-1 -4) = -5/-5 = 1
<u>Perpendicular slope:</u>
<u>Perpendicular line passes through Q(-1, 5):</u>
- y - 5 = -(x - (-1)) ⇒ y = -x + 4
The intersection of the two lines is the orthocenter.
<u>Solve the system of equations to get the coordinates of the orthocenter:</u>
- 5/2x + 1/2 = x + 4
- 5x + 1 = -2x + 8
- 7x = 7
- x = 1
<u>Find y-coordinate:</u>
The orthocenter is (1, 3)
If we plot the points, we'll see it is inside the triangle
Answer:
Domain: 0 minutes to time it takes to fill. Range: 0 to a 10,000 gallons
Step-by-step explanation:
The answer is H
Explanation: what I did was change all of the numbers into decimal form so that we can compare them easier, -2 1/2= -2.5, -2.47 stays the same, -2/5 becomes positive .4 because the entire fraction is negative, you can look at it like -2/-5 and a negative divided by a negative is a positive, And then 5 stays a 5, And 21/4 equals 5.25 therefore your answer is H
Oh and by the way if you don’t know how to turn a fraction into a decimal you simply divide the top number by the bottom number for example 1/2 you take 1 and divide it by 2 which gives you .5 or 12/13 = .923076 hope this makes sense and that this helped
The original price is $30 because 40% off of 12 = 30
Answer:
The optimal, vertex, value will be a minimum
Step-by-step explanation:
The given zeros of the quadratic relation are 3 and 3
The sign of the second differences of the quadratic relation = Positive
Whereby the two zeros are the same as x = 3, we have that the point 3 is the optimal value or vertex (the repeated point in the graph of the quadratic relation) of the quadratic relation
Whereby, the table of values for the quadratic relation from which the second difference is found starts from x = 3, we have;
To the right of the coordinate points of the zeros of the quadratic relation, the positive second difference in y-values gives as x increases, y increases which gives a positive slope
By the nature of the quadratic graph, the slope of the line to the left of the coordinate point of the zeros of the quadratic relation will be of opposite sign (or negative). The quadratic relation is cup shaped and the zeros, therefore, the optimal value will be a minimum of the quadratic relation
