There's nothing to substitute, and no solution,
until somebody gives you another equation.
Answer:
The coordinates of point B are (5,-3)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
In this problem
Point A is at (-5, -4) and point M is at (0, -3.5)
substitute in the formula
so
Solve for x_2
Solve for y_2
therefore
The coordinates of point B are (5,-3)
1) Graph the corresponding equation \( x = 2 \); this will split the plane into two regions. One of the region represents the solution set.
2) Select a point situated in any of the two regions obtained and test the inequality. If the point selected is a solution, then all the region is the solution set. If the selected point is not a solution, then the other (second) region represents the solution set.
3) Test: In this example, let us for example select the point with coordinates (3 , 2) which is in the region to the right of the line x = 2. If you substitute x in the inequality \( x ≥ 2 \) by 3 it becomes \( 3 ≥ 2 \) which is a true statement and therefore (3 , 2) is a solution. Hence, we can conclude that the region to the right of the vertical line x = 2 is a solution set including the line itself which is shown as a solid line because of the inequality symbol \( ≥ \) contains the \( = \) symbol. The solution set is represented by the blue hash region in the graph below including the line x = 2.
For #2, the proportion would be .40/.25 and x/15, then you would cross multiply to find x. and for #3 the proportion would be 15/6 and 75/x and again you would cross multiply to find x. (:
You are asked to find the team score, so it is convenient to let a variable represent that value. Let's call it "s", for "score". The problem statement tells you
.. Michaela scored s/5 . . . . . one fifth of the team's points
.. Aleah scored s/10 . . . . . . . one tenth o the team's points
These scores together are (s/5 +s/10) and that amount is 42 points.
.. s/5 +s/10 = 42
.. s(2/10 +1/10) = 42 . . . . . factor out s
.. s(3/10) = 42 . . . . . . . . . . form the sum of the numbers in parentheses
.. s = 42*10/3 = 140 . . . . . multiply by the inverse of the coefficient of s
The team scored 140 points.
______
Michaela scored 140/5 = 28 points; Aleah scored 140/10 = 14 points.
