a. Write a system of equations to model the problem.
b. Is it possible that the water skier could collide with the taxi? Explain
The system of equations to model the problem is y = 0.5(x - 16) for the water taxi's path and y = -5x + 36 for the water skier's path. No collision is possible between the water skier and the taxi.
a. System of Equations:
To model the problem, we need to find the equation of the water skier's path.
Using the two given points, we can find the slope of the water skier's path:
Now that we have the slope, we can use the point-slope formula to find the equation of the water skier's path:
y - y1 = m(x - x1)
Substituting the values x1 = 6, y1 = 6, and m = -5:
y - 6 = -5(x - 6)
Simplifying:
y = -5x + 36
Therefore, the system of equations to model the problem is:
y = 0.5(x - 16) - Equation of the water taxi's path
y = -5x + 36 - Equation of the water skier's path
b. Possibility of Collision:
To determine if the water skier could collide with the taxi, we need to solve the system of equations. If the x-coordinate at the point of intersection is within a certain range, then a collision is possible.
Substitute the second equation into the first equation:
0.5(x - 16) = -5x + 36
Solve for x:
0.5x - 8 = -5x + 36
5.5x = 44
x = 8
The x-coordinate of the point of intersection is 8. Since the water skier's path does not pass through the point x = 8, there is no collision between the water skier and the taxi.
#SPJ2
I realize that the equation is different, but do it in the same way, it'll help! It is given that the water taxi's path can be modeled by the equation y =0.5(x - 14)^2. Therefore, this is one of the equations in this system. Find a linear equation that will model the path of the water skier, which begins at the point (6,6) and ends at the point (8,-4). The slope is (-5). Use the slope and one point on the line to find the y-intercept of the line. The y-intercept of the line that passes through the points (6,6) and (8,-4) is (0,36). Thus, the equation is y=-5x+36. Now, to determine if it is possible for the water skier to collide with the taxi, we have to determine if there is a solution to the system of equations. To determine if there is a solution to the system of equations, solve the system using substitution. First, write the equation that models the water taxi's path in standard form. y=0.5(x - 14)^2-->0.5x^2-14x+98. Use substitution. Substitute for y in the equation and then solve for x. As the expression on the left side of the equation cannot easily be factored, use the Quadratic Formula to solve for x. Do x=-b(plusorminus)sqrrtb^2-4ac/2a. Identify a, b, and c. a=0.5, b=-9, and c=62. Substitute into the Quadratic Formula. If there is a negative number under the radical, there are NO solutions. Thus, the path of the water skier will never cross the path of the taxi.
In conclusion: It is not possible that the water skier could collide with the taxi as the two paths never cross.
A {(-2,5), (6,9), (8,-4), (8,7)}
B{(-1,4),(-5,-2), (6,1),(-2,-2)}
C {(-5, -6),(-5,3), (-7, -8),(-1, -9)}
D{(-8,-4),(-8,-5),(-6, -1), (3,6)}
Answer:
Only set B
Step-by-step explanation:
Look for pairs (x, y) in the set, where the x value is NOT repeated connecting it with a different y value. The only one like that is set B.
All other sets have repeated x values in their pairs: (8, -4), (8, 7)
(-5,-6) (-5, 3)
and (-8,-4) (-8,-5)
Answer:
b
Step-by-step explanation:
the answer is pemdas math
Which steps would allow him to eliminate the y terms in the system of equations?
Multiply 2x+3y=−1 by 3. Multiply 3x−5y=10 by 5. Add the resulting equations together.
Multiply 2x+3y=−1 by 3. Multiply 3x−5y=10 by 2. Add the resulting equations together.
Multiply 2x+3y=−1 by 2. Multiply 3x−5y=10 by 5. Add the resulting equations together.
Multiply 2x+3y=−1 by 5. Multiply 3x−5y=10 by 3. Add the resulting equations together.
Answer:
Multiply 2x + 3y = −1 by 5. Multiply 3x − 5y = 10 by 3. Add the resulting equations together.
Step-by-step explanation:
To eliminate the y-term. we must multiply both equations by values that make the coefficients of y opposite in sign.
2x + 3y = -1 (1)
3x - 5y = 10 (2)
The easiest way to do this is to multiply Equation (1) by 5
and Equation (2) by 3.
5 × [2x + 3y = -1]
3 × [3x - 5y = 10]
Then, add the two equations.
10x + 15y = -5
9x - 15y = 30
19x = 25
Conclusion: Multiply 2x + 3y = −1 by 5. Multiply 3x − 5y = 10 by 3. Add the resulting equations together.
A. 3
B. 1/3
C. -3
D. - 1/3
Answer:
it shod be B. 1/3
Step-by-step explanation:
Answer B: 3 x 7 x7 or 3 x 7^7
Thanks
Answer:
3) 361/11
4) 51
Step-by-step explanation:
for both problems, they give you the length of the segment so you just add both of the segments equal to the length of the whole segment. then for whatever you find as x, plug it into the equation.
ex. 7x+1+4x-3=42
or
5x-8+7x-12=10x-2