Please I really need help with this question it’s due tomorrow!!
Answers
Answer:
THERE
Step-by-step explanation:
a) To determine how far each ostrich ran, we need to calculate the area under the velocity-time graph for each ostrich. Since the graph represents velocity, the area under the graph represents the distance traveled.
For Ostrich Bert:
The area under the graph can be divided into two sections: a triangle and a rectangle. The triangle's base is 3 seconds and its height is 18 m/s, so its area is (1/2) * 3 * 18 = 27 m. The rectangle has a base of 2 seconds and a height of 9 m/s, so its area is 2 * 9 = 18 m. Adding the areas together, Bert ran a total distance of 27 + 18 = 45 meters.
For Ostrich Ernie:
The area under the graph can also be divided into two sections: a triangle and a rectangle. The triangle's base is 4 seconds and its height is 12 m/s, so its area is (1/2) * 4 * 12 = 24 m. The rectangle has a base of 2 seconds and a height of 6 m/s, so its area is 2 * 6 = 12 m. Adding the areas together, Ernie ran a total distance of 24 + 12 = 36 meters.
b) To calculate the average velocity of Bert, we need to divide the total distance he ran (45 meters) by the total time it took (5 seconds). Therefore, Bert's average velocity is 45 meters / 5 seconds = 9 m/s.
c) The initial acceleration of Ernie can be determined by finding the slope of the velocity-time graph during the initial portion. From the graph, we can see that Ernie's velocity increases by 6 m/s over the first 2 seconds. Therefore, his initial acceleration is (change in velocity) / (change in time) = 6 m/s / 2 seconds = 3 m/s^2.
d) Without further calculation, we can determine that Ernie had the greatest initial acceleration. This is because Ernie's velocity increases at a steeper slope during the initial part of the graph compared to Bert's velocity. The greater the slope, the greater the acceleration. Therefore, Ernie had the greatest initial acceleration.
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Please help asap 25 pts
Answers
Answer:
y= (-3/5)x + 3
Step-by-step explanation:
Slope-Intercept form is y = mx + b, where m is the slope and b the y-intercept.
12x-20y=60 Rearrange
20y=60 -12x
20y= -12x + 60
y= (-12/20)x + (60/20)
y= (-3/5)x + 3
If (x1, y1) and (x2, y2) are distinct solutions to the system of equations shown above, what is the sum of the y1 and y2?
Answers
Solving the system we can see that the sum of the y-values of the two solutions is 139.
How to get the sum of y₁ and y₂?
Let's solve the system of equations.
y = 10 + 16x − x²
y = 3x + 50
We can write this as a single quadratic equation:
10 + 16x - x² = 3x + 50
10 + 16x - x² - 3x - 50 = 0
-x² + 13x - 40 = 0
Using the quadratic formula we will get the two solutions for x:
So the two solutions are:
x = (-13 + 3)/-2 = 5
x = (-13 - 3)/-2 = 8
Evaluating the linear equation in these two values we will get y1 and y2.
if x = 5
y₁ = 3*5 + 50 = 65
if x= 8
y₂ = 3*8 + 50 = 74
The sum is:
65 + 74 =139
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Final answer:
The distinct solutions to the system of equations are (5, 65) and (8, 74), and the sum of the y-values is 139.
Explanation:
To find the sum of y-values of the distinct solutions to this system of equations, first, you need to set the two equations equal to each other to find the x-values of the solutions:
10 + 16x − x^2 = 3x + 50.
Then, solve the resulting equation for x:
x^2 - 13x + 40 = 0.
This is a quadratic equation, and it can be solved either by factoring or using the quadratic formula. The solutions for x result in:
x = 5 and x = 8.
These are the two distinct x-values for the intersections of the graphs of the two equations. To find the corresponding y-values, plug these x-values into either of the original equations. We'll use the simpler equation, y = 3x + 50:
For x = 5, y = 65 and for x = 8, y = 74.
Therefore, the distinct solutions to the system of equations are (5, 65) and (8, 74). Finally, the sum of y1 and y2 is 65 + 74 = 139.
Learn more about System of Equations here:
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Answers
It is a rectangular prism and the base has a right triangle with a measure of the following: long leg = 18cm ; short leg = 16cm
We need to look for the hypotenuse because it serves as the long leg of the right triangle where AG is the hypotenuse.
base triangle
a² + b² = c²
(16cm)² + (18cm)² = c²
256cm² + 324cm² = c²
580 cm² = c²
√580cm² = √c²
24 cm = c
2nd triangle: long leg = 24cm ; short leg = 16cm
(24cm)² + (16cm)² = c²
576 cm² + 256 cm² = c²
832 cm² = c²
√832 cm² = √c²
28.8 cm = c
the length of stack AG is 28.8 cm.
Answers
the x coordinate of the vertex is the axis of symmetry
the vertex of an equation in form
y=ax^2+bx+c is
-b/2a=x coordinate
y=1x^2+4x-7
vertex=-4/2=-2
axis of symmetry is x=-2
y=2x^2+3x-4
ertex=-3/(2*2)=-3/4
axis of symmetry is x=-3/4
Answers
Answer:
27 + 6x = 8.25x
Number of movies (x) = 12
Step-by-step explanation:
Given that:
VIP membership :
Membership fee = $27 per year
Amount per movie = $6
Hence ;
Membership fee + (amount per movie * number of movies)
27 + 6x - - - (1)
Non member :
Amount paid per movie = $8.25
amount per movie * number of movies)
8.25x - - (2)
Let Numbe of movies = x
In other to pay the same amount of money :
Equate (1) and (2)
Equation :
27 + 6x = 8.25x
8.25x - 6x = 27
2.25x = 27
X = 12 movies