Please help me I’m desperate!!
1. Which type of function best models the data in the table? Use differences or ratios.
X: 0,1,2,3,4
Y: 0,5.5,22,49.5,88
2. A bird drops a stick to the ground from a height of 75 ft. The function h=-16t^2+75 gives the sticks approximate height above the ground, in feet, after t seconds. At what time does the stick hit the ground?
3. Graph the function f(x)= -2x^2+3
4. Solve. (x-5)(3x+8)=0
The solution is x= ?
(Use a comma to separate answers as needed)
5. During halftime of basketball game come on a slingshot launches T-shirts at the crowd. A T-shirt is launched a reminder 5 feet with her initial upward velocity of 72 ft./s. Use the equation h(t)=-16t^2+72t+5, Where T is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height?
. The T-shirt takes______second(s) to reach the maximum height. (type an integer or a decimal)
. The T-shirts maximum height is ______ feet above the court. (type an integer or a decimal)
6. Solve by factoring.
v^2+11v+18=0
The solution is v=?
7. Solve by factoring.
2m^2-7m-30=0
m=?
8. Use quadratic formula to solve the equation.
8m^2+13m-7=0
- select the correct choice below and, if necessary fill in the answer box complete your choice
A. x=____
B. The solution is not a real number
use a calculater for the factoring and then see if that helps
1. To determine which type of function best models the data in the table, we can examine the differences or ratios between consecutive values of Y.
Let's calculate the differences between consecutive Y values:
Difference between 5.5 and 0 = 5.5 - 0 = 5.5
Difference between 22 and 5.5 = 22 - 5.5 = 16.5
Difference between 49.5 and 22 = 49.5 - 22 = 27.5
Difference between 88 and 49.5 = 88 - 49.5 = 38.5
From the differences, we can see that there is no consistent pattern or constant difference between consecutive Y values. Therefore, differences do not suggest a linear function.
Next, let's calculate the ratios between consecutive Y values:
Ratio between 5.5 and 0 = 5.5/0 ≈ undefined
Ratio between 22 and 5.5 = 22/5.5 = 4
Ratio between 49.5 and 22 = 49.5/22 ≈ 2.25
Ratio between 88 and 49.5 = 88/49.5 ≈ 1.78
From the ratios, we can see that there is no constant ratio between consecutive Y values. Therefore, ratios do not suggest an exponential function.
Since neither differences nor ratios suggest a linear or exponential function, we need to consider other types of functions that might suit the data better, such as quadratic or polynomial functions. Further analysis and calculations would be needed to determine the type of function that best models the data.
2. To find the time at which the stick hits the ground, we need to solve the equation h = 0. In the given function h = -16t^2 + 75, we substitute h with 0:
-16t^2 + 75 = 0
To solve this equation, we can rearrange it to put it in standard quadratic form: at^2 + bt + c = 0. In this case, a = -16, b = 0, and c = 75.
Using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values: t = (0 ± √(0^2 - 4(-16)(75))) / (2(-16))
Simplifying further, we get: t = ± √(0 + 4(16)(75)) / (-32)
t = ± √(0 + 1200) / (-32)
t = ± √(1200) / (-32)
t = ± √(300) / (-8)
t = ± (10√3) / (-8)
Since time cannot be negative in this context, we consider the positive square root, so: t = (10√3) / 8.
Therefore, the stick hits the ground approximately 1.25 seconds after it was dropped.
3. To graph the function f(x) = -2x^2 + 3, we can plot points on a coordinate plane.
Step 1: Choose a set of values for x.
Let's choose a range of x values: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
Step 2: Calculate corresponding y values by substituting the chosen x values into the function.
For each chosen x value, calculate y by substituting it into the function f(x) = -2x^2 + 3.
Example:
For x = -5:
f(-5) = -2(-5)^2 + 3
= -2(25) + 3
= -50 + 3
= -47
Do this calculation for each chosen x value.
Step 3: Plot the points (x, y) on the coordinate plane.
Using the calculated x and y values, plot the corresponding points on the coordinate plane. Then, connect the points with a smooth curve.
4. To solve the equation (x - 5)(3x + 8) = 0, we need to find the values for x that make this equation true by setting each factor equal to zero.
Setting x - 5 = 0:
x = 5
Setting 3x + 8 = 0:
3x = -8
x = -8/3
Therefore, the solutions to the equation are x = 5 and x = -8/3.
5. To find the time it takes for the T-shirt to reach its maximum height and the maximum height itself, we can use the given equation h(t) = -16t^2 + 72t + 5.
1. To find the time it takes for the T-shirt to reach its maximum height, we can use the formula for the vertex of a parabola, which is given by the equation t = -b/2a, where a = -16 and b = 72.
Substituting the values, we get:
t = -(72) / (2(-16))
t = -72 / (-32)
t = 2.25 seconds
Therefore, the T-shirt takes 2.25 seconds to reach its maximum height.
2. To find the maximum height of the T-shirt, we can substitute the time t = 2.25 seconds into the equation h(t) = -16t^2 + 72t + 5.
h(2.25) = -16(2.25)^2 + 72(2.25) + 5
h(2.25) = -16(5.0625) + 162 + 5
h(2.25) = -81 + 162 + 5
h(2.25) = 86
Therefore, the T-shirt reaches a maximum height of 86 feet above the court.
6. To solve the equation v^2 + 11v + 18 = 0 by factoring, we need to find values of v that make this equation true.
We can look for two numbers that multiply to 18 and add up to 11. The numbers that fit these criteria are 2 and 9.
Therefore, we can factor the equation as follows:
(v + 2)(v + 9) = 0
To find the solutions, we set each factor equal to zero:
v + 2 = 0 --> v = -2
v + 9 = 0 --> v = -9
Therefore, the solutions to the equation are v = -2 and v = -9.
7. To solve the equation 2m^2 - 7m - 30 = 0 by factoring, we need to find values of m that make this equation true.
We can look for two numbers that multiply to -60 (product of the leading coefficient and the constant term) and add up to -7 (coefficient of the middle term). The numbers that satisfy these criteria are -10 and 3.
Therefore, we can factor the equation as follows:
(2m + 3)(m - 10) = 0
To find the solutions, we set each factor equal to zero:
2m + 3 = 0 --> 2m = -3 --> m = -3/2
m - 10 = 0 --> m = 10
Therefore, the solutions to the equation are m = -3/2 and m = 10.
8. To solve the equation 8m^2 + 13m - 7 = 0 using the quadratic formula, we can use the formula x = (-b ± √(b^2 - 4ac)) / (2a), where a = 8, b = 13, and c = -7.
Substituting the values, we get:
m = (-13 ± √(13^2 - 4(8)(-7))) / (2(8))
m = (-13 ± √(169 + 224)) / 16
m = (-13 ± √393) / 16
Therefore, the solutions to the equation are:
m = (-13 + √393) / 16
m = (-13 - √393) / 16
1. To determine the type of function that best models the data in the table, let's examine the differences between consecutive y-values:
Diff1: 5.5 - 0 = 5.5
Diff2: 22 - 5.5 = 16.5
Diff3: 49.5 - 22 = 27.5
Diff4: 88 - 49.5 = 38.5
Since the differences between consecutive y-values are not constant, it suggests that the function may involve a higher degree or non-linear relationship. Let's examine the ratios now:
Ratio1: 5.5 / 0 = undefined
Ratio2: 22 / 5.5 = 4
Ratio3: 49.5 / 22 ≈ 2.25
Ratio4: 88 / 49.5 ≈ 1.77
Since the ratios are not constant either, it suggests that a linear function might not be the best fit. Considering the data and the lack of constant differences or ratios, a quadratic function may provide the best model for the data in the table.
2. To find when the stick hits the ground, we set h(t) = 0 and solve for t:
-16t^2 + 75 = 0
We can solve this equation by factoring if possible or by using the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values into the formula:
t = (-(0) ± √((0)^2 - 4(-16)(75))) / (2(-16))
t = ± √(0 - (-4800)) / (-32)
t = ± √4800 / (-32)
t = ± √150 / (-4)
t ≈ ± 12.25 / (-4)
Since time cannot be negative in this context, the stick hits the ground at approximately t = -12.25 / (-4) = 3.0625 seconds.
3. To graph the function f(x) = -2x^2 + 3, we plot points using various x-values and find their corresponding y-values:
When x = -2, f(x) = -2(-2)^2 + 3 = -8 + 3 = -5
When x = -1, f(x) = -2(-1)^2 + 3 = -2 + 3 = 1
When x = 0, f(x) = -2(0)^2 + 3 = 0 + 3 = 3
When x = 1, f(x) = -2(1)^2 + 3 = -2 + 3 = 1
When x = 2, f(x) = -2(2)^2 + 3 = -8 + 3 = -5
Plotting these points on a coordinate system will give the graph of f(x) = -2x^2 + 3.
4. To solve the equation (x-5)(3x+8) = 0, we set each factor equal to zero and solve for x:
x - 5 = 0 or 3x + 8 = 0
x = 5 or 3x = -8
x = 5 or x = -8/3
Therefore, the solutions are x = 5 and x = -8/3.
5. To find the time it takes for the T-shirt to reach its maximum height, we need to determine the vertex point of the quadratic function h(t) = -16t^2 + 72t + 5. The vertex point is given by the formula t = -b / (2a), where a = -16 and b = 72 in this case:
t = -72 / (2(-16))
t = -72 / (-32)
t = 2.25 seconds
So, it takes 2.25 seconds for the T-shirt to reach its maximum height.
To find the maximum height, substitute the value of t back into the equation:
h(t) = -16(2.25)^2 + 72(2.25) + 5
h(t) = -16(5.0625) + 162 + 5
h(t) = -81 + 162 + 5
h(t) = 86 feet
Therefore, the T-shirt's maximum height above the court is 86 feet.
6. To solve the quadratic equation v^2 + 11v + 18 = 0 by factoring, we need to find two numbers whose sum is 11 and whose product is 18. These numbers are 2 and 9. Therefore, we can rewrite the equation as follows:
(v + 2)(v + 9) = 0
Setting each factor equal to zero:
v + 2 = 0 or v + 9 = 0
v = -2 or v = -9
The solutions are v = -2 and v = -9.
7. To solve the quadratic equation 2m^2 - 7m - 30 = 0 by factoring, we need to find two numbers whose sum is -7 and whose product is -30. These numbers are -10 and 3. Therefore, we can rewrite the equation as follows:
(2m - 10)(m + 3) = 0
Setting each factor equal to zero:
2m - 10 = 0 or m + 3 = 0
2m = 10 or m = -3
m = 10/2 or m = -3
m = 5 or m = -3
The solutions are m = 5 and m = -3.
8. To solve the quadratic equation 8m^2 + 13m - 7 = 0 using the quadratic formula, we substitute the values into the formula:
m = (-b ± √(b^2 - 4ac)) / (2a)
In this case:
a = 8, b = 13, and c = -7
m = (-(13) ± √((13)^2 - 4(8)(-7))) / (2(8))
m = (-13 ± √(169 + 224)) / 16
m = (-13 ± √393) / 16
Therefore, the solutions are:
m = (-13 + √393) / 16
m = (-13 - √393) / 16