The three different values of n to demonstrate that 2n + 3n is equivalent to 5n are 1, 4 and 10.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 2n + 3n
On simplifying the equation , we get
A = 5n
when n = 1 , we get
2n + 3n = 2(1) + 3(1) = 2 + 3 = 5
5n = 5(1) = 5
Therefore, both expressions give the same result of 5.
when n = 4 , we get
2n + 3n = 2(4) + 3(4) = 8 + 12 = 20
5n = 5(4) = 20
Again, both expressions give the same result of 20.
when n = 10 , we get
2n + 3n = 2(10) + 3(10) = 20 + 30 = 50
5n = 5(10) = 50
Hence , the equation is solved
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2. Two numbers are such that when the larger number is divided by the smaller number, both the quotient and the remainder are equal to 2. If five times the smaller number is divided by the larger number, both the quotient and the remainder are also equal to 2. Find the two numbers.
Answer:
Let's assume that the smaller number is x and the larger number is y.
From the problem, we can write:
y = 2x + 2 (since the quotient and remainder when y is divided by x are both equal to 2)
5x = 2(y - 2) (since the quotient and remainder when 5x is divided by y are both equal to 2)
Substituting the first equation into the second equation, we get:
5x = 2((2x + 2) - 2)
5x = 4x + 4
x = 4
Substituting x = 4 into the first equation, we get:
y = 2x + 2 = 10
Therefore, the two numbers are 4 and 10
What is the value of 2x3−2x2+2x−82x2−5x if x=−2 ?
The value of the given algebraic expression is -2.
To find the value of the expression 2x³ - 2x² + 2x - 8 / 2x² - 5x when x = -2, we simply substitute -2 for every instance of x in the expression:
2(-2)³ - 2(-2)² + 2(-2) - 8 / 2(-2)² - 5(-2)
= 2(-8) - 2(4) - 4 - 8 / 8 + 10
= -16 - 8 - 4 - 8 / 18
= -36 / 18
= -2
Therefore, the value of the expression 2x³ - 2x² + 2x - 8 / 2x² - 5x when x = -2 is -2.
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Given the function y = 3x^2 - 12x + 9. place a point on the coordinate grid to show each x-intercept of the function. Place a point on the coordinate grid to show the minimum value of the function.
The required graph shows the x-intercepts and the minimum value.
To find the x-intercepts of the function y = 3x² - 12x + 9, we set y = 0 and solve for x:
3x² - 12x + 9 = 0
Dividing both sides by 3 gives:
x² - 4x + 3 = 0
(x - 1)(x - 3) = 0
So, the x-intercepts are x = 1 and x = 3.
To find the minimum value of the function, we can use the formula:
x = -b / 2a
Here a = 3 and b = -12.
Substitute these values gives:
x = -(-12) / 2(3) = 2
So the minimum value occurs at x = 2.
To find the corresponding y-value, we can plug in x = 2 into the original function:
y = 3(2)² - 12(2) + 9 = -3
So the minimum value is y = -3.
Here is a graph showing the x-intercepts and the minimum value.
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A catapult is used to launch a boulder. The height of the boulder h can be modeled by the function 60x40 ft², where t is the time in seconds after the boulder is launched. Assuming that the boulder doesn't hit anything, how many seconds after launch will the boulder hit the ground?
Four seconds after the boulder is hurled, it will hit the ground.
When the boulder hits the ground, its height will be 0. So, we need to solve the equation:
[tex]h(t) = -16t^2 + 64t = 0[/tex]
We can factor out -16t from the expression:
h(t) = -16t(t - 4)
Setting each factor to zero, we get:
-16t = 0 or t - 4 = 0
Solving for t, we get:
t = 0 or t = 4
Since t = 0 represents the time when the boulder is launched, we can ignore it. Therefore, the boulder will hit the ground 4 seconds after it is launched.
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a) A mechanical engineer conducted experiments to investigate the effect of four different types of boxes on compression strength (lb). The sample means from five experiments for each type of box were 650, 750, 700, 650 (unit: lb). Compute the SSTr.
b) In a single-factor ANOVA problem involving 5 populations, the total number of observations is 20, SSTr = 12 and SST = 20. What is the MSTr, MSE, and test statistic f.
a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).
The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:
Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5
Next, we can calculate SSTr using the formula:
SSTr = n * (sample mean - overall mean)^2
where n is the number of observations in each sample. In this case, n = 5 for each sample.
So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5
For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5
For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5
For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5
Therefore, the total SSTr is:
SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750
b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.
df(SSTr) = k - 1 = 5 - 1 = 4
df(SSE) = N - k = 20 - 5 = 15
The mean square for treatments (MSTr) is calculated as:
MSTr = SSTr / df(SSTr) = 12 / 4 = 3
The mean square for error (MSE) is calculated as:
MSE = SSE / df(SSE) = (20 - 5) / 15 = 1
Finally, we can calculate the F-test statistic as:
F = MSTr / MSE = 3 / 1 = 3
Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.
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Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 20 , upper bound is 30.
The point estimate of the population mean is 25 and the margin of error for the confidence interval is 2.04.
To determine the point estimate of the population mean, we take the midpoint of the interval.
Point estimate of population mean = (Lower bound + Upper bound) / 2 = (20 + 30) / 2 = 25
To calculate the margin of error, we need to know the level of confidence for the interval. Assuming a 95% confidence level, we can use the formula:
The margin of error = (Upper bound - Lower bound) / (2 * z-score)
Where the z-score for a 95% confidence level is 1.96.
Margin of error = (30 - 20) / (2 x 1.96) = 2.04
Hence, the population means point estimate is 25, and the confidence interval's margin of error is 2.04 percent.
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A recipe that makes 16 cookies calls for 1/4 cup of sugar and 2/3 cup of flour. Janelle wants to proportionally increase these amounts to get a new recipe using one cup of sugar. Using the new recipe, how much flour should she use and how many cookies can she make with the new recipe?
Answer:
2 2/3 cups flour
Step-by-step explanation:
32 cookies
by my calculations
A circular flower bed is 17 m in diameter and has a circular sidewalk around it that is 4 m wide. Find the area of the sidewalk in square meters. Use 3.14 for . The area of the sidewalk is m². (Round to the nearest whole number as needed.)
The area of the sidewalk is 264 sq. m.
What is area of a circle?A circle is a figure that is bounded by curved line called its circumference. Its area is the amount of space that he circle will cover on a 2 dimensional plane. It can be determined by:
area of a circle = πr^2
where r is the radius of the circle.
In the given question,
area of the circular flower = πr^2
r = d/2 (d is the diameter)
= 17/ 2
r = 8.5 m
area of the circular flower = 3.14*(8.5)^2
= 226.865 sq. m
area of the circular flower with sidewalk = πr^2
d = 4 + 17 + 4 = 25 m
so that,
r = 25/ 2 = 12.5 m
area of the circular flower with sidewalk = 3.14*(12.5)^2
= 490.625 sq. m
Area of the sidewalk = area of the circular flower with sidewalk - area of the circular flower
= 490.625 - 226.865
= 263.76 sq. m
The area of the sidewalk is 264 sq. m.
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solve
2|x| = 3 i need help
Answer: [tex]x_1 = -\frac{3}{2} \\x_2 = \frac{3}{2} \\\\[/tex]
X could equal either -3/2, or 3/2 because x is made into an absolute value
Answer:
[tex]x = 1 \frac{1}{2} \: \\ x = - 1 \frac{1}{2} [/tex]
Step-by-step explanation:
If we're solving for x, then we should divide both sides by 2 and then simplify.
[tex](2 |x| = 3) \div 2[/tex]
[tex] |x| = \frac{3}{2} [/tex]
This gives us the final answer of
[tex]x = ±\frac{3}{2} [/tex]
Which can be simplified into:
[tex]x = 1\frac{1}{2} , \: - 1\frac{1}{2} [/tex]
PLEASE HURRY
Let a = apple and c = cherry.
Mathland Bakery sells apple pies for $7.00 and cherry pies for $11.00.
The total number of pies sold in one day was 36. If the amount collected for all the pies that day was $304.00, how many of each type were sold?
Answer:
23 apple pies and 13 cherry pies were sold.
Step-by-step explanation:
Let's use the variables a and c to represent the number of apple and cherry pies sold, respectively.
From the problem, we know that:
The total number of pies sold is 36: a + c = 36
The total revenue from pie sales is $304.00: 7a + 11c = 304
We now have two equations with two unknowns. We can use substitution or elimination to solve for a and c. Here's one way to use substitution:
Solve the first equation for a: a = 36 - c
Substitute a = 36 - c into the second equation: 7(36 - c) + 11c = 304
Simplify: 252 - 7c + 11c = 304
Simplify further: 4c = 52
Solve for c: c = 13
Substitute c = 13 into the first equation to solve for a: a + 13 = 36
Simplify: a = 23
Therefore, 23 apple pies and 13 cherry pies were sold.
A line sgement has endpoints at (-3,2) amd (42,32). What is the x-coordinate of the point that is 2/3 the distance from (-3, 2) to (42, 32)
Answer:x = midpoint_x - (midpoint_x - (-3)) * (sqrt(5)/6) = 19.5 - (22.5 * sqrt(5))/6 = 19.5 - 3.75sqrt(5)
Step-by-step explanation:To find the x-coordinate of the point that is 2/3 of the distance from (-3, 2) to (42, 32), we first need to find the coordinates of that point.
The distance between the two endpoints of the line segment is:
d = sqrt((42 - (-3))^2 + (32 - 2)^2) = sqrt(45^2 + 30^2) = 15sqrt(45)
The distance from (-3, 2) to the desired point is:
(2/3)d = (2/3)sqrt(45^2 + 30^2)
Let's call the desired point (x, y). We can use the midpoint formula to find the coordinates of the midpoint of the line segment:
midpoint = ((-3 + 42)/2, (2 + 32)/2) = (19.5, 17)
The midpoint is halfway between the two endpoints, so the distance from (-3, 2) to the midpoint is:
sqrt((19.5 - (-3))^2 + (17 - 2)^2) = sqrt(22.5^2 + 15^2) = 15sqrt(5)
To find the coordinates of the desired point, we can use similar triangles. The ratio of the distance from (-3, 2) to the midpoint to the distance from (-3, 2) to the desired point is:
15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = 15sqrt(5) / 30sqrt(45) = sqrt(5)/6
The ratio of the distance from (42, 32) to the midpoint to the distance from (42, 32) to the desired point is the same:
15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = sqrt(5)/6
TALL BUILDING Rob wants to estimate how tall his school building is. The building casts a shadow that is 30 feet long. If Rob' is 6 feet tall and casts a shadow 2 feet long, how tall is the building?
The height of the building, found using the equivalent ratios of the corresponding sides of the similar triangles formed by Rob, the building and the shadows is 90 feet
What are similar triangles?Similar triangles are triangles that have the same shape but may have different sizes.
The length of the shadow cast by the building = 30 feet
Rob's height = 6 feet
The length of Rob's shadow = 2 feet long
The height of the building can be found from the similar right triangles formed by the building and the building's shadow and the triangle formed by Rob and Rob's shadow as follows;
Let h represent the height of the building, we get;
h/30 = 6/2 = 3
h = 30 × 3 = 90
The height of the building is 90 feet tall
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Here is a Venn Diagram with sets B, D, and the universal set U . Shade (BUD)’ on the Venn diagram.
The Venn diagram is attached in the solution.
Given that, a Venn Diagram with sets B, D, and the universal set U, we need to Shade (BUD)’ on the Venn diagram,
We know that, the complement of a set is the set that includes all the elements of the universal set that are not present in the given set.
Therefore, (BUD)’ = U - (BUD)
therefore, we will shade all the portion except (BUD),
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Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when
copying a design x times. Use the graph to write the equation modeling this relationship.
1 2 3 4 5
Enter the correct answer in the box by replacing the values of a and b.
Note that the graph of the function f(x) = a(b)^x is attached accordingly. Here a = 8 and b = 5
How is this so?f(x) = a(b^x)......1
from the graph we can see that
When x = 0, y = 8
f(0) = 8
8 = a(b^0)
8 = a x 1
a = 8
f(1) = 4
4 = a(b^1)
4 = ab
8b = 4
b = 0.5
Thus a = 8 and b = 5
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Full Question:
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship
Enter the correct answer in the box by replacing the values of a and b.
f(x) = a(b)^x
ayer compre 3/4 y hoy 1/2 cuantos kilogramos tengo en total porfaaaaaaaaaaa
Based on the above, Since Ana bought 3/4 kg of lanzones and 1/2 kg of apples, Ana bought 1 1/4 kilograms of fruits in all.
What is the kilograms?To be able to find out how many kilograms of fruits Ana bought in total, you have to add the amount of lanzones and apples she have.
Ana = 3/4 kg of lanzones
Ana = 1/2 kg of apples
So it will be:
3/4 + 2/4 = 5/4
Therefore, Ana will have bought a total of 5/4 kilograms of fruits.
To convert it to a mixed number, you need to divide the numerator by the denominator:
5 ÷ 4 = 1 remainder 1
So, the mixed fraction will be 1 1/4 kg.
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See full question below
Ana bought 3/4 kg of lanzones and 1/2 kg of apples. How many kilograms of fruits did she buy in all?
Question 1: There are two agents (A and B) in the economy. They demand for two goods:
1 and 2. Agent A's utility is UA (x₁, x₂) = ln x₁ + 2ln x2; agent B's utility is UB (x1, x₂) =
2 lnx₁ + Inx2. We also know agent A's endowment is (1,2), which means that she has
one unit of good 1 and two units of good 2. In addition, agent B's endowment is (2,1).
Suppose the prices for goods 1 and 2 are p₁ and p2, respectively.
1. Derive agent A's demands for goods 1 and 2: x4 and x.
2. Derive agent B's demands for goods 1 and 2: x and x2.
3. Derive agent A's excess demands for goods 1 and 2: z and z.
4. Derive agent B's excess demands for goods 1 and 2: z
and 22.
5. Derive aggregate excess demands for goods 1 and 2: Z₁ and Z₂.
6. Obtain the Walrasian equilibrium prices for goods 1 and 2: p₁ and p2.
7. Comment on your findings.
For points A and B in the economy:
x₁ = 2p₂/p₁ and x₂ = p₂/p₁.
x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.
2 - p₂ / p₁
1 - p₁ / p₂
2 - p₂ / p₁ + 1 - p₁ / p₂
The market clears for both items at the Walrasian equilibrium, and the aggregate excess demands are zero.
How to determine demand of goods?1. To derive agent A's demands for goods 1 and 2, maximize her utility subject to her budget constraint:
max ln x₁ + 2ln x₂
s.t. p₁x₁ + p₂x₂ ≤ p₁(1) + p₂(2)
Using Lagrange multiplier method:
1/x₁ = p₁/(2p₂)
1/x₂ = p₁/p₂
Solving for x₁ and x₂:
x₁ = 2p₂/p₁
x₂ = p₂/p₁
So, agent A's demands for goods 1 and 2 are x₁ = 2p₂/p₁ and x₂ = p₂/p₁.
2. To derive agent B's demands for goods 1 and 2, maximize her utility subject to her budget constraint:
max 2ln x₁ + ln x₂
s.t. p₁x₁ + p₂x₂ ≤ p₁(2) + p₂(1)
Using Lagrange multiplier method:
2/x₁ = p₁/p₂
1/x₂ = p₂/p₁
Solving for x₁ and x₂:
x₁ = 2p₁/p₂
x₂ = p₁/p₂
So, agent B's demands for goods 1 and 2 are x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.
3. Agent A's excess demands for goods 1 and 2 are:
z₁ = 1 - x₁ = 1 - 2p₂ / p₁
z₂ = 2 - x₂ = 2 - p₂ / p₁
4. Agent B's excess demands for goods 1 and 2 are:
z₁ = 2 - x₁ = 2 - 2p₁ / p₂
z₂ = 1 - x₂ = 1 - p₁ / p₂
5. The aggregate excess demands for goods 1 and 2 are:
Z₁ = z₁ᵃ + z₁ᵇ = 1 - 2p₂ / p₁ + 2 - 2p₁ / p₂
Z₂ = z₂ᵃ + z₂ᵇ = 2 - p₂ / p₁ + 1 - p₁ / p₂
6. At Walrasian equilibrium, Z₁ and Z₂ are both equal to zero. So, solve the system of equations:
1 - 2p₂ / p₁ + 2 - 2p₁ / p₂ = 0
2 - p₂ / p₁ + 1 - p₁ / p₂ = 0
Solving for p₁ and p₂:
p₁ = 2
p₂ = 1
So, the Walrasian equilibrium prices for goods 1 and 2 are p₁ = 2 and p₂ = 1.
7. At the Walrasian equilibrium, the market clears for both goods and the aggregate excess demands are zero. This means that the prices are set such that both agents are willing to buy exactly what is being sold in the market.
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Solve for the roots in the following equation. Hint: Factor both quadratic expressions.
(x4 + 5x2 - 36)(2x2 + 9x - 5) = 0
The roots of equation are 2 , -2, 3i, 1/5 and -5.
We have,
([tex]x^4[/tex] + 5x² -36)(2x² + 9x-5)=0
Now, factories each equation as
([tex]x^4[/tex] + 5x² -36)
= ([tex]x^4[/tex] + 9x² - 4x² -36)
= x²(x² + 9) - 4(x² + 9)
= (x² - 4)(x² + 9)
= (x-2)(x+2)(x²+9)
and, 2x² + 9x-5
= 2x² + 10x - x -5
= 2x(x+5)- (x+5)
= (2x -1)(x+5)
So, the factored form is (x-2)(x+2)(x²+9) (2x -1)(x+5)
and, the roots of equation are 2 , -2, 3i, 1/5 and -5.
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3 more than the difference of 20 and a number m
Step-by-step explanation:
(20 - m) + 3
that's it. there is not more to it.
The algebra expression can be expressed as: 3 + (20 - m)
How to solve Algebra word problems?Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. The equations we need to write will only involve basic arithmetic operations. and a single variable. Normally, the variable represents an unknown quantity in a real-life scenario.
We are told that 3 more than the difference of 20 and a number m.
This can be expressed as:
3 + (20 - m)
That is the literal expression of the algebra word problem.
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I'm Serena. For a science project, my friend Jack and I are launching three model rockets, one after another. We launch the first rocket, and then 3 seconds later, we launch the next one. And we're launching the final rocket three seconds after that, from a platform that is 20 feet high.
For our project, we need to predict the paths for all three rockets. We also need to estimate when they will all be in the air at the same time. [A graph that shows "Height of rocket (feet)" on the y-axis and "Time (seconds)" on the x-axis is shown. A red downturned parabola is shown and labeled "Path of the first rocket."]
We have calculated the path of the first rocket. It looks like this: a parabola that opens down. The y-axis is the height of the rocket in feet, and the x-axis is the time in seconds.
My friend Jack thinks we need to recalculate the graphs for the other two model rockets. But since the rockets are all the same, I think we can just shift the graph of the first rocket to find the graphs for the other two. [The graph is duplicated in green and shifts to the right, and then again in blue and shifts to the right and up. Then the rockets blast off again.]
What do you think? How can we use the graph of the first rocket to create the graphs of the second and third rockets? When will all three rockets be in the air at the same time?Evaluate the Conjectures:
2. Do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions? Or do you think that Jack is correct that you need to recalculate the other two? Explain. (2 points)
Analyzing the Data:
Suppose that the path of the first model rocket follows the equation
h(t) = −6 • (t − 3.7)2 + 82.14,
where t is the time in seconds (after the first rocket is launched), and h(t) is the height of each rocket, in feet.
Compare the equation with the graph of the function. Assume this graph is a transformation from f(t) = –6t2. What does the term –3.7 do to the rocket's graph? What does the value t = 3.7 represent in the science project? (What happens to the rocket?)
Again assuming a transformation from f(t) = –6t2, what does the term 82.14 do to the rocket's graph? What does the value h(t) = 82.14 represent in the science project? (What is happening to the rocket?) (2 points)
Serena and Jack launch the second rocket 3 seconds after the first one. How is the graph of the second rocket different from the graph of the first rocket? Describe in terms of the vertical and horizontal shift.
What is the equation of the second rocket?
They launch the third rocket 3 seconds after the second rocket and from a 20-foot-tall platform. What will the graph of the third rocket look like? Describe in terms of the vertical and horizontal shift.
What is the equation of the third rocket?
Answer the following questions about the three rockets. Refer to the graph of rocket heights and times shown above.
a. Approximately when is the third rocket launched?
b. Approximately when does the first rocket land?
c. What is the approximate interval during which all three rockets are in the air?
Answer:
Regarding the conjecture of Serena and Jack:
Serena suggests that they can use the graph of the first rocket and shift it to find the graphs for the other two rockets. This means that the paths of the rockets are similar, and the only difference is the time of launch. Jack suggests that they need to recalculate the graphs for the other two rockets, which means that the paths of the rockets are different.
In this scenario, Serena is correct. Since the rockets are identical, they will follow the same path, but with a different time of launch. Thus, they can use the graph of the first rocket and shift it to the right to get the graph of the second rocket and shift it further to the right and up to get the graph of the third rocket.
Analyzing the equation:
The equation for the first rocket's path is h(t) = -6(t-3.7)^2 + 82.14. Assuming that the graph is a transformation from f(t) = -6t^2, the term -3.7 shifts the graph horizontally to the right by 3.7 seconds. This means that the first rocket was launched 3.7 seconds before the time t in the equation. The value t = 3.7 represents the time when the first rocket was launched.
The term 82.14 shifts the graph vertically up by 82.14 feet. This means that the initial height of the rocket is 82.14 feet above the ground. Therefore, the value h(t) = 82.14 represents the initial height of the rocket.
Equation of the second rocket:
The second rocket is launched 3 seconds after the first rocket. This means that the graph of the second rocket is a horizontal shift of the first rocket's graph by 3 seconds. Therefore, the equation of the second rocket is:
h(t) = -6(t-6.7)^2 + 82.14
This is because the launch time of the second rocket is t = 6.7 seconds (which is 3 seconds after the first rocket's launch).
Description of the third rocket's graph:
The third rocket is launched 3 seconds after the second rocket and from a 20-foot-tall platform. This means that the graph of the third rocket is a horizontal shift of the second rocket's graph by 3 seconds and a vertical shift upwards by 20 feet. Therefore, the equation of the third rocket is:
h(t) = -6(t-9.7)^2 + 102.14
This is because the launch time of the third rocket is t = 9.7 seconds (which is 3 seconds after the second rocket's launch).
Answers to the questions:
a. The third rocket is launched at approximately t = 9.7 seconds.
b. The first rocket lands when h(t) = 0. Solving -6(t-3.7)^2 + 82.14 = 0 gives t = 5.16 seconds (approximate).
c. The approximate interval during which all three rockets are in the air is from t = 6.7 seconds (when the second rocket is launched) to t = 14.46 seconds (when the first rocket lands).
what can you say about the end behavior of the function f(x)=-4x6 -52
The end behavior of the given function is Both ends of the graph goes down(In the same direction),
The degree and the leading coefficient (The coefficient of the highest degree monomial) of a function shows the end behavior of its graph.
if Degree is even and leading coefficient is negative then the end behavior of the function f(x) is,
f(x)---> -∞, as x---> -∞
f(x)---> -∞, as x---> + ∞
That is, Both ends of the graph goes down(In the same direction)
Here, the given function is f(x)=-4x⁶+6x²-52
Degree = 6(even), leading coefficient = -4 (negative)
Thus, the end behavior of the given function is Both ends of the graph goes down(In the same direction),
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You want to purchase a new car in 6 years and expect the car to cost $12,000. Your bank offers a plan with a guaranteed APR of 6.5% if you make regular monthly deposits. How
← much should you deposit each month to end up with $12,000 in 6 years?
T
You should invest $ each month
(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed
Answer:
To calculate the monthly deposit required, we can use the formula for future value of an annuity, which is:
FV = Pmt x (((1 + r)^n - 1) / r)
where FV is the future value, Pmt is the monthly payment, r is the monthly interest rate, and n is the number of months.
In this case, we want to find the monthly payment required to achieve a future value of $12,000 in 6 years, or 72 months. The monthly interest rate is the annual percentage rate (APR) divided by 12, so:
r = 6.5% / 12 = 0.00541666667
Substituting these values into the formula, we get:
12,000 = Pmt x (((1 + 0.00541666667)^72 - 1) / 0.00541666667)
Solving for Pmt, we get:
Pmt = 12,000 / (((1 + 0.00541666667)^72 - 1) / 0.00541666667)
≈ $164.41
Therefore, you should deposit $164.41 each month to end up with $12,000 in 6 years
What does the acronym VAT represent?
Answer:
Value-Added Tax
Step-by-step explanation:
Value-added tax (VAT) is a consumption tax on goods and services that is levied at each stage of the supply chain where value is added, from initial production to the point of sale.
Which box plot matches the data set?
Option A correctly matches the data set.
First, by looking at the numbers and description of the numbers; I notice that it starts at 10, ending at 48.
Second, I see that the first quartile (Q1) is 20, eliminating option D
Third, I see the third quartile (Q3) is 45, eliminating option C.
Lastly, I look at the median (Q2) is 30, eliminating option B.
Since I have eliminated option B, C, and D; only option A remains.
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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
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Samuel runs around a 100 meter track.He uses the linear equation y=200+5x to describe how far he runs after he has already jogged two laps. Which of the following best describes the slope of the linear equation?
Samuel runs 5 meters per second best describes the slope of the linear equation
Given that Samuel runs around a 100 meter track.
He uses the linear equation y=200+5x to describe how far he runs after he has already jogged two laps.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
y=200+5x
y=5x+200
Slope is 5
Hence, Samuel runs 5 meters per second best describes the slope of the linear equation
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(4 radical 3)- 4i in polar form
The solution is the number in polar form 4 - 4i is
4 Root(2) (cos(-45) + i sin(-45)).
We know that,
Polar form of a complex number is r( cos(theta) + i sin(theta) )
r is equal to the total distance created by the rectangular coordinates of the complex number
r = Root(4^2 + (-4)^2) = Root(32) = 4 Root(2)
To find theta, if a > 0, use arctan(b/a), where:
a = the first number
b = the second number
arctan (-4/4) = -45 degrees (-0.7854 radians)
The answer is 4 Root(2) (cos(-45) + i sin(-45))
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complete question;
Express the number in polar form 4 - 4i
Given the table of values below from a quadratic function, write an equation of that function.
X | 0 | 1 | 2 | 3 | 4 |
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Y | 4 | 10 | 12 | 10 | 4 |
this is a answer, thanks
Answer:
Step-by-step explanation:
Tessa’s gpa for three semesters was 3.35 for 46 course units and for her fourth semester gpa was 3.74 for 12 course units. What is Tessa’s cumulative gpa for all four semesters
Tessa's cumulative GPA for all four semesters is 3.44.
To find Tessa's cumulative GPA, we first need to calculate the total number of course units she has taken. For the first three semesters, she took 46 course units. For the fourth semester, she took 12 course units. So, in total, she has taken 46 + 12 = 58 course units.
Next, we need to calculate her total grade points. To do this, we multiply her GPA for each semester by the number of course units she took in that semester, and then add up the results. For the first three semesters, her total grade points are:
3.35 x 46 = 154.1
For the fourth semester, her total grade points are:
3.74 x 12 = 44.88
So her total grade points for all four semesters are:
154.1 + 44.88 = 198.98
Finally, we divide her total grade points by the total number of course units she has taken:
198.98 / 58 = 3.44
Therefore, Tessa's cumulative GPA for all four semesters is 3.44.
45 teachers teach math and 9 teachers teach science. What is the ratio of science teachers to math teachers?
The ratio of science teachers to math teachers is 1:5.
The ratio of science teachers to math teachers can be found by dividing the number of science teachers by the number of math teachers.
The ratio of science teachers to math teachers = (Number of science teachers) / (Number of math teachers)
Here, the number of science teachers is 9 and the number of math teachers is 45.
The ratio of science teachers to math teachers = 9 / 45
Simplifying this ratio by dividing both the numerator and denominator by 9, we get:
The ratio of science teachers to math teachers = 1 / 5
Therefore, the ratio of science teachers to math teachers is 1:5.
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Find the equation of the line perpendicular to y=1/2x-1 and passes through the point (5,6)
The equation of line perpendicular to "y = (1/2)x - 1" and passing through point (5,6) is y = -2x + 16,
The equation of the line is y = (1/2)x - 1, is in slope-intercept form "y = mx + b", where m is slope,
To find the slope of the given line, we see that it is in the form y = mx + b, where m = 1/2.
We know that, slope of a line perpendicular to this line will be the "negative-reciprocal" of this slope.
So, the slope of the perpendicular line will be -2.
Now we use the point-slope form of the equation of a line to find the equation of the perpendicular line passing through the point (5, 6). The point-slope form is : y - y₁ = m(x - x₁),
where (x₁, y₁) is given point and "m" is slope of the line;
Substituting the values, we get:
⇒ y - 6 = -2(x - 5),
⇒ y = -2x + 16,
Therefore, the equation of perpendicular line is y = -2x + 16.
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Identify an equation in standard form for a hyperbola with center (0, 0), vertex (6, 0), and focus (10, 0).
Answer:
Step-by-step explanation: