Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
Create a graph of the polynomial function you selected from Question 2.
Answers
From the information given about the polynomial function, It is correct to state that there is a way for both of them to be correct. See the explanation below and the attached for the graph related to the second question.
What is the explanation for the above?A polynomial could only have a number of zeros equal to its degree. A third degree polynomial can thus have three zeroes, but Ray claims the polynomial has four Intercepts.
While the words "zeroes" and "intercepts" are sometimes used interchangeably, a zero is officially an x-intercept. A function can also have a y-intercept, therefore a cubic can have four intercepts in total, albeit only three will be zeroes.
The zeros of g(x)= x3-x2-4x+4 are -2,2, and 1. End behavior, the Y- intercept, the axis of symmetry, and the vertex are other important characteristics of polynomial functions.
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Related Questions
The record low temperature in Fargo, ND is -35 degrees. The record high is 114 degrees. What is the difference in the record high and the record low temperatures?
Answers
The difference between the record high and low temperatures is 149 degrees.
What is the difference between the temperatures?A negative number is a number that is less than zero. A negative number usually has a minus sign in front of it. An example of a negative number is -35. A positive number is a number that is greater than zero. An example of a positive number is 10.
In order to find the difference between two or more numbers, subtract the numbers from each other.
Difference between the temperature = record high temperature - record low temperature
114 - -35
114 + 35 = 149 degrees
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What is the ratio for 3 rectangles and 4 ovals in its simplest form?
Answers
The ratios for the rectangles and the ovals is 4 : 3
Calculating the ratios for the rectangles and the ovalsFrom the question, we have the following parameters that can be used in our computation:
Rectangle = 4
Oval = 3
The ratio can be represented as
Ratio = Rectangle : Oval
When the given values are substituted in the above equation, we have the following equation
Rectangle : Oval = 4 : 3
The above ratio cannot be further simplified
This means that the ratio expression would remain as 4 : 3
Hence, the solution is 4 : 3
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I just need the answer for letter b
Answers
If f(x) = 1/343, then x = -3. The point on the graph of f when f(x) = 1/343 is (-3, 1/343).
How to explain the valueA point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph. Each point is identified by both an x and a y coordinate.
If f(x) = 1/343, then x = -3. This is because 343 = 7³, therefore the inverses is 1/343. The point on the graph of f when f(x) = 1/343 is (-3, 1/343
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In the figure, what percentage of the circles are shaded?
Answers
Answer: E. 25%
Step-by-step explanation: There are 12 circles in total. 3 out of those twelve are shaded in, making it in fraction form 3/12. dividing both the numerator in the denominator by 3 simplifies it into 1/4. which is subsequently, 25%
Find the distance between (2, 5) and (-5, 8).
58
√58
2√43
2
Answers
Answer:
d = [tex]\sqrt{58}[/tex]
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )
d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]
= [tex]\sqrt{(-7)^2+3^2}[/tex]
= [tex]\sqrt{49+9}[/tex]
= [tex]\sqrt{58}[/tex]
A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions
Answers
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
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Write the coordinates of the vertices after a dilation with a scale factor of 1 2 , centered at the origin.
Answers
The coordinates of the vertices after a dilation of the scale factor would be:
W' = (2.5, 5)V' = (0, -5)U' = (2.5, -5)How to dilate the vertices ?To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.
Given the vertices:
W = (5, 10)
V = (0, -10)
U = (5, -10)
After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:
W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)
V' = (0 * 1/2, -10 x 1/2) = (0, -5)
U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)
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15(2x -10) + 4x= -3(15x + 4)
Answers
The value of x in the equation 15(2x - 10) + 4x = -3(15x + 4) is 1.7
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Given the equation:
15(2x - 10) + 4x = -3(15x + 4)
Solving the parenthesis:
30x - 150 + 4x = -45x - 12
Collect like terms:
30x + 4x + 45x = -12 + 150
79x = 138
Dividing both sides by 79:
x = 1.7
The value of x is 1.7
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The slope of a line of best fit is undefined when _____.
select all that apply
(1) the x values of the data set are constant
(2) the y values of the data set do not change when the x values change
(3) the slope of the line of best fit is vertical
(4) the slope is of the line of best fit is horizontal.
(5) the x values of the data set increase at an unspecified rate as the y values decrease
Answers
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. This is because a horizontal line has a slope of zero
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. A line of best fit is a straight line that is used to represent the data on a scatter plot. It is the line that best fits the data points in a scatter plot.
The slope of a line of best fit is the rate of change of the y-coordinate relative to the x-coordinate.. In other words, there is no rate of change of the y-coordinate relative to the x-coordinate when the line is horizontal.
The x values of the data set increase at an unspecified rate as the y values decrease. This means that the line of best fit has a negative slope. A negative slope means that the y-coordinate decreases as the x-coordinate increases.
In other words, there is a rate of change of the y-coordinate relative to the x-coordinate. The slope of the line of best fit is the value of this rate of change.
The slope of a line of best fit is used to determine the direction and strength of the relationship between two variables.
A positive slope means that the variables are directly proportional, while a negative slope means that they are inversely proportional. The slope of a line of best fit can be calculated using the formula y2 - y1 / x2 - x1.
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On a standardized exam, the scores are normally distributed with a mean of 300 and
a standard deviation of 40. Find the z-score of a person who scored 280 on the exam.
Answer:
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Answers
The z- score of a person who scored 280 on the exam can be found to be - 0. 5.
How to find the z - score ?A z-score indicates how many standard deviations an element is from the mean.
The formula is:
Z = ( X - μ ) / σ
The details here are:
X = 280, μ = 300, and σ = 40
The z - score is therefore :
Z = (280 - 300) / 40
= -20 / 40
= -0.5
In conclusion, the z - score of a person who scored 280 on the exam is -0.5. This means that their score is half a standard deviation below the mean.
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Can someone please answer and provide an explanation for these problems?
Answers
Answer:
50) Midpoint: (5.5, 0)
51) Midpoint: (6, -8)
Step-by-step explanation:
We can find the midpoint between two points using the midpoint formula, which is m = (x1 + x2) / 2, (y1 + y2) / 2, where
m is the midpoint,(x1, y1) are one point,and (x2, y2) are another point50) We can allow (10, 10) to be our (x1, y1) point and (1, -10) to be our (x2, y2) point:
x-coordinate of midpoint of (10, 10) and (1, -10):
(10 + 1) / 2
11 / 2
5.5
y-coordinate of midpoint of (10, 10) and (1, -10):
(10 + (-10)) / 2
(10 - 10) / 2
0 / 2
0
Thus, the midpoint of the line segment with the endpoints (10, 10) and (-1, 10) is (5.5, 0).
51) We can allow (3, -6) to be our (x1, y1) point and (9, -10) to be our (x2, y2) point:
x-coordinate of midpoint of (3, -6) and (9, -10):
(3 + 9) / 2
12 / 2
6
y-coordinate of midpoint of (3, -6) and (9, -10):
(-6 + -10) / 2
(-16) / 2
-8
Thus, the midpoint of the line segment with the endpoints (3, -6) and (9, -10) is (6, -8).
You deposit $5000 in an account earning 3% interest compounded continuously. How much will you have in the
account in 15 years?
Answers
Answer:
$7841.56----------------------
Use the compound interest formula:
[tex]A = Pe^{rt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 3% = 0.03;t = time period in years = 15.Plugging in the values, we get:
[tex]A = 5000*e^{0.03*15}[/tex][tex]A = 7841.56[/tex]A bag contains 14 blue marbles, 6 green marbles and 8 purple marbles. What is the likelihood of randomly drawing a blue marble?
Answers
Answer:
0
Step-by-step explanation:
because 6 plus 8 eqaul 14
What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
Answers
The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
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The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
Given: KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
Prove:
An incomplete flowchart proof is shown.
Answers
By ASA congruency triangle KBH is congruent to triangle NWH.
Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.
From the given figure,
Consider ΔKBH and ΔNWH,
∠KHB=∠NHW (Vertically opposite angles)
∠HKB=∠HWN (Interior alternate angles parallelogram)
KH=HW (Diagonals bisect each other)
By ASA congruency ΔKBH ≅ ΔNWH
Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.
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Please solve this question
Answers
The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.
We have,
The vertex form of a parabola is given by the equation y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
Now,
Given that the parabola passes through (-2, 4) and has a vertex (0, 8), we can substitute these values into the equation to find the value of 'a'.
Using the vertex (0, 8):
8 = a(0 - 0)² + 8
8 = a(0) + 8
8 = 8
Since the coefficient of the squared term is 'a', which remains unchanged, we can conclude that a = 1.
Therefore,
The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.
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A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 75 cubic yards. Rectangular prism
B has a length of 7 yards and a width of 3 yards. The total volume of the solid figure is 180 cubic yards. What is the height of
rectangular prism B?
Answers
The height of rectangular prism B is 5 yards.
Let's first find the volume of rectangular prism B:
The volume of the solid figure = Volume of prism A + Volume of prism B
180 = 75 + length × width × height of prism B
105 = length × width × height of prism B
We know that the length of prism B is 7 yards and the width is 3 yards,
Substitute those values:
105 = 7 × 3 × height of prism B
105 = 21 × height of prism B
height of prism B = 105/21
height of prism B = 5
Therefore, the height of rectangular prism B is 5 yards.
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Based on the March expense statement, how much did Maria spend using her credit card?
A. $181.18
B. $117.57
C. $507.59
D. $25.28
Answers
Please someone help me with this. Simplify. The expression in the picture no negative exponents should be added in the answer
Answers
A simplification of the given expression is 1/m¹⁶.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we would have the following simplified expression:
[tex](m^{\frac{4}{5}} \cdot m^{\frac{4}{5}} )^{-10}\\\\(m^{\frac{4}{5} +\frac{4}{5} } } )^{-10}\\\\(m^{\frac{8}{5} } )^{-10}\\\\(m^{\frac{8 \times -10}{5} } )\\\\(m^{\frac{-80}{5} } )\\\\m^{-16}[/tex]
1/m¹⁶
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Esther ran round the playground and 12 times. The playground is 240 m by 160 m. what distance did she cover?
Answers
The total distance she cover after running is 9600 meters
How to calculate the total distance she cover?From the question, we have the following parameters that can be used in our computation:
Number of times = 12 times
Dimensions of the playground = 240 m by 160 m
The perimeter of the playground is calculated as
Perimeter = 2 * sum of dimensions
substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (240 + 160)
The total distance she cover is calculated as
total distance = 12 * 2 * (240 + 160)
Evaluate
total distance = 9600 meters
Hence, the total distance she cover is 9600 meters
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A simple gable roof is to cover a span of 32 feet. If it is to have a 7:12 pitch, how tall will the ridgeline be above the house?
Answers
The ridgeline will be 18.67 feet above the house.
What will be the height of the ridgeline above the house?Generally, a height refers to the measurement of someone or something from head to foot or from base to top.
To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span
Given data:
Pitch = 7
Span = 32 feet
Inputting the values, we have:
Height = (7 / 12) * 32
Height = 0.5833 * 32
Height = 18.6656
Height = 18.67 feet.
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factorise fully
1) 3x² - 27y²
2) 2014² - 2013²
please help
Answers
Answer: 3x² - 27y² = (3x²) - (27)(y²) = 3(x² - 9y²) = 3(x - 3y)(x + 3y), and 2014² - 2013² = (2014 + 2013)(2014 - 2013) = (3127)(1) = 3127
Im not 100% sure of this answer cause I'm not that good at stuff like this but I still think this is right fr fr
Which of the following is not the solution of system of inqualities
(1,0) (8,0). (0,4). (3,0)
Answers
The points (1,0) (8,0). and. (3,0) are not the solution of system of inqualities
How to deterine which is not the solution of system of inqualitiesFrom the question, we have the following parameters that can be used in our computation:
The graph
Also, we have the following ordered pairs
(1,0) (8,0). (0,4). (3,0)
From the graph, we have the following ordered pairs in the shaded region
(0, 4)
Other points (1,0) (8,0). and. (3,0) are not in the shaded region
This means that (1,0) (8,0). and. (3,0) are not the solution of system of inqualities
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I need help please guys
Answers
The solution is :
After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
Here, we have,
The designated sum can replace either row. Consult your curriculum materials for the intent.
Here, we'll replace row 2 with the sum.
3(2, -2, 5) +(-6, 3, -4) = (3(2)-6, 3(-2)+3, 3(5)-4) = (0, -3, 11)
After the row operation replaces the second row, the augmented matrix is ... [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
Hence, The solution is :
After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
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Lydia has four straws of different lengths, and she is trying to form a right triangle. The lengths are 8, 9, 15, and 17 units. Which three lengths should she use? Justify your answer.
Answers
The set of 3 lengths that make a right triangle is {8, 15, 17}
Which three lengths should she use?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.
So if the 3 sides are A, B, and C, such that:
A < B < C
We will have:
A² + B² = C²
Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:
8² + 15² = 17²
289 = 289
That equationis true, thus, these 3 lengths make a right triangle.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
2=a
7=b
Step-by-step explanation:
a+14=6a+4
-a
14=5a+4
-4
10=5a
/5
2=a
9b+8=10b+1
-1
9b+7=10b
-9b
7=1b
/1
7=b
Answer:
WZ=7
XY=7
WX=2
ZY=2
Step-by-step explanation:
9b+8=10b+1
Take 9b to 10b and 1 to 8 to form the equation
8 - 1 =10b - 9b
7 = b
a + 14 =6a + 4
Take a to 6a and 4 to 14 to form the equation
14 - 4 =6a - a
10 =5a
Simplify the answer
10/5 =5a/5
Five divide by five 1 and 10 divided by 5 is 2
Answer is therfore
2 = a
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
Answers
The required exact value of sin(585 degrees) is -0.707
The sine function is periodic with a period of 360 degrees.
Therefore,
= sin(585 degrees)
= sin(585 degrees - 360 degrees)
= sin(225 degrees).
The sine function has a negative value in the third quadrant, and 225 degrees is in the third quadrant.
Therefore,
sin(225 degrees) = -sin(45 degrees)
= -(1/sqrt(2)) = -0.7071.
Therefore, the exact value of sin(585 degrees) is -0.7071.
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Before the new carpet is installed, all
the walls and the ceiling will be painted
with primer. If one gallon of primer
covers 300 square feet, how many
gallons of primer will be needed?
44 ft
8 ft
32 ft
Answers
You would need to purchase 6 gallons of primer.
how many cubes that are 1" x 1" x 1" could fit into a box that is 8" x 8" x 8"
Answers
Answer:
512
Step-by-step explanation:
To determine how many 1" x 1" x 1" cubes can fit into an 8" x 8" x 8" box, we need to calculate the volume of the box and then divide it by the volume of a single cube.
The volume of the box is calculated by multiplying its length, width, and height:
Volume of the box = 8" x 8" x 8" = 512 cubic inches.
The volume of a single cube is 1" x 1" x 1" = 1 cubic inch.
To find out how many cubes can fit, we divide the volume of the box by the volume of a single cube:
Number of cubes = Volume of the box / Volume of a single cube
Number of cubes = 512 cubic inches / 1 cubic inch
Number of cubes = 512
Therefore, 512 cubes that are 1" x 1" x 1" can fit into an 8" x 8" x 8" box.
If you have a cube that is 1x1x1 and a box that is 8x8x8, then you would multiply the 8x8x8 and get 512 because the cube is only 1x1x1 and when you multiply 8x1 you still get 8.
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.18. The probability that it will not rain and the flight will leave on time is 0.8. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
Answers
The probability that it is raining if the flight has been delayed is 0.07, or 7%.
How to calculate the probabilityWe can use the following formula to calculate the probability that it is raining if the flight has been delayed:
P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)
We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):
= 0.07 * 0.18
= 0.0126.
Substituting these values into the formula, we get:
P(Rain|Delayed) = 0.0126 / 0.18 = 0.07
Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.
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