The polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² has one possible positive real zero according to Descartes' Rule of Signs. We observe one change of sign in the coefficients. Thus, there is a maximum of one positive real root.
Determining the Number of Possible Positive Real Zeros:
To determine the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x², we can use Descartes' Rule of Signs. This rule helps us to count the number of sign changes in the polynomial and thus infer the number of positive real roots.
First, let's observe the original polynomial:
[tex]2x^{4}[/tex] + 14x³ - 35x²
We examine the coefficients: 2, 14, and -35. By running our eye across these coefficients:
From 2 to 14: No sign change (positive to positive).From 14 to -35: One sign change (positive to negative).The polynomial has one sign change. According to Descartes' Rule of Signs, there is a maximum of one positive real root.
Therefore, the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² is one.
if g (x)= x^2-5, where does the graph g (x) cross the x-axis?
Tiana takes 3 hours to drive to the coast without stopping. How many minutes will it take her to reach the coast if she stops to ready for 20 minutes
60 minutes in an hour
3 x 60 = 180 minutes
180 +20 = 200 minutes total
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This is according to the intersection of two tangent theorem. The theorem states that given a circle, if X is any point within outside the circle and if Y and Z are points such that XY and XZ are tangents to the circle, then XY is equal to XZ.
Final answer:
Two tangent segments to a circle that share a common endpoint outside the circle are congruent, meaning they have the same length. This is a fundamental concept in circle geometry, illustrating the unique properties of tangents and their interactions with circles.
Explanation:
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This means the lengths of the two tangent segments from the common external point to their respective points of tangency on the circle are equal. This concept is important in the study of circle geometry, as it helps in understanding relationships between tangents and circles.
A tangent to a circle is a line that touches the circle at exactly one point, ensuring it does not cross the circle at that touchpoint. This property of tangents being congruent when they share an external point is proven using the properties of right triangles and the fact that tangents from a point outside the circle to the circle are perpendicular to the radius at the point of tangency.
An example of this concept in action is if you draw two tangents from a single point outside of the circle to any two points on the circle's boundary, the segments of these tangents from the external point to the points of tangency will have the same length.
Are the two functions parallel, perpendicular, the same equation, or none of these choices? -x-3y= -18 9x-3y= -27
the sum of two numbers is 15 one number is twice as large as the second number what are the tw numbers which let statement would you use
x +2x =15
3x=15
x=15/3
x=5
2x=2*5=10
10+5=15
the two numbers are 5 & 10
I don't know how to do this
Which of the following show the factored equivalent of f(x) = (2x2 +7x + 3)(x - 3) and its zeros?
f(x) = (x + 5)(x + 7)(x - 3); -5, -7, 3
f(x) = (x + 3)(2x + 1)(x - 3); -3, -0.5, 3
f(x) = (x + 5)(x + 7)(x - 3); 5, 7, -3
f(x) = (x + 3)(2x + 1)(x - 3); 3, 0.5, -3
Final answer:
The factored equivalent of [tex]f(x) = (2x^2 +7x + 3)(x - 3)[/tex] is f(x) = (x + 3)(2x + 1)(x - 3), and its zeros are -3, -0.5, and 3.
Explanation:
The factored equivalent of the polynomial f(x) = (2x2 +7x + 3)(x - 3) and its zeros can be determined by factoring [tex]2x^2 + 7x + 3[/tex]. We notice that this quadratic can be factored into (2x + 1)(x + 3). Therefore, when we include the (x - 3) term, we get the fully factored form,
f(x) = (2x + 1)(x + 3)(x - 3). To find the zeros, we set each factor equal to zero:
2x + 1 = 0 gives a zero of -0.5;
x + 3 = 0 gives a zero of -3; and,
x - 3 = 0 gives a zero of 3. Thus, the correct answer is
f(x) = (x + 3)(2x + 1)(x - 3); -3, -0.5, 3.
The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with a mean of 6.7 minutes and a standard deviation of 2.2 minutes. for a door selected at random, what is the probability the assembly time will be:
a.5 minutes or less?
b.10 minutes or more?
c.between 5 and 10 minutes?
Someone please help, I'm stuck!
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x: 3, 1, -1, -3
y: 1, 2, 3, 4
(A) No; the domain values are at regular intervals and the range values have a common sum 1.
(B) No; the domain values are not at regular intervals.
(C) Yes; the domain values are at regular intervals and the range values have a common factor 2.
(D) Yes; the domain values are at regular intervals and the range values have a common sum 1.
Does anyone know how to do this problem? Thanks.
Choose the correct simplification of (5x3 − 5x − 8) + (2x3 + 4x + 2).
Answer:
7x^3+x+6
Step-by-step explanation:
Its answer choice A on a test.
In rectangle JKLM, angle JML is 3x - 15. Find the value of x.
Write the event as set of outcomes. We flip three coins and obtain more tails than heads.
$15 represents 20% of the spending money Arie is saving for camp this summer. What is the total amount of money she hopes to take to camp?
Answer: $75
Step-by-step explanation: i got it right on my quiz
Which method of reasoning reaches a general conclusion on the basis of a number of observations that form a pattern?
deductive reasoning
inductive reasoning
complementary reasoning
supplementary reasoning
Answer:
Deductive reasoningStep-by-step explanation:
Deductive reasoning can be defined as the process of reasoning based on premises to reach a specific conclusion.
So, in this case, the statement indicate a method of reasoning based on a number of observations that can lead to a conclusion. That's just deductive reasoning, because those number of observations form the system of premises, from which a deductive logic is developed to get to the conclusion.
Therefore, the right answer is the first choicem, deductive reasoning.
Complete the equation of variation where y varies inversely as x and y = 0.125 when x = 8.
The word that best describes two acute angles of a right triangle is:
inductive.
supplementary.
vertical.
complementary.
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
(9x + 7)(4x + 1)(3x + 4) = 0
Answer:
3
Step-by-step explanation:
please simplify 9/3-2i.
(05.01 LC)
The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes
Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?
fraction 30 over 2
fraction 2 over 30
fraction 30 over 8
fraction 8 over 30
the first dot is on 2 for number of sprays and 30 for time
so the expression would be number of sprays over time so 2 over 30
2/30 that would reduce to 1/15 meaning each spray happens every 15 minutes
In this exercise we have to interpret the reported graph of an increasing linear function, we find that:
Letter B
Recalling the concepts of an increasing linear function as:
Linear functions happen those whose diagram is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function bear individual independent changing and individual dependent changeable. The independent changeable is x and the helpless changing happen y.With this explanation we have:
Expression would be number of sprays over time so 2 over 30, will be equal to:
[tex]30/2=15[/tex]
See more about linear function at brainly.com/question/5245372
What is the monthly payment for $280000 mortgage with an interest of 6% compounded monthly for 20 years?
What is the differnce between union and intersection in math
Final answer:
Union and intersection are two operations used in set theory to combine sets or find common elements.
Explanation:
Union and intersection are two operations used in set theory. In mathematics, a set is a collection of distinct objects. The union of two sets A and B, denoted by A ∪ B, is the set that contains all the elements that are in either A or B or in both. The intersection of two sets A and B, denoted by A ∩ B, is the set that contains all the elements that are common to both A and B.
For example, let's consider two sets: A = {1, 2, 3} and B = {2, 3, 4}. The union of A and B is {1, 2, 3, 4}, as it contains all the elements from both sets. The intersection of A and B is {2, 3}, as those are the elements that are common to both sets.
What is the sum of the integers between the square root of 12 and 40?
Find the area of a regular hexagon with a perimeter of 42 feet. Round to the nearest tenth if necessary. Select one: a. 128.1 units2 b. 256.2 units2 c. 42.7 units2 d. 21.35 units2
NEED AN ANSWER ASAP
Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?
A. (x,y)→(y,−x)
B. (x,y)→(y,x)
C. (x,y)→(−y,x)
D. (x,y)→(−y,−x)
Answer:
A. [tex](x,y)\rightarrow (y,-x)[/tex]
Step-by-step explanation:
We have been given that figure ABCD is a rectangle with point A (−2, 5). We are asked to choose the rule that would rotate the figure 90° clockwise.
We know that rule of rotating a figure 90 degrees clockwise is: [tex](x,y)\rightarrow (y,-x)[/tex]
Upon looking at our given choices we can see that option A is the correct choice.
After rotating our given point 90 degree clockwise, the coordinates of point A would be:
[tex](-2,5)\rightarrow (5,--2)=(5,2)[/tex]
The perimeter of a rectangular slab of concrete is 24 meters. If the length of the
rectangular slab is 2 meters longer than its width, what is the width of the slab?
Answers:
A) 5 meters
B) 6 meters
C) 7 meters
D) 8 meters
The answer is 5 meters but i don't know how to get that. HELP
The width of the slab is 5 meters which is correct option(A).
What is perimeter of rectangle?Perimeter of rectangle is defined as addition the lengths of the rectangle's four sides.
Let length of slab is L, width is W,
The perimeter of a rectangular slab = 24
2(length) + 2(width) = 2L + 2W = 24
If the length of the rectangular slab is 2 meters longer than its width
= width + 2
So, the equation L = W+2
Now substitute, L= W+2 in equatioin of perimeter,
2(W+2) + 2W = 24
2W + 4 + 2W = 24
4W = 24-4 = 20
W = 20/4 = 5
W = 5
Hence, the width of the slab is 5 meters.
Learn more about Perimeter of rectangle
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The survey of study habits and attitudes (ssha) is a psychological test that measures the motivation, attitude, and study habits of college students. scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. you suspect that incoming freshmen at your school have a mean μ which is different from 115 because they are often excited yet anxious about entering college. to test your suspicion, you decide to test the hypotheses h0: μ = 115 versus ha: μ ≠ 115. you give the ssha to 25 incoming freshmen and find their mean score to be 116.2. what is the value of the test statistic?
Final answer:
The value of the test statistic in this scenario is 0.24, calculated using the z-score formula based on the provided sample mean, population mean, standard deviation, and sample size.
Explanation:
The value of the test statistic for a hypothesis testing can be calculated using the formula for the z-score, which is (sample mean - population mean) / (standard deviation / √sample size). In this case, given that the sample mean is 116.2, the population mean is 115, the standard deviation is 25, and the sample size is 25 students, the test statistic can be calculated as follows:
(116.2 - 115) / (25 / √25)
This computation yields a z-score of:
(1.2) / (25 / 5)
(1.2) / 5 = 0.24.
Therefore, the value of the test statistic is 0.24.
How many different sums can be made with a penny nickel dime quarter?
Sally has 5 red flags, 3 green flags, and 4 white flags. how many 12-flag signals can she run up a flag pole
To solve for the total number of 12 – flag signals Sally can make, we need to make use of the formula:
total flags = d! / (a! b! c!)
Where,
d = is the number of flags to create a signal = 12
a = number of red flags = 5
b = number of green flags = 3
c = number of white flags = 4
We can observe from the equation that the individual number of flags is factored out (or divided from) that is because all the 5 red flags are similar, all the 3 flags are similar and all 4 flags are similar.
Going back into the equation, by substituting and calculating:
total flags = 12! / (5! 3! 4!)
total flags = 27,720
Therefore there are about 27,720 different 12-flags signals.
A person is standing exactly 36 ft from a telephone pole. There is a 30 degree angle of elevation from the ground to the top of the pole. What is the height of the pole?
By using the tangent function in trigonometry, we find that the height of the telephone pole is approximately 20.78 feet. This was calculated using the given angle of elevation and the distance from the pole.
To find the height of the telephone pole, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
Given:
Distance from the person to the base of the pole (adjacent side) = 36 ftAngle of elevation from the ground to the top of the pole = 30 degreesWe know that:
tan(30°) = opposite / adjacent
So,
tan(30°) = height / 36 ft
From a trigonometric table or calculator, tan(30°) ≈ 0.5774.
We can set up the equation as:
0.5774 = height / 36 ft
Solving for the height of the pole:
height = 0.5774 * 36 ftheight ≈ 20.78 ftTherefore, the height of the pole is approximately 20.78 feet.