Answer:- The total number of roots in the given polynomial function is 2.
Explanation:-
We know that corollary of Fundamental Theorem of Algebra tells that polynomial will have exactly as many roots(m) as its degree(m>0).
The given polynomial function [tex]g(x)=5x-12x^2+3[/tex] is a quadratic polynomial with degree 2.
Thus by corollary of Fundamental theorem of algebra
The total number of roots in the given polynomial function must be 2.
Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.
A) 14.2 feet
B) 17.1 feet
C) 47.6 feet
D) 55.2 feet
Answer:
its 14.2
Step-by-step explanation:
Carly is 3 times her brother's age. The sun of their age is no more than 24 years.
brothers age = x
carly's age = 3x
3x +x <=24
4x<=24
x<=24/4 = 6
brothers age is x<=6
What is the domain and range of f(x) = |x + 6|?
domain: (negative infinite,infinite); range: f(x) (greater than or equal to) 0
domain: x (less then or equal to)-6; range: (negative infinite,infinite)
domain: x(greater than or equal to)-6 ; range: (negative infinite,infinite)
domain:(negative infinite,infinite) ; range: f(x) (less than or equal to) 0
Answer:
domain: (negative infinite,infinite); range: f(x) (greater than or equal to [tex]0[/tex]
Step-by-step explanation:
we have
[tex]f\left(x\right)=\left|x+6\right|[/tex]
The vertex of the function is the point [tex](-6,0)[/tex]
The domain is the interval--------> (-∞,∞)
The domain is all real numbers
The range is the interval ------> [0,∞)
[tex]f(x)\geq 0[/tex]
The range is all real numbers greater than or equal to zero
To better understand the problem see the attached figure
The sum of two numbers is 67. the smaller number is 3 less than the larger number. what are the two numbers?
The initial volume of a gas cylinder is 750.0 ml. if the pressure of a gas inside the cylinder changes from 840.0 mm hg to 360.0 mm hg, what is the final volume the gas occupies?
Answer:
[tex]V_2=1.75L[/tex]
Step-by-step explanation:
Use the Boyle's law which states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant. Mathematically this is:
[tex]P_1*V_1=P_2*V_2[/tex] (1)
Where:
[tex]P_1=Initial\hspace{3}pressure\\P_2=Final\hspace{3}pressure\\V_1=Initial\hspace{3}volume\\V_2=Final\hspace{3}volume[/tex]
Before attempting to solve the problem, let's do the pertinent conversions:
[tex]840mmHg*\frac{1torr}{1mmHg} *\frac{1Pa}{133.32torr} =6.3Pa[/tex]
[tex]360mmHg*\frac{1torr}{1mmHg} *\frac{1Pa}{133.32torr} =2.7Pa[/tex]
[tex]750ml*\frac{1L}{1000ml}=0.75L[/tex]
So, we got:
[tex]P_1=6.3Pa\\P_2=2.7Pa\\V_1=0.75L[/tex]
Now, let's isolate [tex]V_2[/tex] from (1) in order to find the final volume:
[tex]V_2=\frac{P_1*V_1}{P_2} \\\\V_2=\frac{6.3*0.75}{2.7} = 1.75L[/tex]
Find x if et = 3x+2 and em = 5x
Answer:
x = 6
Step-by-step explanation:
The centroid (T) always splits the lines so one side is 2/3 and the second is 1/3 of the entire median line. This can also be written as 2x + x. That being said, ET isn't equal to EM, it's only equal to 2/3 of EM so that's what you have to write.
3x + 2 = 2/3 * 5x
3x + 2 = 10/3 x
*3 (3x+2) = *3(10/3x)
9x+6 = 10x
-9x -9x
x = 6
The value of x is 6.
TrianglesThe polygon has three sides. the sum of all the internal angles is 180 degrees.
Given
ET = 3x+2
EM = 5x
To findThe value of x.
How to find the value of x?We know that the centroid of triangles divides it into 2:3.
Then
[tex]\begin{aligned} \dfrac{ET}{EM} &= \dfrac{2}{3} \\\\ \dfrac{3x+2}{5x} &= \dfrac{2}{3} \\\\ 3x+2 &= \dfrac{2}{3} * 5x \\\\ 3x+2 &= \dfrac{10x}{3} \\\\ 3x - \dfrac{10x}{3} &=-2\\\\ \dfrac{-x}{3} &= -2 \\\\ x &= 6\end{aligned}[/tex]
Hence the value of x is 6.
Thus the value of x is 6.
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If you know that two triangles are congruent, you know that any unmarked corresponding parts are also congruent by
What is the solution to the system of equations below? 2x - 5y = 11 and -2x + 3y = -9
In a certain county, the number of charter schools is 10 less than twice the number of alternative schools. We know that there are 46 charter schools in the county. How many alternative schools are in the county?
what is the answer for 5kx+6=7kx solve for x
There are 10 red marbles and 8 green marbles in a jar. if you take three marbles from the jar (without replacement), the probability that they are all red is:
There are 10 red marbles and 8 green marbles in a jar. So, the probability that all three marbles taken from the jar are red is 0.147.
Given :
Number of red marbles = 10
Number of green marbles = 8
Probability is the department of mathematics concerning numerical depictions of how likely the event is to happen or how likely it is that suggestion is genuine. The probability of an event could be number between 0 and 1 , where o shows difficulty of the event and 1 shows certainty.
Total number of marbles in a jar = 10 + 8 = 18
Total number of red marbles in a jar = 10
So, the probability that all three marbles taken from the jar are red is:
[tex]= \dfrac{10}{18}\times\dfrac{9}{17}\times\dfrac{8}{16}[/tex]
[tex]= 0.147[/tex]
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¿A Sandra qué le gusta hacer los viernes?
A A Sandra le gusta comer papas fritas los viernes.
B A Sandra le gusta comer agua los viernes.
C A Sandra le gusta beber pizza los viernes.
D A Sandra le gusta beber galletas los viernes.
All sides are congruent, opposite sides are parallel, and opposite angles are congruent (but not 90) describes which shape
What is the y-intercept of the line represented by the equation
Y=-3x+7
Write (7 + 3i) + (6 − i) as a complex number in standard form.
13 + 2i is (7 + 3i) + (6 − i) in standard form.
What are mathematical operations?
The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To add two complex numbers in standard form, we simply add the real parts and the imaginary parts separately.
(7 + 3i) + (6 − i) = (7 + 6) + (3i − i) = 13 + 2i
Therefore, (7 + 3i) + (6 − i) in standard form is 13 + 2i.
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The sum of 6 times petra's age and 8 times kathy's age is 162. kathy is 1 year more than twice as old as petra is. find each of their ages.
The saginaw bay tides vary between 2 feet and 8 feet. the tide is at its lowest point when time (t) is 0 and completes a full cycle in 16 hours. what is the amplitude, period, and midline of a function that would model this periodic phenomenon? amplitude = 3 feet; period = 16 hours; midline: y = 5 amplitude = 3 feet; period = 8 hours; midline: y = 3 amplitude = 6 feet; period = 16 hours; midline: y = 5 amplitude = 6 feet; period = 8 hours; midline: y = 3
Answer:
Option A
amplitude = 3 feet; period = 16 hours; midline: y = 5 amplitude = 3 feet;
Step-by-step explanation:
Given that The saginaw bay tides vary between 2 feet and 8 feet.
When we correspond these to sine curve we can say minimum 2 ft max 8 ft middle value being 5 ft
Period = 16 hours (since it completes one full cycle in 16 hours_
Amplitude = maximum - middle value or middle value-minimum
=[tex]8-5 = 5-2 = 3 ft[/tex]
Thus the equation would be as[tex]y = 3sin \frac{8}{\pi}+5[/tex]
Thus we find that minimum =2, max =8 middle line y=5
Amplitude = 3 ft and period = 16
Hence option A is right.
Which two segments are a base and its associated altitude of parallelogram QRST?
A. Segment T S is the base, and segment S R is the altitude.
B. Segment Q R is the base, and segment T U is the altitude.
C. Segment T S is the base, and segment T Q is the altitude.
D. Segment Q T is the base, and segment T U is the altitude.
Answer :- Option B is the right answer "Segment QR is the base, and segment TU is the altitude".
Explanation:-
The altitude or height of a parallelogram is the perpendicular line segment from the base to the opposite side (which may have to be extended) of the parallelogram. In the given figure, we can see that the altitude is TU=18 inches which is perpendicular to the base QR=20 inches.
Thus , option B is the correct answer. Segment QR is the base, and segment TU is the altitude.
in a survey respondents were asked which type of movie they watched most often. the bar graph shows how many males and how many females said they watched each type of movie most often.
how many more males said they watched action movies than drama movies
2
4
5
8
Answer:
Option D) 8
Step-by-step explanation:
We are given the following information in the question:
A bar graph is given that shows how many males and how many females said they watched each type of movie most often.
To find:
We have to find that how many males said that they watched action movies than drama movies .
In the bar graph:
Number of action movies watched by males = 13
Number of drama movies watched by males = 5
Number of males males said that they watched action movies than drama movies = 13 - 5 = 8
Males watched 8 action movies more than the drama movies.
Hence, the correct option is D.
Solve x + 9 = 18 - 2x
The solution to the equation x + 9 = 18 - 2x is x = 3.
What is the solution to the equation?Given the equation in the question:
x + 9 = 18 - 2x
To solve the equation x + 9 = 18 - 2x, first, collect and combine the x terms on one side of the equation and the constant terms on the other side:
x + 9 = 18 - 2x
Add 2x to both sides of the equation:
x + 2x + 9 = 18 - 2x + 2x
x + 2x + 9 = 18
3x + 9 = 18
Subtract 9 from both sides of the equation:
3x + 9 - 9 = 18 - 9
3x = 18 - 9
3x = 9
Isolate x by dividing both sides by 3:
x = 9/3
x = 3
Therefore, the value of x is 3.
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Plz Answer ASAP
1.) Danielle pays a car insurance of $126 every three months. Danielle pays her teenage daughter's $342 car insurance twice a year.
How much should Danielle include for car insurance in her monthly budget?
A. $70
B. $88
C. $99
D. $105
2.) Which of the following is a variable expense?
A. Car insurance
B. rent
C. Retirement contribution
D. Home repair
Joanna, Dana and Tracy shared some trail mix. Joanna ate 0.125 pound of trail mix, Dana ate 0.1 pound and Tracy ate 0.12 pound of trail mix. List the friends in order from least to greatest amount of trail mix eaten
We are given the following values:
0.125 pound
0.1 pound
0.12 pound
All values start with the same number which is 0.1, therefore the 0.1 is the smallest.
Next the two values are followed by 0.12, so 0.12 is the next smaller number.
So the largest number is 0.125.
Arranging from least to greatest amount of trail mix eaten:
Dana, Tracy, Joanna
secured debts must have?
they must have a collateral
Can someone please help me with math
Measurement is ___________ when it yields the same values across repeated measurement of the same event.
The answer is reliable. A measure is assumed to have a high reliability if it yields parallel results under steady conditions. It is the characteristic of a set of test scores that relates to the quantity of accidental or random error from the measurement procedure that might be rooted in the scores. Marks that are highly reliable are precise, reproducible, and constant from one testing time to another. To be exact, if the testing method were to be repeated with a different group of test takers, fundamentally the same results would be gotten.
The starting salaries of individuals with an mba degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. refer to exhibit 6-4. what is the probability that a randomly selected individual with an mba degree will get a starting salary of at least $30,000
The probability that a randomly selected individual with an MBA degree will receive a starting salary of at least $30,000, considering the mean salary is $40,000, and standard deviation is $5,000, is approximately 97.72%.
Explanation:The question pertains to the use of the normal distribution in probability, particularly in determining the probability of a randomly selected individual with an MBA degree getting a starting salary of at least $30,000. Given that the mean starting salary is $40,000 and the standard deviation is $5,000, we first need to standardize the salary amount to a z-score using the formula z = (X - μ) / σ. In this context, X refers to the salary amount in question, μ is the mean salary, and σ is the standard deviation.
So, z = (30,000 - 40,000) / 5000 = -2. This means the $30,000 salary is 2 standard deviations below the mean. When we look at the standard z-table, we find that the area to the left of z = -2 is approximately 0.0228. However, because we are looking for the probability of a salary being at least $30,000, we need to consider the area to the right, which is 1 - 0.0228 = 0.9772. So, the probability that a randomly selected MBA graduate will have a starting salary of at least $30,000 is approximately 97.72%.
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The mean weight of a litter of kittens is 3.1 pounds, with a standard deviation of 0.9 pound. Lawrence wants to know the weight of the kitten he is buying, but the seller only has the z-score of 1.22. How much does the kitten weigh?
The weight of kitten is 4.198 pounds
What is z-score?A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units.
Given that, the mean weight of a litter of kittens is 3.1 pounds, with a standard deviation of 0.9 pound, Lawrence wants to know the weight of the kitten he is buying, but the seller only has the z-score of 1.22.
Let x be the weight of the kitten
We know that,
z = (x- mean)/σ
Therefore,
1.22 = (x-3.1)/0.9
(1.22)(0.9) = x -3.1
x = 4.198
Hence, the weight of kitten is 4.198 pounds
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parallel lines intersect? true or false
Seventeen members of Troy's family are going to an amusement park during the week of their family reunion. Adult tickets cost $39.50 each and child tickets cost $31 each. If the total cost for admission to the part is $578, how many adults went to the park?
The equations y = -0.38x + 56.6 and y = 0.38x + 43.4 represent the percent of men and women, respectively, receiving bachelor's degrees, where x is the number of years since 1968. in approximately what year did the same percent of men and women receive bachelor's degrees?