The rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 can be found using the Rational Root Theorem.
The Rational Root Theorem states that if a polynomial has a rational root, it will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is -1 and the leading coefficient is 1. The factors of -1 are -1 and 1, and the factors of 1 are 1. Therefore, the possible rational roots of this polynomial are -1/1, 1/1, or -1 and 1.
We can test these possible roots by plugging them into the polynomial and seeing if the result is 0.
P(-1) = (-1)^3 + 3(-1)^2 + (-1) - 1 = -1 + 3 - 1 - 1 = 0
P(1) = (1)^3 + 3(1)^2 + (1) - 1 = 1 + 3 + 1 - 1 = 4
Therefore, the only rational root of this polynomial is -1.
So, the rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 are -1.
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Use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 13x + 5 as ordered pairs.
O (1, 18), (2, 31), (3, 44), (4, 57)
O (19, 1), (20, 2), (21, 3), (22, 4)
O (1, 19), (2, 20), (3, 21), (4, 22)
O (18, 1), (31, 2), (44, 3), (57, 4)
The solutions of the equation as ordered pairs is:
(1, 18), (2, 31), (3, 44), (4, 57)
How to use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 13x + 5 as ordered pairs?
In order to use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 13x + 5 as ordered pairs, substitute the values of x into the equation and calculate y. That is:
when x = 1:
y = 13(1) + 5 = 18
when x = 2:
y = 13(2) + 5 = 31
when x = 3:
y = 13(3) + 5 = 44
when x = 4:
y = 13(4) + 5 = 57
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Fabian is 3 years younger than twice Yemia's . If Fabian is 27 years old how old is Yemia?
Answer:
Yemia is 60
Step-by-step explanation:
Answer:
Yemia is 60
Step-by-step explanation:
(27 + 3) x 2 = 60
You want to show that KML is similar to FGH using Side-Side-Side Similarity Theorem. Complete the extended proportion that can be used to show such a similarity.
KM/?=?/FH=ML/?
A.) Fill in the blank: KM/?
B.) Fill in the blank: ?/FH
C.) Fill in the blank: ML/?
The extended proportion that can be used to show such a similarity is:
KM/ FG = KL/ FH = ML/ GH
What are similar triangles?Two or more triangles are said to have similar relations if on comparing their corresponding sides and measure of angles, there exist some common relations among them. Similarity of triangles can be expressed by some common terms in relation to their sides and angles.
In the given question, it has been stated that the triangles are similar using Side-Side-Side similarity theorem. Thus on comparison, the extended proportion that can be used to show such a similarity is:
KM/ FG = KL/ FH = ML/ GH
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State the degree of the polynomial.
x²y + x²y² − xy
Enter your answers in the boxes.
Answer:
Factor:
[tex]xy(xy+x-1)[/tex]
Evaluate:
[tex]xy(xy+x-1)[/tex]
This polynomial is a quadratic polynomial.
Step-by-step explanation:
TREES From point A,
the angle of elevation to the top of a pine tree is 42°.
From point B,
on the same side of the tree, the angle of elevation to the top of the tree is 50°.
If point A
and point B
are located 12
feet apart and are both at ground level, what is the approximate height of the tree to the nearest foot?
feet
Answer:
44 ft
Step-by-step explanation:
You want to know the height of a tree whose top is at angles of elevation of 42° and 50° from points 12 feet apart.
TangentThe tangent of an angle is related to the side lengths of a right triangle by ...
Tan = Opposite/Adjacent
This tells us the length of the side adjacent to the angle of elevation is ...
Adjacent = Opposite/Tan
ApplicationHere, the height of the tree is the side of the triangle opposite the angle of elevation, and the difference of adjacent sides is 12 ft:
12 = h/tan(42°) -h/tan(50°)
h = 12/(1/tan(42°) -1/tan(50°)) ≈ 12/(1.11061 -0.83910) ≈ 44.197
The approximate height of the tree is 44 feet.
If r varies inversely as t, but directly as the square of m. If r=32 when m-8 and 1-2, find r when m=6 and t=2.
The value of r is equal to 18.
How to determine the value of r?Mathematically, a proportional relationship or direct variation can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.x, and y represents the variables of a proportional relationship.Based on the information provided, we have the following:
r ∝ m²/t
r = km²/t
In order to have a proportional relationship and equivalent ratios, the variables r, m, and t must have the same constant of proportionality:
Constant of proportionality (k) = tr/m²
Constant of proportionality (k) = (2 × 32)/8²
Constant of proportionality (k) = 1.
For the value of r, we have:
r = km²/t
r = 6²/2
r = 18.
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What is the answer to this?
Answer:
$24,000
Step-by-step explanation:
20,000x(1+0.05x4)=20,000x1.2=24,000
Kendra's aunt sent her $50 for her birthday 10 years ago. At the time,
Kendra wasn't sure what she wanted to do with the money so she put
it in a piggy bank and forgot about it. She just found this $50 in the
piggy bank when she was cleaning her room. Over the past ten years
yearly inflation has averaged 2.46%. How much is Kendra's birthday
money worth now?
Because of the inflation of 2.46%, the $50 of Kendra is not worth of $62.3 after 10 years.
What is inflation?The amount that a collection of products and services have increased in price during a specific time frame, typically a year, is measured by inflation. One of the most well-known words in economics, perhaps.
Countries have experienced protracted periods of instability due to inflation.
Prices for goods and services are always subject to change in a market economy.
Some prices increase while others decrease.
When prices of products and services grow broadly rather than just for a few specific items, it is said to be inflation.
This means that today, for the same amount of money, you can buy less than you could yesterday.
So, we have: $50
Now, the inflation rate is 2.46%.
Then, 50/100 * 2.46
1.23
1.23 * 10
12.3
12.3 + 50 = $62.3
Therefore, because of the inflation of 2.46%, the $50 of Kendra is not worth of $62.3 after 10 years.
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An airplane climbs at an angle of 40 degrees with the ground. What is the ground distance it has traveled (to the nearest 100 ft) when it has attained an altitude of 2400ft
The airplane has traveled a ground distance of 2900 ft when it has attained an altitude of 2400 ft at an angle of 40 degrees with the ground.
Determine ground distanceThe ground distance that the airplane has traveled can be found using the trigonometric function of tangent. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the altitude (2400 ft) and the adjacent side is the ground distance we are trying to find.
We can use the formula:
tan(angle) = opposite/adjacent
Plugging in the given values:
tan(40) = 2400/adjacent
Solving for the adjacent side (ground distance):
adjacent = 2400/tan(40)
Using a calculator, we can find the value of tan(40) and then divide 2400 by that value to get the ground distance:
adjacent = 2400/0.8391
adjacent = 2860.67 ft
Rounding to the nearest 100 ft, the ground distance is 2900 ft.
Therefore, the airplane has traveled a ground distance of 2900 ft when it has attained an altitude of 2400 ft at an angle of 40 degrees with the ground.
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The graph of a quadratic function with vertex (0,3) is shown in the figure below find the domain and range
The domain of this quadratic function is {-∞, ∞}.
The range of this quadratic function is {3, ∞}.
How to determine of this quadratic function?In Mathematics, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Generally speaking, the domain of this quadratic function are all the x-values (independent value) that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞}.
Range = {3, ∞}
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What is the equation of this graph
Charlotte is enjoying a sunny day in the garden on the top of her apartment building. She hears a siren and
is curious where it is coming from. She looks over the edge of the roof and spots an ambulance stopped at
the park down the street from her apartment building. The angle of depression to the ambulance is 3.4°
and her apartment building is 40 feet tall. How far away is the ambulance from the front door of her
apartment building? Round your answer to the nearest tenth. Draw a picture to help you solve the problem.
?
Solving the provided question we can say that by Pythagorean theorem the ambulance from the front door of her apartment building is [tex]YT^2 = -252[/tex] .
what is Pythagorean theorem?The Pythagorean Theorem, often known as the Pythagorean Theorem, is the fundamental Euclidean geometry relationship between the three sides of a right triangle. The area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the right angle equals the sum of the squares that span its sides. It is sometimes written as the general algebraic notation a2 + b2 = c2.
Since XY is tangent to circle O at T, we know that angle OYT is a right angle.
Using the Pythagorean theorem in triangle OYT
[tex]YT^2 = OT^2 - OY^2 \\YT^2 = 18^2 - 24^2\\YT^2 = 324 - 576\\YT^2 = -252[/tex]
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A sketch of y= cos x° for-360 ≤x≤ 360 is shown.
a) State the coordinates of A.
A00
b) State the coordinates of B.
B(00
B
Y₁
Ax
The Coordinates for A is (π/2, 1).
and, the Coordinates for B is (-π, 0).
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
We have y= cos x.
So, when x = π/2 sin x have the maximum value which equals to 1.
Then ,the coordinates is (π/2, 1).
and, when x=π or x=-π then sin x =0
Then ,the coordinates is (-π, 0).
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What is the solution to the system of equations?{y=−5x+1}{−5x−y=−3}
Answer: [tex](0.2,2)[/tex]
Step-by-step explanation:
[tex]-5x-y=-3[/tex]
add y on both side of the equation
[tex]-5x=y-3[/tex]
add 3 on both side of the equation
[tex]y=-5x+3[/tex]
Then insert [tex]-5x+3[/tex] as y in the equation [tex]y =5x+1[/tex]
[tex]5x+1=-5x+3[/tex]
add 5x on both side of the equation
[tex]10x+1=3[/tex]
minus 1 on both side of the equation
[tex]10x=2[/tex]
divide by 10 on both side of the equation
[tex]x=0.2[/tex]
That is how you get x
To get y, you would sub 0.2 for x in the equation [tex]y=5x+1[/tex] or[tex]-5x-y=-3[/tex], I prefer the first equation
[tex]y=5x+1[/tex]
sub 0.2 for x
[tex]y=5(0.2)+1[/tex]
multiply 5 by 0.2
[tex]y=1+1[/tex]
add them up
[tex]y=2[/tex]
and there you go for y
The solution would be in a [tex](x,y)[/tex] form. So, [tex](0.2, 2)[/tex] would be our answer.
If f(x)=x squared +4x-5
show that (x-3) is a factor of the polynomial h(x)=f(x)-f(3)
Answer:
To show that (x-3) is a factor of the polynomial h(x) = f(x) - f(3), we need to use the definition of a polynomial factor. A polynomial factor is a polynomial that, when multiplied by another polynomial, results in the original polynomial.
First, let's evaluate f(3) to find the value of h(3).
h(3) = f(3) - f(3) = 0
Now let's examine the value of h(x) for any x other than 3.
h(x) = f(x) - f(3)
If (x-3) is a factor of h(x), then for any value of x other than 3, h(x) should be equal to zero.
So,
h(x) = (x-3)g(x)
where g(x) is another polynomial.
Therefore, by definition, (x-3) is a factor of h(x) = f(x) - f(3).
The cost of an air conditioner is $110. The cost to run the air conditioner is $0.35 per
minute.
What is the range of the situation above?
A function that models the total cost of running the air conditioner for the first 400 minutes is .
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Let the number of minutes be m.
Let the total cost be T.
Given the following data:
Cost of air conditioner = $130
Running cost = $0.25 per minute
Time = 400 minutes.
To write a function that models the total cost of running the air conditioner for the first 400 minutes:
How to solve a word problem.
First of all, we would write an equation to models the total cost of running the air conditioner for the first 400 minutes:
For the total time:
0.25m
For the total cost:
T= 130 + 0.25m
For the domain:
The value of m is the domain and it can be chosen from 0 to 130.
Domain (m) = [0, 130].
For the range:
A range represents the minimum and maximum value of a data set.
Thus, the value of T would be between 130 and 230.
Range = [130, 230].
For the intercept:
when x = 0, we have:
y = 130 + 0.25(0)
y = 130.
Intercept = [0, 130]
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Greta is a contestant on the kids' game show, Spend or Switch! When she makes it up on stage, host Guy Granger takes out a stack of one hundred-dollar bills. He divides the bills evenly among all 5 contestants on stage. Each contestant receives 4 one hundred-dollar bills. Which equation can you use to find the number of bills b in Guy Granger's stack?
Answer:
Step-by-step explanation:
If Guy Granger's gave each contestant 4 bills and there are 5 contestants, then you would multiply 4x5 which would give you 20. This is the amount of bills in Guy Granger's stack.
The quadrilateral is a trapezoid. What is the value of x?
A. 4
B. 5
C. 48
D. 25
If the quadrilateral is a trapezoid , then the value of x is = (b) 5 .
We know that the Midsegment of a trapezoid is parallel to each of the base and it's length is one half the sum of the lengths of the bases.
From the figure , we can observe that ⇒ side lengths are 21 units, 27 units , and the sides are parallel to each other.
From the given diagram of the trapezoid , the below expression is true:
that means : ⇒ 5x-1 = (21 + 27)/2 ;
⇒ 2(5x - 1) = 21 + 27 ;
⇒ 10x = 48 + 2 ;
⇒ 10x = 50
On Divide both sides by 10 ;
we have ;
⇒ x = 50/10 ;
⇒ x = 5 .
Therefore , for the quadrilateral the value of x is = 5 .
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The given question is incomplete , the complete question is
The quadrilateral in the below figure is a trapezoid. What is the value of x ?
(a) 4
(b) 5
(c) 48
(d) 25
Find the measure of the missing angle
Answer:
Step-by-step explanation:
a= 180-130
= 50 (angles on a straight line)
What is the least common multiple between of 5 and 9
whats the missing number?
Answer:180
Step-by-step explanation:
1-------60
2-------120
3-------x
4------240
n-------60*n
so, 3-----60*3=180
How many 750ml to ounces ?
There are 25.36 fluid ounces in 750 milliliters (mL). To convert mL to fluid ounces, multiply the volume in mL by the conversion factor of 0.033814.
There are 25.36 fluid ounces in 750 milliliters (mL).
To convert mL to fluid ounces (fl oz), you can use the conversion factor of 0.033814, which is the number of fluid ounces in one milliliter. Multiplying the volume in mL by this conversion factor gives the result in fluid ounces.
So, to convert 750 mL to fluid ounces, you can multiply 750 by 0.033814, which gives:
750 mL * 0.033814 = 25.36 fl oz
Therefore, 750 mL is equivalent to 25.36 fluid ounces.
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2. ALGEBRA LaToya Barnes' credit card uses the average-daily-
method of computing finance
balance-including-purchases
charges. Her card has a monthly periodic rate of 1.76% and
shows a finance charge of $7.64. Find her average daily balance
for the past billing cycle.
If ALGEBRA LaToya Barnes' credit card uses the average-daily-
method of computing finance balance-including-purchases charges. her average daily balance for the past billing cycle is 434.
What is the her average daily balance?The average daily balance can be found by using the formula:
Average Daily Balance = (Finance Charge / Monthly Periodic Rate)
Now we can plug in the values and solve for the average daily balance:
Average Daily Balance = (7.64 / 0.0176)
Average Daily Balance =434
Therefore, LaToya Barnes' average daily balance for the past billing cycle was 434.
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What do you call a nine sided polygon?
Answer:
a nonagon
Step-by-step explanation:
Fill The Blank ?a function is a rule that assigns to each value of the_____
In essence, a function is a rule that assigns to each value of the input set (also known as the domain), a unique value of the output set (also known as the range).
A function is a fundamental mathematical concept that is used to describe the relationship between two sets of values.
To understand the idea of a function, imagine a machine that takes in an input and produces an output. The input values are the domain of the function, and the output values are the range. A function can be represented as an equation, a graph, or a table. For example, the equation f(x) = x + 3 represents a function that takes in an input value x and produces an output value that is 3 greater than the input value.
One of the key features of a function is that each input value must have a unique output value. This means that if you input the same value into the function twice, you should get the same output value both times. In mathematical terms, we say that a function is well-defined if it has a unique output value for each input value.
Functions are used in a wide range of mathematical applications, from algebra and calculus to statistics and data analysis. They provide a powerful tool for describing and analyzing relationships between different sets of values.
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The company plans to find the center of the data an give a 5% raise to the employees who have been employee for at least those number of years.Find the mean and median,and explain which will be better from the employees prescriptive.
Number of years of each employed {11,6,32,7,18,4,9,1,15,9,5,27}
The mean is 11.25 and median is 8, and from the employees' perspective, the median would be a better measure of central tendency to use for determining the raise cut-off point.
The mean and medianTo find the mean and median, we can start by arranging the data in ascending order:{1, 4, 5, 6, 7, 9, 9, 11, 15, 18, 27, 32}
Mean:The mean is the average value of the dataset. We can find the mean by summing up all the values and dividing by the total number of values:
mean = (1 + 4 + 5 + 6 + 7 + 9 + 9 + 11 + 15 + 18 + 27 + 32) / 12
= 135 / 12
= 11.25
Therefore, the mean of the dataset is 11.25.
Median:The median is the middle value in the dataset. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
In this case, the dataset has 12 values, so we need to find the average of the 6th and 7th values:
median = (7 + 9) / 2
= 8
Therefore, the median of the dataset is 8.
From the employees' perspective, the median would be a better measure of central tendency to use for determining the raise cutoff point. This is because the median is not affected by outliers as much as the mean.
In this dataset, the value of 32 is much larger than the other values and could skew the mean upward, which would result in a higher cutoff point for the raise. On the other hand, the median is not affected by the outlier and provides a better representation of the central value of the dataset.
A 5% raise for employees who have been employed for at least 8 years (the median) would be more fair and reasonable for all employees.
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If 5x+2=52, then what does x equal?
Answer:
x=10
Step-by-step explanation:
If we subtract 2 from 52 we get 50 and ten mutiplys into 50.
How do I need to work this the answer at the bottom is 160
Answer:
178ft
Step-by-step explanation:
Split the shape up into pieces. If you make an invisible cut vertically from the 14 ft length you will realise you have a small triangle attached to a rectangle.
You can assume that the height of the triangle is equal to the 20 - 14 as the left side must equal the right side for this shape thus this invisible length is equal to 6 ft
Area of triangle: (6ft x 6ft)/2 = 18 ft^2
Area of rectangle: 20ft x 8ft = 160 ft^2
Area of total shape = 160 + 18 = 178ft
So you're correct
At the neighborhood grocery, 2.52.5 pounds of chicken breast cost \$23.50$23.50. Caroline spent \$34.78$34.78 on chicken breast. How many pounds of chicken breast did she buy, to the nearest hundredth of a pound?
What is the value of 156 kg in lbs?
The formula for converting kilograms (kg) to pounds (lbs) is to multiply the mass in kilograms by 2.20462262.The calculation for converting 156 kg to lbs is 156 x 2.20462262 = 344.7382612 lbs.
Thus, the value of 156 kg in lbs is 344.7382612 lbs.To better understand, we can break down the formula into steps. We start by multiplying the kilograms (kg) by 2. This results in 312, which is twice the mass in kilograms. We now add 0.20462262 to the result (312). This gives us a total of 312.20462262, which is the equivalent of 156 kg in lbs.The result of the formula is a unit of mass in the imperial system of measurement. The imperial system of measurement is used in the United States and Great Britain, and is based on pounds (lbs).To further illustrate, one kilogram is equal to 2.20462262 pounds. Thus, 156 kg is equal to 156 x 2.20462262 = 344.7382612 lbs.In conclusion, it is possible to convert kilograms (kg) to pounds.
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