Write a polynomial function f of least degree that has rational coefficients, a leading
coefficient of 1, and the given zeros of -1, 2, and -3i. Show all work.
The least degree polynomial function with rational coefficients and the given zeros, -1, 2 and 3i is f(x) =[tex]x^{2} -x -2(\sqrt{x} -9)[/tex]
What do we mean by polynomial function?
A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
For example, 2x+5 is a polynomial with an exponent of one.
So given zeroes are -1 , 2 and 3i
We have,
x = -1
x +1 =0
Similarly for 2
x = 2
x -2 = 0
Again, For 3i
We have, x = 3i
Rewrite as x = [tex]\sqrt{-9}[/tex]
For easy calculation, squaring on both sides
[tex]x^{2} = -9[/tex]
[tex]x^{2} +9[/tex] =0
So, the polynomial has the function:
(x + 1)(x - 2) ([tex]\sqrt{x} -9[/tex])
[tex]x^{2} - 2x +x -2 (\sqrt{x} -9)\\x^{2} -x -2(\sqrt{x} -9)\\[/tex]
Therefore, the least degree polynomial function with rational coefficients and the given zeros, -1, 2 and 3i is f(x) =[tex]x^{2} -x -2(\sqrt{x} -9)[/tex].
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graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to c is 4/5. in other words a change of 1 unit in x corresponds to a change of 4/5 units in y
The graph that represents the proportional relationship between x and y with a unit rate of 4/5 is shown in the image below.
How to Graph the Line of a Proportional Relationship?If the relationship between x and y is a proportional relationship, the equation that models the relationship between x and y can be expressed as y = mx. Here, the unit rate is represented by the value of in the equation.
This means that, the graph that represents the proportional relationship between x and y would have a slope of the value of m. m, which is the slope of the line, is the ratio of the rose of the line to the run of the line.
Thus, where m = 4/5, the equation that represents the proportional relationship would be:
y = 4/5x.
Therefore, the graph below shows the proportional relationship between x and y which is represented by the equation, y = 4/5x.
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32 oz for 3.29 or 24 oz for 2.59 find the better buy round to the nearest cent or hundreth.
Determine the unit price of 32 oz for $3.29.
[tex]\begin{gathered} \frac{3.29}{32}=0.1028 \\ \approx0.10 \end{gathered}[/tex]Determine the unit price for 24 oz for $2.59.
[tex]\begin{gathered} \frac{2.59}{24}=0.1079 \\ \approx0.11 \end{gathered}[/tex]The unit price of 32 oz for $3.29 is less. So the better buy round is 32 oz for $3.29.
Find the equation of a parabola with a focus of (0, 15) and directrix y = –15.
The equation of the parabola is x² = 60y after applying the concept of the parabola.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
Focus of (0, 15) and directrix y = –15.
Let (x, y) be on the parabola:
The distance between focus and (x, y):
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\rm d=\sqrt{(x-0)^2+(y-15)^2}[/tex]
[tex]\rm d=\sqrt{x^2+(y-15)^2}[/tex]
Directrix y = -15
y + 15 = 0
[tex]\rm \sqrt{x^2+(y-15)^2} = |y + 5|[/tex]
Squaring both sides:
x² + (y - 15)² = (y + 15)²
x² + y² -30y + 225 = y² + 30y + 225
x² -30y = 30y
x² = 30y + 30y
x² = 60y
Thus, the equation of the parabola is x² = 60y after applying the concept of the parabola.
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the ratio to use to find the area of the sector is ____.the area of the circle is ____. the area of the sector is ____.
Ratio = 1/6
Area of circle = 64π
Area of sector = 64π/6 = 32π
Explanation:Area of sector when measured in degrees:
[tex]Areaof\sec tor\text{ = }\frac{\theta}{360}\times\pi r^2[/tex]The ratio here is the ratio of the central angle to 360
ratio = 60/360 = 1/6
the ratio to use to find the area of the sector is 1/6
Area of a circle = πr²
r = radius = 8
Area of a circle = π × 8² = π × 8 × 8
Area of the circle = 64π
Area of sector:
θ = 60°
Area of sector when measured in degrees:
[tex]Areaof\sec tor\text{ = }\frac{\theta}{360}\times\pi r^2[/tex][tex]\begin{gathered} =\frac{60}{360}\times\pi\times8^2 \\ =\frac{1}{6}\times\pi\times8^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of sector = }\frac{64}{6}\pi\text{ (in simplest form)} \\ \text{Area of sector = }\frac{64}{6}\pi\text{ = }\frac{32}{3}\pi \end{gathered}[/tex]Plot the points on your graph paper to answer the question.
Answer:
y=2x
y=x+2
there's ur answer.
A person 1.85 m tall walks towards a lamppost on level ground at a rate of 0.5 m/sec. The lamp on the post is 5 m high. At which rate is the tip of the person's shadow moving toward the lamppost when the person is 4 I from the post? Please enter your answer in decimal format with three decimal places.
Using the Pythagorean Theorem and implicit differentiation, it is found that the tip of the person's shadow is moving toward the post at a rate of 0.393 m/sec when the person is 4 m from the post.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom that relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, we have that:
The distance d between the person's shadow and the lamp is the hypotenuse of a right triangle.The legs are the person shadow and the lamp.Hence the following relation between these variables is established:
d² = x² + y².
Applying implicit differentiation, the rate of change of the distance is given as follows:
[tex]d\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The height remains constant, hence:
[tex]\frac{dy}{dt} = 0[/tex]
The other parameters are given as follows:
y = 5 - 1.85 = 3.15 m (vertical distance).x = 4 m (distance of the person from the post).dx/dt = 0.5 m/s (velocity of the person).Hence the distance at the desired instant is:
d² = 4² + 3.15²
d = sqrt(4² + 3.15²)
d = 5.091 m
The rate of change of the distance is found as follows:
5.091dd/dt = 4 x 0.5
dd/dt = 2/5.091
dd/dt = 0.393 m/sec.
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Jerome is constructing a table of values that satisfies the definition of a function.
It is important to know that a function associates to every elemento of x a unique element of y. In other words, x-values should no repeat. Having said that, we can't fill the blank with -1, 0, 11, or 17.
Hence, the answers are -5 and 2. Find the value of p if the sum of negative 4
and the quantity p divided 5 is sixteen.
A. 4
B. -60
C. 60
D. 100
Answer:
100
Step-by-step explanation:
[tex] - 4 + \frac{p}{5} = 16[/tex]
Multiply through by the LCM which is 5
[tex] 5 \times \frac{ - 4}{1} + 5 \times \frac{p}{5} = \frac{16}{1} \times 5[/tex]
[tex] - 20 + p = 80[/tex]
[tex]p = 80 + 20[/tex]
[tex]p = 100[/tex]
can someone please help me out with consumer math. please and thank you
currency-
exchange rate- c
extrinsic value - g
fiat monetary system- e
gold standard - a
intrinsic value
trade
Order the following functions by growth rate
The following functions have the following growth rates:
2/N < 37 <√N < N < N log log N < N log N < N log(N^2) < N . log^2 . N < N^1.5 < N^2 <N^2. log N < N^3 < 2^N/2 < 2^N
How can you determine a function's growth rate?
The present value is divided by the past value, multiplied to the 1/N power, and then one is subtracted to get the formula for the average growth rate over time approach.
How may the growth rates of two functions be compared?
Determine the limit limxf(x)g(x) lim x f (x) g (x) given the functions f(x) and g(x).The growth rate of f(x) is a times the growth rate of g(x) for sufficiently large x if the limit in Step 1 is a finite constant a0 a 0.To learn more about functions click on the link below:
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Jolene invests her savings in two bank accounts, one paying 4 percent and the other paying 12 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 8740 dollars. How much did she invest at each rate?Amount invested at 4 percent interest is $Amount invested at 12 percent interest is $
We will have the following:
First, we recall that the simple interest formula is given by:
[tex]A=P(1+rt)[/tex]Now, for the accounts that are described in the problem we will have that:
[tex]\begin{gathered} A_1+2P=2P(1+(0.04)(1))\Rightarrow A_1+2P=2P(1.04) \\ \\ A_2+P=P(1+(0.12)(1))\Rightarrow A_2+P=P(1.12) \end{gathered}[/tex]Now, we have that:
[tex]A_1+A_2=8740[/tex]Then:
[tex]\begin{gathered} A_1+A_2+2P+P=2P(1.04)+P(1.12) \\ \\ \Rightarrow8740+3P=3.2P\Rightarrow8740=0.2P \\ \\ \Rightarrow P=43710 \end{gathered}[/tex]So, the amount invested at 4% interest is $87 420.
And, the amount invested at 12% interest is $43 710.
one afternoon the shadow of a flagpole is 21 feet long at the same time the shadow of 109 foot high building is 54 feet long what is the approximate Height of the flag pole
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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What is the contrapositive of the following sentence?If two triangles are congruent, then their corresponding angles are congruent.
Given:
If two triangles are congruent, then their corresponding angles are congruent.
Contapositive statement:
If two triangles are not congruent , then their corresponding angles are not congruent.
Option C is the correct answer
If 5 friends want to share 1.25 of a pizza evenly how much pizza would each person get?
Answer:
0.25
Step-by-step explanation:
1.25 ÷ 5 = 0.25
Answer = 0.25
Hope this helps!
Btw, Brainliest if correct, thanks!
g(9)+h(-14) if g(x)=14-2/3x and h(x)=-x-7?
The value of g(9) + h(-14) is 15.
We are given two functions, h(x) and g(x).The function h(x) is defined as given below:The function h(x) equals -x - 7.The function g(x) is defined as given below:The function g(x) equals 14 - (2/3)x.We have to find the sum of g(9) and h(-14).To find g(9), replace "x" with 9 in the definition of function "g".g(9) = 14 - (2/3)*9g(9) = 14 - (2*3)g(9) = 14 - 6g(9) = 8To find h(-14), replace "x" with -14 in the definition of function "h".h(-14) = -(-14) - 7h(-14) = 14 - 7h(-14) = 7g(9) + h(-14) = 8 + 7g(9) + h(-14) = 15To learn more about functions, visit :
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Use the drawing tool(s) to form the correct answer on the provided graph.
The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x) = 2 f (x - 1)
ights reserved
Drawing Tools
Select
Line
Click on a tool to begin drawing
-8
-6 4
Undo
Reset
The finished graph of g(x) = 2f(x - 1) would be as seen in red.
What is defined by the term transformation?Image transformations usually involve the modification of various bands of data, either from a single source images or from two or more images acquired at different times of the same area.We were provided a graph of the function f(x).
g(x) = 2f is another function definition (x -1).
Now we must use the drawing tool(s) to create the proper graph of a function g(x) = 2f (x -1).
which can be discovered through transformation.
f(x) becomes f (x-1)
Then, f(x-1) becomes 2f (x-1)
f(x-1) shifts this same graph of f(x) by one unit to the right.
Whereas 2f(x-1) extends the graph of f(x-1) by a factor of 2. So we just need to double the y-coordinates of the points on the graph.
As a result, the finished graph of g(x) would be as seen in red.
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how do I graph r=6+3sintheta ?
Given:
[tex]r=6+3\sin \theta[/tex]Let's graph the equation.
Apply the formula:
[tex]r=a\pm b\sin \theta[/tex]Where:
a = 6
b = 3
Thus, we have the following:
Subsitute -θ for θ to know thw axis of symmetry:
[tex]\begin{gathered} r=6+3\sin (-\theta) \\ \end{gathered}[/tex]Now, solve for θ = 1 and -1:
[tex]\begin{gathered} r=6+3\sin (1) \\ r=6.05 \\ \\ r=6+3\sin (\text{ -1)} \\ r=5.94 \end{gathered}[/tex]Since sinθ is not equal to sin(-θ), the pole will be the point of symmetry.
To find the x-intercept, substitute 0 for θ:
[tex]\begin{gathered} r=6+3\sin \theta \\ \\ r=6 \end{gathered}[/tex]Hence, the limacon will cross the x-axis on both sides at x = 6 and -6.
Since the addition is with the sine function, the limacon will face down.
Now, input different values for θ and solve for r.
We have:
When θ = pi/2:
[tex]r=6+3\sin (\frac{\pi}{2})=9[/tex]When θ = pi:
[tex]r=6+3\sin (\pi)=6[/tex]When θ = 9pi/6:
[tex]r=6+3\sin (\frac{9\pi}{6})=3[/tex]Thus, we have the points:
[tex](\frac{\pi}{2},9),(\pi,6),(\frac{9\pi}{6},3)[/tex]Using the coordinates we have the graph:
The x-intercept of 2x + 3y = 12 is (0,4).A.TrueB.False
The x intercept is the value of x when y = 0
Looking at the equation,
2x + 3y = 12
If we substitute y = 0 into the equation, it becomes
2x + 3*0 = 12
2x + 0 = 12
2x = 12
x = 12/2
x = 6
Therefore, the statement is false
Which triangle is similar to △JKH?
1. △MKN
2. △JOG
3. △MQL
4. All triangles are similar to △JKH
Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN
What are similar triangles in geometry?Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.
The given parameter is Line a is parallel to Line b, which gives: a║b
Two triangles are similar if they satisfy the following conditions:
Two angles in one triangle are equal to two angles in the other triangle.Each of the three corresponding sides of the two triangles are proportional.Two sides of one triangle are proportional to the corresponding two sides on the other triangle, and the included angle between the specified two sides in both triangles are congruent.According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN
Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN
Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.
The correct option for the triangle similar to ΔJKH is option 1. ΔMKN
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Which equation represents a proportional relationship A y=3x/4B y=3/4x C y=3x/4 +1D y=3/4x +1
Answer: Out of the given options, we need to pick a relationship that is proportional:
In general, an equation that represents a proportional relationship has the following form:
[tex]y=kx[/tex]Therefore, the following is a proportional equation:
Option-(A)
[tex]\begin{gathered} y(x)=\frac{3}{4}x \\ k=\frac{3}{4} \end{gathered}[/tex]Explanation:
Because there is a constant multiple or a coefficient, and it indeed matches the form of equations that are proportional.
when Angel left his house in the morning his cell phone battery was partially charged. Let B represent the charge remaining and Angels battery, as a percentage, T hours since Angel left his house. A graph of B is shown below. Write an equation for fee then State the slope of the graph and determine its interpretation in the context of the problem
Graph the system of equations 2y=8x+18 24+4y=x
Answer:
draw the graphic vertical and edges line
put the dot on line
And put the 2y=8×+18 24+4y=×
5) Determine the probability distribution's missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
For the given probability distribution, the missing value is 5/17.
What is probability distribution?A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.
For the given distribution,
Let the missing value be x
we know that sum of probabilities = 1
⇒ 0 + 0 + 7/17 + x + 5/17 = 1
⇒ 12 / 17 + x = 1
⇒ x = 1 - 12/17
⇒ x = 5 / 17
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Find the scale factor of APMN to AZXY. * X 4 b Z 6 10 9 NV
Answer:
The scale factor is 5 / 2
Explanation:
The scale factor is the ratio of the side lengths of the bigger triangle to the smaller triangle.
The scale factor is also the ratio of the corresponding sides of the two traingles.
The ratio of MP to XZ is
[tex]\frac{MP}{XZ}=\frac{10}{4}[/tex]Simplification gives
[tex]\frac{5}{2}[/tex]Hence, the scale factor is 5 /2 or 2.5.
using trig to find sides
Step 1: Problem
Find the measure of
Step 2: Concept
Use trigonometry ratio to find the value of angle x.
Step 3: Method
Given data
Opposite = 3.2 side facing given angle
Adjacent = 5
[tex]\begin{gathered} U\sin g\text{ tagent formula} \\ \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \tan x\text{ = }\frac{3.2}{5} \\ \tan x\text{ = 0.64} \\ x\text{ = }\tan ^{-1}\text{ 0.64} \\ x\text{ = 32.6} \end{gathered}[/tex]Step 4: Final answer
What is the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}?
O {1, 2, 3, 4)
O {2, 4, 6}
O (2, 4)
O {1, 2, 3, 4, 6}
Answer:
(b) {2, 4, 6}
Step-by-step explanation:
You want the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}.
RangeThe range of a relation is the set of possible output values. When values are listed as ordered pairs, it is the set of second numbers of those pairs.
The list of second numbers is ...
2, 4, 2, 6
When these are expressed as a set, duplicates are removed, and they are listed in order:
{2, 4, 6} . . . . the range of the relation
Divide. Reduce your answers to lowest terms.5/8 divide (-3 3/4)
Given data
5/8 divided by (-3 3/4)
Firstly, convert the mixed fraction into an improper fraction
[tex]\begin{gathered} -3\text{ }\frac{3}{4}\text{ can be converted to the below improper fraction} \\ -3\text{ }\frac{3}{4}\text{ = -}\frac{(4\text{ x (3) + 3}}{4} \\ -\text{ 3}\frac{3}{4}\text{ = - }\frac{12\text{ + 3}}{4} \\ -\text{ 3 }\frac{3}{4}\text{ = - }\frac{15}{4} \\ \text{Therefore, 5/8 divided by - 15/4} \\ \frac{5}{8}\text{ / -}\frac{15}{4} \\ \frac{5}{8}\text{ x -}\frac{4}{15} \\ =\text{ }\frac{-20}{120} \\ =\text{ - }\frac{1}{6} \end{gathered}[/tex]Answer = - 1/6
A triangular pane of glass has a height of 48 inches and an area of 432 square inches. What is the length of the base of the pane? The length of the base of the pane is inches.
We can express the area of a triangle as half the product of its base and height:
[tex]A=\frac{b\cdot h}{2}[/tex]Then, we can express the base in function of the known variables (area and height) as:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ 2A=b\cdot h \\ b=\frac{2A}{h} \end{gathered}[/tex]We replace with the known values (A=432 sq in, h=48 in) and calculate the base b:
[tex]b=\frac{2\cdot432\text{ in}^2}{48\text{ in}}=18\text{ in}[/tex]Answer: the base is 18 inches.
NEED HELP URGENTLY!!!!!
20. Write a word problem such that the equation
to be formed for solving the problem is
QUESTION 6x +4(x - 10) = 140.
OPEN
In linear equation, x = 18 is the value of x in equation .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.6x +4(x - 10) = 140.
6X + 4X - 40 = 140
10X = 140 + 40
10x = 180
x = 180/10
x = 18
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