Step-by-step explanation:
"integral" means here that the factors in the polynomial are integers.
we have 3 zeros.
the least degree of a polynomial with 3 zeros is 3.
and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).
or 4 zeros (at least 4th degree).
it in general n zeros (at least nth degree).
constructing this out of the given zeros is easy.
what happens, when I multiply something by 0 ? the total result will be 0.
and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.
what expression in x turns 0, when x = -1/3 ?
well : x + 1/3 or with integers 3x + 1 (multiplied by 3)
and for x = 2/3 ?
x - 2/3 or with integers 3x - 2
and for x = -1/4 ?
x + 1/4 or with integers 4x + 1
so, our polynomial function (of at least 3rd degree) is then
(3x + 1)(3x - 2)(4x + 1)
basically this could be already the result, depending on what your teacher wants.
for the fully extended form we need to do the multiplications :
(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2
(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =
= 36x³ - 3x² - 11x - 2
the requested polynomial function is
f(x) = 36x³ - 3x² - 11x - 2
. The number or expression that remains when an expression divides another expression.
Answer:
thanks for the imformation
A general formula for a parabola is y2=4px. what is the value of p in the equation y2=−4x?
The value of p is -1 in the given equation of of parabola.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point called focus and a line called the directrix.
Equation for a Parabola
The general formula or the equation for representing a parabola is given by,
y² = 4px
Here, (h,k) being the vertex of the parabola,
y = a(x-h)² + k
x = b(y-k)² + h
The focus of this parabola is given by (p, 0).
The directrix of the parabola is the line drawn perpendicular to the y-axis and traversing the point (-p, 0). The directrix is parallel to the parabola's axis.
What is the value of p in the equation for parabola?
The given equation is,
y² = -4x
Comparing this equation with the general formula of the parabola, we get,
p = -1
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In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-port
shots. In he second half, he player scored the same number of 3-point shots as the number of 2 point slots scored n
the first half. Which expression represents the total number of points the player scored in the game?
O 2r + 3r + 9
© 2r + 3 + 9
O 2r + 3r + 9x
© 2 + 3r + 9
Save
Answer: I thin The first one 2r+3r+9
Step-by-step explanation: Because he scored a number of 2 port shots which means he scored more than one but the 9 points is just 9 points from free throws which gives only 1 point each and 3 port shots and much as 2 point shots so 3r also
2r+3r+ just 9
explain please thanks
Answer:
26542%
Step-by-step explanation:
12,209,400/46,000 = 265.421
265.421 × 100 ≈ 26542%
What is the variable of f(3) in the function below? f(x) =2^x
Hello !
We replace x by 3.
[tex]f(3) = {2}^{3} = 8[/tex]
Have a nice day ;)
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We have the expression -:
[tex]\boldsymbol{\sf{f(x)=2^x}}[/tex], and we're asked to find
[tex]\boldsymbol{\sf{f(3)}}[/tex].
To do that we put in the value for x (3)-:
[tex]\boldsymbol{\sf{f(3)=2^3}}[/tex].
Evaluate-:
[tex]\boldsymbol{\sf{f(3)=2\times2\times2=8}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
A llhe intersects the points
(4, -2) and (3, 3).
m = -5
Write an equation in point-slope form
using the point (4, -2).
y- [?] =[?]
(x-[?])
Answer:
y + 2 = -5(x - 4)
Step-by-step explanation:
Point-slope form is the following: [tex]y-y_{1}=m(x-x_{1})[/tex], where m is the slope of the line and [tex](x_{1}, y_{1} )[/tex] is a point on the line. We are already given all of the information we need, so all we have to do is write it out. We are told that the slope (m) is -5, and the point the question wants us to use is (4, -2), though either of the points given would work. If we plug in the quantities, we get that y - (-2) = -5(x - 4), or y + 2 = -5(x - 4)
what happens when the multiplicity of a real root is even
a. the graph crosses the y-axis
b. the graph crosses the x-axis
c. the graph is tangent to the y-axis
d. the graph is tangent to the x-axis
When the multiplicity of a real root is even, the graph of the function neither crosses nor is tangent to the x-axis. The correct answer is (c) the graph is tangent to the y-axis.
When a real root has an even multiplicity, it means that the corresponding factor appears multiple times in the factored form of the polynomial. In terms of the graph of the function, this means that the graph touches the x-axis at that root but does not cross it.
Since the graph touches the x-axis without crossing it, it remains on one side of the axis. This behavior indicates that the graph is tangent to the x-axis at the root with even multiplicity.
However, the graph can still intersect or cross the y-axis at a different point depending on other factors or terms in the polynomial. Therefore, option (a) "the graph crosses the y-axis" may or may not be true depending on the overall behavior of the function. The statement in option (b) "the graph crosses the x-axis" is incorrect for an even multiplicity root. Option (d) "the graph is tangent to the x-axis" is also incorrect for an even multiplicity root. Hence, option (c) "the graph is tangent to the y-axis" is the correct choice.
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Maureen says that if a system of linear equations has three equations, then there could be exactly two solutions to the system. Is
Maureen correct? Justify your reasoning.
Answer:
Yes, Maureen is correct. If a system of linear equations has three equations, then there could be exactly two solutions to the system. This is because, in general, a system of linear equations with three variables will have three equations. However, if two of the equations are the same, then there will only be two equations. In this case, there will be two solutions to the system.
Step-by-step explanation:
Find the value of x for which ABCD must be a parallelogram.
1
7
14
28
Note:This better be worth my 27 points
Answer:
A. 1
Step-by-step explanation:
18-4x=7x+7
Use this equation to find x.
Simplify.
18-4x=7x+7
Subtract 7 from both sides.
11-4x=7x
Add 4x to both sides.
11=11x
Divide 11 from both sides.
x=1
Hope this helps!
CAN SOMEONE HELP ME PLEASE:)<3
Answer: D. Cannot be determined
Step-by-step explanation: There are 3 postulates we can use for determining similar triangles.
There is Side Side Side (SSS) Postulate, which requires you have 2 sides of each triangle that are the same proportion as the other triangle. For example, in a triangle ABC, if 2 sides are 5 and 7, and in a triangle DEF, if 2 sides are 10 and 14, then the proportions 5/10 ( 1/2) and 7/14 (1/2) are equal. Thus these are similar triangles and the scale is 1/2.
There is Angle Angle (AA) postulate. If 2 angles are the same to another 2 angles in another triangle, then the two triangles are automatically similar.
The last is Side Angle Side (SAS), which requires you to have an angle that is congruent to another angle in a different triangle, and the angle is in between 2 sides that are proportionally equal to another triangle that also has the same angle in 2 sides. For example, if triangles ABC have angles A, B and C, and angle A is the same equal degrees to another angle in a triangle D, and both A and D are in between 2 sides (i.e DE and AB) that are proportionate (e.g DE and AB are proportionate.) The triangles are then similar.
None of these postulates can be applied to our given problem. Let's see why.
For Angle-Angle, we don't have 2 congruent angles. We have 2 right angles, but that's only 1 angle.
For Side Side Side, we don't have 2 sides given on each triangle, let alone proportionate ones.
For Side Angle Side, we don't even have 2 sides for each triangle given, so this cannot be used either.
Express in exponential form.
log(10)0.001 = -3
Answer:
this gvfyftvyccg c
Step-by-step explanation:
Triangles P and Q are similar.
Find the lengths of the sides:
Triangle P—> CA=9cm AB=4cm BC=?
Triangle Q—> XY=16cm YZ=48cm ZX=?
Answer:
if i labeled the triangle correctly BC= sqrt 97, ZX=32sqrt 2
Step-by-step explanation:
join my stream and tell me how to label the triangle
(ChildOfHermes)
A bag has 20 cubes in it. 6 of the cubes are
green.
You take one cube out of the bag at random.
Which four values below show the probability
that you take out a cube that is green?
6
14
6%
0.3
30% 0.6
3 6
5 20
6
10
60%
3
10
0.03
6
26
Answer: 0.3, [tex]\frac{6}{20}[/tex], [tex]\frac{3}{10}[/tex], 30%
Step-by-step explanation:
We will divide wanted outcomes by possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes, green cubes}}{\text{possible outcomes, cubes in bag}} =\frac{6}{20}[/tex]
Now, we will find four values equivalent to [tex]\frac{6}{20}[/tex]. See attached.
helppp pleaseee quick points
The required algebraic expression is Y = 3X + 2
This table describe the relation between x and y
x = 2 3 4 5
y = 8 11 14 17
What is algebraic expression?Alegebraic expression consists of constant and variable. eg x, y, z etc.
As the data given in the table, we conclude that:
1) The difference in the values of y is 3.
2) When we multiply this difference by x and add 2 it gives the next value of y.
so the from above discussion Y = 3X + 2
Thus, The required algebraic expression is Y = 3X + 2
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Use the substitutions u= 1/x^2 and v= 1/y^2 to solve the system of equations. express numbers as integers or simplified fractions.
-5/x^2 + 1/y^2 =-16
13/x^2- 1/y^2 =48
Answer:
-5 u + 1 v = (-16)
12 u - 1v = 48
adding,
7 u = 32
u = 32/7V = (-16) + 5(32/7)
V = (-16) +160/7
V = -112 + 160/7
V = 48/7Work out the rule for the nth term then work out the 100 term
th
a) 3, 5, 7, 9, 11, 13....
b) 12, 20, 28, 36, 44....
c) 19, 29, 39, 49, 59....
d) 7, 10, 13, 16, 19....
e) 14, 20, 26, 32, 38....
f) 55, 60, 65, 70, 75...
g) 8, 17, 26, 35, 44....
3/8 TIMES 2/5 =
SIMPLIFIED
Answer:
3/20
decimal form: 0.15
Question content area top Part 1 Three friends all live on the same street that runs west to east. lives blocks from . lives from . If the street is represented by a number line and 's house is located at 0, what are the possible locations for 's house?
Based on the information, it can be inferred that Carl's house is 6 blocks from Ann's house.
How to identify where each friend's house is?To identify where each friend's house is, we must graph the information provided as shown below.
Once we have made the graph we will identify that Carl's house is 6 blocks east of Ann's house.
Note: This question is incomplete because there is some information missing. Here is the missing information:
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the function f(x) is shown below
Answer: 2
Step-by-step explanation:
A function composed with its inverse outputs the original input.
Allen is horrible at managing his money. For example, he
recently invested $100,000-part of it in a company that
makes "fish-flavored" chicken and the rest in a company
that makes spray-on vitamins. Somehow he managed to earn
a 3% profit on the fish-flavored chicken investment and 1%
profit on the spray-on vitamin deal. If Allen made a profit
of $2,600 from both investments, how much did he invest in
the fish-flavored chicken company?
Answer:
$80,000
Step-by-step explanation:
Define the variables:
Let x = "fish-flavored" chicken company investment (in dollars)
Let y = spray-on vitamins company investment (in dollars)
If Allen invested a total of $100,000:
⇒ x + y = 100000
Given:
3% profit on "fish-flavored" chicken investment 1% profit on pray-on vitamins investmentTotal profit = $2,600⇒ 0.03x + 0.01y = 2600
Rewrite the first equation to make y the subject:
⇒ y = 100000 - x
Substitute into the second equation and solve for x:
⇒ 0.03x + 0.01(100000 - x) = 2600
⇒ 0.03x + 1000 - 0.01x = 2600
⇒ 0.02x + 1000 = 2600
⇒ 0.02x = 1600
⇒ x = 80000
Therefore, Allen invested $80,000 in the "fish-flavored" chicken company.
The sides of this rectangle are marked off in centimeters. If the rectangle is enlarged proportionally so that the longer side is 35 cm, how long will the shorter side be?
PLEASE I REALLY NEED HELP (the answer is not 10)
the length of the shorter side is:L = 13.125cm
how long will the shorter side be?
In the longer side we have 8 segments.
We know that the side measures 35 cm, then each one of the 8 segments measures:
35cm/8 = 4.375cm
Now, we can see that in the shorter side we have 3 of these segments.
Then the length of the shorter side is:
L = 3*(4.375cm) = 13.125cm
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Can someone please help me solve this question? Pls provide a step by step explanation too… Ty!
Answer:B 1/2
I can't type math symbols well in BRAINLY, so I use pictures╯﹏╰
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.
Team Low High Range Mean Median IQR σ
Team L 4 17 13 9.4 9 9.75 4.8
Team M 6 14 8 9.7 9.5 6.25 3.2
Team N 1 20 19 13 14.5 4.75 5.6
Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically.
Answer:
PART A:
The range, the IQR (inter-quartile range) and the standard deviations are measures which are used to measure the spread of a data set.
A dataset is more consistent relative to another data set when the standard deviation is less than that of the other data set.
From the table, it can be seen that Team C has the least standard deviation.
Therefore, If the club wants to award the team that has the most consistent scoring among its team members, team C should be chosen.
PART B
The mean and the median is a measure of center of a data set.
The mean describes the average of a data set.
From the table, it can be seen that Team B has the highest average score.
Therefore, If the club wants to award the team with the highest average score, team B should be chosen.
Question 3(Multiple Choice Worth 1 points) (08.03 LC) A box plot is shown below: A box and whisker plot is shown using a number line from 20 to 45 with primary markings and labels at 20, 25, 30, 35, 40, 45. In between two primary markings are 4 secondary markings. The box extends from 26 to 38 on the number line. A line in the box is at 31. The whiskers end at 20 and 43. The title of the art is Visitors at the Exhibition, and below the line is written Number of Visitors. What is the median and Q1 of the data set represented on the plot? Median = 31; Q1 = 26 Median = 30; Q1 = 26 Median = 31; Q1 = 20 Median = 30; Q1 = 20
The median in the box plot is: 31
Q1 (lower quartile) = 26
What is the Median and Q1 of a a Data in a Box Plot?The median is the value at the vertical line that divides the box.
The Q1 (lower quartile) is the value at the beginning of the edge of the box.
Thus, from the given box plot, we have the following:
Median = 31
Q1 (lower quartile) = 26
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A carnival tent is set up using a 32-foot pole as the center. The Support wires each have an angle of elevation of 38 degrees from the ground to the top of the pole. Approximately how many feet of wire is needed for one support for the tent?
Answer:
about 52 feet
Step-by-step explanation:
The figure is omitted--you may draw it to confirm my answer.
sin (38°) = 32/x
x sin (38°) = 32
x = 32 / sin (38°) = about 52 feet
A, B, and C are midpoints of ∆XYZ. What is the length of yz
Answer:
Step-by-step explanation:
Comment
When you join 2 consecutive midpoints with a line between them, the length of that line is 1/2 the length of the side opposite the line you just drew.
In other words 24 is 1/2 the length of yz.
Solution
1/2 yz = AB
AB = 24
1/2 yz = 24 Multiply both sides by 2
2(1/2 yz) = 2*24
yz = 48
Answer
yz = 48
New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as _____. Group of answer choices joint probability sample information conditional probability expected utility
New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as SAMPLE INFORMATION.
Hence, 2nd option is the best choice.
A statistical concept called joint probability determines the chance that two events will occur simultaneously and at the same time.
A sample is a collection of people, things, or things used in the study that is taken for analysis from a wider population. To enable us to extrapolate the study sample's findings to the entire population, the sample must be representative of the population. Sample information is the collection of the information of the sample.
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
The expected utility of a course of action is a weighted average of the utilities of each of its potential outcomes, where the utility of a potential result indicates how much it is preferred to the alternatives.
In the question, we are asked what will be the new information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities called.
As we are to name the information, it will be called sample information, from the above-discussed points.
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Prove experimentally that an exterior angle is formed by producing a side of a triangle equals to the sum of non adjacent interior angle. .
It is proved in the answer that an exterior angle of the triangle equals the sum of two opposite interior angles.
What is the exterior angle property of a triangle?If a triangle's side is created, the outside angle that results is equal to the product of the two opposite internal angles.
In the figure given below we can see:
∠BCD is the exterior angle of the triangle
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum property of a triangle)
∠BCA + ∠BCD = 180°(Linear pair)
From both equations we can say that:
∠ABC + ∠BAC + ∠BCA = ∠BCA + ∠BCD
∠ABC + ∠BAC = ∠BCD
Hence Proved
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Which graphs do not show a constant rate of change? Check all that apply.
On a coordinate plane, a parabola opens down.
On a coordinate plane, a line has a negative slope.
On a coordinate plane, a horizontal line is graphed.
On a coordinate plane, a curve curves downwards.
Answer:
a horizontal line is graphed
Step-by-step explanation:
It does not change it will always stay at the same y but just different x.
The rate of change/slope is the change in y divided by a corresponding change in x.
Hi. . .
A n s w e r : -
A, and D.
E x p l a n a t i o n :Cause- A, and D do not show the constant rate of the change.
Hope It Helps . . .
The angle between the lines joining the origin to the points of intersection of the straight line y = 3x + 2 with the curve x² + 2xy + 3y² + 4x + 8y - 11 = 0 is?
The angle between the lines joining the origin to the points of intersection of the degenerated elipse and the straight line is approximately 136.635°.
What is the measure of a triangle?
We have the graphs of a degenerated ellipse and a line, which intercept each other at points (x₁, y₁) = (-0.293, 1.121) and (x₂, y₂) = (- 1.707, - 3.121). A representation of the situation is shown in the image attached below.
Now we find the angle between the two lines by dot product:
[tex]\cos \theta = \frac{(- 0.293, 1.121)\,\bullet \,(- 1.707, - 3.121)}{1.159 \,\cdot\, 3.557}[/tex]
[tex]\cos \theta = - 0.727[/tex]
θ ≈ 136.635°
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