find the zeros of each function. State the multiplicity of multiple zeros y=2x^3+x^2-x
Answers
Answer:
Step-by-step explanation:
To find the roots/zeros, set
2
x
3
+
x
2
−
x
equal to
0
and solve.
2
x
3
+
x
2
−
x
=
0
Factor the left side of the equation.
Tap for more steps...
x
(
2
x
−
1
)
(
x
+
1
)
=
0
If any individual factor on the left side of the equation is equal to
0
, the entire expression will be equal to
0
.
x
=
0
2
x
−
1
=
0
x
+
1
=
0
Set the first factor equal to
0
.
x
=
0
Set the next factor equal to
0
and solve.
Tap for more steps...
x
=
1
2
Set the next factor equal to
0
and solve.
Tap for more steps...
x
=
−
1
The final solution is all the values that make
x
(
2
x
−
1
)
(
x
+
1
)
=
0
true. The multiplicity of a root is the number of times the root appears.
x
=
0
(Multiplicity of
1
)
x
=
1
2
(Multiplicity of
1
)
x
=
−
1
(Multiplicity of
1
)
Answer:
-1, 0, 1/2
Step-by-step explanation:
The function can be factored as ...
y = x(2x^2 +x -1)
y = x(2x -1)(x +1)
The factors are unique, so each zero has multiplicity 1. The zeros are the values of x that make the factors zero:
-1, 0, 1/2 . . . . zeros of the function; each with multiplicity 1
Related Questions
The location of Avenger's Tower is important to the safety of our planet. Steve, Natasha, and Bruce happen to all live equidistant from each other. Since Tony is filthy rich and can buy whatever he wants, he has decided to place the tower somewhere between
their houses. Where in this triangle should the tower be located and why? Geometrically, how could you find this spot? (Assume that no super powers or tech will assist these 3 Avengers when they travel to the tower)
Answers
Step-by-step explanation:
it should be located at the midpoint of the triangle.
it is because it is equidistant from all their houses so that they travel the same distance before reaching the tower.
I love marvel comics
find the centre of each line of the triangle then join into its corresponding opposite Vertex then where are the three lines intersect is the midpoint
A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. \( 87,87,215,154,288,235,231 \) Find the median number of newspapers sold.
Answers
The median number of newspapers sold over seven weeks is 223.
The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.
The formula for the median is as follows:
Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)
We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288
The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.
Median = (215 + 231)/2
= 446/2
= 223
In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.
Hence, the median number of newspapers sold over seven weeks is 223.
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Scenario 1A Calculate the following amounts for a participating provider who bills Medicare and has no deductible left. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Coinsurance amount (20% paid by) $ Medicare payment (80 percent of the PFS) $ Provider write-off $ Scenario 1B Calculate the following amounts for a participating provider who bills Medicare and remaining annual deductible for the patient. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Patient pays $100 remaining on their deductible $ Remaining amount for Insurance and patient to pay $ (PFS - $100) Coinsurance amount (20% of remaining amount) $ Total paid by patient (deductible & 20% of remaining) $ Medicare payment (80 percent of the remaining amount) $ Provider write-off $
Answers
Scenario 1A:
Coinsurance amount is $90
Medicare payment is $360
Provider write-off is $290
Scenario 1B:
Remaining amount for Insurance and patient to pay is $350
Coinsurance amount is $70
Total paid by patient is $170
Medicare payment is $280
Provider write-off is $370
Scenario 1A:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Coinsurance amount (20% paid by patient): $
Medicare payment (80% of the PFS): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Coinsurance amount (20% paid by patient):
Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)
Coinsurance amount = 0.2 * $450 = $90
Medicare payment (80% of the PFS):
Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)
Medicare payment = 0.8 * $450 = $360
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $360 = $290
Scenario 1B:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Patient pays $100 remaining on their deductible
Remaining amount for Insurance and patient to pay: $
Coinsurance amount (20% of remaining amount): $
Total paid by patient (deductible & 20% of remaining): $
Medicare payment (80% of the remaining amount): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Remaining amount for Insurance and patient to pay:
Remaining amount for Insurance and patient to pay = PFS - remaining deductible
Remaining amount for Insurance and patient to pay = $450 - $100 = $350
Coinsurance amount (20% of remaining amount):
Coinsurance amount = 20% of the remaining amount
Coinsurance amount = 0.2 * $350 = $70
Total paid by patient (deductible & 20% of remaining):
Total paid by patient = remaining deductible + coinsurance amount
Total paid by patient = $100 + $70 = $170
Medicare payment (80% of the remaining amount):
Medicare payment = 80% of the remaining amount
Medicare payment = 0.8 * $350 = $280
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $280 = $370
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A total of 85 children and adults go to the local fair on Monday. A child's ticket costs
$3.00 each and an adult's ticket costs $5.00 each. The fair collected $325.00 on
Monday. How many adults and children went to the fair on Monday? Use c for child
and a for adult.
Answers
Hope it helped!
Which of the relations given by the following sets of ordered pairs is not a function?
O {(-4,-2), (-1, -1), (-1, 1), (3, 5), (7, 10)}
O {(-8, 3), (-6, 5), (-4, 2), (-2, 7), (-1,4)}
O {(-6,4), (-3, -2), (0, 5), (1, - 2), (2,3)}
O {(5, 0), (4, 0), (3, 0), (2, 0), (1, 0)}
Answers
A function is a type of relation where the x-value do not repeat. Answer choice B through D have no repeating x-values. However, -1 repeats twice in the x-values of the ordered pairs, so it is NOT a function.
The relation given by the set of ordered pair that is a function is;
{(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}
What is the ordered pair?An ordered pair is defined as any pair of numbers for which order is important. Thus, the order of coordinates for a given point is very important for example (6, 3) and (3, 6) represent two very different points on a coordinate system.
here, we have,
For any of the ordered pair to be a function, there needs to be one unique value of y for every x.
Looking at the options, the only correct ordered pair that shows the law of an ordered pair being a function is Option A.
Hence, The relation given by the set of ordered pair that is a function is;
{(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}
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complete question:
Which of the relations given by the following sets of ordered pairs is a function?
O {(-2,5), (7, 5), (-4, 0), (3, 1), (0, -6)}
O {(1, 3), (1, 1), (1, 1), (1, 3), (1,5)}
O {(1, 2), (2, 3), (3, 4), (2, 1), (1, 0)}
O
1
{(2,8), (6,4), ( – 3, 9), (2, 0), (-5,3)}
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for or">=" for >.(0,4)(2,0)-5
Answers
Find the equation of the dotted line:
\(y=mx+b\)1. Find the slope:
\(m=\frac{y_2-y_1}{x_2-x_1}\)\(m=\frac{0-4}{2-0}=-\frac{4}{2}=-2\)2. Find the y-intercept (b): the value of y when the line cross y-axis:
b=4
Then, the eqution of the line is: y=-2x+4
To write the inequality:
When the line is a dotted line you use > or <, whne it is a full line you use ≥ or ≤
When the sahdow area is under the line use < or ≤, when the shadow area is over the line you use > or ≥
Then, as you have a dotted line and the shadow area in under that line, you get the next inequality:
\(y<-2x+4\)Sixteen times a number x is less than -2.
Answers
Answer:
16x<-2
Step-by-step explanation:
given a set x, the relation of equipotence is an equivalence relation on the collection 2x of all subsets of x. the equivalence class of a set with respect to the relation equipotence is called the cardinality of the set.
Answers
The relation of equipotence is an equivalence relation on the collection 2x of all subsets of set x. The equivalence class of a set, under this relation, represents the cardinality of the set, which is a measure of its size or the number of elements it contains.
The relation of equipotence is an **equivalence relation** on the collection 2x, which represents all subsets of set x. The equivalence class of a set, with respect to the relation of equipotence, is known as the **cardinality** of the set.
An equivalence relation is a relation on a set that satisfies three properties: reflexivity, symmetry, and transitivity. Let's explore how the relation of equipotence satisfies these properties.
1. Reflexivity: For any set A in 2x, A is equipotent to itself. In other words, any set is equivalent to itself in terms of its cardinality. This satisfies the reflexivity property of an equivalence relation.
2. Symmetry: If set A is equipotent to set B, then set B is equipotent to set A. The notion of equipotence does not depend on the order or arrangement of elements within sets. So, if A has the same cardinality as B, then B also has the same cardinality as A. This satisfies the symmetry property.
3. Transitivity: If set A is equipotent to set B, and set B is equipotent to set C, then set A is equipotent to set C. If two sets have the same cardinality and one of them has the same cardinality as a third set, then the first set is also equipotent to the third set. This satisfies the transitivity property.
As a result, the relation of equipotence on 2x fulfills all the requirements of an equivalence relation. Each equivalence class, or set of sets, formed by this relation represents the sets that share the same cardinality.
The cardinality of a set is essentially a measure of the "size" or "number of elements" in that set. It is represented by a non-negative integer. For example, if set A has three elements, its cardinality is 3. The equivalence class of set A, with respect to the relation of equipotence, would consist of all sets that have the same cardinality as A, that is, all sets with three elements.
In summary, the relation of equipotence is an equivalence relation on the collection 2x of all subsets of set x. The equivalence class of a set, under this relation, represents the cardinality of the set, which is a measure of its size or the number of elements it contains.
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A. A person goes from a sauna at 1208F to an outside temperature of -208F. What is the change in temperature
Answers
The change in temperature should be 1208 - (-208).
since r is so widely used, it is appropriate to calculate r for nonlinear data.true/false
Answers
since r is so widely used, it is appropriate to calculate r for nonlinear data: False.
The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.
In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.
n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.
When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.
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Find the missing measures in this regular hexagon. a regular hexagon has side lengths of 16 inches. the radius is 16 inches. an apothem is shown. the length of the apothem of the hexagon is about inches. the perimeter of the hexagon is inches. the area of the hexagon is about square inches.
Answers
The apothem, perimeter, and area of the hexagon are 13.86 inches, 96 inches, and 665.11 square inches respectively.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
A regular hexagon has side lengths of 16 inches. the radius is 16 inches.
The length of the apothem (h) of the hexagon is about inches.
\(\rm h = 16\times \sin 60^o\\\\h = 13.8564 \approx 13.86 \ inches\)
The perimeter of the hexagon is inches.
\(\rm Perimeter = 6 \times 16\\\\Perimeter = 96\ inches\)
The area of the hexagon is about square inches.
\(\rm Area = 6 \times \dfrac{1}{2} \times 13.86 \times 16\\\\Area = 665.1075 \approx 665.11 \ inches^2\)
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Answer:
Step-by-step explanation:
The length of the apothem of the hexagon is about
✔ 13.9
inches.
The perimeter of the hexagon is
✔ 96.0
inches.
The area of the hexagon is about
✔ 667.2
square inches.
The vertices of a triangle are located at the points A(0, 1), B(2, 4) and C(3, 0). The triangle is translated 5 units down to obtain triangle A′B′C′. What are the coordinates of the vertices of triangle A′B′C
Answers
Answer:
The coordinates of the vertices of triangle A'B'C' are \(A'(x,y) = (0,-4)\), \(B'(x,y) = (2,-1)\) and \(C'(x,y) = (3,-5)\).
Step-by-step explanation:
According to this statement, triangle ABC must be translated 5 units in the -y direction to form triangle A'B'C'. We need to use the following operations:
\(A'(x,y) = A(x,y) +(0,-5)\) (1)
\(B'(x,y) = B(x,y) +(0,-5)\) (2)
\(C'(x,y) = C(x,y) + (0,-5)\) (3)
If we know that \(A(x,y) = (0,1)\), \(B(x,y) = (2,4)\) and \(C(x,y) = (3,0)\), then the new vertices of the rectangle are, respectively:
\(A'(x,y) = (0,-4)\), \(B'(x,y) = (2,-1)\), \(C'(x,y) = (3,-5)\)
Find the equation of the line passing through (-8,3) and (-6, 7). Write your equation in point-slope AND slope-intercept forms. Use the first point in your point-slope form!
point-slope form:
slope-intercept form:
Answers
Answer:
point-slope form: y - 3 = 2(x+8)
slope-int form: y = 2x + 19
Step-by-step explanation:
For slope-int form, find the slope of the line.
7-3 / -6-(-8) = 4/2 = 2
This becomes y = 2x + b
To find b: plug in a y-coordinate for the y in the equation and plug in an x-coordinate for the x
7 = 2(-6) + b
7 = -24/2 + b
7 = -12 + b
7 + 12 = -12 + 12 +b
19 = b
The final equation is: y = 2x + 19
Find the quotient and remainder when p (x) divides with g (x) question (i) P (x) = x raise to 4 - 3 x square +4x + 5, g (x) = x square +5
Answers
Answer: \(x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}\)
Step-by-step explanation:
P(x) = x⁴ - 3x² + 4x + 5
g(x) = x² + 5
_x²_- 8
x² + 5) x⁴ + 0x³ - 3x² + 4x + 5
-(x⁴ + 0x³ + 5x²) ↓ ↓
-8x² + 4x + 5
-(-8x² + 0x - 40)
4x + 45
\(\dfrac{x^4-3x^2+4x+5}{x^2+5}=\large\boxed{x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}}\)
the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?
Answers
The average speed of a falling object during the first 3 seconds of its fall is h(3)-h(0)/3.
The model of the motion of the body is given by, and the function of the motion of the body is given by h(t) = 300 - 16t².
The speed of object after 3 seconds is given by . The falling speed of object during the first 3 seconds of falling is calculated as follows, v = dh(t)/dt = -32t.
So now the average speed of the movement is calculated as follows,
v = h(3)-h(0)/3.
Option d is therefore the correct option.
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Complete question - the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?
A.) h(3) – h(0)
B.) h(3/3)-h(0/3)
C.) h(3)/3
D.) (h(3)-h(0))/3
A board game uses the deck of 20 cards
shown to the right. Two cards are selected at
random from this deck. Calculate the
probability that both cards selected have a
1, both with and without replacement.
Answers
Using the probability concept, it is found that they are given by:
0.0316 = 3.16%, without replacement.0.04 = 4%, with replacement.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Without replacement, there are 4 out of 20, and then 3 out of 19 cards with a 1, hence:
\(p = \frac{4}{20} \times \frac{3}{19} = 0.0316\)
0.0316 = 3.16% probability that both cards selected have a 1 without replacement.
With replacement, in each trial, 4 out of 20, hence:
\(p = \frac{4}{20} \times \frac{4}{20} = 0.04\)
0.04 = 4% probability that both cards selected have a 1 with replacement.
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Solve the compound inequality.
4x-2 > 14 or 2x+5≤5
Graph the solution on the number line.
Answers
Answer:
so divide the 4x by the diameter in the form of pie
7
Mr. Jones filled his swimming pool with water.
• Mr. Jones began filling the pool at a constant rate.
He turned off the water for a while.
He then turned the water back on at a slower constant rate.
• Mr. Jones turned off the water again for a while.
• He then turned the water back on at the first rate.
Which graph best represents Mr. Jones filling the pool?
SU
Answers
Answer:
A??
Step-by-step explanation:
Its none of the graphs I am seeing which I can only see B C D so I don't know what graph A is, so I am going to say graph A
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE:) 25 + h - 5 lim h > 0 h 1/10 Need Help? Read It Watch It Talk to a Tutor
Answers
The limit of 25 + h - 5 as h approaches 0 is, 20.
To evaluate the limit, we need to simplify the expression and then apply the limit.
First, let's simplify the expression:
25 + h - 5 = h + 20
Now we can apply the limit:
lim h > 0 (h + 20) = lim h > 0 h + lim h > 0 20
Since the limit of a constant is just the constant itself, we can simplify further:
lim h > 0 (h + 20) = lim h > 0 h + 20
Now we can apply the limit to the remaining term:
lim h > 0 h = 0
So the final answer is:
lim h > 0 (h + 20) = 0 + 20 = 20
Therefore, the limit of the expression 25 + h - 5 as h approaches 0 is 20.
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The space is C [0,2π] and the inner product is (fg)= J 2π f(t)g(t) dt Show that sin mt and cos nt are orthogonal for all positive integers m and n. Begin by writing the inner product using the given functions. (sin mt, cos nt) = 2π J0 ___ dtUse a trigonometric identity to write the integrand as a sum of sines.
Answers
We want to show that sin(mt) and cos(nt) are orthogonal with respect to the given inner product.
Using the inner product, we have:
\((sin(mt)) ,(cos(nt)) =\) ∫_0^(2π) sin(mt) cos(nt) dt
We can use the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b) to rewrite the integrand as:
sin(mt)cos(nt) = (1/2)[sin((m+n)t) + sin((m-n)t)]
Substituting this back into the inner product, we get:
(sin(mt), cos(nt)) = (1/2) ∫_0^(2π) [sin((m+n)t) + sin((m-n)t)] dt
The integral of sin((m+n)t) over one period is zero, since the sine function oscillates between positive and negative values with equal area above and below the x-axis.
On the other hand, the integral of sin((m-n)t) over one period is also zero, for similar reasons.
Therefore, we have shown that:
(sin(mt), cos(nt)) = (1/2) * 0 + (1/2) * 0 = 0
This means that sin(mt) and cos(nt) are orthogonal for all positive integers m and n.
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please answer ill give brainliest to the first
Ben recorded the number of customers who shopped at his pet store every day for one week. The results are shown below.42, 35, 56, 29, 42, 39, 23. What is the mean number of customers who shopped at the pet store?
(A)33
(B)38
(C)39
(D)42
Answers
given f(x)=4x+1 describe how the graph of g compares with the graph of f. g(x)=(4x+1)+3
Answers
The description of the graph of function g(x) is 3 units translation up
How to describe the graph of function g(x)?The equations of the functions are given as
f(x) = 4x + 1
g(x) = (4x + 1) + 3
Substitute f(x) = 4x + 1 in the equation g(x) = (4x + 1) + 3
So, we have
g(x) = f(x) + 3
The above rule implies that:
The function g(x) is a translation of the function f(x)
The unit of the translation is 3 and the direction of the translation is up
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What is the difference between -3 and 7? *
Answers
Answer:
4
Step-by-step explanation:
Hope this helped
Answer:
-3 and 7 are different bc -3 is negative and 7 is positive and they have different absolute values and are different distance from 0
Step-by-step explanation:
Hey hoped I helped have a great day and consider marking this brainliest if you do thank you in advanced!
PLEASE HELP!!!
Find the value of x.
A. 13 B. 9 C. 12 D. 10
Answers
Answer:
C. 12
Step-by-step explanation:
\( x \times 3 = 9\times 4\)
\( x \times 3 = 36\)
\( x = \frac{36}{3}\)
\( x = 12\)
can someone help to see if I'm learning it right. would the answer be c=10+5(enter an equation)
Answers
From the statement, we know that cost of:
• the pieces is $10,
,• and the delivery fee is $5.
The total cost of ordering the pieces is the sum of both prices:
\(c=10+5=15.\)AnswerThe total cost of ordering the pieces is $15.
The solution is the equation:
\(10+5=15\)Find the vertex, focus, and directrix of the parabola. 9x2 + 8y = 0 vertex (x, y) = focus (x, y) = directrix Sketch its graph.
Answers
We can start by rearranging the equation of the parabola into vertex form:
9x^2 = -8y
x^2 = (-8/9)y
Completing the square, we get:
x^2 = (-8/9)(y + 0)
x^2 = (-8/9)(y - 0)
The vertex is (0,0), and the parabola opens downwards since the coefficient of y is negative. The distance from the vertex to the focus is given by:
4p = -8/9
p = -2/9
Therefore, the focus is located at (0, -2/9). The directrix is a horizontal line located at a distance of p below the vertex, so it is given by:
y = p = -2/9
To sketch the graph, we can plot the vertex at (0,0) and then use the focus and directrix to draw the parabola symmetrically. The parabola will open downwards and extend infinitely in both directions. Here is a rough sketch of the graph:
```
|
|
-----o-----
|
|
```
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Is y= 8.6x + 1.3 proportional or not- proportional?
Answers
Answer:
Proportional
General Formulas and Concepts:
Algebra I
Any linear line is proportional
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define function
y = 8.6x + 1.3
Step 2: Identify
The given function is a linear equation. It will be proportional
Step 3: Graph
We can see that the x and y is proportional.
help is highly appreciated <3
Answers
Answer:
5(5r - 6)
Step-by-step explanation:
25r - 30
we can factor out a 5 since 25 and 30 are both multiples of 5
so we get 5(5r - 6)
hope this helps!
ps i love ur pfp
help please ..........
Answers
Answer:b would be 19 points
Step-by-step explanation:
Wendy has a $30 to spend at the store. She wants to buy 5 pairs of socks for $1.99 each and a scarf for $20.49, including tax. She uses rounding to estimate the cost: . Wendy says she has enough money to cover the price of everything. Is she correct? Explain.
Answers
Answer:
Wendy does not have enough of money to cover the price of everything
Step-by-step explanation:
If Wendy has $30 and wants to but 5 pairs of socks that cost $1.99($2.00) each and a scarf for $20.49, she wouldn't have enough of money because the 5 pairs of socks would be $10 and if you subtract that from $30, she would only have $20 dollars left, so she wouldn't have enough money to pay for the socks and scarf, which also means she would only have to pick one of the two items she wants, either she pays for the socks, or she pays for the scarf, but she can't pay for both.