Find X-Intercepts And Multiplicity Of The Following: F(X) = 1\15 (X - 5)(X + 1)2(X - 2)2
Answers
The x-intercepts of the function f(x) = (1/15)(x - 5)(x + 1)^2(x - 2)^2 are x = 5, x = -1, and x = 2.
The multiplicity of each x-intercept is as follows:
x = 5 has multiplicity 1 (linear factor).
x = -1 has multiplicity 2 (quadratic factor).
x = 2 has multiplicity 2 (quadratic factor).
To find the x-intercepts of the function, we set f(x) equal to zero and solve for x. In this case, we have:
(1/15)(x - 5)(x + 1)^2(x - 2)^2 = 0
Setting each factor equal to zero, we find the following x-intercepts:
(x - 5) = 0, which gives x = 5.
(x + 1)^2 = 0, which gives x = -1 (with multiplicity 2).
(x - 2)^2 = 0, which gives x = 2 (with multiplicity 2).
The multiplicity of an x-intercept represents the number of times the corresponding factor appears in the function. In this case, we have linear factor (x - 5) with multiplicity 1, and quadratic factors (x + 1) and (x - 2) with multiplicity 2.
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Related Questions
Triangle DEF, shown below, is reflected over the y-axis to form triangle D'E'F'. What are
the coordinates of F'?
Answers
Answer:
The answer is -6, -4
Step-by-step explanation:
The coordinates of F' are (-6, -4).
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
A transformation known as a translation involves moving each point in a figure uniformly and in the same direction.
Given:
Triangle DEF is reflected over the y-axis to form triangle D'E'F'.
now, we have the rule for reflection over y axis
P( x, y)-----> P' (-x, y)
Then the coordinates of D'E'F are
D(4, 1)---------> D'(-4, 1)
E(8, -3)---------> E'(-8, -3)
F (6, -4)----------> F'(-6, -4).
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What percentage of 1hour is 6munites 20seconds
Answers
Answer:
1 minute and 12 seconds is 2 % of an hour.
Step-by-step explanation:
Answer:
12%
Step-by-step explanation:
What are examples of mutually exclusive events in probability?
Answers
Mutually exclusive events are those events that do not occur at the same time. For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.
Examples of mutually exclusive events are:
When a coin is tossed, getting heads and tails are mutually exclusive. Because the probability of getting both heads and tails is 0.
In a six-sided die, the events "2" and "5" are mutually exclusive. We cannot get events 2 and 5 at the same time with one die.
In a deck of 52 cards, drawing a red card and drawing a club are mutually exclusive events because all clubs are black.
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Do all squares have all right angles?
Answers
Answer:
Yes
Explanation:
All squares have right angles.
4. What is the equation of the line that represents your initial climb? Please. Need ASAP. 20pts
Answers
Answer:
y = 2x
Step-by-step explanation:
I am basing this off of your straight line that you drew.
Slope is found by using \(\frac{rise}{run}\) . This means that you change in your y-axis divided by change in your x axis.
This can also be modeled by Δy/Δx
I used point (0,0) and the peak of the slope (100,200)
Your line starts at 0 and rises 200 and runs to the right 100.
Thus, you can write:
y = \(\frac{200}{100}\) x
This simplifies to y = 2x
the if function applies to one or two conditions, but what if you need to apply multiple conditions?
Answers
IF function applies to one or two conditions, but what if you need to apply multiple conditions? Use the IF-Then function O Use the IFor function Use the nesting capabilities of the IF function Use separate IF functions.
The probability of an outcome that lies within 68% of the mean is a good indicator that it lies in which standard deviation?
A. There is a probability that the outcome is within 1 standard deviation of the mean.
B. There is a probability that the outcome is within 3 standard deviations of the mean.
C. There is a probability that the outcome is within 2 standard deviations of the mean.
D. Standard deviations are not reliable, so the probability cannot be determined.
Answers
Answer:
The correct answer is B or option 2.
PLEASE HELP FAST!!! Estimate the line of best fit using two points on the line.
Answers
Answer:
D) y= -1/2x+9
Step-by-step explanation:
if u substitute y with 8 u will get 2
if u substitute y with 5 u will get 8
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}=xy_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (2, 8) and (x₂, y₂ ) = (8, 5)
m = \(\frac{5-8}{8-2}\) = \(\frac{-3}{6}\) = - \(\frac{1}{2}\)
The line crosses the y- axis at (0, 9) ⇒ c = 9
y = - \(\frac{1}{2}\) x + 9 → D
The problem is 44+(7x+12)=180, what is x?
Answers
Answer:
x=
124 /7
Step-by-step explanation:
Answer:
x=8
Step-by-step explanation:
Actually, the problem is 44+2(7x+12)=180. (There are two angles that equal 7x+12).
44+14x+24=180
68+14x=180
14x=180-68
14x=112
x=8
the quotient property of radicals requires the indices of the radicals to be the same. does this mean that it is not possible to write as a single radical? explain.
Answers
The quotient property of radicals requires the indices of the radicals to be the same. Thus, it is not possible to write the expression (5√3 + 2√2) as a single radical.What is the quotient property of radicals?
The quotient property of radicals states that for any non-negative numbers x and y with y ≠ 0, if n is an integer greater than 1, then the following property holds:√(x/y) = √x/√yNow let's take a look at the question at hand. We can see that the two radicals have different indices. Therefore, the quotient property of radicals does not apply. As a result, it is not possible to simplify the expression as a single radical. Therefore, the expression (5√3 + 2√2) cannot be written as a single radical.
The quotient property of radicals states that when dividing radicals, the indices (or roots) of the radicals involved must be the same. In other words, for the quotient property to be applicable, the radicals being divided must have the same root.
If the radicals have different indices, it is generally not possible to simplify the expression into a single radical. This is because the rules of radical arithmetic require the indices to be the same in order to combine or simplify radicals.
For example, let's consider the expression √2 / √3. Here, the radicals have different indices (square root and cube root), so we cannot combine them into a single radical using the quotient property. The expression √2 / √3 cannot be simplified further because the indices do not match.
However, it's important to note that even though the quotient property does not apply in such cases, it does not mean that the expression is mathematically invalid or cannot be manipulated further. It simply means that the expression cannot be simplified into a single radical using the quotient property. Other algebraic techniques or operations may be necessary to further simplify or manipulate the expression if desired.
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The given information is the quotient property of radicals requires the indices of the radicals to be same.
Yes, it is not possible to write \($8\sqrt{2}+5\sqrt{3}$\) as a single radical because the quotient property of radicals requires the indices of the radicals to be the same.
The quotient property of radicals is a mathematical concept that explains how to divide two radicals with the same index. If r is a non-negative number and s is a non-negative number, then:
\((\frac{r}{s})^{n}=\frac{r^{n}}{s^{n}}\)
The property of quotient states that the quotient of the same degree radicals is equal to the same degree root of the quotient of the radicands. If a and b are non-negative numbers and n is an integer greater than 1:
\((\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}\sqrt[n]{\frac{a}{b}}\)
\(=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\)
If you look at the terms \($8\sqrt{2}$ and $5\sqrt{3}$\), you can tell that their indices are not the same. The term \($8\sqrt{2}$\) has an index of 2 while the term \($5\sqrt{3}$\) has an index of 3. The quotient property of radicals requires the indices of the radicals to be the same. Therefore, you cannot add or subtract two radicals that do not have the same index.
Example: \($8\sqrt{2}+5\sqrt{3}$\) can be rearranged as \($8\sqrt{2}+0\sqrt{3}+5\sqrt{3}$\). Then using distributive property, it can be written as \($(8+0)\sqrt{2}+5\sqrt{3}$\). In conclusion, it is not possible to write \($8\sqrt{2}+5\sqrt{3}$\) as a single radical.
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2. if a sample has a mean of 100 and standard deviation of 6, what value would correspond the the z-score of 2?
Answers
The z-score of 2 for a sample has a mean of 100 and a standard deviation of 6 is 112.
The value that would correspond to the z-score of 2 for a sample with a mean of 100 and standard deviation of 6 can be calculated using the formula for z-score:
z = (x - mean) / standard deviation
In this case, we want to find the value of x that corresponds to a z-score of 2. We can rearrange the formula to solve for x:
x = (z * standard deviation) + mean
Substituting the values given in the question:
x = (2 * 6) + 100
x = 12 + 100
x = 112
Therefore, the value that corresponds to the z-score of 2 for this sample is 112.
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Anyone know how to do this?
Answers
Answer:
Is it 90 degrees
Step-by-step explanation:
The straight up and down line gives it away.
A T-shirt printing company sells T-shirts for $15 each. The
company has a fixed cost for the machine used to print the
T-shirts and an additional cost per T-shirt. Use the table to
estimate the number of T-shirts the company must sell in order
for the income to equal expenses.
T-Shirt Printing Cost
Printing Machine $3000.00
Blank T-Shirt $5.00
Write an equation to represent the income and the expenses. Then
solve to find how many T-shirts need to be sold for both values to
be equal.
Answers
The linear function that models the problem of T-shirt printing company sales is
y = 2.50x + 3.50
The number of T-shirts to be sold to have equal income and expense is 300 T-shirts
How to model the required equationA linear function consists of functions where the variables has exponents of 1. The relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function below
c = y intercept is the cost of the Printing Machine = $3000.00
m = cost of blank T-shirts = $5
assuming number of T shirts is x
y = expenses = 5x + 3000
income = 15x
For income to be equal to expenses
5x + 3000 = 15x
3000 = 15x - 5x
3000 = 10x
x = 300
300 T-shirts should be sold to have equal income and expense
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Daniel expanded the expression as shown. Negative 2 (Negative 8 x minus 4 y + three-fourths) = negative 10 x minus 8 y minus 1 and one-fourth What errors did he make? Select three options. The first term should be positive. The second term should be positive. The last term should be Negative 1 and one-half, not Negative 1 and one-fourth. He divided Negative 8 by Negative 2 instead of multiplying Negative 8 by Negative 2. He did not simplify the expression completely.
Answers
Answer:
Options A, B and C are correct.
Step-by-step explanation:
The given expression is
\(-2\left(-8x-4y+\dfrac{3}{4}\right)\)
Using distributive property, we get
\(-2(-8x)-2(-4y)-2\left(\dfrac{3}{4}\right)\)
\(16x+8y-\dfrac{6}{4}\)
\(16x+8y-\dfrac{3}{2}\)
\(16x+8y-1\dfrac{1}{2}\)
It is given that Daniel expanded the expression as
\(-2\left(-8x-4\dfrac{3}{4}\right)=-10x-8y-1\dfrac{1}{4}\)
The first term should be positive.
The second term should be positive.
The last term should be Negative 1 and one-half, not Negative 1 and one-fourth.
Therefore, options A, B and C are correct.
Answer:
Option 1,2,3
Step-by-step explanation:
got it right
It takes a toy train 6 minutes to travel 2 times around a 25ft track. Assuming it moves at a constant speed, how long does it take the train to travel 100 yards?
Answers
Answer:
It takes the toy train 36 minutes to travel 100 yards.
Step-by-step explanation:
100 yards = 300 feet
300 / (divided by) 25 = 6
meaning 300 = 25 x 6
So: 6 x 6 = 36 minutes
(sorry if this was confusing, I'm not the best at explanations lol)
The only information you have about a certain function f[x] is:
-1 ≤ f[x] ≤ 1
for all the x's between -[infinity] and [infinity].
Is it possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity]?
Why?
Answers
Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].
Explanation:
We can approximate f(x) as a Fourier series, as follows:
\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)
If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.
We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:
\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)
For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.
However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.
Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:
\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)
Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].
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Find the amount of time. I=$70, P=$350, r=4%
Answers
Answer:
5years
Step-by-step explanation:
I=70
P=350
R=4
I=PRT/100➜PRT=100 I
➜T=100 I/PR
➜100×70/350×4
➜7000/1400
➜5years
Somebody help me cause I'm lost
Answers
Answer:
I think it might be (-12,7)
Step-by-step explanation:
This needs to be simplified
Answers
Answer:
7.5x+20y
Step-by-step explanation:
2.5( 3x+8y)
Distribute
2.5 * 3x + 2.5* 8y
7.5x+20y
Answer:
7.5x+20y
Step-by-step explanation
Multiply the parentheses by 2.5
Work out 0.5 + 1.1 x 1.6
Answers
Answer:
=2.26
Step-by-step explanation:
0.5+1.1x1.6
multiply first (pemdas)
0.5+1.76
add
=2.26
i hope this helps :)
Answer:
0.5 + 1.1 x 1.6 = 2.26
Step-by-step explanation:
check it in a calculator so it's correct
Billy earned $150 from a summer job to buy new clothes for school. He found several items he would like to buy, but is trying to decide if he has enough money to buy all the items he likes. He found two pairs of shorts for $20 each and four shorts with an average cost of $18 per shirt. He will have to pay 6.5% sales tax.If he buys all of the items, how much sales tax will he has to pay?
Answers
Answer:
Billy went from rich to broke.
Step-by-step explanation:
What is the Slope and Y-intercept?
Answers
Answer:
slope: -3
y-int: -4
Step-by-step explanation:
find the slope by taking any 2 points and finding the difference of their y-values over the difference of their x-values:
(1,-7) and (0,-4)
slope = -7-(-4) / 1-0
slope = -3/1
the y-intercept is the y-value that is associated with an x-value of zero; in this case, -4
what is the slope of the line that passes through these two points? (1, -2) (3, 4)
Answers
\( \to \rm m = \dfrac{y_2 - y_1}{x_2 - x_1} \)
\( \\ \\ \)
\( \to \rm m = \dfrac{4 - ( - 2)}{3 - 1} \)
\( \\ \\ \)
\( \to \rm m = \dfrac{4 + 2}{3 - 1} \)
\( \\ \\ \)
\( \to \rm m = \dfrac{6}{2} \)
\( \\ \\ \)
\( \to \rm m = \cancel \dfrac{6}{2} \)
\( \\ \\ \)
\( \to \rm m =3\)
Required Answer:-3
The number less than zero are called
Answers
Answer:
Step-by-step explanation: Negatives because a number lower than 0 go like this -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 see? so the answer is Negatives.
i)
\(3 \sqrt{3} \times \sqrt{3} \)
Answers
Answer:
9Step-by-step explanation:
\(3\sqrt{3}\times\sqrt{3}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a\\\\\sqrt{3}\sqrt{3}=3\\\\=3\times\:3\\\\=9\)
Explanation:
3 sqrt(3) • sqrt(3)
= 3 sqrt(3 • 3)
= 3 sqrt(9)
= 3 sqrt(3^2)
= 3 x 3
= 9
subtract. write your answer in scientific notation.
(7.15×105)–(5.964×105)
Answers
Answer:
124.53
Step-by-step explanation:
7.15×105=750.75
5.964×105=626.22
750.75-626.22= 124.53
lmk if this is right or not :)
Answer with step-by-step explanation:
(7.15 × 105) - (5.964 × 105) = 124.53
750.75 - 626.22 = 124.53
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find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm2.
Answers
Let's call the length of the rectangle "L" and the width "W". We know that the width is 10 cm shorter than the length, so we can write.
W = L - 10
We also know that the area of the rectangle is 200 cm 2, so we can write:
A = L x W
Substituting W = L - 10, we get:
A = L x (L - 10)
Expanding the brackets, we get:
A = L^2 - 10L
Now we can substitute in A = 200 and solve for L:
200 = L^2 - 10L
0 = L^2 - 10L - 200
We can use the quadratic formula to solve for L:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -10, and c = -200. Plugging in these values, we get:
L = (10 ± sqrt(10^2 - 4(1)(-200))) / 2(1)
L = (10 ± sqrt(1100)) / 2
L = (10 ± 10sqrt(11)) / 2
L ≈ 19.9 or L ≈ -9.9
We can disregard the negative solution since we're dealing with lengths, so the length of the rectangle is approximately 19.9 cm.
Now we can use W = L - 10 to find the width:
W = 19.9 - 10
W ≈ 9.9 cm
Therefore, the length of the rectangle is approximately 19.9 cm and the width is approximately 9.9 cm.
To find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm², follow these steps:
1. Define the variables: Let the length of the rectangle be L cm, and the width be W cm.
2. Use the given information: Since the width is 10 cm shorter than the length, we can write the equation W = L - 10.
3. Use the formula for the area of a rectangle: The area of a rectangle is given by the formula A = L × W.
4. Substitute the given area and the equation from step 2: In this problem, the area is 200 cm², so we have 200 = L × (L - 10).
5. Solve the equation for L: Expand the equation to get 200 = L² - 10L. Rearrange the equation to L² - 10L - 200 = 0.
6. Factor the quadratic equation or use the quadratic formula: (L - 20)(L + 10) = 0. This gives two possible values for L: L = 20 cm or L = -10 cm.
7. Discard the negative value: Since the length of a rectangle cannot be negative, we discard the value L = -10 cm. So, the length L is 20 cm.
8. Find the width using the equation from step 2: W = L - 10 = 20 - 10 = 10 cm.
Thus, the length and width of the rectangle are 20 cm and 10 cm, respectively.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Subtract the binomials.
On simplifying (-3y2 − 8) − (-5y2 + 1), we get ----------
y2 − ------
. Lines are for the two answers
Answers
The simplified expression is 2y² - 9.
To subtract the binomials (-3y^2 - 8) - (-5y^2 + 1), we need to distribute the negative sign to the terms inside the second set of parentheses:
(-3y^2 - 8) - (-5y^2 + 1) = -3y^2 - 8 + 5y^2 - 1
Next, we combine like terms by adding or subtracting the coefficients of the same degree:
-3y^2 + 5y^2 - 8 - 1 = (5y^2 - 3y^2) + (-8 - 1) = 2y^2 - 9
Therefore, the simplified expression is 2y² - 9.
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Find all values of the scalar k for which the following vectors are orthogonal: u=[k,k,−2],v=[−5,k+2,5]
Answers
The vectors u and v are orthogonal when k equals 5 or -2.
Two vectors u and v are orthogonal if their dot product is equal to zero. The dot product of two vectors u and v is given by the formula:
u · v = u₁ × v₁ + u₂ × v₂ + u₃ × v₃
where u₁, u₂, u₃ are the components of vector u, and v₁, v₂, v₃ are the components of vector v.
Let's calculate the dot product of u and v:
u · v = (k × -5) + (k × (k + 2)) + (-2 × 5)
= -5k + k² + 2k - 10
= k² - 3k - 10
For the vectors to be orthogonal, the dot product must be zero:
k² - 3k - 10 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula:
(k - 5)(k + 2) = 0
From this equation, we can see that the values of k that satisfy the equation are:
k = 5 or k = -2
Therefore, the vectors u and v are orthogonal when k equals 5 or -2.
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Meghan sells handmade sweaters and hats at her store. Let A represent the event that a randomly selected customer buys hat, and let B
represent the event that a randomly selected customer buys a sweater.
What does the notation P(AJB) represent in terms of the context?
A the probability that a customer buys a hat or a sweater
B the probability that a customer buys both a hat and a sweater
C the probability that a customer buys a hat given that the customer has bought a sweater
D the probability that a customer buys a sweater given that the customer has bought hat
Answers
Answer:
Step-by-step explanation:
C the probability that a customer buys a hat given that the customer has bought a sweater.