Answers
The polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6 is f(x) = x³ - x² - 30x.
To find a polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6, we start by using the factor theorem. This theorem tells us that if a polynomial function has a zero at some value c, then it is divisible by the linear factor (x - c).
Therefore, the polynomial with zeros at -5, 0, and 6 can be written as:
f(x) = a(x + 5)(x - 0)(x - 6)
where a is a constant coefficient that we need to determine. Since the leading coefficient of the polynomial is 1, we set a = 1.
Multiplying out the factors, we get:
f(x) = (x + 5)(x)(x - 6)
= x³ - x² - 30x
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Related Questions
Use the Law of Cosines. Find length x.
(Round the final answer to one decimal place as needed. Round all intermediate values to two decimal places as needed.)
Answers
18.2
Step-by-step explanation:
AB² =AC² + CB² -2(AC)(CB)CosA
X²=(17)² + (10)² - 2 (17)(10) Cos80
x² = 289 + 100- 340 cos 80
x= √289+100-340cos80
x= 18.2
Calculate standard deviation for the following by direct and shortcut method.assume mean as 32
Serial no.of workers
1
2
3
Answers
The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.
How to find the standard deviation?Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.
To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.
Direct method:
Calculate the mean wage (F) for the distribution:
Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10
Mean = 34
Calculate the differences between each wage and the mean wage:
20 - 34 = -14
22 - 34 = -12
27 - 34 = -7
30 - 34 = -4
31 - 34 = -3
32 - 34 = -2
35 - 34 = 1
45 - 34 = 11
40 - 34 = 6
48 - 34 = 14
Square each of the differences:
(-14)² = 196
(-12)² = 144
(-7)² = 49
(-4)² = 16
(-3)² = 9
(-2)² = 4
1² = 1
11² = 121
6² = 36
14² = 196
Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756
Divide the sum of the squared differences by the number of workers: 756/10 = 75.6
Take the square root of the result to get the standard deviation:
√75.6 = 8.739
Shortcut method:
The mean wage (F) for the distribution:
(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34
The sum of the squares of the differences between each wage and the mean wage:
(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756
Divide the sum by the number of workers: 756/10 = 75.6
Take the square root of the result to get the standard deviation:
Standard deviation = √75.6 = 8.739
Therefore,
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Complete question is:
Calculate standard deviation for the following
distribution by direct and shortcut method.
Assume mean as 32.
Serial No. of Workers
1
2
3
4
5
6
7
8
9
10
Wage (F)
20
22
27
30
31
32
35
45
40
48
Can someone help me with this please
Answers
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 must assume a value of -1.
A valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the matrix is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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For the following exercises, convert the angle measures to degrees.
9π/5 b) - π/3
(round to two decimal places)
Answers
a) The measure of 9π/5 radians in degrees is approximately 324 degrees.
b) The measure of -π/3 radians in degrees is approximately -60 degrees.
To convert the given angle measures from radians to degrees, we can use the formula:
angle in degrees = (angle in radians) × (180/π)
a) To convert 9π/5 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (9π/5) × (180/π) ≈ 324 degrees (rounded to two decimal places)
b) To convert -π/3 radians to degrees, we can substitute the given value in the above formula as:
angle in degrees = (-π/3) × (180/π) ≈ -60 degrees (rounded to two decimal places)
In general, we can convert an angle measure from radians to degrees by multiplying it by 180/π. Since π is an irrational number, the conversion factor 180/π is an irrational number as well. Therefore, when we round the result to two decimal places, we are actually approximating the true value of the angle measure.
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Can you please help me with this?
Answers
The triangles represented in the picture attached are acute, obtuse, acute and right triangles respectively.
Understanding different types of trianglesAcute Triangle is a triangle in which each of the three angles are less than 90°.
In fact all angles in an acute triangle are can be equal and sum to 180°.
Right Triangle is a triangle in which one of the angles is exactly 90°, often denoted as a "square corner".
The side opposite the right angle is called the hypotenuse and it is the longest side.
Obtuse Triangle is a triangle in which one of the angles is greater than 90°.
In other words, one of the angles in an obtuse triangle is "blunt" or greater than a right angle.
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Answers
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
Ox(x²-5) + 6(x² - 5)
Ox(x²+5)-6(x²+ 5)
O x²(x - 5) + 6(x - 5)
O x²(x+5)-6(x+ 5)
Answers
Answer:
x^2(x+5)-6(x+5)!!!!!!!!
A scientist has two solutions, which she has labeled solution a and solution
b. each contains salt. she knows that solution a is 65% salt and solution b is 80% salt. she wants to obtain 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
Answers
We know that the total amount of mixture needed is 150 ounces, so we can write:
x + y = 150
To achieve a 70% salt mixture, we can write the equation:
0.65x + 0.8y = 0.7(150)
To solve for x and y, we can use substitution or elimination. Let's use substitution to solve for x.
From the first equation, we have:
x = 150 - y
Substituting this into the second equation:
0.65(150 - y) + 0.8y = 105
Simplifying:
97.5 - 0.65y + 0.8y = 105
0.15y = 7.5
y = 50
Now that we know y, we can find x using either of the original equations:
x + y = 150
x + 50 = 150
x = 100
Therefore, the scientist should use 100 ounces of solution a and 50 ounces of solution b to obtain 150 ounces of a mixture that is 70% salt.
What are some common order of operation mistakes that students make when evaluating expressions? Make a list and share two examples in the Discussion Board; then explore the lists your peers have posted and respond to one that you find particularly insightful.
Answers
Some of the common order of operation mistakes that students make when evaluating expressions are the use of basic mathematical operations.
What is a mistake?You should know that an error or fault results from defective judgment, deficient knowledge, or carelessness.
A combination of numbers, letters, and relational operators containing at least one operation is deemed a mathematical expression. Additionally, it must also include variables and/or numbers, excluding an equal sign.
Some prevalent errors include using both a positive and a negative sign, using two negative signs, and misusing brackets.
By being unable to comprehend the problems accurately, learners often commit significant errors while assessing formulations, which underscores the importance of employing fundamental mathematical operations.
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Category: nr percentages
question_id: 5782
Alex is really upset. He invested a lot of money in shares and only has $72,800 left of his original
investment. His shares dropped in value by 35% in 4 days. What amount did Alex pay for his shares
to being with?
Answers
After a 35% drop in value, Alex's shares are worth 65% of their original value.
So, we can write the equation:
0.65X = 72800
Solving for X, we divide both sides by 0.65:
X = 72800 / 0.65
X ≈ $112,000
Therefore, Alex paid around $112,000 for his shares to begin with.
Answer:
Let's start by using algebra to solve for the original amount that Alex paid for his shares.
Let X be the original amount that Alex paid for his shares.
We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:
0.65X = $72,800
Solving for X:
X = $72,800 / 0.65
X = $112,000
Therefore, Alex paid $112,000 for his shares to begin with.
helppp me its need to be done quick
Answers
Answer:
100
Step-by-step explanation:
The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.
Therefore, the answer is 100.
Find the missing information for both parts below.
Answers
The unknown angles in the circle are as follows:
a. m∠AEB = 73°
b. arc angle VW = 155°
How to find arc angles in a circle?a.
If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
m∠AEB = 1 / 2 (99 + 47)
m∠AEB = 146 / 2
m∠AEB = 73 degrees
b.
If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .
Therefore,'
arc angle VW = x
55 = 1 / 2 (x - 45)
55 = 0.5x - 22.5
0.5x = 55 + 22.5
0.5x = 77.5
divide both sides by 0.5
x = 77.5 / 0.5
x = 155 degrees
Therefore,
arc angle VW = 155 degrees
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someone pls help i really need help with this
Answers
Answer:
50° F
Step-by-step explanation:
35 - -15= 50
Check
-15 + 50 = 35
And 35 - 50 = -15
I need help with this please.
1/2 x 3 x 3 = 4.5
I just need help on how 4.5 is the answer.
Answers
Answer:
3
Step-by-step explanation:
3 * 3 = 6
1/2 * 6 = 3 not 4.5
Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.
The 3 x 3 part turns into 9
So we have 1/2 x 9 or 9/2
Use long division to find that 9/2 gives a quotient of 4 and remainder 1
Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.
The "remainder 1" then leads to 1/2 = 0.5
quotient = 4
remainder = 1 ---> decimal portion = 1/2 = 0.5
So that's how we get to 4+0.5 = 4.5
You can use a calculator to see that 9/2 = 4.5
Use the substitution u = 1/y and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. -3/x + 4/y = 5 and 1/x - 2/y = -3
Answers
-3/x + 4/y = 5
1/x - 2/y = -3
We can use the substitutions u = 1/y and v = 1/x to rewrite the equations in terms of u and v:
-3v + 4u = 5 (multiply both sides by uv)
v - 2u = -3
Now we can solve this system of equations in terms of u and v. One way to do this is to multiply the second equation by 4 and add it to the first equation, eliminating the v variable:
-3v + 4u = 5
4v - 8u = -12
_____________
u = -1/2
Next, we can substitute this value for u into one of the equations to solve for v. Using the second equation, we get:
v - 2u = -3
v - 2(-1/2) = -3
v + 1 = -3
v = -4
Now we have the values of u and v:
u = -1/2
v = -4
To find the solution set in terms of x and y, we can back substitute these values into the original substitutions:
u = 1/y
-1/2 = 1/y
y = -2
v = 1/x
-4 = 1/x
x = -1/4
Therefore, the solution set to the original system of equations is:
x = -1/4
y = -2
2010 2008
$971 $812
$977 $943
$900 $873
$1071 $1023
$501 $486
2. What is the median weekly earnings of workers in the occupations listed for
2010?
Answers
The median weekly earnings of the data set of the workers in the occupations listed for 2010 is calculated as: $971.
How to Find the Median Weekly Earnings?To find the median weekly earnings for the occupations listed in 2010, we need to first arrange the earnings in order from least to greatest:
$501, $900, $971, $977, $1071
The median is the middle value in this ordered list. Since there are an odd number of values, the median is simply the middle value.
Therefore, the median weekly earnings of workers in the occupations listed for 2010 is $971.
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Which of the following accurately graphs the points listed in the table above?
Answers
Answer:
Correct ANSWER IS A
Step-by-step explanation:
For each coordinate pair (r,θ) listed in the table, first identify the ray on the graph created by the angle θ. On this ray, plot a point a distance of r from the pole.
Can you help me rewrite this in other words?
Part a
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
2. The chi square equals 1947 with one degree of freedom and the p-value being a non-zero number.
3. Since the p-value is less than the significance level, which would be .05, we rejected null hypothesis that would show that there is a significant association between climate change and a certainty.
Part 2
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
2. The chi square was 119.864 with 12 different degrees of freedom the p value for this is also a non-zero number.
3. Since the p value is less than .05, we would reject to null hypothesis, which would make sense that there is a significant association between sleeping and income class.
Answers
The discussion for both cases is shown below.
Part a:
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.
The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.
Part 2:
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.
Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.
In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.
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Exercise 17.5 Calculate the curved surface a cone whose height is 8 cm and base radius 5cm
Answers
The curved surface area of the cone is 148 cm².
Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,
The curved surface area gives the area of the face of an object.
The CSA of a cone = π × radius × slant height.
Slant height = √r²+h²
= √64+25
= 9.43 cm.
Now the csa = 3.14 × 5 × 9.43
= 148
Hence the curved surface area of the cone is 148 cm².
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A washer and a dryer cost $770 combined. The washer costs $70 more than the dryer. What is the cost of the dryer?
Answers
Answer:
d = $350
Step-by-step explanation:
If we allow d to represent the cost of the dryer and w to represent the cost of the washer, we know that the total cost of the washer and dryer is
d + w = 770.
Since we're told that the washer costs $70 more than the dryer, we know that
w = d + 70
We can substitute equation for w in the original equation to find d:
d + d + 70 = 770
2d + 70 = 770
2d = 700
d = 350
If you went on to find w, you'd see that it'd be 420 since 770 - d = w and 770 - 350 = 420
We know that the dryer costs $350 and the washer costs $420. 420 is indeed $70 more than $350 so our answer for the cost of the dryer is correct.
Find the inequality represented by the graph.
Answers
The inequality represented by the given graph as required to be determined in the task content is; y ≥ 0.5x.
Which inequality is represented by the given graph?It follows from the task content that the inequality which is represented by the given graph is required to be determined.
By observation; the slope of the border line is; 0.5 and the y-intercept is; 0.
Ultimately, the corresponding equation to the border line is; y = 0.5x.
Hence, since the region above the line is shaded and the line is a solid line; the required inequality is; y ≥ 0.5x.
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The bells obtain a 30-year, $90,000 conventional mortgage at a 10.0% rate on a house selling for $120,000. Their monthly mortgage payment, including principal and interest, is $783.00. They also pay 2 points at closing.
A)What is total amount the Bells will pay for their house.
B) How much of the cost will be interest (including the 2 points)?
C) How much of the first payment on the mortgage is applied to the principal?
Answers
The total amount that the Bells will pay for their house would be $313, 680.
The cost that would be interest is $193, 680
The amount of the first payment going to mortgages is $165. 24
How to find the total amount paid ?Find the down payment :
Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000
Then the points paid at closing :
= $ 90,000 x 0. 02 = $1,800
Total amount paid = Total mortgage payments + Down payment + Points cost
= 281, 880 + 30, 000 + 1, 800
= $ 313, 680
The total that is interest is:
Total interest paid = Total interest paid through monthly payments + Points cost
Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680
The amount of the first payment going to principal is:
Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24
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Write two numbers that multiply to the value on top and add to the value on bottom.
8
8
−
6
−6
×
×
+
+
Answers
a + b = -9......a = -9 - b
b(-9 - b) = -70
-b^2 - 9b + 70 = 0
(-b + 5)(b + 14) = 0
-b + 5 = 0
5 = b
b + 14 = 0
b = -14
ur numbers are -14 and 5
-14 * 5 = -70
-14 + 5 = -9
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answers
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.
What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?
Answers
The measure of ∠ADC is equal to 180 degrees.
The measure of ∠ABC is equal to 90 degrees.
What is a circle?In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.
In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.
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The sequence is geometric.
1, 6, 30, 60, . . .
Answers
The sequence 1, 6, 30, 60, . . . is not a geometric sequence
Checking if the sequence is geometricFrom the question, we have the following parameters that can be used in our computation:
1, 6, 30, 60, . . .
To check if the sequence is geometric, we calculae the common ratio of the sequence using
r = next term/previous term
Using the above as a guide, we have the following:
r = 6/1 = 6
r = 30/6 = 5
r = 60/30 = 2
The common ratios of the sequence calculated above are different
This means that the sequence is not geometric
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Solve for x. Round to the nearest tenth, if necessary.
50 points
Answers
Answer: 8.7
Step-by-step explanation:
Given:
hypotenuse = 9
Angle x =75
opposite of angle = x
Solution:
From SOH CAH TOA, use SOH
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] > substitute
sin 75 = [tex]\frac{x}{9}[/tex] > multiply both sides by 9
9*sin 75 =x
x=8.7
For her geography project, Karen built a clay model of a
volcano in the shape of a cone. Her model has a diameter
of 12 inches and a height of 8 inches. Find the volume of
clay in her model to the nearest tenth. Use 3.14 for pi
Answers
Answer:
301.4 in^3
Step-by-step explanation:
Divide 12 by 2 to get the radius
12/2=6
Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.
6^2=36 36*3.14=113.04
We now have the area of the base.
Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.
113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.
limit x->oo (sqrt(x^2-9x+1)-x)=?
I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.
Answers
Note that the limit of the expression as x approaches infinity is 1/2.
How did we arrive at this conclusion ?start by multiplying both the numerator and denominator by the conjugate expression
√ (x ² - 9x + 1) + x,
this will eliminates the root in the numerator
lim x->∞ [(√(x ² - 9x + 1) - x) * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)
Expanding the numerator
lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)
Simplifying further:
lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)
we can see that the 1/x ² term approaches zero, and the expression simplifies to
lim x->∞ [(1 - 0)] / (√(1 - 0) + 1)
= 1/2
So it is correct to state that the limit of the expression as x approaches infinity is 1/2.
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Helppppppp pleaseee
The loudness of sound in decibels perceived by the human ear depends on the intensity levels according to
D=10log(I/lo)
Find the decibel level when I is 63, 096 times Io.
The decibel is -------------- dB when I is 63, 096 times Io.
Round your answer to the nearest whole number.
Answers
Answer:
We can use the given formula to calculate the decibel level D when the intensity level I is 63,096 times Io:
D = 10log(I/lo)
Where Io is the reference intensity level and is typically taken to be the threshold of hearing, which is 10^−12 watts/m^2.
So, substituting the values, we get:
D = 10log(63,096*Io/Io) = 10log(63,096)
Using a calculator, we find:
D ≈ 47.1 dB
Rounding this to the nearest whole number, we get:
The decibel level is 47 dB when I is 63,096 times Io.
I hope this helps mate.