sec(9x + 2) = csc(-x + 24)
Answers
Consider the given expression,
\(\begin{gathered} \sec (9x+2)=\csc (-x+24) \\ \sec (9x+2)=\csc (24-x) \end{gathered}\)Consider the formulae,
\(\begin{gathered} \sec \theta=\frac{1}{\cos\theta} \\ \csc \theta=\frac{1}{\sin\theta} \\ \sin (90-\theta)=\cos \theta \end{gathered}\)Then the expression is transformed as,
\(\begin{gathered} \frac{1}{\cos(9x+2)}=\frac{1}{\sin (24-x)} \\ \sin (24-x)=\cos (9x+2) \\ \sin (24-x)=\sin \mleft\lbrace90-(9x+2)\mright\rbrace \\ \sin (24-x)=\sin \lbrace90-9x-2\rbrace \\ 24-x=88-9x \\ 9x-x=88-24 \\ 8x=64 \\ x=8 \end{gathered}\)Consider another formula,
\(\sin (90+\theta)=\cos \theta\)This will give the other value of 'x',
\(\begin{gathered} \frac{1}{\cos(9x+2)}=\frac{1}{\sin(24-x)} \\ \sin (24-x)=\cos (9x+2) \\ \sin (24-x)=\sin \mleft\lbrace90+(9x+2)\mright\rbrace \\ 24-x=90+9x+2 \\ 9x+x=24-88 \\ 10x=-64 \\ x=-6.4 \end{gathered}\)Thus, the given trigonometric equation has two solutions 8 and -6.4
Solve for the first angle as,
\(\begin{gathered} 9x+2=9(8)+2=72+2=74 \\ 9x+2=9(-6.4)+2=-57.6+2=-55.6 \end{gathered}\)Solve for the other angle as,
\(\begin{gathered} -x+24=-(8)+24=16 \\ -x+24=-(6.4)+24=17.6 \end{gathered}\)
Related Questions
A parobola has the equation y=x²+2x-3
What are the coordinates of the turning point of the parabola? what is the equation of the axis of symmetry for this parabola?
Answers
Answer:
(-1,-4) is the vertex
x = -1 is the equation of symmetry;
Step-by-step explanation:
See attached image.
Answer:
(- 1, - 4 ) and x = - 1
Step-by-step explanation:
given a parabola in standard form
y = ax² + bx + c ( ax≠ 0 )
then the x- coordinate of the vertex is
x = - \(\frac{b}{2a}\)
y = x² + 2x - 3 ← is in standard form
with a = 1, b = 2 , then
x = - \(\frac{2}{2}\) = - 1
substitute x = - 1 into the equation for corresponding y- coordinate
y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4
vertex = (- 1, - 4 )
this is an upward opening parabola ( a > 0 )
the axis of symmetry is a vertical line passing through the vertex with equation
x = c ( c is the value of the x- coordinate of the vertex ), then equation is
x = - 1
I need help with my homework
Answers
Answer:
1.) 10
2.) 8
3.) 24
4.) 4
5.)39
6.) 45
7.) 15
8.) 6
Step-by-step explanation:
1.) 9+8= 17, 17-7=10
2.) 7-5=2, 2+6=8
3.) 4(-1)= -4, -6(-4)=24
4.)8/4=2, 2(2)=4
5.) 6+7=13, 3(13)=39
6.) 10-1=9, 5(9)=45
7.) 72/9=8, 8+7=15
8.) 4+4=8, 48/8=6
Hope this helps.
Step-by-step explanation:
9+8-7=(9+8)-7=17-7=10
7-5+6=(7-5)+6=2+6=8
-6*4(-1)=-6*(-4)=24
8/4*2=2*2=4
3(6+7)=3*13=39
5(10-1)=5*9=45
72/9+7=8+7=15
48/(4+4)=48/8=6
A line starts at (negative 2, 0), goes to (5, question mark), and then goes down to (6, 0). What would the height need to be for this curve to be a density curve? One-fourth One-half StartFraction 1 Over 8 EndFraction StartFraction 1 Over 16 EndFraction
ANSWER
One-half
A density curve is a continuous curve that describes the probability distribution of a continuous random variable. In order to be a density curve, the curve must meet several conditions:
The curve must be non-negative everywhere, meaning it must have a y-value of at least 0 at every point.
The curve must have a total area of 1 under it.
The curve must be symmetrical around the mean of the distribution.
In this case, the curve starts at (negative 2, 0) and goes to (5, question mark). It then goes down to (6, 0). For the curve to be a density curve, the y-value at x=5 must be at least half the distance from the x-axis to the top of the curve. This is because the curve must have a total area of 1 under it, and the area under the curve between x=-2 and x=6 must be 1. Since the curve starts at y=0 and ends at y=0, the curve must reach its maximum height at x=5. Therefore, the height at x=5 must be at least one-half in order for the curve to be a density curve.
Answers
The height of the curve must be 1/2 in order for it to be a density curve.
How to determine the height needed for the curve to be a density curve?In order for the curve to be a density curve, it must meet the following criteria:
1. The curve must be nonnegative everywhere, meaning that the y-value of the curve must be greater than or equal to 0 at all points.
2. The area under the curve must be equal to 1.
Since the curve starts at (negative 2, 0) and goes to (5, question mark), and then goes down to (6, 0), the area under the curve will be a trapezoid with a height of question mark and bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).
The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:
area = ((3 + 1) × question mark) / 2
Since the area under the curve must be equal to 1, we can set up the equation:
1 = ((3 + 1) × question mark) / 2
Solving for question mark, we get:
question mark = 2/4
question mark = 1/2
Therefore, the height of the curve is 1/2
Learn more about density curve on:
https://brainly.com/question/24244167
#SPJ1
The specifications for a manifold gasket that installs between two engine parts calls for a thickness of 2.500 mm + 020 mm. The standard deviation of the process is estimated to be 0.004 mm. The process is currently operating at a mean thickness of 2.50 mm. (a) What are the upper and lower specification limits for this product? (b) What is the Cp for this process? (c) The purchaser of these parts requires a capability index of 1.50. Is this process capable? Is this process good enough for the supplier? (d) If the process mean were to drift from its setting of 2.500 mm to a new mean of 2.497, would the process still be good enough for the supplier's needs? R
Answers
The upper specification limit is 2.520 mm, and the lower specification limit is 2.480 mm. The process is not capable according to the purchaser's requirement of a capability index of 1.50.
(a) The upper specification limit (USL) is calculated by adding the process mean (2.500 mm) to the upper tolerance (0.020 mm), resulting in 2.520 mm. The lower specification limit (LSL) is calculated by subtracting the lower tolerance (0.020 mm) from the process mean, resulting in 2.480 mm.
(b) The process capability index (Cp) is calculated by dividing the tolerance width (USL - LSL) by six times the standard deviation. In this case, the tolerance width is 0.040 mm (2.520 mm - 2.480 mm) and the standard deviation is 0.004 mm. Therefore, Cp = 0.040 mm / (6 * 0.004 mm) = 1.25.
(c) The purchaser requires a capability index (Cpk) of 1.50, which measures how well the process meets the specification limits. Since Cp (1.25) is less than the desired Cpk (1.50), the process is not capable according to the purchaser's requirement. It is not good enough for the supplier either, as the Cp is less than the desired level.
(d) If the process mean were to drift to 2.497 mm, the Cp value would remain the same at 1.25. Since the Cp value is still less than the desired Cpk of 1.50, the process would still not be good enough for the supplier's needs, even with the changed process mean.
Learn more about standard deviation here:
https://brainly.com/question/29115611
#SPJ11
a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 45 ft from the base of the pole?
Answers
The most appropriate choice for similarity of triangles will be given by -
Speed of tip of the shadow of woman = 6 ft/s
What are similar triangles?
Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.
Here,
The diagram has been attached here
Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.
Height of street light = 18 ft
Height of woman = 6ft
The two triangles are similar [As height of woman is parallel to the height of pole]
\(\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\\)
To find the speed, we have to differentiate both sides with respect to time 't'
\(\frac{dy}{dt} =\frac{3}{2}\frac{dx}{dt}\\\frac{dy}{dt}=\frac{3}{2} \times 4\\\frac{dy}{dt} = 6\)
Speed of tip of her shadow = 6 ft
To learn more about similarity of triangles, refer to the link-
https://brainly.com/question/14285697
#SPJ4
Find an equation of the parabola with the focus and directrix given. \left(0, \frac{1}{2}\right), y=-\frac{1}{2}
Answers
To find the equation of a parabola given the focus and directrix, we can use the definition of a parabola.
The focus of the parabola is given as (0, 1/2), and the directrix is given by the equation y = -1/2.
Step 1: Find the vertex of the parabola.
The vertex of the parabola is the midpoint between the focus and the directrix. In this case, the y-coordinate of the vertex is the average of the y-coordinates of the focus and the directrix. Therefore, the y-coordinate of the vertex is \((1/2 + (-1/2))/2 = 0.\)
Step 2: Determine the distance between the vertex and the focus.
Since the vertex is at (0, 0), the distance between the vertex and the focus is the y-coordinate of the focus, which is 1/2.
Step 3: Write the equation of the parabola in vertex form.
The equation of the parabola in vertex form is \((y - k)^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.
In this case, the vertex is (0, 0), so the equation becomes \(y^2 = 4a(x - 0)\).
Step 4: Determine the value of 'a'.
Since the distance between the vertex and the focus is 1/2, we know that 4a = 1/2. Solving for 'a', we find a = 1/8.
Step 5: Substitute the value of 'a' into the equation.
Substituting a = 1/8 into the equation, we get\(y^2 = (1/8)(x - 0)\), which simplifies to \(y^2 = 1/8x\).
Step 6: Simplify the equation.
To simplify the equation, we can multiply both sides by 8 to eliminate the fraction, resulting in \(8y^2 = x\).
So, the equation of the parabola with the given focus and directrix is \(8y^2 = x\).
The equation of the parabola with the focus (0, 1/2) and the directrix\(y = -1/2 is 8y^2 = x.\)
To find the equation of a parabola given the focus and directrix, we can use the definition of a parabola. The focus of the parabola is given as (0, 1/2), and the directrix is given by the equation y = -1/2. We start by finding the vertex of the parabola, which is the midpoint between the focus and the directrix. The y-coordinate of the vertex is the average of the y-coordinates of the focus and the directrix, which in this case is (1/2 + (-1/2))/2 = 0.
Next, we determine the distance between the vertex and the focus, which is the y-coordinate of the focus, 1/2. With the vertex at (0, 0), the equation of the parabola in vertex form becomes y^2 = 4a(x - h), where (h, k) is the vertex. Substituting the values, we get \(y^2 = 4a(x - 0)\). To find the value of 'a', we use the fact that the distance between the vertex and the focus is 1/2. Thus, 4a = 1/2, and solving for 'a', we find a = 1/8.
Substituting this value back into the equation, we get \(y^2 = (1/8)(x - 0)\), which simplifies to y^2 = 1/8x. Multiplying both sides by 8, we eliminate the fraction and the equation becomes\(8y^2 = x\). Therefore, the equation of the parabola with the given focus and directrix is \(8y^2 = x\).
The equation of the parabola with the focus (0, 1/2) and the directrix \(y = -1/2\)is\(8y^2 = x\).
To know more about vertex :
brainly.com/question/32432204
#SPJ11
What is the value if Y is between C and Z , XY= 3a, XZ=5a-4, and YZ.
a=??
Please help!
Answers
The value of a is gotten from the equation 5a - 4 = 3a + 14 which gives a = 9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Y is between X and Z, hence:
XZ = XY + YZ
XY= 3a, XZ=5a-4, and YZ = 14, therefore substituting gives:
5a - 4 = 3a + 14
a = 9
The value of a is gotten from the equation 5a - 4 = 3a + 14 which gives a = 9
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
please help i need to pass math class
Answers
Answer:
4. (B)
5. (C)
6. (C)
7. (B)
8. (B)
9. (D)
10. (B)
Hope this helps! Have a nice day!
Step-by-step explanation:
Is the following sometimes, always, or never true? If two lines intersect to form congruent adjacent angles, then the lines are perpendicular.
Answers
Answer:
sometime
Step-by-step explanation:
Which table represents a function?
Answers
Answer:
table 1
Step-by-step explanation:
table one, because you have different value of x (inputs) with no repetition for the same value
Write 55 as a product of its prime factors
Answers
Answer:
55 = 5 × 11
Step-by-step explanation:
The only prime factors of 55 are 5 and 11, thus
55 = 5 × 11
Answer:
To express 55 as a product of its prime factors you do long division
After you've done that you will get this as your final answer
55= 5×11
Three less than the product of 2 and a number is equal to 5
Answers
Answer:
3<2*x=5
Step-by-step explanation:
Hope this helped, Have a Wonderful Day/Night!!
( btw the astric means multiplication )
The unknown number will be equal to 4.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that three is less than the product of 2 and a number is equal to 5. The unknown number will be calculated as:-
2x - 3 = 5
2x = 5 + 3
2x = 8
x = 8 / 2 = 4
Therefore, the unknown number will be equal to 4.
The complete question is given below:-
Three less than the product of 2 and a number is equal to 5. Calculate the unknown number.
To know more about an expression follow
https://brainly.com/question/4344214
#SPJ2
who wants 15 points?
Answers
Answer:(:
Step-by-step explanation:
MEEEEEEEEE!!!!!
Answer: Me ty lol
Step-by-step explanation:
11. Write a function rule for the area of a rectangle with a length 7 m more than three
times its width. What is the area of the rectangle when its width is 3 m?
Answers
The area of the rectangle when its width is 3 m is 39m².
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
A function rule for the area of a rectangle with a length 7 m more than three times its width.
Area of rectangle = Length(Width)
Area of function = (w) (3w+7)
Area of function = 3w² + 7w
If w = 3m
Area of function = 3(3)² +7(3)
Area of function = 3(9) + 21
Area of function = 18 + 21
Area of function = 39
the area of the rectangle when its width is 3 m is 39m².
To learn more about area, visit:
https://brainly.com/question/27683633
#SPJ13
Superman begins flying at a constant rate of 100 miles per hour. After one mile he increases his flying rate by 20% and maintains the new rate for the duration of the second mile. He continues this pattern, increasing his rate by 20% at the beginning of each mile. During which mile does his rate first become at least 200 miles per hour
Answers
Superman begins flying at a constant rate of 100 miles per hour. After one mile he increases his flying rate by 20% and maintains the new rate for the duration of the second mile.
Increasing his rate by 20% at the beginning of each mile. During which mile does his rate first become at least 200 miles per hour?
The rate of Superman when he begins to fly is constant. He starts at 100 mph, and for every mile he flies, he increases his speed by 20%.
In the first mile, his speed would remain at 100 miles per hour.
In the second mile, he will be able to fly at a speed of 120 miles per hour.
Let's make a table for better understanding:
Mile Rate (in mph) | 1 | 100 | 2 | 120 | 3 | 144 | 4 | 172.8 | 5 | 207.36 |
Hence, the rate of Superman becomes at least 200 miles per hour in mile number 5.
Answer: 5
To know more about speed ,visit:
https://brainly.com/question/17661499
#SPJ11
When a dilation is applied to a geometric figure, the pre-image and image are similar to each other.
True or False? ^^
Answers
Answer:
false
Step-by-step explanation:
Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.
Answers
The average rate of change is 4.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The rate of change in interval [0, 2]
r=[h(2)-h(0)]/2
h(2)=(2)²+2(2)-6
h(2)=4+4-6
h(2)=2
h(0)=(0)²+2(0)-6
h(0)=0+0-6
h(0)=-6
So, r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(8)/2
r=4
Learn more about this concept here:
https://brainly.com/question/9645290
#SPJ1
![Find the average rate of change of each function over the interval [0, 2]. Match each representation](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/Mk2pIgBmUxKvUt972vzMARCGHawWetHq.png)
PLEASE HELP MEE !!
Marcus made $500 working a 40 hour shift last week. He also runs a side business selling t-shirts for $12 each. How much money will Marcus have earned if he saves the $500 from last week, works another shift of 30 hours this week, and sells 22 t-shirts online?
Marcus will have a total of ____ dollars saved.
Answers
Answer:
764
Step-by-step explanation:
12x22=264+500=764
hope this helps
You have to find the common difference, the term named in the problem, and the explicit formula.
Answers
Question 1
Given the sequence
31, 61, 91, 121,...
An arithmetic sequence has a constant difference 'd' and is defined by
\(a_n=a_1+\left(n-1\right)d\)
computing the differences of all the adjacent terms
61 - 31 = 30, 91 - 61 = 30, 121 - 91 = 30
The difference between all the adjacent terms is the same and equal to
d = 30
As the first term of the sequence is:
a₁ = 31
now substituting a₁ = 31 and d = 30 in the nth term of the sequence
\(a_n=a_1+\left(n-1\right)d\)
\(a_n=30\left(n-1\right)+31\)
\(a_n=30n+1\)
Now, putting n = 36 to determine the 36th term
\(a_n=30n+1\)
\(a_{36}=30\left(36\right)+1\)
\(a_{36}=1080+1\)
\(a_{36}=1081\)
Thus, the 36th term is:
\(a_{36}=1081\)
Question 2
Given the sequence
-34, -44, -54, -64, ...
An arithmetic sequence has a constant difference 'd' and is defined by
\(a_n=a_1+\left(n-1\right)d\)
computing the differences of all the adjacent terms
\(-44-\left(-34\right)=-10,\:\quad \:-54-\left(-44\right)=-10,\:\quad \:-64-\left(-54\right)=-10\)
The difference between all the adjacent terms is the same and equal to
\(d=-10\)
As the first term of the sequence is:
a₁ = -34
now substituting a₁ = -34 and d = -10 in the nth term of the sequence
\(a_n=a_1+\left(n-1\right)d\)
\(a_n=-10\left(n-1\right)-34\)
\(a_n=-10n-24\)
Now, putting n = 26 to determine the 36th term
\(a_n=-10n-24\)
\(a_{26}=-10\left(26\right)-24\)
\(a_{26}=-260-24\)
\(a_{26}=-284\)
Thus, the 26th term is:
\(a_{26}=-284\)
y = -2x + 1d: {-4, -3, -2, -1} ri{Blank 1:Blank 2:Blank 3:Blank 4:
Answers
Problem
y = -2x + 1
d: {-4, -3, -2, -1} ri{
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Solution
For this case we just need to find the range with the domain given like this:
Blank 1: -2(-4) +1= 8+1 =9
Blank 2: -2(-3) +1= 6+1=7
Blank 3: -2(-2) +1= 4+1=5
Blank 4: -2(-1) +1= 2+1=3
it is known that 20% of products on a production line are defective. products are inspected until first defective is encountered. what is the probability that the first defective was found after inspecting exactly 3 products?
Answers
= 0.0655.
This is stated in a different way and i would take this as 3 non defective before first defective on the 6th inspection. That would be 0.8^3*0.2 = 0.0655.
You can learn more about this through the link below:
https://brainly.com/question/14210034#SPJ4
Solve: (x2−x−6/x2)=(x-6/2x)+(2x+12/x)
After multiplying each side of the equation by the LCD and simplifying, the resulting equation is: ?
Answers
To solve the equation (x² - x - 6) / x² = (x - 6) / (2x) + (2x + 12) / x, we need to multiply each side of the equation by the least common denominator (LCD) to eliminate the fractions.
The LCD of the equation is x² * 2x * x = 2x⁴.
Multiplying both sides of the equation by the LCD, we get:
2x⁴ * (x² - x - 6) / x² = 2x⁴ * (x - 6) / (2x) + 2x⁴ * (2x + 12) / x
Simplifying each term:
2x⁴ * (x² - x - 6) / x² = 2x⁴ * (x - 6) / (2x) + 2x⁴ * (2x + 12) / x
2x² * (x² - x - 6) = x³ * (x - 6) + 4x⁵ * (2x + 12)
Expanding the expressions:
2x⁴ - 2x³ - 12x² = x⁴ - 6x³ + 8x⁶ + 48x⁵
Rearranging the terms:
0 = 8x⁶+ 48x⁵ - x⁴ + 6x^3 - 12x² + 2x³ - 2x⁴
Combining like terms:
0 = 6x⁶ + 46x⁵ - 3x⁴ + 8x³ - 12x²
So, after multiplying each side of the equation by the LCD and simplifying, the resulting equation is 6x⁶+ 46x⁵ - 3x⁴ + 8x³- 12x² = 0.
In this case, the resulting equation is a sixth-degree polynomial equation, and solving it further may require factoring, using the rational root theorem, or employing other methods depending on the specific instructions or context of the problem.
For more information on polynomial equation visit:
brainly.com/question/28947270
#SPJ11
which statement is equivalent to the inequality | x-3 | > 5
Answers
Find two numbers whose sum is 11 and whose product is a maximum. The two numbers are (Simplify your answer. Use a comma to separate answers as needed.)
Answers
To find two numbers whose sum is 11 and whose product is maximum, we can use a mathematical approach.
Let's denote the two numbers as x and 11 - x, where x represents the first number. The sum of these numbers is 11, so we can write the equation x + (11 - x) = 11. Simplifying this equation gives us 2x = 11, and solving for x results in x = 11/2 or 5.5. Therefore, the two numbers are 5.5 and 5.5.
To explain this answer, we can consider the properties of quadratic functions. When we multiply two numbers, their product is maximized when the numbers are equal. By representing one number as x and the other as 11 - x, we ensure that their sum is 11. We then set up an equation using the sum constraint and solve for x. In this case, we find that x = 5.5, indicating that both numbers are 5.5. As a result, their product is maximized at 30.25.
To learn more about product click here: brainly.com/question/31815585
#SPJ11
What is the value of x in the diagram?
Answers
Answer:
Simplifying
6x = 36
Solving
6x = 36
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '6'.
x = 6
Simplifying
x = 6
Explain how to find the zeros of the given polynomial: x3+3x2–x−3
What are the zeros?
Answers
Answer:
Step-by-step explanation:
The zero (root) of a function is any value of the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x-axis.
~~~~~~~~~
f(x) = x³ + 3x² - x - 3
f(-3) = ( - 3 )³ + 3( - 3 )² - ( - 3 ) - 3 = 0
f(-1) = ( - 1 )³ + 3( - 1 )² - ( - 1 ) - 3 = 0
f(1) = ( 1 )² + 3( 1 )² - ( 1 ) - 3 = 0
Answer:
The zeroes of the function are x = -3, x = -1, and x = 1.
Step-by-step explanation:
We are given a polynomial and asked to find the zeroes of the polynomial. Our given polynomial is:
\(x^3 + 3x^2 - x - 3\)
The zeroes of a polynomial are the solutions or roots of the function. This is where if the line were graphed, the line would intersect the x-axis at those points (sometimes there will only be one).
This is a cubic polynomial. We can use a factoring technique referred to as grouping, which is most effective when factoring a trinomial with the only satisfaction met is: a > 1.
However, it can also be used when a > 1 is not true.
We can work with an example polynomial first and then work through solving the given polynomial.
An example polynomial would be:
\(10x^2 + 8x - 9 = 0\)
In grouping, our main goal is to factor as quickly as possible. If you examine the polynomial, there is no common factor between 10x², 8x, or -9, so we cannot take out a GCF and need to use another factoring technique.
Since a > 1, we can instantly jump to using the grouping factoring technique.
Please note that the parent function for a quadratic is \(ax^2 + bx + c = 0\).
To group:
We want to find the product of the terms a and c. So, with our example polynomial, a is 10, b is 8, and c is -9. Therefore, let's find the product of 10 and -9.Using ac, we will list all available factors. After doing this, we will find two factors of ac that will add up to give us b.These two factors are then substituted with b and c in the following parent equation: \(ax^2 + bx + cx + d\).Finally, the equation is factored using parentheses in the following format: \((ax^2 + bx)(+ cx + d) = 0\)After we group the function, we take the GCF out of both parentheses sets and write it as a coefficient to the remaining bit of the parentheses. The two GCFs are a set of terms and the remaining portion is the other set of terms.Let's use grouping to solve \(x^3 + 3x^2 - x - 3\).
Because we already have four terms, we can skip steps one through three and go straight to step four.
\((x^3 + 3x^2)(-x - 3)\)
Now, we need to take the GCF of both parentheses sets. Let's do this with our first set of terms.
You can divide x² out of both x³ and 3x², so x² is the GCF, leaving x and 3 behind.Then, we can also do this with our second set of terms.
There is a -1 implied in front of x, and there is no other common term between -x and -3, so -1 is our GCF, leaving x and 3 behind.Because our remaining terms for both sets match, we have grouped our polynomial correctly. Now, let's combine our GCFs into one term and list our common term as the second term.
\((x^2-1)(x+3)\)
Now, we can break apart x² - 1 into more factors.
This is the difference of two squares. The formula for the difference of two squares is \((a^2-b^2)=(a+b)(a-b)\)
Our perfect squares are every integer in the spectrum of numbers, so 1 is a perfect square. Therefore, x² becomes x and 1 becomes ±1.
Our new terms would therefore be \((x+1)(x-1)(x+3)\).
Finally, to find zeroes of a function, x needs to equal something. Therefore, we can set our terms equal to zero and solve for x.
Term 1 (x + 1)
\(x + 1 = 0\\\\x + 1 - 1 = 0 - 1\\\\\boxed{x = -1}\)
Term 2 (x - 1)
\(x - 1 = 0\\\\x - 1 + 1 = 0 + 1\\\\\boxed{x = 1}\)
Term 3 (x + 3)
\(x + 3 = 0\\\\x + 3 - 3 = 0 - 3\\\\\boxed{x = -3}\)
Therefore, our zeroes are listed above. To finalize our answer, we want to list them in increasing order, so this will be most negative to most positive. Therefore, our final answer is x = -3, -1, 1.
standard error of an estimator is not affected by the multiple choice question. population standard deviation. sample size. population size
Answers
The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.
The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.
It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)
where , n --> sample size
σ --> population standard deviations
Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.
For more information about standard error, visit :
https://brainly.com/question/14467769
#SPJ4
Complete question:
standard error of an estimator is not affected by the multiple choice question.
a) population standard deviation
b) sample size
c) population size
160 m of fencing to enclose a quadrilateral shape pen (3 sided) for a children's play area. Determine the shape of the children's play area that gives the maximum area.
Answers
Answer:
A square of side length 40 m will give the maximum area of the play area
Step-by-step explanation:
Mathematically, it has been established that a square gives the maximum area of a quadrilateral
Hence, for us to have a maximum area of the given perimeter, we have to divide the perimeter by 4 to get the side length of the square
From what we have, we know that the perimeter of the fencing is 160 m
To get the side length, we divide the perimeter by 4
Side length of the shape would be 160/4 = 40 m
In a family with 7 children, excluding multiple births, what is the probability of having 7 boys? Assume that a girl is as likely as a boy at each birth. Let E be the event that the family has 7 boys, where the sample space S is the set of all possible permutations of girls and boys for 7 children. Find the number of elements in event E, n(E), and the total number of outcomes in the sample space, n(S). n(E) = n(S)=
Answers
The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.
To find the probability, we need to calculate n(E) and n(S).
In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.
This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.
Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.
Learn more about Probability click here : brainly.com/question/30034780
#SPJ11
why is change management a significant challenge for many organizations during enterprise system implementation?
Answers
Change management is a significant challenge for many organizations during enterprise system implementation due to various factors such as resistance to change, organizational culture, lack of employee engagement, and inadequate communication and training.
Determine the enterprise system implementation?During enterprise system implementation, organizations typically undergo significant changes in processes, roles, and technologies. This can lead to resistance from employees who may be accustomed to existing ways of working. Resistance to change can hinder the adoption and utilization of the new system, affecting its success.
Organizational culture also plays a role. If the organization has a rigid or hierarchical culture that is resistant to change or lacks a culture of innovation and learning, it becomes difficult to implement and integrate the new system effectively.
Lack of employee engagement and involvement in the implementation process can further impede change. Employees need to understand the reasons behind the change, how it will benefit them and the organization, and be provided opportunities for input and feedback.
Inadequate communication and training can be a major obstacle. Employees must be informed about the changes, their roles and responsibilities, and be provided with sufficient training to effectively use the new system. Insufficient communication and training can lead to confusion, frustration, and resistance.
Overall, change management is crucial during enterprise system implementation to address these challenges and ensure a smooth transition, user acceptance, and successful adoption of the new system.
To know more about innovation, refer here:
https://brainly.com/question/30929075#
#SPJ4