Answer:
Step-by-step explanation:
The Rational Zeroes Theorem states that if a polynomial equation has a rational solution (a solution that can be expressed as a fraction of two integers), then that rational solution must be of the form p/q, where p is a factor of the constant term (in this case 36) and q is a factor of the leading coefficient (in this case 4).
Step 1: Find the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: For each factor of 36, divide it by each factor of 4 to get a list of possible rational solutions.
Step 3: Test each of the possible rational solutions by plugging them into the polynomial equation and seeing if they make the equation equal to zero. If a solution makes the equation equal to zero, it is a root of the polynomial.
Step 4: Once you have found all of the roots of the polynomial, you can use them to write the polynomial in factored form.
Note: This method only works for polynomials with real coefficients and will only give you the real solutions of the equation. If the polynomial has complex solutions, you will need to use a different method to find them.
Jason decides to sell his band's CD. It required an investment of $3349 for computer hardware and it will cost $3.65 for materials for each disk. If each CD sells for $13.50, how
many must he sell to break even?
196 CDs
340 CDs
339 CDs
195 CDs
Answer:
340 CDs
Step-by-step explanation:
To answer this question, we're dealing with three functions for one problem, namely the revenue function, the cost function, and the profit function.
The revenue function is R(q) = pq, where p is the price of a certain good and q is the quantity sold.
The cost function is C(q) = variable cost + fixed cost, where variable costs changes depending on the quantity of goods produced and fixed cost is a one-time cost for the producer (e.g., an investment, rent, etc.).
The profit function is P(q) = R(q) - C(q) and is simply the cost function subtracted from the revenue function.
The "break-even point" is the point at which profit = $0 and the point at which cost = revenue.
From the problem, we see that Jason invested $3349 (once) for his CDs and each disk requires $3.65 for the materials so our cost function is C(q) = 3.65q + 3349
Furthermore, we see that each disks sells for $13.50, so our revenue function is R(q) = 13.5q
Our profit function then is P(q) = 13.5q - (3.65q + 3349) = 13.5q - 3.65q - 3349 = 9.85q - 3349.
Thus, to find the break-even point, we set profit = 0 and solve for q:
[tex]0=9.85q-3349\\3349=9.85q\\340=q[/tex]
Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the greatest measure
• B. second-longest side
• C. shortest side
• D. angle with the smallest measure
The longest side of a triangle is always opposite the,
A. angle with the greatest measure.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
We know, The length of the largest side in a triangle is opposite to the largest angle.
The statement, The longest side of a triangle is always opposite the
angle with the greatest measure.
Because A longer angle will be more spread out and hence the opposite side will be longer too.
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If f(r)=√, which equation describes the graphed function?
The equation that describes the graphed function is given as follows:
A. y = f(-x + 3).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]y = \sqrt{x}[/tex]
The function was reflected over the y-axis, hence it is given as follows:
[tex]y = \sqrt{-x}[/tex]
Then it was moved 3 units right, hence the definition is given as follows:
[tex]y = \sqrt{-(x - 3)}[/tex]
[tex]y = \sqrt{-x + 3}[/tex]
Hence:
y = f(-x + 3), as x was replaced by -x + 3.
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An electrician charges a set fee of $100 for every house call and then charges an
additional $60 per hour. Make a table of values and then write an equation for C, in
terms of t, representing the total cost of the electrician's services if the electrician
spends t hours at the house working.
Answer:
C = 60t + 100
Step-by-step explanation:
our flat fee is 100 dollars, meaning you're charged straight up $100, and then for each hour the electrician works, you're charged another $60
this means that 100 stays constant, while the amount of times you multiply 60 changes based on the amount of hours the electrician works
therefore, our equation will be C = 60t + 100, where C represents the total cost while t represents the hours the electrician works
for our table, we can use the equation we just found to make one
the easiest and most reasonable numbers will be 1, 2, 3, 4, and 5, because it's unreasonable to charge a proportional amount for something such as 1.2948 hours
using the equation, we plug 1, 2, 3, 4, and 5 into C = 60t+100 to find C for t
C = 160, 220, 280, 340, 400
T = 1, 2, 3, 4, 5
A grade distribution for a particular math class is shown below.
Grade distribution
Quizzes,
30%
Homework
15%
Test, 30%
Classwork
25%
According to the circle graph, what must be true?
O Tests are weighed the most when determining a grade.
O
Homework is worth twice as much as quizzes.
More than half the grade is based on tests and quizzes combined.
If someone never does their classwork it is possible for them to earn an 80 % in the class.
The statement is true; Tests are weighed the most when determining a grade.
What is Graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given in the question that:
Grade distribution
Quizzes, 30%
Homework 15%
Test, 30%
Classwork 25%
The total giving 100%.
A particular student scored the following;
87.9% on exams, 77.8% quiz, 90% Home work and 100% on class participation
Calculating the percentages the student had for each
Exam total = 50 x 0.879 = 43.95% earned
Quiz = 30 x 0.778 = 23.34% earned
Home work = 15x 0.9 = 13.5% earned
Class participation = 5*1 = 5% earned
Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%
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When Cheryl's phone battery is 55% charged, she knows it will last for another 1.5 hours. If Cheryl's
phone battery loses its charge at a constant rate, how long, in hours, will it last when it is fully charged?
The battery will last 2.73 hours when it is fully charged
How to determine how long it will last when it is fully charged?The unit rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, the unit rate is one quantity divided by the other quantity
Since Cheryl's phone battery is 55% charged and it will last for another 1.5 hours. Thus, the rate will be:
rate = 1.5 hours/55% = 3/110 hour per %
When it is fully charged, that is 100%. Thus, it will take:
Time for 100% = (3/110) * 100% = 2 8/11 hours = 2.73 hours
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HelpThe ratio of the perimeters of two similar quadrilaterals is 2:4. What is the ratio of their areas? PLLLLLLLLLLSSSSSSss
a.1:2
b. 4.8
c. 2:4
d. 4:16
e. 5:3
The ratio of the areas of the quadrilaterals is 1:2. Option A
What is the ratio of the perimeter?Let's assume that the two similar quadrilaterals have side lengths of x and 2x, respectively. The ratio of their perimeters is then 2x + 2x + 2x + 2x = 8x : 2 * (2x + 2x + 2x + 2x) = 4 * 8x = 32x. The ratio of the perimeters is 2:4, so we can write the equation:
8x/32x = 2/4
Solving for x, we find that x = 4.
So the ratio of the areas of the two similar quadrilaterals is (x^2)/(2x)^2 = (4^2)/(2 * 4^2) = 16/32 = 1/2.
Therefore, the ratio of the areas of the two similar quadrilaterals is 1:2.
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solve for x, 11, 31°
The value of x is 21.4.
What is right-angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.
The sine of an angle is the ratio of height to the hypotenuse.
Therefore,
sin 31° = height/hypotenuse
sin 31° = 11/x
Multiply x with both sides:
x sin 31° = 11
Divide sin 31° with both sides:
x = 11/ sin 31°
x = 21.35
x ≈ 21.4 units
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Can someone do all of this and explain each one
Answer: no exact answer
Step-by-step explanation:
Linda and Rob charged a $67.44 restaurant bill on their credit card. They gave the card to the waitress, who accidentally transposed two digits and charged them $76.44. They did not notice this until they received their statement later that month. Their card has an 18% APR.
They plan to pay their monthly statement amount in full, but they need to deduct the amount they were overcharged, plus the finance charge that was based on the incorrect amount. If the overcharged amount was on their statement for 18 of the 31-day billing cycle, how much should they deduct from this monthly statement, including the amount they were overcharged?
Answer:
Step-by-step explanation:
a
As a technical engineer, you must calculate the elevation of a Point marked on a topographic map. The distance between the 420-foot and 440-foot contour lines is 0.5 inches, and the marked point between them is 0.2 inches from the 420-foot contour. What is the elevation, in feet, of the marked point?
A.100
B.424
C.428
D.430
E432
Answer:
The correct answer is C, 428 feet.
To calculate the elevation of the marked point, we need to interpolate between the two contour lines. The difference in elevation between the two contour lines is 20 feet (440 - 420 = 20). And since the distance between the two contour lines is 0.5 inches, each 0.1 inch increment represents a 4-foot change in elevation (20 feet ÷ 0.5 inches = 40 feet per inch ÷ 10 = 4 feet per 0.1 inch).
Since the marked point is 0.2 inches from the 420-foot contour, the elevation of the marked point can be calculated by adding 8 feet (4 feet x 0.2 inches) to the 420-foot contour line: 420 + 8 = 428 feet.
Solve this problem using Rational Zeroes Theorem (but explain it, please).
What are the real zeroes of the polynomial function:
f(x) = 4x^4 - 8x^3 - 19x^2 + 23x - 6?
The real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
What do you mean by Polynomial?In mathematics, a polynomial is an expression consisting of variables and coefficients, which are combined using the operations of addition, subtraction, and multiplication. A polynomial can have one or more terms, where each term is the product of a coefficient and one or more variables raised to non-negative integer powers. For example, the polynomial 2x² - 3x + 1 has three terms: 2x², -3x, and 1.
For the given polynomial function, the constant term is -6 and the leading coefficient is 4. Therefore, the possible rational zeroes of the function are of the form p/q, where p is a factor of -6 and q is a factor of 4.
The factors of -6 are ±1, ±2, ±3, and ±6. The factors of 4 are ±1, ±2, and ±4. So the possible rational zeroes are:
±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±3/2
To determine which of these possible rational zeroes are actual zeroes, we can use synthetic division or long division to evaluate the function at each possible zero. Doing so, we find that the actual zeroes of the function are:
x = 1/2, x = 1, x = 3/2, x = 2
Therefore, the real zeroes of the polynomial function f(x) = 4x⁴ - 8x³ - 19x² + 23x - 6 are 1/2, 1, 3/2, and 2.
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-3x+y=11,4x+3y=7 use stubstitution to solve
On solving the given system of equations →
Eq { 1 } : - 3x + y = 11
Eq { 2 } : 4x + 3y = 7
using substitution, we get {x} = -2 and {y} = 5.
What is a system of equations?In mathematics, a system of equations is a pair of equations which have a common set of solutions.
Given is the system of equations as -
- 3x + y = 11
4x + 3y = 7
The given system of equations is -
- 3x + y = 11
4x + 3y = 7
Now, we can write -
y = 11 + 3x
So -
4x + 3(11 + 3x) = 7
4x + 33 + 9x = 7
16x = - 26
{x} = - 2
Then, we can write -
- 3 x - 2 + y = 11
{y} = 5
Therefore, on solving the given system of equations using substitution, we get {x} = -2 and {y} = 5.
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What is the value of w in the solution to the following system of linear equations?.
The value of 'w' in the solution of the following system of linear equations is -[tex]\frac{1}{6}[/tex]
we can solve for a variable say 'v' then put the value of 'v' in the other equations and solve them for the value of 'w'
5v + 4w = 1
5v = 1 - 4w
v = [tex]\frac{1-4w}{5}[/tex]
now, when we put the value of 'v' in the second equation, we get:
3([tex]\frac{1-4w}{5}[/tex] ) - 6w = 2
3([tex]\frac{1-4w}{5}[/tex] ) = 2 + 6w
[tex]\frac{3-12w}{5}[/tex] = 2 + 6w
3 - 12w = 10 + 30w
-42w = 7
w = [tex]\frac{7}{-42}[/tex]
w = -[tex]\frac{1}{6}[/tex]
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1.6.3 Quiz: Graphs of Polynomial Functions
Question 8 of 10
How many zeros does the graphed polynomial function have?
A. 3
B. 1
OC. 4
D. 2
2
-10
-15-
8
0
19
The zeros of the given polynomial function are 3
Zeros of a polynomial:Zero of a polynomial are numerical values at which the polynomial will equal zero. In other words, zeros of a polynomial are numerical values of the variable which give zero when we plug into the polynomial.
For example, for a polynomial p(x) the zeros are the value of 'x' which satisfies p(x) = 0. This means by identifying the x-intercepts, we may determine the polynomial's zeros.
In the case of a graph, we can determine the zeros of a polynomial by observing the points at which the graph line will cut the x-axis. In simple words, we can say that the x-coordinates of the points where the graph meets the x-axis are the zeros of the polynomial.
Here we have a graph
In the given graph the polynomial function meets the x-axis three times at three different points.
Therefore,
The zeros of the given polynomial function are 3
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Sarah has 275 red beads and 3 times as many blue beads. She uses a total of 156 beads to make a bracelet. How many beads are left?
Answer: 994 beads
Step-by-step explanation:
Red Beads = 275
Blue Beads = 825 (275 x 3)
825 + 275 = 1100 beads (total)
1100 - 156 = 994 beads
In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°. Find the length of f, to the nearest 10th of a centimeter.
The length of side f is 12.0 inches
How to determine the length of side fFrom the question, we have the following parameters that can be used in our computation:
In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°
The sum of angles in a triangle is 180 degrees
Using the above as a guide, we have the following:
E = 180 - 72 - 61
E = 47
Using the law of sines, we have
f/sin(F) = e/sin(E)
substitute the known values in the above equation, so, we have the following representation
f/sin(72) = 9.2/sin(47)
So, we have
f = sin(72) * 9.2/sin(47)
Evaluate
f = 12.0
Hence, the length is 12.0 inches
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PLEASE HELLLP IM TAKING A QUIZ!!Cory is making popcorn. He knows that 3 identical scoops of unpopped
kernels produce 6 quarts of popcorn.
R
Which table most likely represents the total amount of popcorn, in quarts,
produced by x scoops of unpopped kernels?
Answer: C
Step-by-step explanation:
I am fairly certain this is the right answer. Good luck on your quiz!
Answer:C
Step-by-step explanation:
I remember this from class one time hope it helps:)
Solve the system of inequalities by graphing.
y < 3x+3
3x-y ≤ 4
The solution to the inequality are the region in the shaded area
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y < 3x+3
3x-y ≤ 4
Represent properly
y < 3x + 3
3x - y ≤ 4
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (0.2, 2)
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The sum of two numbers is 17 and their product is 60 what are the two numbers?
Answer:
12 and 5
Step-by-step explanation:
12+5=17
12x5=60
Answer:
Step-by-step explanation:
5 12 step by step
A certain model car has a keypad with 5 numbers on the door. To open the door, 5 numbers must be entered in the correct order and no number can be used more than once. What is the probability that someone could guess the correct code?
Answer:
Step-by-step explanation:
The probability that someone could guess the correct code for the car model with a keypad of 5 numbers is 1 in 120,000, or approximately 0.0000083.
To calculate this, we need to determine the total number of possible combinations of 5 numbers (without repetition) from a set of 5 numbers. This can be calculated as 5!/(5-5)! = 5! = 5x4x3x2x1 = 120.
So, the probability of guessing the correct code is 1/120 or 0.0000083. This means that the chances of guessing the correct code are very low and the car's security system is fairly secure.
What is the percentage, to the nearest tenth, of 29-year olds with some degree of heart disease?
The function P(x)= 120/1+372e^-0.133x models the percentage, P(x), of Americans who are x years old and have some degree of heart disease.
To the nearest tenth, 13.55% of people aged 29 have some form of cardiac disease.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
The function for the estimation of the percentage of heart disease is,
[tex]P =\dfrac{ 120}{1+372e^{-0.133x}}[/tex]
The percentage will be calculated as:-
[tex]P =\dfrac{ 120}{1+372e^{-0.133x}}[/tex]
[tex]P =\dfrac{ 120}{1+372e^{-0.133\times 29}}[/tex]
P= 120 / ( 1 +7.85)
P = 13.55%
Therefore, 13.55% of adults aged 29 have a heart condition, to the closest tenth.
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What shape is this, why?
The shape is most specifically a trapezoid because it has a pair of parallel sides
How to determine the type of the shapeFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we have the following highlights:
The sides with lengths 21 and 24 are parallel sideThe other sides are non parallelUsing the above as a guide, we have the following:
The shape is most specifically a trapezoid
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A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?
sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2
The total area of the quilt is: 112.5 square inches
How to determine the total area of the quilt?The six-sided figure is given, and we can deduce the following parameters from the question:
The shape is made of a triangle and a rectangle
The side lengths derived from the question are:
The triangle on top:
base: 5 inches and height: 5.18 inches
The rectangle at the bottom:
Base: 16 inches with a height of 7.5 inches
So, we have the total area of the figure to be
Area of figure = 1/2 * 5 * 6 + 13 * 7.5
Area of figure = 112.5
Based on the parameters, the total area is 112.5 square inches
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Help me with this Quadratic Functions graph it
1. In the figure below, a line intersects two parallel lines. Fill in the missing about how you might solve for the measurement help ASAP
Angle b is equal to 35°, angle a and angle e are each equal to 145°
What is an angle?An angle is formed when two lines intersect at a point. Types of angles are acute angle, obtuse angle and right angle. Vertical opposite angles are always congruent to each other. The sum of angles along a straight line is supplementary (add up to 180 degrees)
From the diagram:
b = 35° (vertical opposite angles are congruent)
a + b = 180° (sum of angles along a straight line)
a + 35 = 180
a = 145°
a = e = 145° (vertical opposite angles are congruent)
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The graph below is the function f(x)
The value of lim x -> -1- f(x)= -1
What is the Limit of a function?The behavior of a function at a specific input is described by its limit, a crucial concept in calculus and analysis.
Hence,
As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.
As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.
The one-sided limits do not match, so the two-sided limit does not exist.
But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.
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The graph below is the function f(x)
Find lim x -> -1- f(x)=
-0.2x+3 / 2 = -0.6 ??
Answer:
Step-by-step explanation:
-0.2x+3 / 2 = -0.6 =>
-0.2x = -(3/2) - 0.6 => (facotorize out -1)
x = ((3/2)-0.6)/0.2 =>
x = 4.5
We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
. We would like to be 99.5% confident that the estimate is within 0.1 of the true population mean. How large of a sample size is required?
n=
Answer:
5,144,079
Step-by-step explanation:
[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]
Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).
Click the bookings sheet tab and select cell f5. Calculate average revenue per passenger by dividing the fee by the number of passengers.
In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:
In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5
If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.
In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.
mean = sum of values / number of values
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