P is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P if P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P() = 0). (x).
The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.
What does the theorem of rational zeros state?According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(xconstant )'s term and q is a factor of P's leading coefficient (x).
What does rational number theorem determines?Finding the rational solutions to a polynomial equation is done using the rational root theorem, as its name suggests (or zeros or roots of a polynomial function). The answers obtained from any polynomial equation are referred to as the roots or zeros of polynomials. It's not necessary for a polynomial to have rational zeros.
So, to find rational zero theorem states:
If P(x) is a polynomial with integers coefficients and if is a zero of P(x)(P()=0), then
P is a factor of the constant term of P(x) and q is a factor of of the leading coefficient
Of P(x).
To find all the rational zero of a polynomial we can use the rational zeros theorem
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7. (01.03 LC) A craft store marks up all sewing machines 45%. What is the selling price of a sewing machine that costs $155.00 before the markup? (1 point) $169.75 $224.75 $245.50 O $278.25
The selling price is $224.75.
What is Percent?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Cost price= $155
Cost marks up = 45%
Then the selling price is
=155 + 155 x 45/100
= 155 + 155 x 0.45
=155 + 69.75
= $224.75
Hence, The selling price is $224.75.
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Please thank you :(Use the functions f(x) = x ^ 2 - 1 and g(x) = x + 11 to answer parts (a) - (g)
Answer:
(a) {-1, 1)
(b) {-11}
(c) {-3, 4}
***(d) { x < -1 or x > 1, I am not sure how else to put it, try {-1, 1} if you are not allowed to put in > or < signs
(e) (-∞, -11] or x ≤ -11
(f) {-3, 4}
(g) ( -√2, √2)
***I know the correct solution sets but I am not sure how to represent all of them given the one box you have in your solution for (a). Maybe the solution boxes for the other parts are different. Without knowing that I am only able to provide what is the correct expression
Step-by-step explanation:
We have
f(x) = x² - 1
g(x) = x + 11
(a) f(x) = 0
=> x² - 1 =
=> x² = 1
x = ± 1
Answer (a): The solution set is {-1, 1}
(b)
g(x) = 0
=> x + 11 = 0
=> x = -11
Answer (b): Solution set: {-11}
(c)
f(x) = g(x)
=> x² - 1 = x + 11
=> x² -x -12 = 0
This is a quadratic equation which can be solved by factoring:
=> (x - 4)(x+3) = 0
=> x = 4, x = -3
{-3, 4} Answer
(d) f(x) > 0
=> x² - 1 > 0
Add 1 to both sides
x² > 1
x < -1 or x > 1
[tex]\left(-\infty \:,\:-1\right)\cup \left(1,\:\infty \:\right)[/tex]
(e) g(x) ≤ 0
=> x + 11 ≤ 0
=> x ≤ -11
{-∞, -11}
(f)f(x) > g(x)
=> x²-1 > x +11
=> x² -x - 12 > 0
=> (x + 3)(x +4) > 0
=> x + 3 >0 and x - 4 > 0
=> x > -3 and x < 4
{-3, 4}
(g) f(x) ≥ 1
=> x² - 1 ≥ 1
=> x² ≥ 2
=> x ≥ ± √2
=> x ≤ -√2 or x ≥ √2
=> { -√2, √2}
In the above derivations note that if x² ≥ 1 then two possibilities are
x < - 1 or x > 1
Here are two right circular cylnders. The radius of the smaller cylinder on the left is 4 cm, and its height is 8 cm. The radius of the larger cylinder on the right is 16 cm, and its height is 8 cm. The volume of the larger cylinder is how many times as large as that of the smaller cylinder?
The larger cylinder is 16 times as large as the smaller cylinder.
Volume of cylinderThe formula for calculating the volume of cylinder is expressed according to the equation;
V = πr²h
where:
r is the radius
h is the height.
Determine the volume of the smaller cylinder;
V = π(4)²(8)
V = 128π cm^3
Determine the volume of the larger cylinder;
V = π(16)²(8)
V = 2048π cm^3
Determine the ratio
Ratio = 2048π/ 128π
Large/Small = 16
Large = 16 Small
This shows that the volume of the large cylinder is 16 times greater than that of smaller cylinder.
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Find the distance between (-12, 1) and (12, -1).
If the coordinates of two points are (x_1,y_1) and (x_2,y_2), the distance between them is given by the formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute for the coordinates: (-12,1) and (12,-1):
[tex]\begin{gathered} d=\sqrt[]{(12-(-12))^2+(-1-1)^2} \\ =\sqrt[]{(12+12)^2+(-2)^2} \\ =\sqrt[]{(24)^2+4} \\ =\sqrt[]{576+4} \\ =\sqrt[]{580} \\ =2\cdot\sqrt[]{145} \\ \approx24.08318916\ldots \end{gathered}[/tex]Therefore, the distance between (-12,1) and (12,-1) is approximately 24.08.
Carlos has a smart phone data plan that costs $20 per month that includes 7 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carlos have to pay in a month where he used 4 GB over the limit? How much would Carlos have to pay in a month where he used went over by x GB?
Answer:
Carlos will end up paying 80£ in that month, the standard data plan cost 20£ plus 60£ the price of the extra 4 GB of data used.
Carlos has to pay total $80 in a month if he uses 4 GB data over the limit and if he uses x GB data over the limit then have to pay $20+15x.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Cost of 7 GB data plan = $20,
Cost for extra data = $15 per GB.
Since, Carlos use extra 4 GB data in a month,
Cost of 1 GB extra data = $15
Cost of 4 GB extra data = $60
Total cost = cost of 7 GB data plan + Cost of 4 GB extra data
= $20 + $60
= $80
Total $80 Carlos have to pay, where he used 4 GB over the limit.
If Carlos uses x GB extra data,
Then cost of x GB extra data = $15x
Total cost = cost of 7 GB data plan + Cost of x GB extra data
= 20 + 15x
Total $20+15x Carlos have to pay, where he used x GB over the limit.
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A rectangular dog pen is constructed using a barn wall as one side and 120m of fencing for the other three sides. a) give a sketch of the situation. b) express the area in terms of x. c) sketch the graph. d) find the value of x that gives the greatest area. e) find the dimensions of the pen. f) state the domain.
Answer:
see the attachments for the sketch and the graphA = x(120 -2x)x = 30 maximizes the areadimensions: 30 m by 60 mdomain of x: [0, 60]Step-by-step explanation:
You want an expression for area, maximum area, and dimensions of a rectangular pen fenced on three sides with a total of 120 m of fencing.
a) SketchThe first attachment shows a sketch of the pen with x defined as the dimension the pen extends from the barn wall. The total length of fence is 120 m, so the side parallel to the barn will be (120 -2x) m in length.
b) AreaThe area is the product of the length and width of the rectangle:
A = (x)(120 -2x)
c) GraphThe second attachment shows a graph of the area as a function of x.
d) Greatest areaThe value of x that gives the greatest area is the x-coordinate of the vertex of the parabola. It is halfway between the zeros at x=0 and x=60. The maximum area will be had when x=30.
e) DimensionsThe dimensions of the pen are ...
x = 30
120 -2x = 120 -2(30) = 60
The pen is 30 m by 60 m, with the 60 m dimension parallel to the barn wall.
f) DomainThe area function only makes sense for values of x between 0 and 60 meters.
The domain of x is 0 ≤ x ≤ 60.
The amount of a radioactive isotope present at time t is given by A(t) = 500e^ -0.028171
grams.
How many grams remain after 40 years?
According to the radioactive isotope disintegration model, the remaining mass of the radioactive isotope after 40 years is approximately equal is 129.622 grams.
What is the amount of the mass of a radioactive isotope after a period of 40 years?
The deceasing exponential expression described in the statement models the mass of the radioactive isotope (m), in grams, as a function of time (t), in years, which represents the solution of an ordinary differential equation that represents a simple disintegration.
Now, we need to evaluate the function at t = 40 to find the amount remaining after 40 years:
A(40) = 500 · exp(- 0.028171 · 40)
A(40) = 129.622
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Use the picture shown to solve for inequalities in two triangles
GIVEN
Two triangles ABC and ACD where two corresponding sides of the two triangles are equal.
SOLUTION
The two triangles have equal sides such that:
[tex]\begin{gathered} AB=AD \\ and \\ AC=AC \end{gathered}[/tex]By this, the length of the remaining sides BC and DC are related such that the side opposite the greater angle has the greater length.
Since [tex]BC>DC[/tex]Substitute known values into the inequality:
[tex]\begin{gathered} DC=11x-33 \\ BC=77 \\ \therefore \\ 77>11x-33 \end{gathered}[/tex]Solving the inequality:
[tex]\:x<10[/tex]Recall that the side DC has to be greater than 0. Therefore:
[tex]\begin{gathered} 11x-33>0 \\ \therefore \\ x>3 \end{gathered}[/tex]Combining both solutions:
[tex]3ANSWERA’ (,)
B, (,)
C’ (,)
Please answer I give brainliest
The image's coordinates are:
A = (-2,5),
B = (3,-3),
C = (-4,-1).
What is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair od numerical coordinates, that are the signed distances from two lines that are fixedly perpendicular to the point and are measured in the same length.
How do you find coordinates on a plane?The reverse is done in order to determine a point's coordinates in a coordinate system. Start at the point and move along a vertical line either up or down to the x-axis. Your x-coordinate is located there. To get the y-coordinate, repeat the previous steps while following a horizontal line.
According to the given data:The graph's coordinates are as follows:
A = (-2,5)
B = (3, -3)
C = (-4,-1)
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Juan is a teacher who has an annual salary of $65,798. He has to pay state income tax of 5%. What is the amount that Juan pays in state income tax?
Responses
Answer:
$3,289.90
Step-by-step explanation:
65,798 times 5%
Lynette is making candles for her online store the wholesale cost of the materials for one candle is $5.35 if she sells a candle for $12 what is the percent markup round to the nearest percent
The percent markup is 124.30%.
The wholesale cost of one candle is $5.35
The selling price of the candle is $12
The profit she earns = 12 - 5.35
= $6.65
Here we have to find the percent markup.
The formula for the percent markup =( profit/ wholesale cost )× 100
Markup percent = 6.65 / 5.35 × 100
= 1.24299 × 100
= 124. 30%
Therefore the markup percentage is 124.30%.
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Three times the first of two numbers decreased by the second number equals 9. Twice the first number increased by the second number equals 11. Find the two numbers
As per the given condition for the system of equation, the two numbers are equal to 4 and 3.
As given in the question,
To begin with the solution, let the two unknown numbers be x and y. Now, translating the two mathematical statements into system of equations,
When three times the first of two numbers decreased by the second number equals 9.
3 x - y = 9 ____(1)
Twice the first number increased by the second number equals 11,
2 x + y = 11 ____(2)
By solving resultant system of equations we get,
3 x - y = 9
2 x + y = 11
5x = 20 (by adding the two equations)
=> x = 4
Substituting the value of x in second equation,
y = 11 - 2x
= 11 - 2(4)
= 11 - 8 = 3
Therefore, as per given condition for the system of equation, the two numbers are equal to 4 and 3.
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a) What is the difference between a 90º counterclockwise rotation and a 90º clockwise rotation?
b) If you use the letter C, what letter will each of those rotations look like...
...a 90º counterclockwise rotation?
...a 90º clockwise rotation?
Answer: answer to A: Clockwise rotations clockwise, while counterclockwise rotations rotate in the opposite direction
Answer to B: i have no idea but i hope the first one helps
Step-by-step explanation:
Find the inverse and determine if it is true or false.
Statement : Obtuse angles are not right angles.
The inverse statement is If an angle is not obtuse, then it is a right angle False. Option C
What is an inverse statement?An inverse statement can be defined as a type of conditional sentence having a prompt or immediate inference made from original statement.
It carries the negation of both the hypothesis and conclusion from the
It states the opposite of the original statement given.
The statement is formed by negating the hypothesis and conclusion of a given conditional statement.
An inverse statement is expressed the form:
Original statement: If p, then q
Inverse statement: If not p, not q
Given the statement as;
Obtuse angles are not right angles
The inverse statement is:
If an angle is not obtuse, then it is a right angle
Hence, the inverse statement is False. Option C
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Graph the following features: Y-intercept = -4 slope is -1/3
The equation of the line is y = -1/3x - 4
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation of the line?The given parameters are
Slope, m = -1/3
y-intercept, c = -4
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = mx + c
So, we have
y = -1/3x - 4
Hence. the linear equation is y = -1/3x - 4
See attachment for the graph
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I want the answer for this question pls...
Simplify 72h ÷ 9h
Answer:
8
Step-by-step explanation:
[tex] \frac{72h}{9h} = 8[/tex]
The h is common in the numerator and the denominator, so it cancels out. We are left with 72/9 = 8.
Write the domain and range of the function using interval notation.
The domain of the function using interval notation is 4 ≤ y < 8 and the range of the function using interval notation is 4 ≤ y < 6.
What is a domain?A domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
By critically observing this graph of a function shown, we can reasonably infer and logically deduce the following:
Domain = (4, 8).Range = (4, 6).In interval notation, the domain of this function can be rewritten as 4 ≤ y < 8. In interval notation, the range of this function can be rewritten as 4 ≤ y < 6.
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Write the numbers in the blanks that make this equation true.
( 2 + 1 ) + 3 = 2 + ( _ + _ )
Can somebody please help me
We were given the following details:
Car registration = $90
Car Insurance (annual) = $520
Home Insurance = $1020
Since we are to calculate for the monthly amount to budget for Car Insurance, we have:
[tex]\begin{gathered} CarInsurance(monthly)=\frac{CarInsurance\mleft(annual\mright)}{No\mathrm{}of\mathrm{}months} \\ CarInsurance(monthly)=\frac{520}{12}43.33\approx43.00 \\ CarInsurance(monthly)=\text{\$}43.00 \end{gathered}[/tex]herefore, the correct nanswer is A. ($43.00 per month)
Which of these strategies would eliminate a variable in the system of equations?
2x + 3y = -5
2x - 3y = 10
Choose all answers that apply:
Answer:
jhhuibhhhiihhuuuuuuuuuuuuuuuuuuuuuuuu
A company charges $120 for an accident policy. If the person is injured by a vehicle, the company will pay $500. If the person is injured on the job, the company will pay $800. It has been found that five out of 900 claims are filed for vehicular injury and seven out of 900 claims are for an on the job accident. What is the expected annual profit for this policy for the company? Answer:
Assuming that the total number of people that pay the $120 are the 900 that claim the policy, and assuming that out of the 900 cases only the vehicular and job related policies are covered, then the profit for this policy will be:
[tex]p=900(120)-5(500)-7(800)\Rightarrow p=99900[/tex]So, under those assumptions, the profit would be $99 900.
A square has a perimeter of 120 cm what is the length of one side of the square
Shelby, Allen, and Denise printed their digital photos each requested the same size prints. Allen paid $3.24 for 11 prints. Denise paid $4.05 for 20 prints describe how you would write the equation for the relationship between the number of photos ordered and the amount paid
Taking x and y as the price for each photo, then the equation that represents each situation would be:
For Allen
[tex]11x=3.24[/tex]For Denise
[tex]20y=4.05[/tex]I have another question for brainly users out there.
Determine the value of y in the inequality.
12 + 4y < 32
Will mark brainliest.
Answer:
y = 3x-8
Step-by-step explanation:
What is the y-intercept of the given graph?
A) -4
B) 3
C) 4
D) None of these choices are correct.
Answer:
Answer should be 3
Step-by-step explanation:
prove me wrong
A truck rental company rents a moving truck for one day by charging $23 plus $0.09 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven.
What is the cost of renting the truck if the truck is driven 107 miles? 419 miles?
A linear equation is an algebraic equation of the form y = mx + b. The cost of renting the truck if the truck is driven 107 miles exists $32.63.
What is meant by linear equation?A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
Number of miles travel exists represented by "x"
cost per mile is represented by "c"
therefore we have equation,
c = 23 + 0.09 x
For 1 mile that is x = 1, cost c = $25.07
For 220 miles that is x = 220
c= 23 + 0.09 × 107
c= $32.63
For 107 miles the cost will be $32.63.
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Can someone explain how I would get the answer to this?
We are given the following values of the function to be
[tex]\begin{gathered} f(x)=7x^2-2x+5 \\ g(x)=-x+2 \end{gathered}[/tex]To find (f.g)(x)
We will find the product of f(x) and g(x)
[tex]f(x)\times g(x)=(7x^2-2x+5)\times(-x+2)_{}[/tex]Upon expanding, we will have
[tex]\begin{gathered} =7x^2\mleft(-x\mright)+7x^2\cdot\: 2-2x\mleft(-x\mright)-2x\cdot\: 2+5\mleft(-x\mright)+5\cdot\: 2 \\ =-7x^3+16x^2-9x+10 \end{gathered}[/tex]Thus, the answer is:
[tex]=-7x^3+16x^2-9x+10[/tex]How can you use the Product of Powers, Power of a Product, and Power of a Power Laws to evaluate and write equivalent numerical expressions with whole-number exponents?
The product of powers, power of a product, and power of a power laws can be used to evaluate the equivalent numerical expressions such as:
2² × 2³ = 2^5 = using product of Powers2² × 3² = (2×3)² = 6² = using power of a Product(2²)³ = 2^6 = using power of a powerHow to illustrate the information?According to the Power of a Product Property, you can distribute the exponent to each factor if a term is raised to one.
According to the rule of a power, when a base is raised to a power and then raised to another power, the exponents are multiplied while the base is left unchanged.
According to the product of powers rule, you can multiply two words with the same base by simply adding their exponents to get the result.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 40% pure fruit juice, and the second type is 65% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 70 pints of a mixture that is 55% pure fruit juice?
By using the concept of weighted averages, 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice are needed to produce 70 pints of 55 % pure fruit juice.
How to produce a quantity of a given concentration from two quantities of different concentrations?
The situation describes a mixing process with two fruit juices of different concentrations. All pure fruit percentages are known and we are asked to determine the numbers of pints of 40 % pure fruit juice and 65 % pure fruit juice to produce 70 pints of 55 % pure fruit juice. This can be determined by means of the concept of weighted average:
(55 / 100) · 70 = (40 / 100) · x + (65 / 100) · (70 - x)
38.5 = 0.4 · x + 45.5 - 0.65 · x
0.15 · x = 7
x = 46.667
We need 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice to produce 70 pints of 55 % pure fruit juice.
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Need help with this !!!!
The equation of the line in slope intercept form is y = -7x/2 - 5.
What is termed as the slope intercept form?A straight line's slope-intercept form is y = mx + b. In the equation y = mx + b for a straight line, m is known as the slope and b is known as the y-intercept. where y = mx+by = how much further up or down the line is,x = how far along the line is it,b = value of y when x equals 0 andm = indicates how steep this same line is.This is calculated using m = (distinction in y coordinates)/ (difference in x coordinates).For the given question,
The graph of the straight line is given.
Select two points which lies on the line.
(x₁, y₁) = (0, -5)
(x₂, y₂) = (-2, 2)
Find the slope using the formula.
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 + 5)/(-2 - 0)
m = -7/2
The equation of the line in slope intercept form is given as;
y - y₁ = m(x - x₁)
Put the values.
y + 5 = (-7/2)(x - 0)
y = -7x/2 - 5
Thus the equation of the line in slope intercept form is y = -7x/2 - 5.
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