The expression on being divide by x-1 gives -5 as remainder and quotient (x²-x+2)
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x²-5x+11
Given here: The expression as x³-2x²+3x-7 which is to be divide by x-1
Thus dividing using the long divsion method we get
x-1)x³-2x²+3x-7(x²-x+2
x³-x²
-________
0-x²+3x
x²+x
-________
2x-7
2x-2
-__________
-5
Thus The expression can be written as x³-2x²+3x-7 =(x-1)×(x²-x+2)-5
Hence, On dividing the given expression by x-1 by long divison method we get the remainder as 2.
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Find all non-empty finite sets of integers A and B with the following properties:
i) whenever x is in A, x+1 is in B
ii) whenever x is in B, x^2-4 is in A
Hence, find all positive integers a and b such that there are non-empty finite sets A and B with the property that whenever x is in A, x+a is in B, and whenever x is in B, X^2-b is in A.
Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinality (or the cardinal number) of a set. Let us take an example:
A = {1, 2, 3, 4, 5 }
Since a set is usually represented by the capital letter. Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets. Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5. Some commonly used sets are as follows:
N: Set of all natural numbers
Z: Set of all integers
Q: Set of all rational numbers
R: Set of all real numbers
Z+: Set of all positive integers
A non empty is a set that has one or more elements.A “set” is just a well-defined collection of distinct objects, and their union—the set—is an object itself. A set can contain anywhere from 0 to an infinite number of items.
Finite sets are sets having a finite/countable number of members. Finite sets are also known as countable sets, as they can be counted. The process will run out of elements to list if the elements of this set have a finite number of members
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What does the law of demand state?
Answer:
In economics, the LOD or Law of Demand states that as the price increases on a good or service, there are less people that are willing and able to purchase that good or service.
Here is an example
On the image attached there is a Price Quantity Demanded Graph. The Line on the graph represents demand. The furthur right the line of the graph goes, the larger the quantity of demand for a good is, vice versa. The Law Of Demand is demonstrated on the graph and the table, when price (Px) is at 5, then only Quantity Demanded (Dx) equals 100. When Px = 1 then Dx = 500. As price decreases, demand increases.
Hope this helped :)
the fed is most likely to use which tool(s) to conduct monetary policy? group of answer choices open market operations discount rate interest on reserves (ior) rate required reserve ratio
The Federal Reserve uses three main tools to conduct monetary policy: Open Market Operations, the Discount Rate, and Interest on Reserves (IOR).
Open Market Operations involve the buying and selling of government securities in the open market, which impacts the money supply and interest rates. The Discount Rate is the interest rate the Federal Reserve charges commercial banks to borrow from it. A lower Discount Rate encourages borrowing, while a higher Discount Rate discourages borrowing. Interest on Reserves (IOR) is the interest rate the Federal Reserve pays commercial banks on their excess reserves. A higher IOR rate encourages banks to keep more of their funds in the form of reserves, while a lower IOR rate encourages banks to lend out more of their funds. The Required Reserve Ratio is also used to affect the money supply, as it determines the amount of reserves banks must keep on hand. An increase in the Required Reserve Ratio reduces the money supply, while a decrease in the Required Reserve Ratio increases the money supply.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours | Total Number of Students
0 | 1
1 | 8
2 | 2
3 | 5
4 | 9
5 | 7
6 | 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for exactly 1 hour is 0.23
How to determine the probability that a student studied for exactly 1 hour?Probability is a measure of the likelihood of a particular event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
From the given table, you need notice that the number of students who study for 1 hour is 8.
In order to determine the probability that a student studied for exactly 1 hour, we need to find total number of students. That is:
Total number of student = 1 + 8 + 2 + 5 + 9 + 7 + 3 = 35
probability (exactly 1 hour) = number of exactly 1 hour/Total number
probability (exactly 1 hour) = 8/35 = 0.23
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Answer:
B
Step-by-step explanation:
admission to the movies is x dollars, and a bag of popcorn costs $4. write an expression to represent total cost for two people to go to the movies three times and sharing a bag of popcorn each time.
Answer: The total cost for two people to go to the movies three times is 3x2 = 6x dollars.
The cost of a bag of popcorn is $4 and they share one bag of popcorn each time they go to the movie, so the total cost of popcorn is 4*3 = $12 dollars.
So the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12
So an expression to represent the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12.
Step-by-step explanation:
NO SPAM OR LINKS!!! WILL MARK BRAINLEST
Review the Monthly Principal & Interest Factor chart to answer the question:
FICO Score APR 30-Year Term 20-Year Term 15-Year Term
770–789 5.5 $5.68 $6.88 $8.17
750–769 6.0 $6.00 $7.16 $8.44
730-749 6.5 $6.32 $7.46 $8.71
710–729 7.0 $6.65 $7.75 $8.99
690–709 7.5 $6.99 $8.06 $9.27
Calculate the monthly payment, for a 15-year term mortgage, after a 15% down payment on a $315,200.00 purchase price, for a household with a 711 credit score. (2 points)
$1,776.29
$1,984.39
$2,173.56
$2,408.60
Answer: c
Step-by-step explanation:
A city has a population of 310,000 people. Suppose that each year the population grows by 8%. What will the population be after 14 years?
round your answer to the nearest whole number.
Asha pulls five tiles out of a bag that contains only positive and negative x and x² tiles. She simplifies the resulting polynomial and gets x². What are all the possible sets of five tiles that she could have pulled out?
The possible sets of five tiles that she could have pulled out are (2,3),(3,2)
How to find the factors of a quadratic expression?If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]
Then writing b in terms of alpha and beta would help us getting common factors out.
Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any trial and error.
Given;
Number of tiles asha pulled out=5
Bag contains only positive and negative x and x² tiles
So, the equation will be
-x^2+x=5
x^2-x+5=0
Now,
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
x= 1 +[tex]\sqrt{1-4*-1*-5}[/tex])/2
x=2,3
x=3,2
Therefore, the quadratic equation solution will be (2,3),(3,2)
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Which are which help asap..
Answer:
H = 20
Step-by-step explanation:
Looks like you got everything correct. Nice!
For your last one, let's get H by itself. Since 1/2 is division, let's multiple it by 2 to turn it into one. Because you multiply by 2 on the left side, you have to on the right side also...
(1/2)(2) = 1
(1)(h) = h
On the other side, 10(2) = 20.
Combining the 2, H = 20
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-3,0)
(5,-2)
solve it to find the value of X. also find the actual length of each square[tex]perimeter of square 40cm,(x+2)cm[/tex]
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
What is the perimeter of the square?The product of the four and the edge length of the square or the sum of all the sides of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,
4(x + 2) = 40
Simplify the equation, then we have
4(x + 2) = 40
(x + 2) = 10
x = 10 - 2
x = 8
The equation will be 4(x + 2) = 40 and the value of the variable 'x' will be 8.
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help this is the only question i have left help bsf help
Why do you think insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage?
We can actually think that insurance companies offer uninsured/ underinsured coverage at a cheaper rate than collision coverage because the risk of a claim is typically lower for uninsured/underinsured coverage.
What is insurance?An agreement to provide compensation to another party in the event of a certain loss, damage, or injury is known as insurance, and it is a way to safeguard against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.
Collision coverage is for damage to the policyholder's own vehicle, while uninsured/underinsured coverage is for damage caused by another driver who does not have enough insurance to cover the costs of an accident. Since fewer drivers are uninsured or underinsured, the likelihood of a claim being made under that coverage is lower, and thus the cost is less.
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In the linear equation 4x-3y=6, the slope of the line is
arrange the following numbers in ascending order: 147, 772,324,256,9199,946,4342,493,891,4
10
Solve for x.
8
6
X
will give brainliest!!!
Answer:
7.5
Step-by-step explanation:
Since the segments are parallel, the side segment lengths are proportional.
8/10 = 6/x
4/5 = 6/x
4x = 30
x = 7.5
Express the formula v=pie r^2 • H in terms of height, H. Use that formula to find the height when the volume is 45pid and the radius is 3
Option (b) is the correct option i.e. The height is 5 units.
What precisely are volume and height?The height of an object is determined by measuring the distance between its base and its top.
As opposed to length, width, and height for a rectangular shape's area, the basic formula for volume is length, breadth, and height. The calculation is unaffected by how the different dimensions are referred to; for example, "depth" can be used in place of "height."
Given, V = πr².H
V/πr² = H
So, It can be written in terms of height, H as V/πr².
Now, If r = 3 units and V= 45π then,
H = V/πr² = 45π / π(3)²
= 45π/9π
= 5 units.
Hence, height is 5 units.
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Carter has 10 fewer marbles than April. Nicholas has 3 times as many marbles as April. If April has m marbles, which expression BEST represents how many marbles Carter and Nicholas have altogether?
Which one of these?
4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.
What is Expression?An expression is combination of variables, numbers and operators.
Let m be the number of marbles.
The number of marbles April has be m.
Given that Carter has 10 fewer marbles than April.
If Carter has 10 less than m, that's m - 10.
Nicholas has 3 times as many marbles as April.
3m
marbles Carter and Nicholas have altogether
m-10+3m
4m-10
Hence, 4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.
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find the area of the shaded part given below where the diameter is 14 cm.
Answer:
area of sector = 49π/6 cm² ≈ 25.7 cm²
Step-by-step explanation:
area of sector = (n/360°)πr²
where n = central angle of sector, and r = radius of circle
Here, we have:
n = 60°
r = d/2 = 14 cm / 2 = 7 cm
area of sector = (60°/360°)π(7 cm)²
area of sector = (1/6)π(49 cm²)
area of sector = 49π/6 cm² ≈ 25.7 cm²
55oz to ____ lb ____ o
What type of triangle and are they congruent
Answer: AAS and both triangles are congruent
Step-by-step explanation: Hello! Since you are given two angles and one side that are congruent in both triangles, you know that they are either congruent by ASA (angle side angle congruence postulate) or AAS (angle angle side) congruence postulate. The way you tell the difference between the two is by how the congruent angles and the congruent side is shown. In ASA, the congruent side would be the included side between both congruent angles. Since the congruent side is not in between both angles and both angles do not share the congruent side to the other triangle, the triangles are congruent by AAS. The triangles two given shared angle and given congruent side is in the order of angle angle side, so the triangles are related by AAS. This means that the triangles are congruent.
Fun fact:
By CPCTC, you know that corresponding parts are congruent in congruent triangles. If you know two or more triangles are congruent, then each of their angles and sides are congruent as well.
I hope this helps you!
The longer leg of a right triangle is 3cm longer than the shorter leg. The hypotenuse is 6cm longer than the shorter leg. Find the side lengths of the triangle.
In a case whereby longer leg of a right triangle is 3cm longer than the shorter leg and hypotenuse is 6cm longer than the shorter leg then the side lengths of the triangle is 9 inches.
How can the lenght be calculated?The concept that will be used is pythagoras theorem.
We can make s = the length of the shorter leg.
Where the longer leg can be expressedas (s + 3),
Then the hypotenuse is( s + 6).
From pythagoras theorem, a^2 + b^2 = c^2.
then we have s^2 + (s + 3)^2 = (s + 6)^2
[s^2 + (s + 3)(s + 3)] =[ (s + 6)(s + 6) ]
s^2 + s^2 + 6s + 9 = s^2 + 12s + 36
If we collect like terms we have
s^2 - 6s - 27 = 0
Then if we factorize we have
(x - 9)(x + 3) = 0
then
we can set the whole left side to equal 0.
x - 9 = 0, then x = 9
x + 3 = 0, then x = -3.
But we can only have positive value which sis 9, hence shortest side is 9 inches.
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For a particular company the salaries of five employees are: $45,000 $52,000 $67,000 $42,000 $56,000 A new employee is hired and her salary is $280,000. What word best describes this data set with the new employee included?
section 7.5 substitution page 15 pdf answer key 7c i can solve a linear system of equations by substitution.
Yes, substitution can be used to solve a linear system of equations.
Linear System of Equations:
A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution. For example, is a system of three equations in the three variables x, y, z.
The substitution technique involves separating out a single variable from one equation and utilizing that expression to replace the variable in the other equation (s). This will enable you to solve for the remaining variable or variables and discover the system's answer.
Yes, a linear system of equations can be solved via substitution.
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Need help with questions 12!
Answer:
So the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
Step-by-step explanation:
We can use algebra to solve for the width and length of the rectangle. Let's call the width of the rectangle "w" and the length "l".We know that the perimeter of the rectangle is the sum of all four sides, so we can use the formula:P = 2l + 2wwhere P is the perimeter and l and w are the length and width of the rectangle. We know that P = 312 feet.Also, we know that the length is seven times the width, so we can express the length as:l = 7wNow we can substitute this value of l into the perimeter equation:312 = 2(7w) + 2w312 = 14w + 2w312 = 16ww = 19.5 feetNow we can use this value of w to find the length:l = 7w = 7(19.5) = 136.5 feetSo the width of the rectangle measures 19.5 feet and the length measures 136.5 feet.
4
MP.1 Make Sense and Persevere Alicia
measured 1/4 yard of the Blue Diamonds fabric and5/6
yard of the Yellow Bonnets fabric to make a quilt.
Rename each length of fabric. Use the number of
inches in a yard as a common denominator.
HINT: 1 yard = 3 feet; 1 foot = 12 inches
Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
Describe the length.The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.
Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.
5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.
Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
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Find the length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
The length of the midsegment of the trapezoid with the vertices A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0) is; 3√2
How to find the distance between two coordinates?The length of the mid-segment of a trapezoid is half the sum of the lengths of the two parallel sides, AB and CD. T
The vertices are;
A(0,3) ,B(2 , 5) ,C(6,4) ,D(2,0)
Thus;
Length of sides AB and CD
length = √(x₂ - x₁)² + (y₂ - y₁)²
AB =√(2 - 0)² + (5 - 3)²
AB = 2√2
length = √(x₂ - x₁)² + (y₂ - y₁)²
CD = √(2 - 6)² + (0 - 4)²
CD = 4√2
Formula to use for the mid segment is;
Mid segment = (AB + CD)/2
= (2√2 + 4√2) / 2
= 3√2
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Simplify 3y-(2y-3)÷4
The solution to the algebraic expression 3y - (2y - 3) ÷ 4 is; (10y + 3)/4
How to simplify algebraic expressions?The algebraic expression is given as;
3y - (2y - 3) ÷ 4
With the aid of order of operations named PEMDAS which is an acronym for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction. Thus, we can rewrite the expression as;
3y - (2y - 3)/4
The common denominator is 4 and when we distribute we will have;
(4(3y) - 2y + 3)/4
= (12y - 2y + 3)/4
= (10y + 3)/4
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each of the following situations, determine whether or not the given random variabas a binomial or geometric distribution. then, find the probability
The probability of 5 heads in 10 flips.
A coin is flipped 10 times and we want to find the probability of getting exactly 5 heads.
This situation is a binomial distribution because it involves a fixed number of trials (10) and each trial has a fixed probability of success (1/2). . The probability of obtaining exactly 6 successes in 10 trials is given by the formula P(x) = nCx * px * (1-p)n-x. In this situation, the probability is P(x) = 10C6 * 0.26 * 0.84 = 0.17496. The probability of getting exactly 5 heads can be calculated using the formula P(X=5) = 10C5 * 0.5^5 * 0.5^5 = 0.246. This is the probability of 5 heads in 10 flips.
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Complete question:What is the probability of getting 5 heads when you toss a fair coin 10 times?
PLEASE HELP The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch? How many sec after launch did their rocket hit the ground? What was their rockets maximum height in meters??
The rocket was at a height of 19.75 meters after 0.5 seconds
The rocket hit the ground after 8.02 seconds
The maximum height is 81 m.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The height (h) of the rocket t seconds after launch is modeled by:
h(t) = -5t² + 40t + 1
a) After 0.5 seconds:
h(0.5) = -5(0.5)² + 40(0.5) + 1 = 19.75 meters
b) The rocket hit the ground when h(t) = 0, hence:
-5t² + 40t + 1 = 0
t = 8.02 s
c) The maximum height is at h'(t) = 0
h'(t) = -10t + 40
-10t + 40 = 0
10t = 40
t = 4 s
h(4) = -5(4)² + 40(4) + 1 = 81 meter
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