(i) 0 is the remainder when x³ + 3x² + 3x + 1 is divided by (x +1)
(ii) 27/8 is the remainder when x³ + 3x² + 3x + 1 is divided by (x - 1/2)
(iii) 1 is the remainder when x³ + 3x² + 3x + 1 is divided by x
(iv) -π³ + 3π² - 3π + 1 is the remainder when x³ + 3x² + 3x + 1 is divided by (x + π)
(v) -27/8 is the remainder when x³ + 3x² + 3x + 1 is divided by (5 + 2x)
What is remainder?The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.
Let a be any real number and let p(x) be any polynomial with degree greater than or equal to one.
Now, if a polynomial p(x) is divided by (x - a) then the remainder is p(a).
Assume, p(x) = x³ + 3x² + 3x + 1
Now,
(i) The root of x + 1 = 0 is -1
or, p(-1) = (-1)³ + 3(-1)² + 3(-1) + 1
or, p(-1) = -1 + 3 - 3 + 1
or, p(-1) = 0
Hence by the remainder theorem, 0 is the remainder when, x³ + 3x² + 3x + 1 is divided by x + 1. We can also say that x + 1 is a factor of x³ + 3x² + 3x + 1.
(ii) The root of x - (1/2) = 0 is 1/2.
or, p(1/2) = (1/2)³ + 3(1/2)² + 3(1/2) + 1
or, p(1/2) = 1/8 + 3/4 + 3/2 + 1
or, p(1/2) = (1 + 6 + 12 + 8)/8
or, p(1/2) = 27/8
Hence by the remainder theorem, 27 / 8 is the remainder when x³ + 3x² + 3x + 1 is divided by x.
(iii) The root of x = 0 is 0
or, p(0) = (0)³ + 3(0)² + 3(0) +1
or, p(0) = 0 + 0 + 0 + 1
or, p(0) = 1
Hence by the remainder theorem, 1 is the remainder when x³ + 3x² + 3x + 1 is divided by x.
(iv) The root of x + π = 0 is - π
or, p(-π) = (-π)³ + 3(π)² - 3π + 1
or, p(-π) = -π³ + 3π² - 3π + 1
Hence by the remainder theorem, (-π)³ + 3(π)² - 3π + 1 is the remainder when x³ + 3x² + 3x + 1 is divided by x + π.
(v) Now, the root of 5 + 2x = 0 is -5/2
or, p(-5/2) = [(-5/2)³ + 3(-5/2)² + 3(-5/2) + 1]
or, p(-5/2) = [(-125/8) + (75/4) + (-15/2) + 1]
or, p(-5/2) = (-125 + 150 - 60 + 8) / 8
or, p(-5/2) = (-185 + 158) / 8
or, p(-5/2) = -27/8
Hence by remainder theorem, -27/8 is the remainder when x³ + 3x² + 3x + 1 is divided by 5 + 2x.
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The complete question is as follows:
Find the remainder when x³ + 3x² + 3x + 1 is divided by
i) x + 1 ii) x - (1/2) iii) x iv) x + π v) 5 + 2x
Determine whether the lines are parallel, perpendicular, or neither
X+7y = -3 and y= 7x + 25
Answer:
perpendicular
Step-by-step explanation:
7y = -x - 3
y = -1/7 x - 3/7
-1/7 is the reciprocal of the opposite, so the lines are perpendicular
someone pls help me answer this question!!!! look through the directions and give a thorough explanation. thank you!
The sailboat and the medical aid should meet at the points
(0, 7) and (5, 12).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
The intersection point between the two graphs y = - x² + 6x + 7 and y = x + 7 is the point where they meet each other.
Now, For the equation y = - x² + 6x + 7,
When x = 0, y = 7 ⇒ (0, 7).
when x = 1, y = 12 ⇒ (1, 12).
Now for y = x + 7,
when x = 1, y = 8 ⇒ (1, 8).
when x = 2, y =9 ⇒ (2, 9).
Now by taking the graph paper with each box of 1 square unit will plot these points and we obtain that at (0, 7) and (5, 12) these graphs intersect each other.
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How many terms are there in the expression 5xy² 3xyz?
The number of terms in the expression 5xy² 3xyz is 1.
What are terms in equations?Various parts of an algebraic expression , which are separated by + or – are called terms of the algebraic expression.
Calculation:
The given expression 5xy²3xyz.
Step 1: Write down the given expression
The given expression is 5xy²3xyz.
Step 2: Find number of terms in the expression
We know that Various parts of an algebric expression , which are separated by + or – are called terms of the algebric expression.
In the expressions the term is 5xy²3xyz.
Hence number of terms in the expression 5xy²3xyz is 1.
The number of terms in the expression 5xy² 3xyz is 1.
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A model airplane in Yesinia's collection is at a 1:40 scale to the actual plane. If the model is 7.5 inches long, what are the dimensions of the actual airplane in feet?
The dimension of actual plane is 300 inches.
What are ratios?
A ratio is the comparison of quantities which have same parameters or units of measurement.
Why are calculation of ratios significant?
It helps to identify how big or small a quantity is as compared to other thing having same parameter of measurement.
NOTE: Things which have different measurement cannot be compared by ratio;
Example: 1 litre of milk cannot be in ratio with 1 kg of sand, as milk is measured in volume and sand is in weight.
Solution:
Given, ratio of model of plane and actual plane = 1 : 40
x = 7.5 inches
Let, x be the dimension of model of the airplane
y be the dimension of actual airplane
Using the formula by equating the ratios,
1/40 = x/y
⇒ 1 x y = 40x
⇒ y = 40 x 7.5
⇒ y = 300 inches
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How do you read a 4 quadrant graph?
Four areas known as quadrants are created by the coordinate axes.
What is the name of a graph with four quadrants?The four quadrants of the coordinate plane can be discussed in depth and for a very long time. Encourage your students to think of further applications for it, such as in an animation or video game.As an alternative, you may show your students a variety of graphs that you've taken from readings and other assignments and invite them to talk about what they see and wonder about. A visual approach of displaying connections between numbers is coordinate graphing.On a coordinate plane, the relationships are shown. Two perpendicular axes, or lines, that are labelled similarly to number lines make up a coordinate plane. Each axis may be extended in two directions if the number system is expanded to include negative numbers. Typically, the x-axis is used to refer to the horizontal axis. Typically, the vertical axis.To learn more about quadrant graph refers to:
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What is the 4th equivalent fraction to 3/5
Answer:
If you are refering to the 4th in a sequence being 3/5 the first.
3/5, 6/10, 12/20, 24/40
24/40 would be your answer.
If you are looking for 3/5 in 4ths
2.4/4
See the similar shape below and find the length of /YZ/
Answer:
YZ = 20 cm
Step-by-step explanation:
Δ XYZ and Δ CBA are similar ( AA postulate )
The corresponding sides are then in proportion , that is
[tex]\frac{YZ}{BA}[/tex] = [tex]\frac{XY}{CB}[/tex] ( substitute values )
[tex]\frac{YZ}{8}[/tex] = [tex]\frac{25}{10}[/tex] = 2.5 ( multiply both sides by 8 )
YZ = 8 × 2.5 = 20 cm
What is the difference between continuous function and discontinuous function?
A continuous function is a function that is defined for all values of the independent variable, and its graph has no breaks or jumps. A discontinuous function is a function that is not continuous, meaning there are values of the independent variable at which the function is undefined or has a break or jump in its graph.
A continuous function is a function that can be graphed without any breaks or jumps. This means that the graph of a continuous function is a single, unbroken curve that passes through all its points. Furthermore, a continuous function is defined for all values of the independent variable. This means that the function is defined for all points in its domain. On the other hand, a discontinuous function is a function that is not continuous, meaning there are values of the independent variable at which the function is undefined or has a break or jump in its graph. This means that the graph of a discontinuous function will have jumps or breaks. Furthermore, a discontinuous function is not defined for all values of the independent variable, meaning that there are certain points in the domain for which it is not defined. In conclusion, the main difference between continuous and discontinuous functions is that a continuous function is defined for all values of the independent variable and has no jumps or breaks in its graph, whereas a discontinuous function is not defined for all values of the independent variable and has jumps or breaks in its graph.
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The amount P of pollution varies directly with the population N of people. City A has a population of 468,000 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce, if we know that its population is 350,000.
Answer: you should expect 218,750 tons of pollutants from City B.
Step-by-step explanation:
When two variables vary "directly", it means that they fit into the equation y=mx, where y varies directly with x, with the multiplier m to be determined by the information you are given.
For this problem, P (pollutants) varies directly with N (people) so the equation is P=mN for their relation.
You are given that City A has P = 260,000 tons of pollutants and N = 416,000 people. Plug these into the equation above (P=mN) and you get 260,000=(m)(416,000). If we divide each side by 416,000, you get that m=0.625. So now you have the multiplier for your equation: P=(0.625)N.
Use the complete equation now to find out how many P (pollutants) City B will produce.
P=(0.625)N
P=(0.625)(350,000) [[350,000 was the given "N" or amount of people in City B]]
P=218,750 tons of pollutants
The cafeteria at Midtown Middle School surveyed 575 students about their favorite food. Find the number of students that responded for each of the following.
salad = 20%
Which answer is correct?
20
11.5
460
115
Answer:
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
20% of 575 is 116
a sponsor will donate $0.15 for every meter merissa walks in a charity event. Merissa walks 5 kilometers in the charity event. How much does the sponsor donate to merissa's walk
The sponsor will donate 750 dollars.
1 kilo is 1000 meters
5 kilos is 1 kilo x 5
1000 meters x 5 is 5000 meters
0.15 x 5000 = 750
Answer:
12345678900987654321
Ramon's dad is an architect. He is designing a new house for his family. Yesterday, he brought home a model of a house that they will build. In the model ½ inch represents 2 feet and Ramons room measures 2.5 inches by 4 inches. Ramon wants to purchase a rug that will take up 169 square feet of space. Provide mathematical reasoning explaining why Ramon should or should not purchase the rug. (Hint: Draw the room)
Ramon should buy the rug of 169 square feet area because the room area is 160 square feet.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in the model ½ inch represents 2 feet and Ramons room measures 2.5 inches by 4 inches. Ramon wants to purchase a rug that will take up 169 square feet of space.
1/2 inch = 2 feet
1 inch = 4 feet
2.5 inch = 10 feet
4 inch = 16 feet
Area of room = L x W
Area of room = 10 x 16
Area of room = 160 square feet
The area of the rug is 169 square feet and the area of the room is 160 square feet which will cover the whole area.
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Why does the midpoint partition a segment into a 1 1 ratio?
In a company, 60% of the workers are men. If 1,880 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
4700 workers
Step-by-step explanation:
We know that 60% of the worker are men
1880 people work for the company who aren't men
100% - 60% = 40%
40% of workers = 1880
40% = 0.4
If 0.4 = 1880
100% of the workers x
100% = 1
We have equations
0.4 = 1880
1 = x
Cross multiply
0.4x = 1880
Divided both sides by 0.4
x = 4700 workers total
To find the number of men workers, we take
4700 - 1880 = 2820 men workers
So, there are a total of 4700 workers!
1880 women workers & 2820 men workers!
If you can, please give me a Brainliest; thank you!
Answer:
FIRST SOLUTION: (proportion)60% are men. 40% women
x - amount of men, 1 880 amount of women
60:x = 40:1 880
40x = 60(1 880)
40x = 112 800
x = 2 820
First solution said that there are 2 820 men and 1 880 womenthere are 4 700 workers all in allSECOND SOLUTION: base rate percentagePercentage = Rate / Base
= 1 880 / (1 - 0.60) (1-0.60 to find out the percent of not men)
= 1 880 / 0.40
= 4 700
There are total of 4 700 workers because there are 1 880 women meaning 4 700 - 1 880 = 2 820There are 2 820 womenCHECKING:Women: 4 700 * 0.4 = 1 880 (this statement is true)
Men: 4 700 * 0.6 = 2 820 (therefore, it is too)
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What are the vertical asymptotes of f/x 10 /( x 2 1?
Taking the function given in the question [tex]f(x) = \frac{10}{x^{2} +1}[/tex] , there are no vertical asymptotes since there no any real values for x , which makes the function undefined.
What is vertical asympotote?A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.
How to calculate vertical asymptote of a function?To calculate the vetical asymptotes of a function simply equate the denominator of the equation to zero , which when solved gives the values of x at which the function is undefined. Thus the obtained values of x are the vertical asymptotes to the given function.
In the given function f(x), let's equate the denominator to zero to find the vertical asymptotes,
[tex]x^{2} +1 =0[/tex]
Solving the above equation, we get
x = [tex]\sqrt{-1}[/tex]
which is imaginary, hence there is no vertical asymptote for the given function.
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9 apples and 6 oranges cost $33. 18 apples and 20 oranges cost $80. how much does one apple and one orange cost?
Answer:
Apple: $2.50
Orange: $1.75
Step-by-step explanation:
Let A represent apples and Y represent Orange
We have equations
9A + 6Y = $33
18A + 20 Y = $80
Let's find out the cost of oranges first. Multiply the first equation by -2
-18A - 12Y = $-66
18A + 20 Y = $80
8Y = $14
Y = $1.75
Now let's put 1.75 back in the Y to find the cost of apple
18A + 20(1.75) = $80
18A + 35 = $80
18A = $45
A = $2.50
Answer:2 50
Step-by-step explanation:
Sydney pays a flat rate of $20 plus a
rate of 7 cents per minute in her phone
plan. Which function shows the cost, "C",
of Sydney's plans as a function of time
in minutes?
Answer:
The answer is C(t)=0.07t+20
Step-by-step explanation:
20 is the starting value, or y-intercept in this case. The rate of change is 7 cents, or, 0.07. If we put this in y=mx+b format, it will come out as:
C(t)=0.07t+20
Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.95. Each refill is $1.50. She also decided to get a bagel for $3.00. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$9.95
$9.45
$8.65
$7.95
Answer: $9.45
Step-by-step explanation:
The first cup is $3.95
2 refills are $1.50 times 2 = $3
A bagel is $3
3.95+3+3 - 0.50 = $ 9.45
Answer:
$9.45
Step-by-step explanation:
add 3.95, 1.50, 1.50, and 3.00, then subtract the $.50 and you get 9.45
Mateo has a piece of fabric that is 2 1/4 yards long. He cuts it into pieces that are each 3/8 yard long. How many pieces of fabric does Mateo cut?
Answer:6
Step-by-step explanation: 2 1/4 is a mixed fraction and needs to be changed into an improper fraction:
The whole number 2 is multiplied by the denominator 4 which gives 8 and we add 1 from the numerator this gives 9 and we put this over the denominator 9/4
9/4÷3/8=
The first fraction stays the same and we flip over the second fraction and use the multiplication sign in between
9/4 x 8/3=72/12=6
The tops of the fractions are multiplied together to give 72
The bottoms of the fractions are multiplied together to give 12
Zach scores a ringer 40\%40%40, percent of the time that he throws a horseshoe. Let rrr be the number of throws it takes zach to score his first ringer in a game. Assume the results of each throw are independent. Find the probability that it takes zach 555 or more throws to score his first ringer.
There is about a 7.3% probability that it will take Zach 555 or more throws to score his first ringer.
To solve this problem, we can use a geometric distribution, which models the number of trials it takes to get a success in a series of independent Bernoulli trials (trials with two outcomes: success or failure) with a fixed probability of success.
In this case, the probability of success is 40% (the probability of scoring a ringer), and the probability of failure is 60% (the probability of not scoring a ringer). We can use the formula for the probability mass function of a geometric distribution to calculate the probability that it takes Zach 555 or more throws to score his first ringer:
P(X ≥ 555) = 1 - P(X < 555)
= 1 - (P(X = 1) + P(X = 2) + ... + P(X = 554))
= 1 - (0.4 + (0.4 * 0.6) + (0.4 * 0.6^2) + ... + (0.4 * 0.6^554))
To calculate this probability, we can use a computer to sum up the series, or we can use a calculator with a geometric distribution function. Using a calculator, we get P(X ≥ 555) ≈ 0.073, or about 7.3%.
This means that there is about a 7.3% probability that it will take Zach 555 or more throws to score his first ringer.
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In this case, the probability of success is 40% (the probability of scoring a ringer), and the probability of failure is 60% (the probability of not scoring a ringer). We can use the formula for the probability mass function of a geometric distribution to calculate the probability that it takes Zach 555 or more throws to score his first ringer:
P(X ≥ 555) = 1 - P(X < 555)
= 1 - (P(X = 1) + P(X = 2) + ... + P(X = 554))
= 1 - (0.4 + (0.4 * 0.6) + (0.4 * 0.6^2) + ... + (0.4 * 0.6^554))
To calculate this probability, we can use a computer to sum up the series, or we can use a calculator with a geometric distribution function. Using a calculator, we get P(X ≥ 555) ≈ 0.073, or about 7.3%.
Which is not a test for similarity 1 SSS 2 SAS 3 AAA 4 Asa?
The correct option is option (4) ASA is not a test for similarity
Triangles' similarities can be described based on their features. If two triangles have corresponding sides and have the same ratio and their corresponding angles are equal, then two triangles are said to be similar. The following are the criteria that are used to determine the similarity between two triangles:
1. AAA (Angle-Angle-Angle)
2. SSS (Side-Side-Side)
3. SAS (Side-Angle-Side)
The criteria ASA does not prove the similarity between two triangles as this property does not guarantee that the rest of the sides of one triangle will be similar to those of the other triangle. Thus, ASA criteria are not used to check the similarity between two triangles.
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How do you prove that two right triangles are similar?
We can prove that two right triangles are similar by:
Hypotenuse-Leg (HL) Theorem.
Leg-Acute (LA) Angle Theorem.
Hypotenuse-Acute (HA) Angle Theorem.
Leg-Leg (LL) Theorem.
Two triangles are congruent if they have the same three sides and exactly the same three angles. Two right triangles can be considered to be congruent, if they satisfy one of the following theorems.
Theorem 1 : Hypotenuse-Leg (HL) Theorem :
If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.
Theorem 2 : Leg-Acute (LA) Angle Theorem :
If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.
Theorem 3 : Hypotenuse-Acute (HA) Angle Theorem :
If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
Theorem 4 : Leg-Leg (LL) Theorem :
If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.
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Why we use mean method?
The assumed mean method is used to determine the mean or arithmetic mean of grouped data. If there is a large amount of data available, this method is suggested over calculating the mean directly.
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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according to us postal regulations, the perimeter of the smallest end plus the length of a parcel sent by mail may not exceed 108 inches. what is the largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail? what are the dimensions of the parcel of largest volume?
The largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail according to USPS regulation is 11664 cubic inches.
The volume of a rectangular parcel with dimensions l, w, and h is lwh. We can express the volume of the rectangular parcel in terms of one variable, say l, as lwh = l(108 - 2l)h. We want to maximize this expression subject to the constraint that l is a positive number less than 54 (the maximum value for l that still allows the parcel to fit within the 108-inch limit).
Taking the derivative of the volume with respect to l and setting it equal to zero, we find that the maximum volume occurs when:
l = (27 inches)
At this value, the dimensions of the parcel are:
l = 27 inches
w = 27 inches
h = 2(108 - 2l) = 2(72) = 144 inches
The volume of the parcel is then:
lwh = (27)(27)(144) = 11664 cubic inches
This is the largest possible volume of a rectangular parcel where the smallest end is a square that can be sent by mail according to USPS regulations.
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How do you find the base of an isosceles triangle with legs?
We can find the base of the isosceles triangle with legs using the formula:
2 × sqrt ((hypotenuse) ^ 2 - (altitude)^2) = base
Let us assume that the leg of the isosceles triangle is 'h' and one side is 'a'. Let the base be 'x'.
As there is a leg (altitude) in the isosceles triangle, then it forms a right triangle in the isosceles triangle, such that the sides form the hypotenuse.
Therefore, by using the Pythagoras' theorem,
hypotenuse ^ 2 = (altitude)^2 + (base / 2)^2
Hence, we get the base by deriving this expression from the above formula:
2 × sqrt ((hypotenuse) ^ 2 - (altitude)^2) = base
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What angle is bigger than right?
Answer:
look this up next time..with this said, obtuse
Step-by-step explanation:
What are the possible rational roots of x³ X² 10x 8 0?
The Possible rational roots of the equation "x³- x² - 10x - 8 = 0" are x = -1 , x = -2 and x = 4 .
The Rational roots of the equation are defined as the values of the variable such that value of the entire equation becomes 0 .
the function is f(x) = x³- x² - 10x - 8 ,
By the Rational Roots Theorem , we know that is p/q is the root of the equation , then p is a factor of 8 and q is a factor of 1 .
the possible values of p are ±1 , ±2 , ±4 , ±8 , and
the possible values of q are ±1 .
So , the possible rational roots (p/q) are ±1 , ±2 , ±4 , ±8 .
So , on substituting the all the possible values of the rational roots ,
we get ;
f(1) = (1)³- (1)² - 10(1) - 8 = -18
f(-1) = (-1)³- (-1)² - 10(-1) - 8 = 0
f(2) = (2)³- (2)² - 10(2) - 8 = -24
f(-2) = (-2)³- (-2)² - 10(-2) - 8 = 0
f(4) = (4)³- (4)² - 10(4) - 8 = 0
f(-4) = (-4)³- (-4)² - 10(-4) - 8 = -48
f(8) = (8)³- (8)² - 10(8) - 8 = 360
f(-8) = (-8)³- (-8)² - 10(-8) - 8 = -446.
we get , the value as 0 at x = -1 , -2 and 4 .
Therefore , the possible rational roots are x = -1 , x = -2 and x = 4 .
The given question is incomplete , the complete question is
What are the possible rational roots of x³- x² - 10x - 8 = 0 ?
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The lengths of the sides of a triangle are three consecutive integers. The perimeter of the triangle is 48 in. What is the length of the longest side of the triangle?.
The required lengths of side of triangle are 15 in, 16 in and 17 in.
Given :
The sum of the angles of a triangle is always 180°
Given that :
Sides of a triangle are consecutive integers.
Also given that,
Perimeter of triangle is 48.
Let the sides of triangle are x, x + 1 and x + 2.
x + x + 1 + x + 2 = 48
3x = 48 - 3
3x = 45
divide by 3 on both sides
x = 15
The length of the triangles
x + 1 = 15 + 1 = 16
x + 2 = 15 + 4 = 17
The side lengths of the triangle are 15, 16 and 17.
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What is a hole of a function?
In the graph of a function there exist a point where function is not defined is known as a hole of a function.
Hole of a function is defined as:
A point where the function does not defined.In the rational function when the common factor of the numerator and denominator get cancel with each other .Common factor of numerator and denominator represents hole.In the graph of a function hole represents it approaches to the given point but in reality does not exist.Hole exist in the rational function when we input the value and it approaches to zero.Therefore, the hole of a function is a point where function does not defined only approaches.
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Help me please with this
The domain and the range of this function shown in the graph include the following;
Domain = -5 ≤ x < 1.Range = -4 ≤ y < 7.How to identify the domain and range of this graph?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Note: Each interval on this graph represent 1 unit and the less than or equal to (≤) would be used because the dotted point is shaded (closed).
By critically observing the graph shown above, we can reasonably and logically deduce the following:
Domain = -5 ≤ x < 1 or [-5, 1].
Range = -4 ≤ y < 7 or [-4, 7].
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