Factorization is a step in the process of locating the roots of a quadratic equation.
Why is quadratic equation by factoring?Finding the roots of a quadratic equation involves the process of factorization. When factoring quadratic equations, the original quadratic expression is changed into the product of two linear factors.
A quadratic function has the formula f(x) = ax² + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.
Breaking down the factors, or numbers, that multiply to create another number is a frequent mathematics operation known as factoring. Various things affect some figures.
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A motorist takes 4. 5 hours to reach his destination at 80km/ h.
If he wants to complete his journey in 4 hours at what speed must he travel
Answer:
71.11 km/h
Step-by-step explanation:
D = S/T
D = distance
S = Speed
T = Time
The motorist is going 80km/h and takes 4.5 hours to reach his destination.
80/4.5 = 17.77km
The motorist travels 17.77km
Now find how fast he'll have to go to reach 17.77km in 4 hours.
17.77 * 4 = [71.11 km/h]
Given f(x)= 11x^3+4x^2-2x+3 G(x)= 3x^3+6x^2-10x+8 find: I) f(x)- 2G(x) ii) 2f(x)+3G(x) iii) 1/2f(x)+ G(x)
A function is a mathematical relation between two sets of values that assigns a unique output to each given input.
What is a function?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
I) f(x)- 2G(x) = 5x³-8x²+18x-13
II) 2f(x)+3G(x) = 31x³+26x²-34x+30
III) 1/2f(x)+ G(x) = 17/2x³+8x²-12x19/2
Here, we have
f(x)= 11x³+4x²-2x+3, G(x)= 3x³+6x²-10x+8
We have to find I) f(x)- 2G(x), ii) 2f(x)+3G(x), iii) 1/2f(x)+ G(x)
I) f(x)- 2G(x) = 11x³+4x²-2x+3 -2(3x³+6x²-10x+8 )
= 11x³+4x²-2x+3 - 6x³-12x²+20x-16
= 5x³-8x²+18x-13
Hence, the value of f(x)- 2G(x) is 5x³-8x²+18x-13.
II) 2f(x)+3G(x) = 2(11x³+4x²-2x+3)+3(3x³+6x²-10x+8 )
= 22x³+8x²-4x+6+9x³+18x²-30x+24
= 31x³+26x²-34x+30
Hence, the value of 2f(x)+3G(x) is 31x³+26x²-34x+30.
III) 1/2f(x)+ G(x) = 1/2(11x³+4x²-2x+3) + (3x³+6x²-10x+8)
= 11/2x³+2x²-2x+3/2+3x³+6x²-10x+8
= 17/2x³+8x²-12x19/2
Hence, the value of 1/2f(x)+ G(x) is 17/2x³+8x²-12x19/2.
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which expression gives the closest estimate of 327+171
The expression that gives the closest estimate of 327+171 is 325+175.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Here, we have
Given: 327+171
We have to find the closest estimate of the given expression.
We concluded that the closest estimate of the given expression is 325+175.
327 is close to 325.
175 is close to 325.
Hence, The expression that gives the closest estimate of 327+171 is 325+175.
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Which of the following represents the additive inverse of 2/3
A. -2
B. 2/3
C. -2/3
D. 3
Answer: C. -2/3
Step-by-step explanation:
What is the name of the system if there are fewer equations than variables Mcq?
The system is a consistent system with an infinite solutions.
There are two types of system of equations - consistent and inconsistent.
Inconsistent means that it has no solution , i.e. the solution does not exist.
Consistent system means a solution of the equation exists.
Further, this is of type , a consistent system may have a unique solution or an infinite number of solutions where we need to assign an arbitrary value to a free variable.
For e.g. let us consider the system -
x + y+ z = 0
2x + 3y + 4z = 1
Since , (0,0,0) is a solution to this system , we can't say its an inconsistent system .
Also, for a system to be consistent , either a unique solution exists or an infinite solutions exist. There is no particular number of solutions.
Also, we see that (-1,1,0) is also a solution other than the zero solution.
So, such a system is a consistent system with infinite solutions.
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The Washington monument is one of the tallest structures in the United States. It is about 555 feet tall. How many yards is this?
Answer: 185 yards
Divide it by 3 to convert to yards
The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated. What is the mean of the sampling distribution of the sample mean for samples of size 16 ? 1.7 3.2 3.2 V16 1.7 16 1.7 16
The mean of the sampling distribution of the sample mean for samples of size 16 is 3.2 V16, which is equal to the population mean of 3.2 divided by the square root of 16 (V16). This represents the expected mean of the sample mean when samples of 16 are taken from the population.
Step 1: Calculate the population mean (μ):
μ = 3.2 pets per student
Step 2: Calculate the standard deviation of the population (σ):
σ = 1.7 pets per student
Step 3: Calculate the sample size (n):
n = 16 students
Step 4: Calculate the mean of the sampling distribution (μx):
μx = μ / √n
μx = 3.2 / √16
μx = 3.2 / 4
μx = 0.8
Therefore, the mean of the sampling distribution of the sample mean for samples of size 16 is 0.8.The mean of the sampling distribution of the sample mean for samples of size 16 is 3.2 V16. This is calculated by dividing the population mean (3.2 pets per student) by the square root of the sample size (16). The square root of 16 is 4, which gives us a final result of 0.8. This means that the expected mean of the sample mean when samples of 16 are taken from the population is 0.8. This is a useful measure for understanding the variability of the sample mean, as it indicates how much the sample mean is likely to vary from the population mean.
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every 10 years, the u.s. census bureau attempts to count every person living in the united states. to check the accuracy of their count in a certain city, they draw a sample of census districts (roughly equivalent to a city block) and recount everyone in the sampled districts. what kind of sample is formed by the people who are recounted?
Answer: The sample formed by the people who are recounted in the U.S. Census Bureau's accuracy check is a random sample. This is because the census districts are selected in a random manner, with each district having an equal chance of being selected. Random sampling is a method of selecting a sample from a larger population in which each member of the population has an equal chance of being selected. This ensures that the sample is representative of the population as a whole and allows for the estimation of population characteristics with a known degree of precision.
Step-by-step explanation:
twice the length decreased by 5. (grade 7)
Answer: 2x-5
Step-by-step explanation: twice=2 the lenght=x We don't know the length, and decreased= subtract sign
2x-5
what's the height of the prism? h, 6 square inches, volume=42 cubic inches
Answer:64
Step-by-step explanation: i did the test
Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete
your choice, please help and explain
The Mean is 391.75, the Median is 441, and no mode.
What is a mean median and mode?
The mean is the average of a set of numbers, calculated by adding all the numbers together and dividing by the number of items in the set. The median is the middle value in a set of numbers, or the average of the two middle values if the set has an even number of items. The mode is the most frequently occurring value in a set of numbers.
Data: $436, $403, $479, and $249.
Mean = SUm of all observation / total no. of observations.
Mean = 436 + 403 + 479 + 249 / 4.
Mean = 391.75
No. of terms n = 4(even)
Median = (n/2+(n/2 + 1)) / 2
Median = 403 + 479 / 2
Median = 441.
Mode is the value repeating the more no. of times
So, there is no mode.
Hence, the Mean is 391.75, the Median is 441, and no mode.
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Tamara likes to run on the treadmill. If she runs at a speed of 5.75 miles per hour for 0.92 hours, how many miles does she run? Recall distance = speed x time. Estimate to check your answer.
PLEASE BE ACCURATE!!! Thank you!!!:)
In order to finish a marathon in 4 hours, your average pace needs to be 9 min, 9.62 sec per mile, or 9:9.62 minutes per mile.
What is meant by marathon?
The marathon is a long-distance foot race that takes place over a distance of 42.195 km (26 mi 385 yards), though it can also be done on trail routes.You can run the marathon or use a run/walk method to finish it. There are several categories for wheelchairs.There are more than 800 marathons organized annually throughout the world, and while larger marathons can draw tens of thousands of competitors, the vast majority of those running them are recreational athletes.In 1896, the marathon was one of the first modern Olympic competitions. Before 1921, the distance was not standardized. The 1983-starting World Athletics Championships also feature the distance.To learn more about marathon refer to
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a fair die is cast until a 6 appears what is the probability that it must be cast more than 5 times times
The probability that the fair die must be cast more than 5 times is 0.4315 or 43.15%.
The probability that it must be cast more than five times is the complement of the probability that it will be cast five or less times.
The probability of getting a 6 on the first roll is 1/6, the probability of not getting a 6 on the first roll is 5/6. The probability of getting a 6 on the second roll, given that it was not obtained on the first roll, is 1/6. The probability of getting a 6 on the third roll, given that it was not obtained on the first and second rolls is 1/6 and so on.
The probability of not getting a 6 in five rolls is (5/6)⁵. The probability of getting a 6 on the fifth roll is 1/6. The probability of getting a 6 on the fifth roll or not getting it on the first five rolls is (5/6)⁵ + 1/6.
So the probability of getting a 6 in five rolls or less is (5/6)⁵ + 1/6.
Therefore, the probability of getting a 6 in more than five rolls is 1 - ((5/6)⁵ + 1/6) = 0.4315
So the probability of having to cast the die more than five times to get a 6 is 0.4315 or 43.15%.
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WHICH EQUATION BEST USES COMPAITABLE NUMBERS TO ESTIMATE 318/38
318/38=9.
What are compatible numbers?
The term "compatible numbers" refers to those that are simple or complimentary. It indicates that the numbers are compatible if they are simple to add, subtract, multiply, or divide. It is also simpler to estimate the answer and solve difficulties because these numbers are near to the real numbers in value.
Step by step explaination:
318/38=8.3
to round of 8.3 to 9
The equation to the compatible number 318/38 is 9
(318/38=9).
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Devoir de maths sur les Rectangle d'or et nombre d'or (énoncé ci-dessous)
Answer:
where the probleme to help
I need help understanding how to find the outer perimeter.
Answer:
im doing the same thinggg okay so to find the outer perimeter you have to divide that shape up so start with the triangle with the right angle.
Step-by-step explanation:
i would just go on yt and watch a vid on how
I need help asap please !!!!!!!!
Answer:
f(x) = x² - 4x - 5
Step-by-step explanation:
given the roots of a parabola x = a and x = b , then the factors are
(x - a) and (x - b)
the function is then the product of the roots , that is
f(x) = (x - a)(x - b)
from the graph the roots ( where graph crosses the x- axis ) are
x = - 1 and x = 5 , then corresponding factors are
(x - (- 1) ) and (x - 5) , that is (x + 1) and (x - 5) , then
f(x) = (x + 1)(x - 5) ← expand using FOIL
= x² - 5x + x - 5
f(x) = x² - 4x - 5
The distance y traveled by a hybrid car using x gallons of gas can be represented by y=42x. Which car gets better gas mileage? Explain.
The car with the better mileage is the hybrid car.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
Compact car:
288 miles with 9 gallons of gas.
This means,
y = 32x
Where y is the distance traveled with x gallons
The distance traveled per gallon.
= 288/9
= 32 miles
Hybrid car:
y = 42x represents the distance traveled with x gallons.
Where y is the distance traveled with x gallons
The distance traveled per gallon.
y = 42 x 1 = 42 miles
Thus,
The hybrid car gets better mileage.
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The complete question is:
A new compact car can travel 288 miles on nine gallons of gas. The distance driven in miles y varies directly with the number of gallons of gas x. This situation can be represented by the equation y= 32x.
The distance y traveled by a hybrid car using x gallons of gas can be represented by y = 42x. Which car gets better gas mileage? Explain.
The distance between two points can be determined by the
of the real number values of the two points.
Answer: The absolute value of the difference
Step-by-step explanation:
Hope this helps
SAA Airbus A340-200 and use your findings to explain why the economy class seating only starts at row number 49 and why the letters B,I and J are not used
Due of the greater legroom, the exit row seats are reserved for the airline's most valuable passengers.
Why do airplanes avoid Row 33?A United Airlines representative told Travel + Leisure that although the end row used to be standardized by skipping row 33 on some maps, it is no longer the case. A mathematical formula, in essence, underlies the justification for having a consensus seating chart.
Airlines frequently omit certain row numbers in order to accommodate more passengers because airplanes are intended to carry the maximum number of passengers possible.
Due of the greater legroom, the exit row seats are reserved for the airline's most valuable passengers.
The complete question is,
How come airlines don't use Row 9?
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What number is 10 more than 90?
The answer of 10 more than 90 is 100.
The answer of 10 more than 90 is 100 which can be derived using simple mathematical calculations.
To find 5 more than 5, you can add 5 to the original number 5.
10 + 90 = 100
It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 10 more than 90 is 100.
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Triangle ABC has vertices A = (1, 5), B = (3, 2), and C = (4, 7). Triangle A'B'C' is formed when triangle ABC is shifted using the rule (x, y) --> (x-3 , y-1). What are the coordinates of triangle A'B'C' ?
How are the four properties of equality alike?
The four properties of equality are alike as all the expression on LHS is equal to all the expression on RHS, x = y.
What are Properties of Equality?
The relationship between two equal quantities is described by the property of equality, and if an operation is used on one side of the equation, it must also be used on the other side to keep the equation balanced.
There are four properties of equality -
Addition Property of Equality
Example - x - 3 = 8
⇒ x - 3 + 3 = 8 + 3
⇒ x = 8 + 3
⇒ x = 11
Subtraction Property of Equality
Example - x + 4 = 7
⇒ x + 4 - 4 = 7 - 4
⇒ x = 7 - 4
⇒ x = 3
Multiplication Property of Equality
Example - x/4 = 6
⇒ (x/4) × 4 = 6 × 4
⇒ x=24
Division Property of Equality
Example - 3x = 6
⇒ (3x/3) = 6/3
⇒ x=2
They are alike as they need to keep the equations balanced.
The left-hand side of the equation and the right-hand side of the equation is always equal in all the properties of the equality.
Therefore, the properties of equality are alike.
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How do you round 15 to the nearest 10?
The Round-off of 15 nearest to the 10th is 20. This process is called rounding off the numbers.
The process is used to simplify the numbers so that the number can easily be calculated, this is called round-off. The Round-off process can take place to the nearest 10, 100,1000, and so on.
In round-off, the numbers 0,1,2,3,4 are considered as nearest to the "0" and the numbers 5,6,7,8,9,10 are considered as nearest to the "10". Just like that, 15 is considered as nearest to the "20".
It can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form.
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01.18.23 Problem Set Practice
1. Quick Photography specializes in enlarging photographs. Mrs. Smith needs a photo
measuring 4 inches wide and 6 inches long to be enlarged proportionally so that the width is
10 inches. What would be the length of the enlarged photo?
A. 14.5 inches
B. 17.5 inches
C. 15 inches
D. 35 inches
After using proportion the enlarged photo length is C)15 inches.
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here According to the question before enlargement the width is 4 inches and length is 6 inches. Taking proportion between before and after enlargement of the measurements then,
=> [tex]\frac{ width}{length}[/tex]
=> [tex]\frac{4}{6}=\frac{10}{x}[/tex]
=> x = [tex]\frac{10\times 6}{4}[/tex]
=> x = 5 × 3 = 15
Hence after enlargement the photo length is 15 inches.
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Please help!! urgent!! 25 points
Answer:
33 15/16
Step-by-step explanation:
What is the log value of 7?
The log value of 7 base 10 is approximately 0.8451.
What is logarithm ?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
The logarithm of a number is the power to which a certain base (in this case we can consider it as base 10) must be raised to produce that number.
The log value of 7 base 10 is approximately 0.8451.
You can calculate it using log10(7) in most of the calculators or programming languages and get the same result.
The log value of 7 base 10 is approximately 0.8451.
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a gas occupies 7.3 liters at 320k. if the volume is allowed to change to 7.4 liters at constant pressure, what will be the new temperature? provide your answer with one decimal place.
The new temperature of a gas will be 324.38k .
The Ideal Gas Equation defines the four gas variables and one constant for a better understanding. The four gas variables are pressure (P), volume (V), number of moles of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the gas constant.
PV=RT
at constant pressure
V∝T
[tex]\frac{V_{1} }{V_{2} } = \frac{T_{1} }{T_{2} }[/tex]
According to the question,
[tex]V_{1} = 7.3 litres[/tex] , [tex]V_{2} = 7.4 litres, T_{1} = 320k[/tex]
⇒ [tex]\frac{7.3}{7.4} = \frac{320}{T_{2} }[/tex] (substitute the values)
⇒ [tex]T_{2} =\frac{320 * 7.4}{7.3}[/tex]
⇒ [tex]T_{2} =324.38[/tex]
Hence, the new temperature will be 324.38k.
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Write a polynomial of least degree with roots 0 and 8.
Write your answer using the variable x and in standard form with a leading coefficient of 1
Answer:
x² - 8x
Step-by-step explanation:
The least degree polynomial with two roots has to be a quadratic polynomial.
Since the roots are 0 and 8, the factors are, (x - 0)(x - 8) = x² - 8x
Cheers
Answer:
The polynomial of least degree with roots 0 and 8 is x(x-8)=0. This can be written in standard form as x2 - 8x = 0.
a company manufactures 15 inch laptops and 17 inch laptops. It takes 3 hours to manufacture a 15 inch laptop and 5 hours to manufacture a 17 inch laptop. The company has 480 hours T of manufacturing time available. Write a linear inequality to model this sceanario
The linear inequality that models this scenario is 3x + 5y ≤ 480
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Inequalities are used to show that an expression containing numbers and variables are not equal.
Let x represent the number of 15 inch laptops and y represent the number of 17 inch laptops.
It takes 3 hours to manufacture a 15 inch laptop and 5 hours to manufacture a 17 inch laptop.
The company has 480 hours T of manufacturing time available, hence:
3x + 5y ≤ 480
The linear inequality is 3x + 5y ≤ 480
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