Answers
The quotient of the expression (10x³ - 2x² + 8x)/2x is (5x² - x + 4).
What is meant by the term factorization?A polynomial can be published as the product of the its factors with degrees below or equal to the degree of the original polynomial. Factorization of polynomials refers to the process of factoring.The basic technique for factoring polynomials is to find the greatest common factor, which simplifies the problem.The second factoring technique is known as grouping. If there is no factor common to all of the terms of the a polynomial, but there are factors common to a few of the terms, this method is used.The given expression is;
= (10x³ - 2x² + 8x)/2x
Take 2x common on the numerator.
= 2x(5x² - x + 4)/2x
Cancel 2x from the numerator and denominator part.
= 5x² - x + 4
Thus, the quotient of the expression is found as 5x² - x + 4.
To know more about the factorization, here
https://brainly.com/question/25829061
#SPJ13
Related Questions
7. A rectangle has a perimeter of 48 inches. Each side is a whole number of inches. What is the difference between the greatest and least areas that the rectangle can have? 2 2 A. 144 in. B. 121 in.? C. 120 in.? D. 110 in. 2
Answers
Given
The perimeter of the reactangle is, P = 48 inches
The objective is to find the difference between the greatest and least areas that the rectangle.
The sum of the length and breadth of the reactangle can be calculated using the formula of perimeter of the rectangle.
[tex]\begin{gathered} 2(l+b)=48 \\ l+b=\frac{48}{2} \\ l+b=24 \end{gathered}[/tex]The various possible pairs for obtaining 24 are,
[tex]\begin{gathered} 23,1 \\ 22,2 \\ 21,3 \\ 20,2 \\ 19,5 \\ 18,6 \\ 17,7 \\ 16,8 \\ 15,9 \\ 14,10 \\ 13,11 \\ 12,12 \end{gathered}[/tex]From the above pairs, consider the first and the last pairs.
The least area of the rectangle will be,
[tex]\begin{gathered} A(l)=23\times1 \\ =23inches^2 \end{gathered}[/tex]The greatest area of the rectangle will be,
[tex]\begin{gathered} A(g)=12\times12 \\ =144inches^2 \end{gathered}[/tex]Then, the difference can be calculated as,
[tex]undefined[/tex]find the probability that a family with 12 children will have at least one boy 
Answers
The probability that a family with 12 children will have at least one boy is 99.97%.
What is probability?The study of random events is the focus of the mathematical field known as probability theory. A random event's outcome can take any of a number of possible forms; it cannot be predicted before it happens. The outcome as it occurs is thought to have been determined by chance.
In everyday language, the word "probability" can mean a number of things. In order to develop and apply the mathematical theory of probability, two of these are particularly crucial. One is the interpretation of probabilities as relative frequencies; simple games involving coins, cards, dice, and roulette wheels serve as examples for this.
Assuming that the outcome of child born as a bopy or girl is 50% then each boy has a probability of 1/2
The odds of having all girls is = 1/2¹² = 1/4096 ≈ 0.000244
The odds of have at least 1 boy = 1 - 1/4096
= 0.999756
Converting to percentage = 99.97%
Thus, the probability that a family with 12 children will have at least one boy is 99.97%.
Learn more about probability
https://brainly.com/question/24756209
#SPJ13
The scatter plot shows the relationship between the number of chapters and the total number of page’s for several books
Answers
we have
x ----> number of chapters
y ---> number of pages
In this problem
we have a proportional relationship between the variables x and y (because the line passes through the origin)
so
The linear equation is of the form
y=Kx
where k is the constant of proportionality
K=y/x
looking at the graph
we take the point (4,40)
so
k=40/4=10
the equation is
y=10x
For y=180
substitute
180=10x
solve for x
x=180/10
x=18
the answer is 18 chaptersFind the value of the test statistic z.The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 430 peas with 126 of them having yellow pods.
Answers
You have to calculate the z-value or value of the test statistic z, for the proportion of yellow pods. The form of the z-statistic used to study the population proportion is:
[tex]Z=\frac{\hat{p}-p}{\sqrt[]{\frac{p(1-p)}{n}}}\approx N(0,1)[/tex]The population proportion of the yellow pods is p=0.25.
From a sample of 430 peas, 126 of them had yellow pods, using this information you have to calculate the sample proportion p-hat (^p)
The sample proportion is equal to the quotient between the number of successful outcomes "x" (number of yellow pods) and the total number of outcomes "n" (number of peas sampled)
[tex]\begin{gathered} \hat{p}=\frac{x}{n} \\ \hat{p}=\frac{126}{430} \\ \hat{p}=0.29 \end{gathered}[/tex]Once determined the sample proportion, you can calculate the z-value as follows:
[tex]\begin{gathered} Z=\frac{0.29-0.25}{\sqrt[]{\frac{0.25(1-0.25)}{430}}} \\ Z=\frac{0.04}{\sqrt[]{\frac{0.25\cdot0.75}{430}}} \\ Z=\frac{0.04}{\sqrt[]{\frac{0.1875}{430}}} \\ Z=1.915\approx1.92 \end{gathered}[/tex]The value of the test statistic is 1.92.
*-*-*-*-*
The standard deviation of the distribution of the sample proportion:
To simplify the calculations you can calculate the standard deviation separately, the formula for this measure is the denominator of the formula of the Z-statistic:
[tex]\sigma=\sqrt[]{\frac{p(1-p)}{n}}[/tex]Using p=0.25
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{0.25(1-0.27)}{430}} \\ \sigma=\sqrt[]{\frac{0.25\cdot0.75}{430}} \\ \sigma=\sqrt[]{\frac{0.1875}{430}} \\ \sigma=\sqrt[]{\frac{3}{6880}} \\ \sigma=0.0208 \end{gathered}[/tex]Then you can replace the result in the denominator of the formula to determine the Z-value:
[tex]\begin{gathered} Z=\frac{\hat{p}-p}{\sqrt[]{\frac{p(1-p)}{n}}} \\ Z=\frac{0.29-0.25}{0.0208} \\ Z=\frac{0.04}{0.0208}\approx1.92 \end{gathered}[/tex]I am in basic math an need help. so what is 2 1/4 divided by 1/2 I keep getting 4 1/2 what an I doing wrong
Answers
In order to divide a mixed number by a fraction we have to take into account:
- It is easier to convert the mixed number into an equivalent fraction.
- Dividing by a fraction is equivalent to multiplying by the reciprocal of that fraction.
In this case, we have to divide the number 2 1/4 by 1/2.
We start by converting it to a fraction:
[tex]2+\frac{1}{4}=\frac{2\cdot4+1}{4}=\frac{8+1}{4}=\frac{9}{4}[/tex]Then, we have to divide it by 1/2. As we state before, this is the same as multiply by the reciprocal: 2/1, so we have:
[tex]\frac{\frac{9}{4}}{\frac{1}{2}}=\frac{9}{4}\cdot\frac{2}{1}=\frac{18}{4}=\frac{16+2}{4}=\frac{16}{4}+\frac{2}{4}=4+\frac{1}{2}[/tex]Answer: 4 1/2
Reduce this fraction to lowest terms.
35/49
Select the correct answer.
5/7
5/6
6/7
4/9
Answers
Answer:
the answer to your problem is 5/7.
A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was $18,100, find the discount and the new price
The discount in price is
Thus, the new price is $
Answers
Write an equation in slope-intercept form for the line with y-intercept 3 and slope 2.
Answers
Answer:
y=2x+3
Step-by-step explanation:
Slope intercept form: y=mx+b
mx(slope)=2
(b)y-intercept=3
y=2x+3
Hope this helps :)
A line passes through (-1, 7) and (1, 3).
Which answer is the equation of the line?
Answers
Answer:
hgg
Step-by-step explanation:
Use the order of operations to evaluate the expression.7 + { 6 + (3 x 2 )} x 5A. 67B. 95C. 97D. 125
Answers
ANSWER
67 (Option A)
EXPLANATION
Given:
[tex]7+\lbrace6+(3\times2)\rbrace\times5[/tex]Desired Outcome:
Evaluate the expression
Using the order of operations
Note: Follow the following ORDER to evaluate the expression
1. The parenthesis are completed first.
2. The exponents come next.
3. Multiplication and division are done from left to right when they are encountered.
4. Addition and subtraction are done from left to right when they are met.
1. Complete parenthesis first
[tex]\begin{gathered} 7+\lbrace6+6\rbrace\times5 \\ 7+\lbrace12\rbrace\times5 \end{gathered}[/tex]2. Multiplication and division are done from left to right when they are encountered.
[tex]\begin{gathered} 7+\lbrace12\rbrace\times5 \\ 7+60 \end{gathered}[/tex]3. Addition and subtraction are done from left to right when they are met.
[tex]\begin{gathered} 7+60 \\ =67 \end{gathered}[/tex]Hence, the answer is 67 (Option A)
Evaluate the expression below for a=2, b=3, and c= -2 a + (b - c)^2
Answers
[tex]a+(b-c)^2[/tex][tex]2+(3-(-2))^2[/tex][tex]2+(3+2)^2[/tex][tex]2+(5)^2[/tex][tex]2+25=27^{}[/tex]
Find a polynomial with integer coefficients that satisfies the given conditions.
Q has degree 3 and zeros
−4
and 1 + i.
Answers
An arithmetic polynomial that meets the requirements.
Q has zeros of degree 3 is -4 and 1+i is Q(x)=x³+4x²-10x+12..
Given that,
We have to find an arithmetic polynomial that meets the requirements.
Q has zeros of degree 3 is -4 and 1+i.
There is a complex number is i.
When working with complex numbers, the following relationship is the most crucial:
i²=-1
A function's zeros:
This polynomial, given by f(x), has roots of x₁, x₂, x₃..... in which an is the leading coefficient and can be represented as a(x-x₁)(x-x₂)(x-x₃).....
Degree 3 and zeros -4 and i+1 make up Q.
Given that complex roots are always complex-conjugate, 1 - i is also a root if 1 + i is a root.
The leading coefficient, as we will mention, is 1.
Q(x)=(x-(-4))(x-(1-i))(x-(1+i))
Q(x)=x³+4x²-10x+12
Therefore, the polynomial we get is Q(x)=x³+4x²-10x+12.
To learn more about polynomials visit: https://brainly.com/question/11536910
#SPJ1
En el supermercado puedes llenar tu propio contenedor de osos
de miel. Un cliente compra 12 oz de
miel por $5.40.
1a) ¿Cuánto cuesta la miel por onza? (comunicar dinero usando un $ al principio, *
sin espacios y sin palabras)
Answers
Question 4Given AGEO 2 AFUMZE = (42.)in/N = 40mZU = 80ånd m_G = 60find the value of a(The problem is sort of messed up because of canvas)
Answers
It is stated in the problem that ΔGEO is congruent with ΔFUN. On the first triangle, the measurement of angle E and angle G is given but the measurement of angle O is not given. Using the congruence relation of the two triangles, it is true that
[tex]m\angle O\cong m\angle N[/tex]The measurement of angle N is provided in the problem, which is equal to 40 degrees. Hence, we can say that angle O has also an angle measurement of 40 degrees base on the statement above.
The sum of the interior angles of the triangle is equal to 180 degrees. This means that if we add up the interior angles of the triangle GEO, we have the following equation
[tex]m\angle G+m\angle E+m\angle O=180[/tex]Substitute the measurement of each angle on the equation above and compute, we get
[tex]\begin{gathered} 60+4x+40=180 \\ 4x+100=180 \\ 4x=180-100 \\ \frac{4x}{4}=\frac{80}{4} \\ x=20 \end{gathered}[/tex]Therefore, the value of x is equal to 20 degrees.
When evaluated for y =8the expression y-3/y^2+14
Answers
Given expression is
[tex]\frac{y-3}{y^2+14}[/tex]It is given that y = 8.
Hence the value of the expression is
[tex]\frac{8-3}{8^2+14}=\frac{5}{78}[/tex]Hence the answer is 3. 5/78
Define integer give me an example of a number that is an integer and a number that is not an integer
Answers
Step-by-step explanation:
An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.
A certain solution has hydrogen ion concentration of 0.0000653 miles per liter write this number in scientific notation.
Answers
Solution:
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. In this case, we have that:
[tex]0.0000653=653x10^{-5}[/tex]so that, the correct answer is:
[tex]653x10^{-5}[/tex]If I got a 92% and there were 40 questions how many did I get wrong?
Answers
Answer: 3.2 were wrong
92% of 40 is 36.8 so you got 3.2 wrong
I hope this helps / Is correct
Keaton needs to fill juice cups for her little sister's birthday party. There are 22 juice cups and each juice cup holds 12 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase?
(1 quart = 32 fluid ounces, 1 gallon = 4 quarts)
Answers
Answer: 3 Gallons
Step-by-step explanation:
To find the total number of ounces she needs of juice we need to multiply the 22 cups by 12 ounces.
22 x 12 = 264
Now to find the number of quarts we need to convert the ounces into quarts by dividing by 32.
264 / 32 = 8.25
To find the number of gallons we need you have to convert it into gallons by dividing by 4.
8.25 / 4 = 2.0625
Because you cannot purchase .0625 of a gallon, we need to round up and purcahse 3.
PENNANT Tameeka is in charge of designing a school pennant for spirit week. She wants the base to be 34 feet and the height to be 6 feet. She has 20 square feet of paper available. Does she have enough paper? Explain.
Answers
Given:
Required base of pennant is, b = 34 ft.
Required height of pennant is, h = 6 ft.
The objective is to fin
1. Make a frequency table for the scores on a ten-point quiz: 5, 5, 7, 8, 8, 6, 7, 8, 7, 7, 8, 10,9
Answers
To make the frequency table we need to count how many of each scores we have, for example we have two fives; 4 sevens, and so on, then the table is:
A paralegal bills a law firm for 19.5 hours of work at a rate of £240 per hour. How much money has the paralegal earned from this job? Include units in your answer.
Answers
The money that the paralegal has earned for this work = £4680
What is the unitary approach for problem solving?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. This technique essentially involves determining the value of a unit from the value of a multiple.
Given, cost of work per hour = £ 240
Duration of work of a law firm = 19.5 hours
Money earned by paralegal for the work = (240*19.5) = £ 4680
Thus, the money that the paralegal has earned for this work = £4680
To learn more about this, tap on the link below:
https://brainly.com/question/28486225
#SPJ9
i need to round to tge narest tenth
Answers
Answer:
[tex]\lbrace8.4,0.6\rbrace[/tex]Step by step explanation:
Solve for x:
[tex]x^2-11x+5=-2x[/tex]As a first step, solve using inverse operations to solve equations:
[tex]\begin{gathered} x^2-11+2x+5=0 \\ x^2-9x+5=0 \end{gathered}[/tex]Now, to solve this quadratic function we need to use the quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where,} \\ ax^2+bx+c=0\text{ is the form of the function} \end{gathered}[/tex]Then, the solutions for the equation:
[tex]\begin{gathered} x_1=\frac{9+\sqrt[]{(-9)^2-4(1)(5)}}{2(1)}=8.4 \\ x_2=\frac{9-\sqrt[]{(-9)^2-4(1)(5)}}{2(1)}=0.6 \end{gathered}[/tex]Aaron buys 5 pounds of potatoes. He divides the potatoes into 1/6 pound portions for dinner. How many portions does Aaron have?
Answers
In one pound, there are 6 portions of 1/6 pounds each one of them because
[tex]1\text{pound}=\frac{6}{6}\text{pound}[/tex]Therefore, in five pounds there are 30 portions of 1/6 pounds each one of them because
[tex]5\text{pounds}=\frac{30}{6}\text{pounds}[/tex]How many portions does Aaron have? He has 30 portions.
Determine if the triangle with the given sides is acute, obtuse, or right.80, 84, 116
Answers
Given: The sides of a triangle below
[tex]\begin{gathered} side1=80 \\ side2=84 \\ side3=116 \end{gathered}[/tex]To Determine: If the triangle is acute, obtuse or right
Solution
If it is right triangle, then the Pythagoras theorem would hold
[tex]\begin{gathered} Pythagoras-Theorem \\ Hypothenuse^2=Opposite^2+Adjacent^2| \\ Hypothenuse=Longest-side \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 116^2=80^2+84^2 \\ 13456=6400+7056 \\ 13456=13456 \end{gathered}[/tex]From the above calculation, we can conclude that the triangle is
RIGHT TRIANGLE
482 + 51.8 =
O 1000
O 430.2
O 533.8
O 100
Answers
It costs $24 to join the health club A,plus an additional $20 per month. It costs $80 to join the healths club B,plus an additional $12 per month. After how many months of membership would it cost the4 same to belong to either health club? What is that cost?
Answers
Answer:
7 months. 164 dollars.
Step-by-step explanation:
Club a = 24 + 20x
Club b = 80 +12x
a = b
24 + 20x = 80 +12x
8x = 56
x = 7
7 months before it is the same.
write an equation parallel to y=3x+6 that passes through the point (4,7).
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is
y = 3x + 6
If we compare the given equation with the slope intercept equation, we can see that slope = 3
If two lines are parallel, it means that they ahve the same slope. Thus, the slope of the line
that passes through the point (4,7) is 3
We would find it's y intercept, c by substituting m = 3, x = 4 and y = 7 into the slope intercept equation. It becomes
7 = 3 * 4 + c
7 = 12 + c
c = 7 - 12
c = - 5
Thus, we would substitute m = 3 and c = - 5 into the slope intercept equation to get the equation of the line. Thus, we have
y = 3x - 5
Two sides of an isosceles triangle have lengths of 3 and 6. What is the length of the third side?A. 6B. 9C. 3D. 5
Answers
It is given that the triangle is isosceles and the sides are 3 and 6.
Since the triangle is isosceles so third side will be either 3 or 6 .
If third side is 3 then we have
[tex]3+3=6[/tex]which is a contradiction to the fact that sum of two sides of a triangle is greater than the third side.
So the third side will be 6.
Hence the correct option is (A).
6r = 726r − 6 = 72 − 6r = 66Is Brooke’s solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given solution
[tex]\begin{gathered} 6r=72 \\ 6r-6=72-6 \\ r=66 \end{gathered}[/tex]STEP 2: Determine whether Brooke's solution is correct
Brooke's solution is incorrect because Brooke subtracted the co-efficient of r which is 6 from both sides. Brooke can not use this method since 6 is multiplied to the unknown value which ir and not added to both sides.
The correct step will be to divide both sides by the coefficient of r as seen below:
[tex]\begin{gathered} 6r=72 \\ Coefficeint\text{ of r is 6} \\ Divide\text{ both sides by 6} \\ \frac{6r}{6}=\frac{72}{6} \\ r=12 \end{gathered}[/tex]