Answers
Hello there. To solve this question, we'll have to remember some properties about dividing polynomials.
Given the polynomials, we want to evaluate the division:
[tex](1+3x+x^4)\div(3-2x+x^2)[/tex]Rewriting it the way we perform long division:
We start with the higher degree terms, namely x^4 and x².
Dividing x^4 by x², we get x². Now we multiply every term from the division by this factor and subtract from the term being divided.
Now, we have a 2x³ as the higher degree term from the term being divided. Dividing it by x², we get 2x. Multiply each term of the divisor and subtract from it.
Finally, the highest degree term from the term being divided is x². Dividing it by x², we get 1. Multiply each term of the divisor and subtract it from the dividend.
Now, the highest degree term from the dividend is -x, when the highest degree term from the divisor is x². We cannot proceed with the long division anymore.
It means that we have a quotient:
[tex]x^2+2x+1[/tex]And a remainder:
[tex]-x-2[/tex]Notice if we rewrite it as:
[tex]x^4+3x^2+1=(x^2-2x+3)\cdot(x^2+2x+1)-x-2[/tex]We have the division P(x)/D(x) written in the form:
[tex]P(x)=D(x)\cdot Q(x)+R(x)[/tex]Where Q(x) and R(x) are the quotient and remainder polynomials.
Related Questions
A catering service offers 8 appetizers, 9 main courses, and 3 desserts. A customer is to select 6 appetizers, 6 main courses, and 2 desserts for a banquet. Inhow many ways can this be done?
Answers
Given:
Number of appetizers offered = 8
Number of appetizers customer is to select = 6
Number of main courses offered = 9
Number of main courses customer is to select = 6
Number of desserts offered = 3
Number of desserts the customer is to select = 2
Let's determine how many ways this can be done.
This is a combination problem.
To determine the number of ways this can be selected, apply the combination formula below:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Thus, we have:
[tex]_nC_r=_8C_6\ast_9C_6\ast_3C_2[/tex]Solving further, let's apply the formula and combine:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(8-6)!}\ast\frac{9!}{6!(9-6)!}\ast\frac{3!}{2!(3-2)!} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(2)!}\ast\frac{9!}{6!(3)!}\ast\frac{3!}{2!(1)!} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7\ast6!}{6!(2\ast1)}\ast\frac{9\ast8\ast7\ast6!}{6!(3\ast2\ast1)}\ast\frac{3\ast2!}{2!(1)} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7}{2\ast1}\ast\frac{9\ast8\ast7}{3\ast2\ast1}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{56}{2}\ast\frac{504}{6}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=28\ast84\ast3 \\ \\ _8C_6\ast_9C_6\ast_3C_2=7056 \end{gathered}[/tex]herefore, there are
24. Jenna wants to purchase a new guitar for $375. She currently has $45 in her savings account. If she plans to save $35 each week, how many weeks will it take her to save enough money to purchase the guitar? Choose the inequality that best represents this situation. A 45 + 35x < 375 B 35 + 45x < 375 C 45 + 35x > 375 D 35 + 45x > 375
Answers
Here, we want to select the inequality that best represents the situation
Let the number of weeks be x
Total value saved in x weeks at $35 per week will be 35 * x = 35x
Adding this to what she had initially, the total expression becomes 35x + 45
This sum must be the same or greater than what she plans to save
The inequality is thus;
[tex]35x\text{ + 45}\ge\text{ 375}[/tex]Find the slope m of the line passing through the given pair of points. (If an answer is undefined, enter UNDEFINED.)
(6, 5) and (−9, 5)
Answers
Answer:
m= 0
Step-by-step explanation:
Since the two points have the same y-coordinates, the line passing through them is a horizontal line. Horizontal lines have a slope of zero.
Prove:
[tex]\boxed{slope = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Slope between (6, 5) and (-9, 5)
[tex] = \frac{5 - 5}{ - 9 - 6} [/tex]
[tex] = \frac{0}{ - 15} [/tex]
= 0
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In a 7-card poker, played with a standard 52-card deck, 52C7, or 133,784,560, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by . Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.
Answers
If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is: 0.999944..
ProbabilityProbability of complement of the event A =P (Ac) = 1- P(A)
A = event of the particular type of hand
Probability of A :
P(A) = n (A) / n(S)
P(A) = 7480 / 133,784,560
Ac = event of not being dealt of this type of hand
Probability of Ac:
P (Ac) = 1- P(A)
P (Ac) = 1- 7480 / 133,784,560
P (Ac) = 133, 777,080 / 133,784,560
P (Ac) = 0.999944
Therefore the probability of not being dealt this type of hand is 0.999944.
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The complete question is :
In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.
The miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, find the number of hours it would take Jack to travel 665 miles.
Answers
If the miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, the number of hours it would take Jack to travel 665 miles is 9.5 hours.
Determining the number of hours to travelLet x represent the number of hours it would take Jack to travel
Formulate an equation
175 / 2. 5 = 665 / x
The denominator cannot equal 0 because the fraction is defined
so,
x ≠ 0
Hence,
1750 × 25x / 25 = 665 × 25x /x
Reduce the fraction
1750x = 665 × 25
1750x = 16,625
Divide both side by 1750x
x = 16,625 / 1750
x = 9.5
Therefore it will take Jack 9.5 hours.
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In 9.5 hours Jack can travel for 665 miles.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost 10 dollars, therefore 1 pen costs (10/2) = 5 dollars.
From this unitary value, we can determine the cost of any no. of pens.
Given, Jack drove 175 miles in 2.5 hours.
∴ In one hour Jack can drive (175/2.5) miles.
= 70 miles.
So, to travel 665 miles Jack needs (665/70) hours.
= 9.5 hours or 9 hours and 30 minutes.
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PLEASE HELP ASAP Solve for y, z, x, or t: z-a=z/b if b does not equal 1
Answers
On solving the equation z-a = z/b if b≠1 , for z we get z=ab/(b-1) .
in the question ,
the equation is given as
z-a = z/b
adding "a" to both the sides
we get
z-a+a = z/b + a
z = z/b + a
subtracting z/b from both the sides , we get
z - z/b [tex]=[/tex] z/b - z/b + a
z - z/b = a
taking z common
z(1-1/b) = a
taking LCM as b and solving further , we get
z (b-1)/b = a
on cross multiplication we get
z = ab/(b-1)
Therefore , on solving the equation z-a = z/b if b≠1 , for z we get z = ab/(b-1) .
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Which of the following numbers could not be used to describe a distance walked? O 19 feet 0-140 feet 0 -125 feet 12 feet
Answers
NSWER
140 Ffeet
EXPLANATION
istance is an absolute value wquantity, so it is expressed either as a positive value or an absolute value of a negative number.
Henry is younger than Cameron. Their ages are consecutive odd integers. Find Henry's age if the sum of Henry's age and 2 times Cameron's age is 85.
Answers
Since we used x and x+2 as consecutive odd integers. "x" to represent Henry's age, Henry's age is 27. Since we used the expression "x+2" to represent Cameron's age, Cameron's age is "27+2" which is just 29.
How to do age sums?So the consecutive odd integers, just means they're separated by a value of 2. This can be generally expressed as "a and a+2" where the these two values would be consecutive odd integers assuming "a" is an integer.
So let's express the Henry's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive odd integer, Cameron's can be expressed as "x+2"
So the equation we need to set up is 2(Cameron's age) + (Henry's age) = 85
So we can substitute variables we defined to express Cameron and Henry's age:
2(x+2)+x= 85
Distribute the 2:
2x+4+x
Add like terms:
3x+4=85
Subtract 4 from both sides:
[tex]3x= 81[/tex]
Divide both sides by 3:
x=27
Since we used "x" to represent Henry's age, Henry's age is 27. Since we used "x+2" to represent the Cameron's age, Cameron's age is "27+2" which is just 29.
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TRUE OR FALSE? For any real number x > 0 log 3 x > log ₂ x.
Answers
======================================================
Explanation:
We can use a counter-example.
Pick any positive real number you want to replace x.
I'll pick x = 7
Use the change of base formula to get the following
[tex]\log_{3}(\text{x}) = \frac{\log(\text{x})}{\log(3)}\\\\\log_{3}(7) = \frac{\log(7)}{\log(3)}\\\\\log_{3}(7) \approx \frac{0.8451}{0.4771}\\\\\log_{3}(7) \approx 1.7713\\\\[/tex]
and
[tex]\log_{2}(\text{x}) = \frac{\log(\text{x})}{\log(2)}\\\\\log_{2}(7) = \frac{\log(7)}{\log(2)}\\\\\log_{2}(7) \approx \frac{0.8451}{0.3010}\\\\\log_{2}(7) \approx 2.8076\\\\[/tex]
---------------------------
So if x = 7, then we have,
[tex]\log_{3}(\text{x}) > \log_{2}(\text{x})\\\\\log_{3}(7) > \log_{2}(7)\\\\1.7713 > 2.8076\\\\[/tex]
The last statement is false, so the first statement is false when x = 7.
It turns out that you could pick any positive real number for x and will always get a false statement when saying [tex]\log_{3}(\text{x}) > \log_{2}(\text{x})[/tex]
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,4) and parallel to x + 2y = 7.a) The equation of the line in slope-intercept form is(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)b) The equation of the line in standard form is(Type your answer in standard form.)
Answers
For this type of question the first step is to calculate the slope of the line given by th equation x+2y=7, for this we recall the slope intercept form ( y=mx+b) and put the equation in that form
[tex]y=-\frac{x}{2}+\frac{7}{2}[/tex]Then, m=-1/2. Now, since the equation of the line we are looking for is parallel to the previous line the slope must be the same, now we recall the point slope equation
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ \end{gathered}[/tex]Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :
[tex]\begin{gathered} y-4=-\frac{1}{2}(x-(-3)) \\ y-4=-\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]Finally to put it in the slope intercept form, we solve the equation for y:
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]For part b) we recall that the standard form of the equation of a line is:
[tex]\begin{gathered} C=Ax+By \\ \text{where C, A and B are real and whole numbers if possible} \end{gathered}[/tex]Now, we solve for the constant of the equation:
[tex]\begin{gathered} \frac{5}{2}=y+\frac{1}{2}x \\ 5=2y+x \end{gathered}[/tex]The last equation is the standard form of the equation of the line.
Type a paragraph in which you use at least two linking commas, two semicolons, and one colon.
Need two commas (,,)
two semicolons (;;)
one colon (:)
and not run on sentences and of course put period.
Answers
There are numerous advantages of involving oneself in sports. First and foremost, as known by all and very definitively, competitions increase the physical fitness of an individual. Additionally, sports also contribute to building stable mental well-being of a person. Various researchers show that people who are in the daily practice of sports in any form record better mental as well as physical health. Moreover, sports also eliminates the risk of a person catching diseases or facing any bodily interruptions. Competitions increase immunity and increase people’s stamina.
a picture is 5inches wide and 8inches tall:A photographer wants to use a scale factor of 2.5to enlarge a picture.what will the area of the picture be after it is elarged
Answers
We can determine the area of the enlarged picture as follows:
*First, we determine the new dimensions, that is:
[tex]5\cdot2.5\text{ = 12.5}[/tex][tex]8\cdot2.5=20[/tex]*Secondly, we find the area using the formula of area for a rectangle, that is:
[tex]A=20\cdot12.5\Rightarrow A=250[/tex]From this, we have that the area of the picture after being enlarged equals 250 in^2.
find the standard error mean if O = 64 and n = 64
Answers
The standard error mean if σ = 64 and n = 64 is 8.
How can we obtain the standard error mean?The standard error mean is given by the formula σ/√N. In the question provided, we need to note that the standard error mean is designated by σM.
Now applying the formula, we will have this:
σM = 64 ÷√64
The root of 64 = 8.
Therefore, the standard error mean is equal to 64 divided by 8 which is 8.
So, we can arrive at the conclusion that given the standard error mean of σ = 64 and n = 64, the standard error mean will be 8.
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Determine if the two figures below are congruent. Use the drop-down menus below to justify why. Which point on Figure 2 corresponds to point CC on Figure 1?
Answers
From the figure, we observe that,
Non-rigid motions are used to map figure 1 onto figure 2.
Here, resizing (stretching horizontally, vertically, or both ways) is a non-rigid transformation.
So, the answer is,
The figures are congruent because non-rigid motions are used to map figure 1 onto figure 2.
The point corresponding to point C is H.
What is the answer to this question?
Answers
In the given angle, the value of x is 9°.
What are angles?In Euclidean geometry, an angle is a shape created by two rays that share an endpoint and are referred to as the angle's sides and vertex, respectively. The plane that contains the rays contains the angles created by two rays. The meeting of two planes can also result in an angle. They are referred to as dihedral angles.As we can see that the two triangles are congruent as 2 pairs of sides are similar to each other.
Hence, the angle between them is also similar.So, with this the equation will be:
3x + 15 = 423x = 42 - 153x = 27x = 27/3x = 9Therefore, in the given angle, the value of x is 9°.
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One morning in Atlanta, Tina observed that the temperature was 72 degrees. Later the temperature rose 21 degrees and then dropped 11 degrees. She then flew to New York where the temperature was 67 degrees.
What was the change in temperature from when Tina left Atlanta and arrived in New York?
A:5°
B:6°
C:14°
D:15°
Answers
If She then flew to New York where the temperature was 67 degrees. The change in temperature from when Tina left Atlanta and arrived in New York is : D:15°.
Change in temperatureGiven :
Beginning temperature = 72 degrees
Increase in temperature = 21 degrees
Decrease in temperature = 11 degrees
Temperature outside Atlanta = 67 degrees
First step is to calculate the temperature in Atlanta using this formula
Temperature = (Beginning temperature + Increase in temperature - Decrease in temperature )
Let plug in the formula
Temperature = 72 + 21 -11
Temperature = 82 degrees
Second step is to calculate the change in temperature
Change in temperature = Temperature in Atlanta - Temperature in New York
Change in temperature = 82 degrees - 67 degrees
Change in temperature = 15 degrees
Therefore the correct option is D.
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The converse of the proposition "If it is cold, then I will not go walking" is:
A. If it is not cold, then I will go walking.
B. If it is not cold, then I will not go walking.
C. If I did not go walking, then it is cold.
D. If I go walking, then it is not cold.
Answers
Answer:
C. If I did not go walking, then it is cold.
Step-by-step Explanation:
A conditional statement is a hypothesis followed by a conclusion. The hypothesis in this example being “If it is cold” and then followed by a conclusion “I will not go walking”.
A converse statement swaps the hypothesis and the conclusion of a conditional statement.
help meeeeeeeeeeeeeee
Answers
Answer: What do you need help with?
Step-by-step explanation:
1: Comment what u need help with
2: We will help you
3: You have been helped :)
Answer:
After doing the math I got 74.44
Gary is buying a $1,250 computer on the installment plan. He makes a down payment of $150. He has to make monthly payments of $48.25 for 2 years. What is the total finance charge?
Answers
The total finance charge on the computer purchased on finance by Gary is $58.00
What is finance charge?
The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150
principal=purchase price-down payment
principal=$1,250-$150
principal=$1,100
total payments=monthly payment*number of months in 2 years
total payments=$48.25
total payments=$48.25*24
total payments=$1,158.00
total finance charge=total payments-principal
total finance charge=$1,158.00-$1,100.00
total finance charge=$58.00
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Factor 8mn2 + 12mn completely. A 42mn’ +3mn) B 4mn(2 + 3n) C 4mn(2mn + 3) D 4mn(2n + 3)
Answers
Question 1Step 1: Problem
[tex]\text{Factor 8mn}^2\text{ + 12mn}[/tex]Step 2: Concept
Factor the highest common factor out.
Step 3: Method
[tex]8mn^2\text{ + 12mn = 4mn( 2n + 3)}[/tex]Step 4: Final answer
4mn(2n + 3)
Question 2
Step 1: Question
[tex]\text{Simplify }\frac{(1.24\text{ }\times10^2\text{ ) (3.6 }\times10^{-3})}{1.8\text{ }\times\text{ 10}}[/tex]Step 2: Concept
Apply laws of exponent
[tex]\begin{gathered} \text{Division law } \\ \frac{m^x}{m^y}=m^{x\text{ - y}}^{} \\ \text{Multiplication law} \\ m^x\text{ }\times m^y=m^{x\text{ + y}} \end{gathered}[/tex]Step 3: Method
[tex]\begin{gathered} =\text{ }\frac{(1.24\text{ }\times10^2\text{ )(3.6 }\times10^{-3})}{1.8\text{ x 10}} \\ =\text{ }\frac{1.24\text{ }\times\text{ 3.6 }\times10^{2\text{ + (-3)}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{2\text{ - 3}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{-1}}{18} \\ =\text{ }\frac{4.464}{18}\text{ }\times10^{-1} \\ =\text{ 0.248 }\times10^{-1} \\ =\text{ 2.48 }\times10^{-2} \end{gathered}[/tex]Step 4: Final answer
Option D is the correct answer
[tex]2.48\text{ }\times10^{-2}[/tex]
Please help for number 1 2 and 3 and an explanation because I don't understand
Answers
The product of the numbers are-
107×11 = 117772×13 = 936466×27 = 12582What is defined as the product of number?In mathematics, a product is defined as the result of multiplying two or more numbers together.The amount of objects in a group is referred to as a multiplicand, and the number of these equal groups is referred to as a multiplier.A multiplier, a multiplicand, as well as the product comprise a multiplication expression.For the given number;
Part a: 107 × 11
1 0 7
× 1 1
---------
1 0 7
+ 1 0 7 x
-------------
1 1 7 7
--------------
Thus, 107×11 = 1177
Part b: 72×13
7 2
× 1 3
---------
2 1 6
+ 7 2 x
-------------
9 3 6
--------------
Thus, 72×13 = 936
Part c: 466×27
4 6 6
× 2 7
---------
3 2 6 2
+9 3 2 x
-------------
1 2 5 8 2
--------------
Thus, 466×27 = 12582
Therefore, product of the number are found.
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What is the slope of a line perpendicular to the line whose equation is 3x-12y=-108
Answers
Answer:
-4
Step-by-step explanation:
Given:
Equation of line is 3x-12y = -108.To Find:
Slope of line perpendicular to the given line.Concept used:
For a line ax+by+c = 0 , the slope is equal to -a/b.Slope of a line perpendicular to a line say ax+by+c = 0 will be b/a.For the given equation, we have
a = 3, b = -12 and c = 108
So, Slope of line perpendicular to given line = -12/3 = -4
So, the slope of required line is -4.
The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation is given below.
3x - 12y = - 108
Convert the equation into a slope intercept, then we have
3x - 12y = - 108
12y = 3x + 108
y = (1/4)x + 9
The product of the slopes of the perpendicular line will be a negative one. Then we have
(1/4)m = -1
m = - 4
The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.
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If you were to write an essay on an eyeball what would you write? Please help me i can’t do this!
Answers
Answer:
Should the essay be 3-5 paragraphs? Also I can't write the essay here or otherwise your school will find out you plagiarized it.
Step-by-step explanation:
I can send it to you privately.
Consider a simple economy where the basket of goods used to calculate the CPI contains two items: shampoo and soap. The basket consists of 1 bottle of shampoo and 2 bars of soap. The prices are shown in the table.
Year Price of a Bottle of Shampoo Price of a Bar of Soap
Year 1 $6.50 $1.25
Year 2 $6.60 $1.30
Type the correct answer in the box. Round your answers to two decimal places, if necessary.
The CPI for year 2 is
.
Answers
In this simple economy where the market basket for CPI contains two items, the CPI for year 2 is 102.22%.
What is the CPI?The CPI means the Consumer Price Index.
The CPI economically indicates the inflationary trend, using a basket of selected consumer goods and services, and computes their total costs for each period.
The base year's total costs set to 100% are used to compare with the current year's.
Price 1 Bottle of 1 Bar of 2 Bars Total Cost
Shampoo Soap of Soap Mkt Basket
(a) (b) (c) (a) + (c)
Year 1 $6.50 $1.25 $2.50 $9.00
Year 2 $6.60 $1.30 $2.60 $9.20
CPI for Year 1 (base year) = 100% ($9/$9 x 100)
CPI for Year 2 = 102.22% ($9.20/$9 x 100)
Thus, year 2's Consumer Price Index is 102.22%, compared to year 1's.
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Answer:
102.22
Step-by-step explanation:
Edmentum.
use the roster method to write the set of natural numbers less than 6
Answers
A circular disc has a circumference of 141 meters. If we multiply the radius of the circular disc by 12, what will be the circumference of the new disc? OA) 168 m OB) 248 m OC) 4147 m OD) 352 m
Answers
3 to 5 men and total of 224 people how many are men
Answers
When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.
How to illustrate the information?From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.
Therefore, it should be noted that the fraction for men that illustrates the information will be:
= 5/(3 + 5) × 224
= 5/8 × 224
= 5 × 28
= 140
Therefore, the number of men is 140 men.
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
The value of x of the Quadratic Equation, (x - 7)² = 36 when the right-hand side is positive is 13 and for the negative right-hand side, it is 1. So the value of x could be 13 and 1 both.
Split into two equations:
(x - 7)² = 36
(x- 7) = √36 or (x- 7) = -√36
For equation (x- 7) = √36 value of x:
x - 7 = √(6)²
x - 7 = 6
x = 13
For equation (x- 7) = -√36 value of x:
x - 7 = -√(6)²
x - 7 = - 6
x = 1
∴ value of x could be 13 and 1 both.
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Renu's brother is 5 years younger than Renu. Now he is 30 years old. Connect their ages
Answers
The age of Renu and her brother is 35 and 30 years respectively.
Let the age of Renu be x
Then,
The age of her brother will be x-5
According to the question,
Age of Renu's brother is 35
So,
x-5 = 30
x = 30+5
x= 35
Hence, the age of Renu and her brother is 35 and 30 years respectively.
This question is related to the topic age problem. These problems aim is to find the age of certain people.
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Need to know what goes in the 4 boxes above, and the last box
Answers
Given that Owen moves half the number of boxes moved by Ariana.
So you can put 2 in the left side upper box, and 1 in the left side lower box.
Now, it is mentioned that Owen mobes 12 boxes. So the corresponding number of boxes moved by Arianna is to be obtained.
So you have to put 12 in the right side lower box. And a variable (say 'x') in the right side upper box.
The vaue of 'x' is to be calculated.
Cross multiply the terms,
[tex]\begin{gathered} 1\cdot x=2\cdot12 \\ x=24 \end{gathered}[/tex]Thus, the value of 'x' is 24.
Therefore, Arianna can move 24 boxes in the time when Owen moves 12 boxes.