The synthetic division solution of (4x² + 3x³ + 9x− -20) / (x + 2) is mathematically given as
3x^2-2x+13-(6/x+2)
This is further explained below.
What is synthetic division?Generally, Synthetic division is a technique that may be used to manually conduct Euclidean division of polynomials.
Compared to long division, the synthetic division requires less writing and fewer calculations to complete. The approach is most often taught for dividing by linear monic polynomials; however, it may be extended to divide by any polynomial.
In conclusion, The synthetic division solution is mathematically given as
3x^2-2x+13-(6/x+2)
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Find the smallest positive integer, n,such that 168n is a square number.
Answer:
n = 42 and the square number is 7056
==============================
Prime factors of 168 are:
168 = 2*2*2*3*7In order to make 168n a square number we need to use each prime factor even number of times.
Add 2, 3 and 7 to the prime factors (as a minimum) to get:
168*2*3*7 = 168*42 = 2⁴*3²*7² = (2²*3*7)² = 84² = 7056The normal cruising speed of a certain airplane is about 250 m/sec. What is this speed in miles per hour? Round to a whole number.
Answer:
900,000 mph
Step-by-step explanation:
I am assuming the m in he problems is standing for miles.
250m/sec x 60 sec/min x 60min/hour The sec cross out and the minutes cross out and you are left with miles be hour.
Write the number name and expanded form for the number of driver ants that could be in two colonies.
Up to 22000 000 driver ants can live in a single colony
Number name = 22 million
Expanded form = 20,000,000 + 2,000,000
How to write a number in expanded form?
To write the number name and expanded form for the number of driver ants that could be in two colonies.
Given that Up to 22,000,000 driver of ants can live in a single colony
Now, from number expressions, we know that;
1, 000, 000 = 1 million
Thus number name is;
22,000,000= 22 million
Expanded form of 22,000,000 = 20,000,000 + 2,000,000
Thus, we conclude that;
Number name = 22 million
Expanded form = 20,000,000 + 2,000,000
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Determine the relationship between the quantities on the given graph.
Wages Earned ($)
OA. The hourly rate depends on the wages earned.
B.
The time worked depends on the wages earned.
C.
The wages earned depends on the time worked.
The time worked depends on the hourly rate.
O D.
Total Wages
Time Worked (hours)
The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct
The graph given in the question shows the time worked on x axis and wages earned on y axis and a ray staring from the origin and moving upward
from the graph we can say that when time worked is zero then wages earned is zero. As the time worked is increasing the wages earned is also increasing .
Hence, it can be said that The wages earned depends on the time worked is the correct relationship between the quantities on the given graph that means option C is correct
The correct question is -Determine the relationship between the quantities on the given graph.
Total Wages
Wages Earned ($)
Time Worked (hours)
OA. The hourly rate depends on the wages earned.
OB. The time worked depends on the wages earned.
OC. The wages earned depends on the time worked.
OD. The time worked depends on the hourly rate.
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Dominie practices the piano 714 minutes in 2 weeks. at what rate did she practice, in minutes per day?
The number of minutes per day that Dominie practise the piano is 51 minutes per day.
What is the rate of practice?The first step is to convert two weeks to days.
1 week = 7 days
2 weeks : 7 x 2 = 14 days
The second step is to divide the total minutes Dominie practices by the total number of days. Division is the mathematical operation that is used in grouping a number into equal parts using another number. The result of a division is known as the quotient. The sign used to represent division is ÷.
Number of minutes they practice per day : total practice / number of days in two weeks
714 / 14 = 51 minutes per day
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I need help with this please
Answer: m<ABC = 45 degrees, m<DBC = 36 degrees
Step-by-step explanation:
set both equations equal to 81 because they add up to form one angle:
5x + 6 + 9x - 9 = 81
Combine like terms
14x - 3 = 81
Add three to both sides
14x = 84
Divide by 14 to find x
x = 6
To find the angles:
Measurement of angle ABC:
9(6) - 9 = 45 degrees
Take the original angle of 81 and subtract the angle you just found to find the remaining angle:
81 - 45 = 36
Therefore, the angle of DBC is 36 degrees
If 6 -x = 12, what is x - 6?
Answer: x - 6 = -12
Step-by-step explanation: first, we'll solve for x in 6 - x = 12. We'll isolate the variable by subtracting 6 from both sides, which gives us -x = 6. Now we'll divide both sides by -1 to get x and we will get -6 = x. So for the expression, we'll sub in the value we got for x from the equation, -6. -6 - 6 = -12.
Answer:
-12
Step-by-step explanation:
(x-j) (5x + k) = 0
How do i find x from this equation
Answer:
x = 5j-k
Step-by-step explanation:
(x-j) (5x+k) = 0
(x-j) * (5x+k) = 0
x - 5j + k = 0
x + k = 5j
x = 5j - k
Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. Is she correct?
Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends. He is incorrect
How to illustrate the information?From the information, Luciana claims that if you add numbers with the same sign, the sum is always greater than each of the addends.
Let's add (-3) + (-4)
It should be noted that the addition is equal to -7.
It should be noted that this doesn't corelate with what Luciana said.
Therefore, she is incorrect. It's only correct for positive numbers.
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help with 5,6,&7 please!! will mark as brailylist
mous this mobail phonffyuuyy
The number of cars a salesman sold each month for a two year period are represented by the box and whisker plot below. Which of the following statements is most likely to be true?
In approximately 50% of the months he sold less than 9 cars.
In approximately 25% of the months he sold less than 12 cars.
In approximately 75% of the months he sold more than 12 cars.
In approximately 25% of the months he sold less than 9 cars.
The true statement is that (a) in approximately 50% of the months he sold less than 9 cars.
How to determine which of the statements is most likely to be true?The given parameter is the box and whisker plot
As mentioned above, the box and whisker plot is a great tool to show the five-number summary.
The five-number summaries are:
MinimumLower quartileMedianUpper quartileMaximumOn the box and whisker plot, we have the following five-number summaries:
Minimum: 0Lower quartile: 4Median: 9Upper quartile: 12Maximum: 19The difference between the quartlles is
Difference = Upper quartile - Lower quartile
So, we have
Difference = 12 - 4
Evaluate
Difference = 8
This means that in approximately 50% of the months he sold 8 cars
8 is less than 9
This means that in approximately 50% of the months he sold less than 9 cars.
Hence, the true statement is that (a) in approximately 50% of the months he sold less than 9 cars.
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A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field?
A.150 feet
B.178 feet
C. 191 feet
D.212 feet
A square field has an area of 22,500 square feet, then the diagonal distance across the field in nearest foot is equal to 212 foot (approximately).
As given in the question,
Area of the square field = 22,500square feet
Let 'a' be the side and 'd' be the diagonal length of the square
a² =22,500
⇒a =150 foot
Using Pythagoras theorem
d² =a² +a²
⇒d² = 2(150)²
⇒d² =45000
⇒d =212.13
≈ 212 nearest foot (approximately)
Therefore, the diagonal distance across the field in nearest foot is 212 foot (approximately) with area of 22,500 square feet as given.
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Subtract. Write your answer as a decimal.
5.5−8.1=
The solution of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex] which is a negative integer in decimal form.
The numbers of the number line are called integers. They include positive numbers, zero, and negative numbers.
Zero is neither considered a negative nor a positive number.
[tex]5.5\\[/tex] is a positive number and a smaller number when compared from [tex]8.1[/tex].
When a smaller number is subtracted from a larger number it results in subtraction with a negative sign.
[tex]5.5 - 8.1 \\= -2.6[/tex]
The subtraction of the given expression [tex]5.5 - 8.1[/tex] in decimal form is [tex]-2.6[/tex].
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Simplify the expression −7+ −5−40 ×−8
The value of the given expression when simplified is equal to 318.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified using the PEMDAS as shown below.
-7 + 5 - 40 × -8
As per the PEMDAS multiplication should be solved first,
= -7 + 5 + 320
Further, solve addition,
= -7 + 5 + 320
= -7 +325
= 318
Hence, the value of the given expression when simplified is equal to 318.
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You are having a dinner catered. You pay a rental fee of $150 for the dining hall, and you pay the caterer $10 for each person who attends the dinner. How much should you charge per ticket if you expect 50 people to attend? (Round your answer to the nearest cent.)
Answer:
$13
Step-by-step explanation:
For 50 people it will cost you 150 + 50(10) or 500
150 +500 = 650 Divide that among 50 people and you get a cost of $13 a person.
5m + n = 10 Solve for m
Answer:
[tex]m = - \frac{1}{5} n + 2[/tex]
For what value of x does 3^2x = g^3x-4?
1
2
3
4
The value of x will be 2. So, Option B is correct for the equation [tex]3^{2x} = 9^{3x - 4}[/tex]
In the given question, the equation is [tex]3^{2x} = 9^{3x + 4}[/tex], we have to find out the value of x. First, we need to re-arrange the equation in order to apply the property of exponents. So,
=> [tex]3^{2x} = 9^{3x -4}[/tex] => [tex]3^{2x} = 3^{2(3x - 4)}[/tex]
We know according to the property of exponents if [tex]x^{m} = x^{n}[/tex], then m = n.
Similarly, in this equation the base of both RHS and LHS are the same, We get
=> 2x = 2(3x - 4)
=> 2x = 6x - 8 => 4x = 8
=> x = 2
We get value of x = 2.
Hence the value of x for this equation will be 2 and option B is correct.
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The weight of an organ, an adult males has a bell shaped distribution with a mean of 320 g and a standard deviation of 45 g use the empirical rule to determine the following
A. About 95% of organs will be between what weights?
B. What percentage of organs weighs between 185 grams in 455 grams?
C. What percentage of organs weighs less than 185 grams or more than 455 grams?
D. What percentage of organs weighs between 275 grams in 410 grams?
For what values of x is x^3+18x^2+92x+120=0 a true statement.
For x = -2,-6, and -10 the value of the polynomial will be satisfied.
What are the roots of an equation?Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.
Given the polynomial,
x³ + 18x² + 92x + 120 = 0
By hit trial method let's put x = -2
-8 + 72 - 184 + 120 = 0
-192 + 192 = 0
0 = 0
Now,divide x³ + 18x² + 92x + 120 = 0 by x + 2
(x + 2)(x²+ 16x + 60) = 0
(x + 2)(x + 6)(x + 10) = 0
x = -2,-6 and -10.
Hence "For x = -2,-6, and -10 the value of the polynomial will be satisfied".
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ole has $1,750 to invest. His bank offers two different types of accounts to choose from. Cole will not make any additional deposits or withdrawals. Which account will earn the most interest at the end of 3 years?
At the end of 3 years second account will earn the most interest, that is $148.38
Given,
The amount Cole has with him = $1750
Two types of account bank offered:
First account has simple interest rate = 2.75% annually
Second account has compound interest rate = 2.75% compounded annually.
Number of years = 3
We have to find the account which earn the most interest at the end of 3 years.
Simple interest = PRT/100
Compound interest = A - P
A is the amount
A [tex]=P(1+\frac{R}{N} )^{NT}[/tex]
Where,
P is the principal amount
R is the rate of interest
T is the time period
N is the number of times interest compounded yearly.
Here,
P = 1750
R = 2.75%
T = 3 years
N = 1
Now,
First account:
Simple interest = PRT/100
SI = (1750 × 2.75 × 3) / 100
SI = 14437.5/100
SI = 144.375
First account offers $144.375 as interest for 3 years.
Second account:
Compound interest = A - P
A [tex]=P(1+\frac{R}{N} )^{NT}[/tex]
A = 1750 [tex](1+\frac{0.0275}{1} )^{1(3)}[/tex]
A = 1750 (1 + 0.0275)³
A = 1750 × 1.0275³
A = 1750 × 1.084789547
A = 1898.381707
A ≈ 1898.38
Compound interest = A - P
CI = 1898.38 - 1750
CI = 148.38
Second account offers $148.38 as interest for 3 years.
So, we can conclude that second account will earn the most interest at the end of 3 years.
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ASAP pls help .....
11 Points
Answer:
0.008 3repeating
Step-by-step explanation:
For the given functions f and g, find the requested function.
Answer:
its 1
Step-by-step explanation:
i just know
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
A. Two
B. One
C. Zero
D. Infinitely many
The two lines have only one intersection
[tex]\therefore[/tex] There are only one solution to the system of equation.
Which could be a possible value of x for the expression below to be a rational number? √9x+4
X=4
X=13
X=14
X=16
18
You buy 8 gallons of gasoline and pay $23.20.
a.) Write an equation to represent this situation.
28
So
b.) Find the price of one gallon of gasoline.
514 gram in kg convert into
Answer:
514 grams is equal to 0.514 kilograms
Solve the equation P(x) = 8.
Answer:
Step-by-step explanation:
Line AL is a perpendicular bisector of segment CM. Which of the following are true
Triangle ABC is an isosceles right triangle.
Because of A(-8,7) B(-4,2) C(1,6)
So AB=√[-8-(-4)]²+(7-2)²
=√41
BC=√(-4-1)²+(2-6)²
=√42
AC=√(-8-1)²+(7-6)²
=√82
AB=BC
AB²+BC²=AC²
So triangle ABC is an isosceles right triangle.
What is isosceles right triangle?
An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.
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If one of the points that this relationship passes through is (,)=(300,10), find the
proportionality constant for this relationship. Round your answer to 3 decimal places.
Answer:
.033
Step-by-step explanation:
When there is a proportional relationship the constant of proportionality is y/x and in this case that would be 10/300 and that would be .033 rounded to three decimal places.
HELP PLEASE
Graph the point (-2,3) and 3 more points using a slope of -1/2
The linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2
How to graph the point (-2,3) and 3 more points using a slope of -1/2?The given parameters are
Slope, m = -1/2
Point, (x1, y1) = (-2, 3)
The linear equation is calculated as:
y = m(x - x1) + y1
Substitute the known values in the above equation
y = -1/2(x + 2) + 3
Expand
y = -1/2x - 1 + 3
Evaluate the sum
y = -1/2x + 2
This means that the linear equation that represents the point (-2,3) and 3 more points with a slope of -1/2 is y = -1/2x + 2
See attachment for the graph of the point and the three other points
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