Answers
According to the given synthetic table, the quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.
Synthetic table:
Basically, the shortcut for polynomial division when the divisor is of the form x – a. And only numeric coefficients of the dividend are used when dividing with synthetic division.
Given,
Here we have the synthetic table.
Now, we have to solve this one.
In order to find the quotient and remainder, we have to do the following steps:
Step-1 : Write down the first coefficient 5
Step-2 : Multiply our root -3 by our last result 5 to get -15 [ (-3) × 5=-15 ]
Step-3 : Add new result -15 to the next coefficient of the dividend 10, and write down the sum -5, [ 10 + (-15)=-5 ]
Step-4 : Multiply our root -3 by our last result -5 to get 15 [ (-3) × (-5)=15 ]
Step-5 : Add new result 15 to the next coefficient of the dividend -12, and write down the sum 3, [ (-12) + 15=3 ]
Step-6 : Multiply our root -3 by our last result 3 to get -9 [ (-3) × 3=-9 ]
Step-7 : Add new result -9 to the next coefficient of the dividend 11, and write down the sum 2, [ 11 + (-9)=2 ]
Step-8 : Multiply our root -3 by our last result 2 to get -6 [ (-3) × 2=-6 ]
Step-9 : Add new result -6 to the next coefficient of the dividend 7, and write down the sum 1, [ 7 + (-6)=1 ]
We have completed the table and have obtained the following coefficients 5,-5,3,2,1
Thus quotient is 5x³ - 5x² + 3x + 2 and remainder is 1.
And all these process are illustrated below.
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Related Questions
suppose the family wise error rate is 0.05, if there are ten levels of one factor but only 5 comparisons are of importance, what would the individual error rate need to be for each of those 5 comparisons?
Answers
The individual error rate needs to be for each of those 5 comparisons is Option B which is 0.01.
Individual error rate = α/m = 0.05/5 = 0.01
The individual error rate is the most extreme likelihood that at least one correlation will inaccurately infer that the noticed contrast is essentially unique in relation to the invalid speculation.
Individual error rates are careful in all cases. Family error rates are careful with equivalent gathering sizes. Assuming that gathering sizes are inconsistent, the true family error rate for Tukey, Fisher, and MCB will be somewhat more modest than expressed, bringing about moderate certainty spans. The Dunnett family error rates are careful with inconsistent example sizes.
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0.875 in 2 decimal places
Answers
Dave i packing 23 weater into boxe. Each box will hold 3 weater. How
many boxe will he need? Explain how
the remainder affect your anwer
Answers
Dave will need 8 boxes, out of which 7 will be completely full and 2 sweaters will be kept in eighth box.
Number of boxes required for 23 sweaters = total number of sweaters ÷ number of sweaters in each box
Keep the values in above mentioned formula to find the number of boxes required for 23 sweaters.
Number of boxes required for 23 sweaters = 23 ÷ 3
On performing division, we get 7 as quotient and 2 as remainder. This indicates that 7 boxes will be accomodate the sweaters and 2 indicates the remaining sweaters.
Thus, there will be need of 8 boxes in total.
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A 13 km stretch of road needs repairs. Workers can repair 3 1/2km of road per week.
How many weeks will it take to repair this stretch of road?
Answers
The workers would need 3.71 weeks to repair the road.
A generalization of arithmetic in which letters representing numbers are combined using arithmetic rules
Given that the total length of the road is 13km. Workers can repair 3.50 roads per week.
To determine the number of weeks required to repair the road, divide the total by per week. The equation would be:
13 ÷ 3.5
= (13 x 10)/35
= 130/ 35
= 3.71
Therefore the workers would need 3.71 weeks to repair the road.
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Consider the diagram shown. what is the angle of x
Answers
By using angles properties (sum of interior angles of a triangle and so) we will see that the measure of angle x is 120°.
How to get the value of angle x?Let's define C as the angle inside the triangle that is adjacent to angle x.
We can see that these two are supplementary angles, then we know that:
C + x = 180°.
We also can see that C is an interior angle of a triangle, and remember that the sum of all interior angles of a triangle is equal to 180°, then we can write
68° + 52° + C = 180°
With that equation, we can find the value of C.
C = 180° - 52° - 68° = 60°
Then.
x + C = 180°
x + 60° = 180°
x = 180° - 60° = 120°
That is the measure of angle x.
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Distance (km) 10 9 8 3 2 1 0 20 40 60 Time (min) 80 100 120 Sara and Sam went for a two-hour drive. According to the graph, between 40 minutes and 80 minutes into their trip, they-- M KO a €
Answers
The correct option regarding Sara's and Sam's position between 40 minutes and 80 minutes is given as follows:
C. Were not moving since there was not a change in position.
What is stated by the graph?The graph is given by the image shown at the end of the answer, and the relation graphed is defined as follows:
Distance x Time.
Hence the input and the output variables are given as follows:
Input variable: Time.Output variable: Distance.Between 40 minutes and 80 minutes, which is a symmetric period around the time of one hour, the graph is constant.
The constant graph means that the position was not changed, that is, they were not moving, hence the correct statement is given by option C.
Missing InformationThe problem is given by the image shown at the end of the answer.
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15.99-15% discount +20%tip =
Answers
Answer:
$16.30
Step-by-step explanation:
15.99-15%=$13.59
13.59x1.20=$16.30
what is the smallest number 4.36,4.3,4.06,4.306
Answers
Answer: its 4.06
Step-by-step explanation:
Name three fractions between 4/5 and 4/6
Answers
The three fractions between 4/5 and 4/6 are 49/30, 73/30 and 69/30
What is Fraction?A fraction represents a part of a whole.
We need to find fractions between 4/5 and 4/6
LCD is 30
4×6/30 + 5×5/30
24/30 + 25/30 = 49/30
The fraction between 4/5 and 49/30
4/5+49/30
LCD of 5 and 30
24+49/30
73/30
The fraction between 49/30 and 4/6
49/30+4/6
49+20/30
69/30
Hence the three fractions between 4/5 and 4/6 are 49/30, 73/30 and 69/30
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Ana is bowling. She pays $4 per game and $7 to rent shoes. After three games, each additional game is free. Is the total cost to bowl a function of the number of games played? Use a table or graph to help explain your answer.
Answers
Answer:
$19.00
Step-by-step explanation:
Between which two consecutive whole numbers does the length of the diagonal fall?
Which whole number is it closer to? Use the drop-down menus to show your answer.
Answers
The length of the diagonal is between 4 and 5.
What is square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The length of the diagonal = √18
Now,
Since, The length of the diagonal = √18
And, √18 = 4.24
Thus, The number 4.24 is lies between two whole numbers 4 and 5 as;
⇒ 4 < 4.24 < 5
⇒ 4 < √18 < 5
⇒ √16 < √18 < √25
Thus, The length of the diagonal is between 4 and 5.
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Find the number that makes the ratio equivalent to 2:3. 8:
Answers
Answer:
12
Step-by-step explanation:
You could think of ratios as fractions :
Whatever we do to the top we must do to the bottom to keep it equivalent .
If we multiply the first thing by something we must do the multiply by the same number to the second.
2 × m = 8
m = 4
3 × m = ?
m = 4
3 × 4 = 12
? = 12
So the number that makes the ratio equivalent is 12
2:3 = 8:12
Hope this helped and have a good day
in the class of 25 students, 15 are girls. express the ratio of boys to girls in this class as a fraction. of two more boys join this class, what will be the new ratio of boys to girls? express the new ratio as a fraction
Answers
Answer:
Girls
Step-by-step explanation:
out of children there are 15 girl therefore percentage of girl = 15 x 100 =60
25
there are 60% girls in class
-69/-11 as a quotient
Answers
Answer: 69/11
Step-by-step explanation:
-69/-11=
-69*(-1)/(-11*(-1))=
69/11
help me quick pls/....................
Answers
Answer:
A
Step-by-step explanation:
First off, "A" is the only one that even has "x cubed minus one" in it. The y squared divided by twenty-four is also present.
write the standard equation for the circle with center (14,-48) and radius of 50
Answers
The standard equation for the circle with center (14,-48) and radius of 50
is [tex](x-14)^{2} +(y+48)^{2} =2500[/tex]
What is the equation of circle?Given the circle's center and radius, the equation of a circle offers an algebraic approach to describe a circle. The formulas used to determine a circle's area or circumference are different from the equation for a circle. Numerous coordinate geometry problems involving circles employ this equation.We need the equation of the circle in order to represent a circle on the Cartesian plane. If we are aware of a circle's center and radius, we can draw it on a piece of paper. Similar to this, if we know the coordinates of the Center and radius of a circle on a Cartesian plane, we can draw it. There are numerous ways to symbolize a circle:General formStandard formParametric formPolar formStandard form: [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
Given, h =14, k = -48 and r = 50
therefore, The standard equation for the circle with center (14,-48) and radius of 50
is [tex](x-14)^{2} +(y+48)^{2} =2500[/tex]
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30.08 rounded nearest 10
Answers
The tenth is the first number after the decimal. When you round 5 and above push the number in front up but 4 and below do nothing
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x)=−x2+10x+9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.
Answers
The irrigation system is positioned 9.5 feet
The spray reaches a maximum height of 34.5 feet
The spray reaches all the way to the ground at about 10.87 feet
How to find the maximum height of the spray
The standard form of a quadratic equation is given by the formula
y = ax^2 + bx + c
compared with the given equation h(x) = −x^2 + 10x + 9.5 the solutions are calculated as follows
The irrigation position refers to the value of h(x) at x = 0
h(x) = −x^2 + 10x + 9.5
h(0) = 0^2 + 10*0 + 9.5
= 9.5
The maximum height is at the symmetry of the parabolic curve, for a curve opening downward.
At the symmetry x = -b/2a
x = -b/2a = -10/(2 * -1) = 5, At x = 5, then y is
h(5) = −(5)^2 + 10 * 5 + 9.5 = 34.5
The maximum horizontal distance is at one of the roots solved as
h(x) = −x^2 + 10x + 9.5
x = 10.87 OR -0.87
The maximum distance is the greatest distance form the origin (0, 0). Therefore maximum distance is at x = 10.87 feet
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complete question
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x^2+10x+7.5 where x is the number of feet away from the sprinkler head (along the ground) the spray is.
The irrigation system is positioned____ feet above the ground to start.
The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
The spray reaches all the way to the ground at about_____ feet away
Given the shape, find the length AD (x)
Answers
The length of AD is 8.58 units
Here triangle CDE and triangle CAB are similar triangles.
We know that the corresponding sides of similar triangles are in proportion.
CD/CA = CE / CB = DE/AB
Consider, CD/CA = DE/AB
15/(15 + x) = 7/11
15 * 11 = 7 * (15 + x)
165 = 105 + 7x
7x = 165 - 105
7x = 60
x = 8.58 units
Therefore, the length of AD is 8.58 units
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Subtract -9x² - x + 9 from 8x² - 6x - 8.
Answers
Answer:
17x^2-5x-17
Step-by-step explanation:
(8x^2-6x-8)-(-9x^2-x+9)
8x^2-6x-8+9x^2+x-9
17x^2-5x-17
A ubmarine tart at 0 unit and ha group of 3 float and group of 4 anchor attached. Which expreion would make the ubmarine float the highet? −532−4 53−2−4 −53−2−4 235−4 −23−5−4 23−5−4 What will it final poition be? 34 unit
Answers
The following are three equivalent expressions for the submarine's final position -(5)(3) - (2)(4), -(5)(3) + (-2)(4) and -(5)(3) + (2)(-4)
What is defined as the equivalent expressions?
Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value.Each float advances by 5 units.
Each group takes a two-unit step.
As a result, the submarine's final position is:
Final = -(5)(3) - (2)(4)
The minus "-" symbol indicates that the submarine is sinking.
Thus, the following are equivalent expressions for the submarine's final position:
-(5)(3) - (2)(4), -(5)(3) + (-2)(4) and -(5)(3) + (2)(-4)
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Write the equation of the line in fully simplified slope-intercept form.
Answers
The equation of the straight line in slope-intercept form is given by
y = -x +6 .
The line of the graph is clearly passing through the points (5,1) and (3,3) .
Hence the slope of the line = (3 - 1) / (3 - 5) = 2 / (-2) = -1
The equation of the straight line will be given by the formula:
y-3 = -1 (x-3)
or, y - 3 = -x +3
or, y + x = 6
One of the most popular ways to display a line's equation is in the slope intercept form, which looks like a straight line.
When the slope of anything like the straight line and in fact the y-intercept are known, the slope intercept formula can be used to determine the equation of a line the y-coordinate of the point where the line crosses the y-axis. A line cannot exist unless every point on the line fulfils an equation.
Hence the equation of the line in slope intercept form is y = -x +6
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I don't know whether this line is a negative or positive. The line is crossing the origin and is in the 1 quadrant and 3 quadrant. Please help!!
Answers
The given line is positive.
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Given that,
The line is crossing the origin and is in the 1 quadrant and 3 quadrant.
This means, the graph of the line starts at the bottom left and goes towards the top right.
If a line has a positive slope, then y always rises when x rises and always falls when x falls (i.e., m > 0). The line's graph thus begins at the bottom left and moves up to the top right.
So, the given line is positive.
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find the mean of the following group of numbers: 6.1, 5.9, 4.2, 5.9, and 10.7. round your answer to the nearest tenth. responses 4.2 4.2 10.7 10.7 6.6 6.6 6.5
Answers
The mean of the given set of group numbers is 6.6
Given,
In the question:
The Group of numbers are as follows:
6.1, 5.9, 4.2, 5.9 and 10.7
To find the mean of the given set of group of numbers.
Now, According to the question:
Given is the following data:
6.1, 5.9, 4.2, 5.9 and 10.7
We can find the mean of the given set of data using the formula-
Mean (M) = Σ a[i]/n = (Sum of all the elements)/(total number of elements)
Now, n = 5
and Σ a[i] = 6.1 + 5.9 + 4.2+ 5.9 + 10.7 = 32.8
Putting the values in the formula, we get:
M = 32.8/5 = 6.56 = 6.6
Hence, The mean of the given set of group numbers is 6.6
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A new bank customer with 5000$ wants to open a money market account. The bank is offering a simple interest rate of 1.2%.
a. How much interest will the customer earn in years?
b. What will the account balance be after years?
i will tap brainliest answer for whoever answers first
Answers
Answer:
A new bank customer with
P = $ 5000
The bank is offering a simple interes rate
r = 1.9%
a) how much interes will the customer earn in 10 years
A = P(1 + rt)
t = 10 years
Calculation:
First, converting R percent to r a decimal
r = R/100 = 1.9%/100 = 0.019 per year.
Solving our equation:
A = 5000(1 + (0.019 × 10)) = 5950
A = $5,950.00
I = A - P = $950.00
b) After 10 years the account balance will be
The total amount accrued, principal plus interest, from simple interest on a principal of $5,000.00 at a rate of 1.9% per year for 10 years is $5,950.00.
Step-by-step explanation:
two numbers that multiply to -34 and add to -4
Answers
Answer: 4 an 34
Step-by-step explanation:
A group of friends were working on a student film that had a budget of $1100. They used 45% of their budget on props. How much money did they spend on props?
Answers
A group of friends were working on a student film. The money did they spend on props is $495.
percentage :
a percentage is a number or ratio expressed as a fraction of 100or A percent is one one-hundredth (1/100) of something.It is denoted by % symbol.budget of group working on a student film = $1100
They used percentage of their budget on props. = 45%
then money spend on props is calculated as :
= 45% of 1100
= (45/100) x 1100
= 45 x 11
= $495
A group of friends were working on a student film. The money did they spend on props is $495.
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Round 57.183 to the nearest whole number tenth and hundredth
Answers
Answer:
Step-by-step explanation: 57.183= to the whole number= 58.183
Tenth= 57.180
Hundredth= 57.200
Answer:
Nearest Whole Number: 57
Nearest Tenth: 57.2
Nearest Hundredth: 57.18
*Note: When rounding to a place value the number after the place value you want determines whether the place value number says the same or goes up by 1. In order for the place value number to stay the same the number after has to be less than 5 and in order for the place value number to go up by 1 the number after has to be greater than or equal to 5.
28 divided by x + 4 = 11
Answers
Answer:
x= -16/11
Step-by-step explanation:
hope this helps
Answer: x=4
Step-by-step explanation:
28 divided by x+4=11
28 divided by x=7
28/7=4
After a shopping trip, the amount of money
Katrina has left can be modeled by the expression
75-9. 5t-11. 75s, where t is the number of t-shirts
and s is the number of pairs of shorts Katrina bought.
a. Describe what each term of the expression
represents in this situation.
b. How many t-shirts and shorts might Katrina have
bought?
Answers
Answer:
66
Step-by-step explanation:
