The division of the given polynomial would be (x^4) + 81.
What is the synthetic division?
Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.
To divide the polynomials using polynomial division, we will use the following steps:
Write the polynomials in descending order of exponents.
(2x^3 + x^4 - 6x^2 + 11x - 10) (x^2 + 2 - x)
Create a grid with the dividend on the left and the divisor on the right.
2x^3 x^4 -6x^2 11x -10
x^2 2 -x
Bring down the leading coefficient of the dividend, which is 2x^3 in this case. Write it in the next row of the grid.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
Multiply the divisor (x^2 + 2 - x) by the leading coefficient (2x^3) and write the result in the next row.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
2x^5 2x^4 4x^3 -2x^4
Subtract the second row from the third row and write the result in the next row.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
2x^5 2x^4 4x^3 -2x^4
0 -x^4 -2x^2 11x -10
Divide the new leading term by the leading term of the divisor, which is x^2, and write the result in the next row.
2x^3 x^4 -6x^2 11x -10
2x^3 x^2 2 -x
2x^5 2x^4 4x^3 -2x^4
0 -x^4 -2x^2 11x -10
-x^2
So the final answer would be (-x^2) + (x^4 + 2x^2 - 11x + 10).
Hence, the division of the given polynomial would be (x^4) + 81.
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Direction Evaluate the Expression
N·58 + (4x12-40) to the power of 2
After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.
What is expression?An expression or mathematical expression is a finite combination of symbols that are well-formed in accordance with context-dependent rules. To help define the logical syntax and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.
Authors frequently distinguish between a formula and an expression, with the former referring to a mathematical object and the latter to a statement about such an object.
We have been asked to evaluate the Expression
58 + (4x12-40) to the power of 2
⇒ (58 + (4x12-40))²
Use (a + b)² = a² + b² + 2ab
= 58² + (4x12-40)² + 2(58)(4x12-40)
= 3364 + (4x12-40)² + 116(4x12-40)
= 3364 + (48-40)² + 116(48-40)
= 3364 + (8)² + 116(8)
= 3364 + 64 + 928
= 4356
= 4.356 ×10³
Thus, After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.
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Write the equation of the line that is parallel to the line 5x- 4y = 4 and passes through one point (-8, 2).
Answer:
y = 5/4x - 8
Step-by-step explanation:
first you convert the equation to y = mx + b
then you add the the -8 into the x and the 2 into the y and solve for b
b = -8 and since it is parallel same slope.
hope this helps :)
The expression 2x + 4x represents the cost of buying the same number of
cases of spring water, sold for $2 per case, and sparkling water, sold for $4
per case. What expression can be used to express the total cost?
Answer:
6x
Step-by-step explanation:
Combine like terms
A trader buys some oranges at #50 each. He finds that six of them are rotten. He sells the rest at #80 each and makes a profit of #450. How many oranges did he buy?
The total number of oranges that the trader bought is 31
How to calculate the total number of oranges that the trader bought?A trader bought some oranges at the price of #50 each
He finds that Six of these oranges are rotten
He sells the remaining at #80
He makes a profit of #450
Therefore the number of oranges that the trader bought is
Let y represent the number of oranges that the trader bought
At a price of #50= 50x
6 oranges were rotten= x-6
Profit = 450
450= 80(x-6)-50x
450= 80x-480-50x
450= 80x-50x-480
450= 30x-480
450+480= 30x
930= 30x
x= 930/30
x= 31
Hence the trader bought 31 oranges
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What can the Learning Center staff help you with?
Staff at the learning center can teach whole groups of students who need extra help or focus on working one-on-one with a specific child. They work on improving knowledge of academic subjects like biology as well as skills like reading comprehension.
What is a learning center instructor?Learning centre instructors work in programmes that assist at-risk students in strengthening their academic skills. Learning centre instructors can work for a private or public learning centre. Learning centre instructors work with students to teach them valuable skills and academic subjects no matter where they work.
Learning centre instructors can teach large groups of students who require extra assistance or work one-on-one with a specific child. They work on improving academic knowledge, such as biology, as well as skills, such as reading comprehension.
They are in charge of creating the overall curriculum and training programme. Learning centre instructors must also have excellent classroom management skills as well as patience in order to work with students who are experiencing difficulties.
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Consider the following triangle.
A
13
C
B
Based on the given information, what is the measure of the missing length, c?
Enter your answer as a number like this: 42.
12
Answer:
5
Step-by-step explanation:
We will use the Pythagorean theorem to solve this problem. We know [tex]a^{2} + b^{2} = c^{2}[/tex]. (a, in this case, will be c) Now, we can substitute in our numbers, giving us:
[tex]a^{2} + 12^{2} = 13^{2}[/tex]
Simplifying:
[tex]a^{2} + 144 = 169[/tex]
Subtract 144 from both sides gives us:
[tex]a^{2} = 25[/tex]
Square rooting both sides gives us:
[tex]a = 5[/tex]
So, the missing measurement (c) is 5.
Hope this helped!
In triangle ABC, ZA=25°, ZC=55° and AB-60. What are the approximate measures of the remaining side lengths of
the triangle?
BCN 31, AC 72
BC 72, AC 31
BC 23, AC 87
O BC 87, AC 23
The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = AC / sin B
In triangle ABC, ∠A = 25°, ∠C = 55° and AB = 60. Then the third angle is given as,
∠A + ∠B + ∠C = 180°
25° + ∠B + 55° = 180°
∠B = 100°
Then the length of BC is given as,
60 / sin 55° = BC / sin 25°
BC = 30.955
BC ≈ 31
Then the length of AC is given as,
60 / sin 55° = AC / sin 100°
AC = 72.134
AC ≈ 72
The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.
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Assume a total current of 2 amperes flows in a circuit with three resistorsR1 has a value of 1400 ohms, R2 has a value of 200 ohms and R3 has a value of 100 ohms , producing a total resistance of 80 ohms for the circuit. What is the amount of the current flow through resistor R3?
Answers:
(A)0.114
(B)0.800
(C)1.600
(D)0.228
1.600 amps of current flow through resistor r3 are measured.
Describe the resistor.A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.
Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.
The parameters are determined by the query:
total current = 2 amperes
Total resistance = 80 ohms
Total current = voltage * Resistance
Total current = 2* 80
= 160V.
Consequently, the current passing through resistor R3 will be
V= IR (Ohms law)
where I (current)= V/R
current = 160/ 100
Current flowing through R3 =1.600 amperes.
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Use the commutative and :or associative properties to simplify 2/5 + 5/12 + (-2/5)
Answer:
5/12
Step-by-step explanation:
Use associative property of addition:
2/5 + 5/12 + (-2/5) = (2/5 + (-2/5)) + 5/12 ==> switch 5/12 and -2/5
(2/5 + (-2/5)) + 5/12 = ==> simplify
(2/5 - 2/5) + 5/12 =
0 + 5/12 = 5/12
Kyle is curious on how long does it take for him to reach school from their house. With that he asked his parents what is their speed as they drive going to school. How long does it take for kyle to reach school if their speed is in constant 40 km/h as they travel 60 km going to school in the northern side of their city? Show your solution.
math/science..
Answer: To find how long it takes Kyle to reach school, we can use the formula:
Time = Distance / Speed
Given that Kyle's parents travel at a constant speed of 40 km/h and the distance from their house to school is 60 km, we can substitute these values into the formula:
Time = Distance / Speed = 60 km / 40 km/h
To convert the answer from hours to minutes we have to multiply the result by 60.
Time = (60 km / 40 km/h) * 60 = 1.5 * 60 = 90 minutes
So it takes Kyle 90 minutes to reach school from their house if their speed is constant at 40 km/h and the distance they are traveling is 60 km.
Step-by-step explanation:
The quadrilateral DEFG,show. On the coordinate plane below is dilated from the origin by a space factor r= 2/3. Identify the coordinates of the dilated figure D^1 E^1 F^1 G^1 and the draw and label on the coordinate plane
The required dilated coordinates of the quadrilateral is given as,
D' {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G' (-2, 2).
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
Initial corrdiantes
D = (-6, 3)
G = (-3, 3)
E = (-4, -3)
F = (5, -2)
Dilated coordinates of a quadrilateral with by scale factor of 2/3 is given as,
D' = (-6 × 2 / 3, 3 × 2 / 3)
D' = {-4, 2}
Similarly,
G = (-2, 2)
E = (-8/3, -2)
F = (10/3, -4/3)
Thus, the required dilated coordinates of the quadrilateral is given as,
D' {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G' (-2, 2).
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i need help
please someone help me
Answer: 1/2 PI actually ez not gonna lie
Step-by-step explanation: We know that pi times radius squared times 45/360 equals 1/2 pi. PI*radius^2*0.125 = 1/2PI. Solve algebra to get r^2 = 4 or radius = 2. We need the diameter to find circumference. D = 2*r or D = 4. D * PI * 45/360 = answer. We get 4 * PI * 0.125 = 1/2 PI
I will give brainliest, if you get this correct
1) What is the probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the I.D's of five students from among ten students of which four are not of legal age?
Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.
Step-by-step explanation:
he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.
The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where:
x = the number of successful outcomes (in this case, the number of minors refused service)
n = the total number of trials (in this case, the number of IDs checked)
p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)
In this case:
x = 3 (the number of minors refused service)
n = 5 (the number of IDs checked)
p = 4/10 (the probability that a randomly chosen student is a minor)
So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:
P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288
Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.
It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.
Based on the triangles shown, Which congruence Statement is correct?
CAB ≈ RWT
ABV ≠ RWT
BCA ≈ RWT
CBA ≈ TWR
statement CBA ≅ TWR is true.
what is congruence theorem?
The theorem that states that two triangle is congruent when there three corresponding sides are equal and all three corresponding angles are also equal.
Which statement is true for congruent triangle?
given, triangle ABC and Triangle RWT both are right-angled.
we examined that three corresponding sides of ABC is equal to the corresponding sides of RWT and same for the three corresponding angles.
we measured, right angle A = right angle R
base length AB = base length RW
hypotenuse BC = hypotenuse WT
Side length AC = side length RT
angle C = angle T
angle B = angle W
as per the properties of congruence theorem ABC and RWT are congruent.
hence the statement CBA ≅ TWR is true.
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A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale
The equation that represents the linear function is y =32x
What is a linear equation explain?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
A linear function is represented as
y = mx + c
The slope is calculated as
m = y₂ - y₁/x₂ - x₁
m = 576 - 64/18 - 2
m = 512/16
m = 32
The linear equation is then calculated as
y = 32( x - 2 ) + 64
y = 32x - 64 + 64
y = 32x
Hence, the equation that represents the linear function is y =32x
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The complete question is -
A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18
Number of Tickets Sold (y) 64 192 576
1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.
bathroom which is also a square and has an area of 900cm². What is the measurement down one side of the mirror? cm
Answer:
30cm
Step-by-step explanation:
it will be the root of 900cm²
=30cm
Set up the equation to solve for the missing side length.
A
5
B
12
с
Answer:
The answer is, 5² + 12² = AC²
This is the Pythagorean theorem which states that sum of the squares of the two sides of a right angled triangle is equal to the square of the hypotenuse.
base² + height² = hypotenuse² or in this case, 5² + 12² = AC²
Pls mark as brainliest. I really need for no apparent reason. Cheers
9. Brenna decided to purchase 4 points in order to lower the interest rate on her
$175,000 mortgage. How much additional money does she need to bring to closing for
the points she wishes to purchase?
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
The percentage of mass of Cs in the sample is 25%
What is percentage?
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage, indicates hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
To calculate the percentage of Cs in the sample
100/400 x 100
=25%
To calculate the percentage of cesium (Cs) in the sample
300/400 x 100
=75%
Hence, 25% is the percentage of Cs in the sample
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Hi can someone help me do this math problem? How would you do it in a ti-84 calculator or by hand?
The value of x, if x is a real number and the expression, [tex]\frac{x + 2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex] is a purely imaginary number is x = -2. The correct option is option b.
b. -2
What is an imaginary number?An imaginary number is a number which is obtained by finding the square root of a negative number.
The specified expression is; [tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex]
Multiplying the numerator and the denominator by the complex conjugate of the denominator, (1 - i), we get;
[tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}\times \frac{1 - \mathbf{i}}{1 - \mathbf{i}} =\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2}[/tex]
[tex]\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2} = \frac{x + (2 - x)\cdot \mathbf{i} + 2}{1 - (-1)} =\frac{x + (2 - x)\cdot \mathbf{i} + 2}{2}[/tex]
Where x is real, for the number to be purely an imaginary number, we get;
[tex]\dfrac{x + (2 - x)\cdot \mathbf{i} + 2}{2} = \dfrac{x +2+ (2 - x)\cdot \mathbf{i} }{2} = \dfrac{0+ (2 - x)\cdot \mathbf{i} }{2}[/tex]
[tex]\frac{0+ (2 - x)\cdot \mathbf{i} }{2} = \frac{(2 - x)\cdot \mathbf{i} }{2} = \frac{(2-x)}{2} \cdot \mathbf{i}[/tex]
Therefore, for the number to be a purely imaginary number, then; x + 2 in the numerator following the multiplication of the numerator and the denominator by the complex conjugate of 1 + i, which is 1 - i, should be 0, and we get;
x + 2 = 0
x = 0 - 2 = -2
x = -2
The value of x such that the expression (x + 2·i)/(1 + i) is a purely imaginary number is; x = -2
The correct option is; b. -2
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complex numbers. see picture for question!!!
Answer:
yes b is a right answer hope it will help you and please make me brainlist
What is the value of 5 to the 4th power
5 raised to the fourth power (written as 5^4) is equal to 5 multiplied by itself 4 times. Mathematically, it can be written as:
5^4 = 5 * 5 * 5 * 5 = 625
So, the value of 5 to the fourth power is 625.
I hope this helps :)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5^4}[/tex]
[tex]\mathsf{= 5 \times 5 \times 5 \times 5}[/tex]
[tex]\mathsf{= 25 \times 25}[/tex]
[tex]\mathsf{= 625}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{625}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Arianys invests money in an account paying a simple interest of 3% per year. If m
represents the amount of money she invests, which expression represents her balance
after a year, assuming she makes no additional withdrawals or deposits?
Adrian must multiply his money by 1.03 to find his total balance in a year in one step.
What is simple interest?Borrowers must pay simple interest to lenders as a fee for a loan. Compound interest is not taken into account while calculating it; just the principal is used. Simple interest is applicable to all loans. It is also the form of interest that banks give their customers on their savings accounts. There are two techniques to compute interest: simple interest and compound interest. The principal, or initial amount of a loan, is used to compute simple interest. Compound interest, sometimes known as "interest on interest," is calculated using both the original amount and the total accumulated interest from prior periods.The following calculation must be done in order to determine what Adrian should multiply his current balance by in order to find his total balance in a year in one step, assuming that no money will be added to or subtracted from the investment. Adrian invests money in an account that offers simple interest of 3% per year.
Current balance = X
Interest = 3% = 3/100 = 0.03
Interest + principal = 1.03
1.03X = Total balance in a year
Therefore, Adrian must multiply his money by 1.03 to find his total balance in a year in one step.
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Sandy's ice cream corner uses 9/10 of a bag of cups every day How many days would 10 bags of cups last?
Answer:
11 days
Step-by-step explanation:
It will last: 10/1 : 9/10 = 10/1 x 10/9 = 100/9 = 11,111... days
Answer: 11.1 days
Step-by-step explanation:
Everyday, Sandy uses 9/10 of a bag of cups.
Use unitary method.
9/10 bag - 1 day
10 bag - 10/(9/10) = 100/9 ≈ 11.1 days
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The triangles are similar.
What is the value of x?
Enter your answer in the box.
Answer:
x = 4
Step-by-step explanation:
We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)
Big triangle:little triangle
25:5
5:1
So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.
Solve for x:
3x+8 = 4(5) [ratio!!]
3x+8 = 20
(subtract 8 from both sides)
3x = 12
(divide both sides by 3)
x = 4
Thus, we have our answer!
A rectangle is [tex]\frac{1}{3}[/tex]yards long and [tex]\frac{2}{3}[/tex] yards wide. What is the area of the rectangle in yd2?.
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]A=lw=\frac{1}{3} \cdot \frac{2}{3}=\frac{2}{9}[/tex]
The cost of 3 dozen oranges is rupee 54 how many oranges can be purchased for rupee 24 ?
Can you explain the steps plsss it’s for my assignment
Answer:
You can buy 17 oranges for rupee 24.
Step-by-step explanation:
3 dozen = 3 x 12 = 39 oranges
54 ÷ 39 = 1.38461538462
1 orange = rupee 1.38
1.38461538462 x 17 = 23.5384615385
17 oranges = rupee 23.54
If you add the cost of 1 more orange it would cost more than rupee 24 so you can only buy 17 oranges for rupee 24.
Hope this helps :)
A survey was given to 280 people asking whether people like dogs and/or cats. 151 said they like dogs 138 said they like cats 47 said they don't like cats or dogs. How many said they liked cats but not dogs?
Answer: 80
Step-by-step explanation:
280-47=233 people who like cats or dogs
153+138=291 people who like cats, dogs, or both
291-233=58 people who like both
People who like cats = 138-58=80
398107.1706 to standard form
Answer:
3.981071706 × 105
Answer:
3.981071706 x 10^5
Step-by-step explanation:
In standard form, a number is written as a decimal multiplied by a power of 10. To convert 398107.1706 to standard form, we can move the decimal point until we have a number between 1 and 10 and a power of 10 that will make the original number.
398107.1706 = 3.981071706 x 10^5
A building has a number of floors of equal helght, as well as a thirty-foot spire above them all. If the
height of each floor In feet is h, and there are n floors in the building, which of the following represents
the building's total height In feet?
A.) n+h+30
B.)nh+30
C.)30n+h
D.)30h+n
The total height of the building would be nh + 30.
Option (B) is correct.
What is a simplification in mathematics?
In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.
The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.
So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:
= n * h + 30
=nh + 30
This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.
Hence, the total height of the building would be nh + 30.
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