how do i solve (4x^3 + 2x - 3) divided by (x - 3) with long division??
Answers
We want to divide 4x³ + 2x - 3 by x - 3 with the long division method
First, we rewrite the polynomial as:
4x³ + 0x² + 2x - 3
Them we divide the first term of the dividend by the highest term of the divisor:
4x²
x - 3 |4x³ + 0x² + 2x - 3
Then we multiply the divisor by this result:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
Now we subtract this result from the dividend:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
|12x² + 2x - 3
Now we can repeat all the previous steps using the last result as dividend:
| 4x² + 12x
x - 3 | 12x² + 2x - 3
12x² - 36x
|38x - 3
And we repeat these steps once more:
4x² + 12x + 38
x - 3 | 38x - 3
34x - 102
|99
The final term is the remainder
Then, we have:
4x³ + 2x - 3 = (x - 3)*(4x² + 12x + 34) + 99
Related Questions
Scott took out a 72 month
loan for $35,000 to purchase
a new boat. If Scott paid
$8,925 in simple interest,
what was the interest rate?
Answers
$8,925 / ($35,000 * 6 years) = 0.0429 or 4.29%
Therefore, the interest rate on Scott's loan was 4.29%.
The interest rate paid by Scott is 4.25% for the 72 months.
We can determine the simple interest of the given problem by the simple interest formula which is given as :
I=PRT
Where,
I=Interest
P=principal
R=rate in decimal
T=time in years
Converting the given 72 months into years we get time t :
1 year = 12months
72 months / 12months = 6 years
t=6
From the given data
I=8925
P=35000
R=r
T=6
Substituting the above values in the simple interest equation we get:
8925 = 35000*r*6
8925 = 210000*r
divide both sides by 210000
R = 0.0425
Therefore, the interest rate is 4.25%
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Parker needs to order some new supplies for the restaurant where he works. The restaurant needs at least 367 glasses. There are currently 151 glasses. If each set on sale contains 8 glasses, use the drop-down menu below to write an inequality representing ss, the number of sets of glasses Parker should buy.
Answers
Answer:
151+8x>_367
Step-by-step explanation:
x=sets of glasses.
151+8x>_367
^is greater than equal to i dont
have a sign for that.
2) You purchase a car using a $23,000 loan with a 4% simple interest rate. Suppose you pay the loan off after 5
years. How much interest do you pay on your loan? Please show your math work and don't forget the unit!
(Calculator is allowed but please write down the numbers that you enter into your calculator).
Answers
The graph below represents a recent 10 meter race between two remote control cars.
A graph titled Remote Control Car Race has seconds after race start on the x-axis and distance from start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).
Which statements about the race are true? Check all that apply.
The red car won the race because it started above the blue car.
The cars crashed at 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.
The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.
The blue car is faster because the slope of its line is steeper than the slope of the line representiong the red car.
The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.
Answers
Answer:
options c d e
Step-by-step explanation:
Answer:
C D E
Step-by-step explanation:
which is the pair of congruent right angles?
Answers
Answer:
CBA =~ DEA
Step-by-step explanation:
They are both right angles.
How do we know?
They both have the square.
Right angles can ONLY be 90 degrees.
Find g(f(−1)).
g(f(−1))
Answers
...........the answer is 64
2. Write a quadratic function given the roots (4,0) and (2, 0) and the point 2 points
(3, 4). (2 pts) *
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\(y = -4(x - 2)(x - 4) \)
\(y = -4 {x}^{2} + 24x - 32 \)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The expression for the quadratic function will be y = -4x² + 24x - 32.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that a quadratic function given the roots (4,0) and (2, 0). The quadratic equation will be formed as below:-
The two roots of the quadratic equation are 2 and 4 then the two factors will be ( x- 2 ) and ( x - 4).
y = -4(x-2)(x-4)
y = -4x² + 24x - 32.
Therefore, the expression for the quadratic function will be y = -4x² + 24x - 32.
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Can someone help me with this? I can't figure it out
Answers
In linear equation, 9 is the constant of variation k.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
given x varies inversely with y then
xy = k ← k is the constant of variation
to find k use the condition x = - 4 when y = - 9, hence
k = -4 × -9 = 36
x = 36/y
when x = 4 , then y = 36/4
x = 9
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what is the quotient of 1/6 and 2/9
Answers
Answer:
3/4
Step-by-step explanation:
Hurry!
The following is a function, true or false?
Answers
Answer:
Step-by-step explanation: true
What is the length of AC on a right triangle 84 156-x 7
Answers
Answer:
144
Step-by-step explanation:
i just took the test
A fair number cube is labeled with the numbers 1 – 6. After rolling the cube 100 times, which would be most likely to occur? Responses The number 6 would never be rolled. The number 6 would never be rolled. All the numbers rolled would be odd. All the numbers rolled would be odd. An even number would be rolled 50 times. An even number would be rolled 50 times. The number 7 would be rolled at least once. The number 7 would be rolled at least once.
Answers
The outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
A fair number cube labeled with the numbers 1 - 6 is equally likely to land on any of its faces when rolled.
Therefore, we can use probability to determine which outcome is most likely to occur after rolling the cube 100 times.
"The number 6 would never be rolled." This outcome is highly unlikely, but not impossible.
If the cube is fair, each number has an equal probability of being rolled, so the probability of rolling a 6 on any given roll is 1/6.
The probability of rolling a non-6 on any given roll is 5/6. The probability of not rolling a 6 in 100 rolls is (5/6)¹⁰⁰, which is approximately 0.0001. So, while it is very unlikely that the number 6 would never be rolled, it is not impossible.
"All the numbers rolled would be odd." This outcome is even less likely than the first one.
The odd numbers on the cube are 1, 3, and 5, each with a probability of 1/2.
The probability of rolling an odd number on any given roll is 1/2.
The probability of rolling an odd number on 100 rolls is (1/2)¹⁰⁰, which is an extremely small number, approaching zero.
"An even number would be rolled 50 times." This outcome is more likely than the first two.
The even numbers on the cube are 2, 4, and 6, each with a probability of 1/2.
The probability of rolling an even number on any given roll is 1/2.
If we assume that each roll is independent of the others, the probability of rolling an even number exactly 50 times in 100 rolls can be calculated using the binomial distribution and is approximately 0.0796.
This means that this outcome is not very likely, but still possible.
"The number 7 would be rolled at least once."
This outcome is impossible since the cube is only labeled with the numbers 1 through 6.
Therefore, the number 7 cannot be rolled.
Hence, Based on the above analysis, the outcome that is most likely to occur after rolling the cube 100 times is that an even number would be rolled around 50 times.
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help pls i'm not good at math
Answers
Answer: x = 56
Step-by-step explanation:
The two angles 'z' and 124 add up to form a straight line. The angle of a straight line is 180 degrees. Therefore, we can say that:
\(z+124=180\)
Subtract 124 on both sides to isolate the angle 'z' to get:
\(z=56\)
Answer:
z=56 degrees
Step-by-step explanation:
in total the line will equal 180 so just do 180-124 and you get 56.
Write these numbers as a product of prime factors, giving your answer in index form: a. 21 b. 128
Answers
Answer:
128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
Step-by-step explanation:
128 = 2 x 64
= 2 x (8 x 8)
= 2 x (2 x 2 x 2) x (2 x 2 x 2)
Write the equation below in standard form and then answer the following questions. If a value is a non-integer type your answer as a decimal rounded to the hundredths place. 16x^2+64x+4y^2-8y+4=0The center is (h,k). h= Answer and k= AnswerThe value for a is Answer . The value for b is Answer .The foci with the positive y value is the point ( Answer, Answer)The foci with the negative y value is the point ( Answer, Answer)
Answers
Answer:
Explanation:
Given the function:
\(16x^2+64x+4y^2-8y+4=0\)This can be written as:
\(16(x+2)^2+4(y-1)^2=8^2\)The center here is:
(h, k) = (-2, 1)
The radius is
Help ASAP please!
The question is attached
Answers
Answer:Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?Nora is going to invest $9,600 and leave it in an account for 8 years.Assuming the interest is compounded continuously, what interest rate,to the nearest hundredth of a percent, would be required in order forNora to end up with $14,400?
help me pls :( I don't understand it!!
Answers
Watch mr morgan math I do the same math book as u. Search the grade and unit. He really good at explaining. I hope this helps.
Find an equation of a line of best fit shown in the figure given below.
Answers
Answer:
C
Step-by-step explanation:
So you can use two points on the line to find the gradient. I used K and G. B and D could've been easily eliminated since the line goes through the origin (0,0) so there's no y - intercept or b value.
M = (Y-y)/(X-x)
M = (8-4)/(14-7)
M = 4/7
And the equation of a line is y = mx + b. There's no b so it's just y = (4/7)x
A square poster has an area measure of 324x^2 + 540x + 225 square units. Determine the side length of the poster.
Answers
\(\huge\text{$(18x+15)$ units}\)
Given the area, we need to find the side length. Let's start with the area equation for a square, where \(s\) is the side length and \(A\) is the area.
\(s^2=A\)
Substitute in the known value.
\(s^2=324x^2+540x+225\)
Now we need to factor the trinomial. The trinomial given for the area is a perfect square trinomial since \(324\) (\(18^2\)) and \(225\) (\(15^2\)) are both perfect squares.
We also know that \(a^2+2ab+b^2=(a+b)^2\), which we can use to factor.
\(s^2=324x^2+540x+225\\s^2=(18x)^2+2(18x)(15)+15^2\\s^2=(18x+15)^2\)
Now, take the square root of both sides to fully isolate \(s\).
\(\sqrt{s^2}=\sqrt{(18x+15)^2}\)
Keep in mind that the square root of any value squared is the original value.
\(s=\boxed{18x+15}\)
let C be the curve y=5sqrtx for 1.1
Answers
We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
We have,
To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:
S = ∫(a to b) 2πy√(1 + (f'(x))²) dx
In this case,
f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).
Let's calculate the surface area:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx
Simplifying the expression inside the integral:
S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx
Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
To find the surface area of revolution about the x-axis of the function
f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:
S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx
Let's calculate the integral:
S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx
To simplify the calculation, let's simplify the expression inside the integral first:
S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx
Next, we can distribute the square root and simplify further:
S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx
Thus,
We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.
We can evaluate the integral using numerical methods or a calculator to find the final answer.
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5 + 2a = a - 9 what does a equal
Answers
Add the negative nine to the five and subtract the 2a from a. Should leave you with 14=-a. Multiply both sides by -1. -14=a
a= -14.
Step-by-step explanation:1. Write the expression.\(5 + 2a = a - 9\)
2. Subtract 5 from both sides of the equation.\(5 + 2a -5= a - 9-5\\ \\2a=a-14\)
3. Subtract "a" from both sides of the equation.\(2a-a=a-14-a\\\\a=-14\)
4. Verify.\(5 + 2(-14) = (-14) - 9\\ \\5-28=-23\\ \\-23=-23\)
Both sides are equal to each other, hence a= -14 is the correct solution.
5. Conclude.a= -14.
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Please help will mark Brainly
Answers
The ordered pair that are solution of the equation 3x-y= 1 is (−2, −7) , (−1, −4)
and (3, 8)
What is ordered pair ?
An ordered pair is a set of two things in mathematics. The pair's objects must appear in a specific order for them to be considered distinct from one another, unless a = b. Ordered pairs are also referred to as 2-tuples, or sequences with a length of 2.
Checking the equation by putting the values of x and y in the given options
1. (-2,-7)
LHS
=3*(-2) - (-7)
= -6+7
=1
LHS = RHS
2. (-1,-4)
LHS
=3*(-1) - (-4)
= -3+4
=1
LHS = RHS
3. (0,1)
LHS
=3*(0) - (1)
= -1
=-1
LHS \(\neq\) RHS
4. (3,8)
LHS
=3*(3) - (8)
= 9-8
=1
LHS = RHS
5. (4,2)
LHS
=3*(4) - (2)
= 12-2
=10
LHS \(\neq\) RHS
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Un bloque de vidrio flint tiene un espesor de 4 cm, ¿qué espesor aparenta tener cuando se le ve desde arriba?
Answers
Answer: El índice de refracción del vidrio flint es mayor que el del aire. Cuando la luz pasa de un medio con un índice de refracción menor (como el aire) a un medio con un índice de refracción mayor (como el vidrio), experimenta un cambio de dirección. Este fenómeno se conoce como refracción.
Cuando observamos el bloque de vidrio flint desde arriba, la luz que proviene del bloque sufre refracción al pasar del vidrio al aire. Debido a la refracción, los rayos de luz se desvían y parecen venir de una posición más alta dentro del vidrio de lo que realmente están. Esto crea una ilusión óptica que hace que el espesor aparente del bloque de vidrio se vea más delgado de lo que realmente es.
La cantidad exacta de adelgazamiento aparente depende del ángulo de incidencia de la luz y de los índices de refracción del vidrio y el aire. Sin más información, no es posible determinar el espesor aparente específico del bloque de vidrio flint cuando se ve desde arriba.
Step-by-step explanation:
A hiker climbs down a mountain that is
84 ft above sea level. It took him 6
hours to make it back to sea level.
What was the average number of
feet that he descended each hour?
A. -78 ft
B. 90 ft
C.-504 ft
D. -14 ft
Answers
Answer:
D.
Step-by-step explanation:
0 - 84 / 6
= -14 ft / hour.
Answer: 84 divided by 6= 14ft
Step-by-step explanation:
4. Gilbert works picking strawberries. He
earns $2.50 for each large basket he fills.
a) Draw a scatter plot to represent the
relationship between the number of
baskets Gilbert fills and the money
he earns.
b) If Gilbert's goal is to earn $360.
how many baskets must he fill?
c) Write an algebraic expression to
describe the relationship.
Answers
Answer:
Graph is attached
144 baskets
\(y=2.5x\)
Step-by-step explanation:
Let y be the total amount of money Gilbert earns and x be the number of baskets filled. So, we get the relation
\(y=2.5x\)
Some points which satisfy the equation is
\(y=2.5\times 1\\\Rightarrow y=2.5\)
\((1,2.5)\)
\(y=2.5\times 3\\\Rightarrow y=7.5\)
\((3,7.5)\)
\(y=2.5\times 5\\\Rightarrow y=12.5\)
\((5,12.5)\)
His goal is to earn $360 so \(y=360\)
\(360=2.5x\\\Rightarrow x=\dfrac{360}{2.5}\\\Rightarrow x=144\)
Hence, to earn $360 he must fill 144 baskets.
The algebraic relation is \(y=2.5x\).
In the following diagram,
What is the measure of
∠x
Answers
Answer:
Step-by-step explanation:
BAD = 42
x + 103 + 42 = 180
x = 180 - 145
x = 35
Can someone please provide a step-by-step explanation for the answer?
If the universe of discourse is the real numbers, give the truth value of each of the
following propositions:
(a) ∀x∃y(x = y²)
(b) ∀x∃y(x² = y)
(c) ∃x∀y(xy = 0)
(d) ∀x∃y(x + y = 1)
Answers
The Propositions are resulting
(a) ∀x∃y(x = y²) is False
(b) ∀x∃y(x² = y) is True.
(c) ∃x∀y(xy = 0) is True.
(d) ∀x∃y(x + y = 1) is True.
(a) ∀x∃y(x = y²)
This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².
Therefore, the proposition (a) is false.
(b) ∀x∃y(x² = y)
For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.
Therefore, the proposition (b) is true.
(c) ∃x∀y(xy = 0)
The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.
Therefore, the proposition (c) is true.
(d) ∀x∃y(x + y = 1)
To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.
Therefore, the proposition (d) is true.
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Challenge A large university accepts 60% of the students who apply. Of the students the university
accepts, 35% actually enroll. If 10,000 students apply, how many actually enroll?
students would actually enroll. (Type a whole number.)
Answers
Answer:
man i cant really say
Step-by-step explanation:
What is the value of cos theta given that (- 5, - 4) is a point on the terminal side of theta ?
Answers
Answer:I believe it's -5√41/41
Step-by-step explanation:
The value of \(cos\theta\) will be \(-0.7813\).
If the point \((-5.-4)\) were rotated around the origin, it would form a circle of radius \(r\). Also, if the point were projected to the x-axis, a right-angled triangle would be formed. Then, the value of \(cos\theta\), could be obtained by the formula
\(cos\theta=\dfrac{x}{r}\)
where
\(x=\text{the side of the triangle opposite the reference angle of }\theta\\r=\text{the radius of the circle}\)
From the point on the terminal side
\((x,y)=(-5,-4)\)
we can directly get the value of \(x\). But we need to calculate the value of \(r\).
To calculate the value of \(r\), make use of Pythagoras theorem
\(r=\sqrt{x^2+y^2}\\=\sqrt{(-5)^2+(-4)^2}\\=\sqrt{25+16}\\\approx6.4\)
We can now proceed to find the value of \(cos\theta\), since we have the values of \(x\), and \(r\). Therefore,
\(cos\theta=\dfrac{x}{r}\\\\=\dfrac{-5}{6.4}\approx-0.7813\)
Learn more about trigonometry here: https://brainly.com/question/23686339
If f ( x ) is a linear function, f ( − 4 ) = − 4 , and f ( 4 ) = − 1 , find an equation for f ( x ) .
Answers
Step-by-step explanation:
linear function
y = ax + b
f(-4) = -4
x = -4
y = -4
-4 = a×-4 + b
f(4) = -1
x = 4
y = -1
-1 = 4a + b
sum both equations
-5 = 0 + 2b
b = -5/2
-1 = 4a - 5/2
3/2 = 4a
a = 3/2 / 4 = 3/8
the function would be
y = 3/8 x - 5/2