what is the quotient of {24a^4 b^2 + 36a^2 b-36ab^2 +48 ab}÷(12ab)?
Answers
To divide this polynomial, we will follow steps below:
Step 1
Arrange
step 2
Divide 24a⁴b² by by 12ab
The result will be 2a³b
Write the result at the top of the root sign
Step 3
Mutiply 12ab by 2a³b, the result will be 24a⁴b²
Write the result in the root sign under 24a⁴b²
step 4
subtract, the result is zero
step 5
Take down 36a²b
Step 6
divide 36a²b by 12ab
The result is 3a
write the result at the top of the root sign
step 7
Multiply 12ab by 3a
The result is 36a²b
Write the result in the root sign under 36a²b
Step8
subtract, the result is 0
step 9
Take down -36ab²
step10
Divide -36ab² by 12ab
The result is -3b
Write the result at the top of the root sign
step11
Multiply 12ab by -3b
The result is -36ab²
Write the result in the root sign under -36ab²
step12
subtract, the result is zero
step 13
Take down 48ab
step 14
divide 48ab by 12 ab
The result is 4
write the result at the top root sign
step 15
Mulltiply 12ab by 4
The result is 48ab
Write the result in the root sign under 48 ab and then subtract
The result is zero
Hence the quotient is : 2a³b + 3a -3b + 4
Related Questions
8 and 7 are like terms true or false
Answers
8 and 7 are like terms, because they share the same power of x:
[tex]\begin{gathered} 8x^0\rightarrow8 \\ 7x^0\rightarrow7 \end{gathered}[/tex]which of the following equations has only one solution? x^2 - 8x + 16 = 0x ( x - 1 ) = 8 x^2 = 16
Answers
Simplify the equation x^2 - 8x + 16 = 0 to obtain the value of x.
[tex]\begin{gathered} x^2-8x+16=0 \\ x^2-2\cdot4\cdot x+(4)^2=0 \\ (x-4)^2=0 \\ (x-4)(x-4)=0 \\ x=4 \end{gathered}[/tex]Equation has one solution, x = 4.
Simplify the equation x ( x - 1 ) = 8 to obtain the value of x.
[tex]\begin{gathered} x(x-1)=8 \\ x^2-x-8=0 \end{gathered}[/tex]This is a quadratic equation which is not a perfect square so it has two solutions.
Simplify the equation x^2 = 16 to obtain the value of x.
[tex]\begin{gathered} x^2=16 \\ x=\sqrt[]{16} \\ =\pm4 \end{gathered}[/tex]Thes equation has two solution x = 4 and x = -4.
So equation x^2 - 8x + 16 = 0 has only one solution and remaining equation has two solutions.
11 Jamal has a sudden medical emergency, and although his doctors do not agree, he is sure that it was caused by an antibiotic he took to prepare for a tooth extraction. Jamal posts a picture of himself in the hospital on his social media with the hashtag #antibioticskill. Although hashtags can raise awareness of important issues, what might happen if Jamal’s post were to go viral? A. People could be influenced into groupthink and reject antibiotics without knowing the facts. B. People would be encouraged to research the side effects that antibiotics cause before accepting them. C. Jamal would be investigated for making unfounded claims about a product online. D. Jamal could cause people to be more willing to listen to their doctor’s advice.
Answers
Answer:
A.
Step-by-step explanation:
A. People could be influenced into groupthink and reject antibiotics without knowing the facts.
Bradley rolls two fair 6-sided dice with faces numbered 1 through 6. What is the probability that the sum of her two rolls has an odd number of factors?
Answers
Answer:
The probability that the sum of her two rolls has an odd number of factors will be;
[tex]P=\frac{7}{36}[/tex]Explanation:
We want to find the probability that the sum of her two rolls has an odd number of factors.
For the two rolls the total number of possible outcomes is;
[tex]6\times6=36[/tex]Let us list out the possible outcomes of the two rolls;
[tex]\begin{gathered} (\text{outcome)= sum= number of factors of the sum} \\ \mleft(1,1\mright)=2=2\text{ factors} \\ (1,2)=3=2\text{ factors} \\ (1,3)=4=3\text{ factors} \\ (1,4)=5=2\text{ factors} \\ (1,5)=6=4\text{ factors} \\ (1,6)=7=2\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (2,1)=3=2\text{ factors} \\ (2,2)=4=3\text{ factors} \\ (2,3)=5=2\text{ factors} \\ (2,4)=6=4\text{ factors} \\ (2,5)=7=2\text{ factors} \\ (2,6)=8=4\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (3,1)=4=3\text{ factors} \\ (3,2)=5=2\text{ factors} \\ (3,3)=6=4\text{ factors} \\ (3,4)=7=2\text{ factors} \\ (3,5)=8=4\text{ factors} \\ (3,6)=9=3\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (4,1)=5=2\text{ factors} \\ (4,2)=6=4\text{ factors} \\ (4,3)=7=2\text{ factors} \\ (4,4)=8=4\text{ factors} \\ (4,5)=9=3\text{ factors} \\ (4,6)=10=4\text{ factors} \\ \end{gathered}[/tex][tex]\begin{gathered} (5,1)=6=4\text{ factors} \\ (5,2)=7=2\text{ factors} \\ (5,3)=8=4\text{ factors} \\ (5,4)=9=3\text{ factors} \\ (5,5)=10=4\text{ factors} \\ (5,6)=11=2\text{ factors} \end{gathered}[/tex][tex]\begin{gathered} (6,1)=7=2\text{ factors} \\ (6,2)=8=4\text{ factors} \\ (6,3)=9=3\text{ factors} \\ (6,4)=10=4\text{ factors} \\ (6,5)=11=2\text{ factors} \\ (6,6)=12=6\text{ factors} \end{gathered}[/tex]From the listed possible outcomes, the number of oucomes with odd number of factors of the sum is;
[tex]n_A=7[/tex]Total number of possibles outcomes is;
[tex]n_T=36[/tex]The probability that the sum of her two rolls has an odd number of factors will be;
[tex]\begin{gathered} P=\frac{n_A}{n_T}=\frac{7}{36} \\ P=\frac{7}{36} \end{gathered}[/tex]Would lines 4x+3y=52 and 3x-4y=44 be perpendicular parallel or neither? I just need a brief explanation with the answer
Answers
Would lines 4x+3y=52 and 3x-4y=44 be perpendicular parallel or neither?
step 1
Find out the slopes of the given lines
4x+3y=52
isolate the variable y
3y=-4x+52
y=-(4/3)x+52/3 ------> m=-4/3
3x-4y=44
4y=3x-44
y=(3/4)x-44/4 ------> m=3/4
step 2
Compare their slopes
m=-4/3 and m=3/4
the slopes are opposite reciprocal
that means
the lines are perpendicularI need help solving this problem any help is appreciated
Answers
If we want to solve this problem we first need to list a few properties of trigonometric functions:
[tex]\begin{gathered} \text{cot }\theta=\frac{\cos\theta}{\sin\theta} \\ \sin^2\theta+\cos^2\theta=1 \end{gathered}[/tex]We are told that cot(θ)=1/2. Using the first equation and this data we obtain the following:
[tex]\frac{1}{2}=\frac{\cos\theta}{\sin\theta}[/tex]We multiply both sides and we get an expression for the cosine of θ:
[tex]\begin{gathered} \frac{1}{2}\sin\theta=\frac{\cos\theta}{\sin\theta}\cdot\sin\theta \\ \cos\theta=\frac{1}{2}\sin\theta \end{gathered}[/tex]Now we are going to take the second property I wrote in the begining and replace the cosine of θ with this new expression that we found:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=\sin^2\theta+(\frac{1}{2}\sin\theta)^2=1 \\ \sin^2\theta+\frac{1}{4}\sin^2\theta=1 \\ \frac{5}{4}\sin^2\theta=1 \end{gathered}[/tex]We must solve this equation for the sine of θ. We can multiply both sides by 4/5:
[tex]\begin{gathered} \frac{4}{5}\cdot\frac{5}{4}\sin^2\theta=1\cdot\frac{4}{5} \\ \sin^2\theta=\frac{4}{5} \end{gathered}[/tex]And we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{\sin^2\theta}=\sqrt{\frac{4}{5}} \\ |\sin\theta|=\frac{2}{\sqrt{5}} \end{gathered}[/tex]We are told that θ is located in quadrant I which means that its sine is positive. Therefore we get:
[tex]\sin\theta=\frac{2}{\sqrt{5}}[/tex]AnswerThen the answer is 2/√5
Solve the following system of equations. How many solutions are there? x + y = 2 5x + 5y = 10 a) There is no solution. b) There are infinite solutions. c) There is one solution.
Answers
we are given the following system of equations:
[tex]\begin{gathered} x+y=2,\text{ (1)} \\ 5x+5y=10,\text{ (2)} \end{gathered}[/tex]Equation (2) can be rewritten dividing by 5 on both sides as:
[tex]\frac{5x}{5}+\frac{5y}{5}=\frac{10}{5}[/tex]Solving the operations:
[tex]x+y=2,\text{ (2)}[/tex]Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.
In 2 years, Ariel wants to buy a bicycle that costs 1,000.00. If she opens a savings account that earns 9%interest compounded quarterly, how much will she have to deposit as principal to have enough money in 2 years to buy the bike?
Answers
Let's first list down the information given in the scenario:
a.) In 2 years ariel wants to buy a bicycle that costs 1,000.00
b.) She opens a savings account that earns 9% interest compounded quarterly
Question: How much will she have to deposit as principal to have enough money in 2 years to buy the bike?
To be able to determine the principal amount Ariel will need to deposit, let's use this formula for Compound Interest:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{r}{n}}{100})^{nt}[/tex]Where:
A = Is the final amount/ cost of the bicycle = 1,000
n = Number of times the interest is being compounded = 4
r = Interest rate = 9%
t = No. of periods elapsed/ No. years the principal money be deposited
P = Principal amount/ amount to be deposited
Let's now find the principal amount:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{4}{n}}{100})^{nt}\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }\frac{\frac{9}{4}}{100})^{4(2)}[/tex][tex]\text{1,000 = }P(1\text{ + }\frac{2.25}{100})^8\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }0.0225)^8\text{ }\rightarrow1,000=P(1.0225)^8[/tex][tex]\text{ P = }\frac{1,000}{(1.0225)^8}\rightarrow\text{ P = }\frac{1,000}{1.19483114181}[/tex][tex]\text{ P = 836.93835 }\cong\text{ 836.94}[/tex]Therefore, Ariel must deposit a principal amount of 836.94 for her to be able to buy the bike in 2 years.
1.question The preimage was(-3, 4) and after the rotation the image was (3, -4). What many degrees counterclockwise did the point rotate?a) 90b) 270c) none aboved) 1802. question
Answers
Answer:
Question 1
d) 180
Question 2:
b T <8, 14>
Explanation:
Here is a graph of the two points.
As can be seen, the two points are on the opposite sides of teacher other, meaning the point (-3,4) has to rotate 180 degrees to get to (3, -4) and vice versa.
Question 2
The coordinates of A and B are
A = (5, 6)
B = (-3, -8 )
If we want to go from B to A, we need to add 8 to the x-coordinate and 14 to the y-coordinate.
Therefore, the translation
[tex]B\rightarrow A\text{ is T<8,14>}[/tex]
Rewrite the following equation y - 7 = -4(x + 1)
Answers
If the factors of a polynomial are x-4 and x-5, which value of x make that polynomial 0?
Answers
Given a polynomial of factors below,
[tex]f(x)=(x-4)(x-5)[/tex]To find the values of x at f(x) = 0, substitute for f(x) into the equation above,
[tex]\begin{gathered} (x-4)(x-5)=0 \\ x-4=0 \\ x=4 \\ x-5=0 \\ x=5 \\ x=4\text{ and 5} \end{gathered}[/tex]C is the right option
Spongebob was trying to fill up Gary's bath with water. He noticed the tub filled up 1 gallon per minute.AContinuousBDiscrete
Answers
given data:
Spongebob was trying to fill up Gary's bath with water. He noticed the tub filled up 1 gallon per minute.
to find what kind of data this is.
it is discrete because it is measurable. that is countiuse while countable.
Thus the answer is discrete.
Express the difference in medians as a multiple of the IQR of EACH dataset.Class A.Class B440506070Height (inches)
Answers
From the given box plot, let's express the difference in the medians of the IQR of each data.
Given:
Median of class A = 56
Q1 of class A = 50
Q3 of class A = 58
Median of class B = 52
Q1 of class B = 48
Q3 of class B = 54
Thus, we have:
IQR for class A = Q3 - Q1 = 58 - 50 = 8
IQR for class B = Q3 - Q1 = 54 - 48 = 6
Diffrence in median = 56 - 52 = 4
Thus, to find the expression of the difference in medians as a multiple of IQR of each data, we have:
[tex]\begin{gathered} \text{Difference class A: 4 = 8}\ast n \\ \\ \text{Difference class B: 4 = 6 }\ast n \end{gathered}[/tex]Let's solve for each difference.
Difference class A:
[tex]n=\frac{4}{8}=\frac{1}{2}[/tex]Difference class B:
[tex]n=\frac{4}{6}=\frac{2}{3}[/tex]ANSWER:
[tex]\begin{gathered} \text{CLass A = }\frac{1}{2} \\ \\ \text{Class B = }\frac{2}{3} \end{gathered}[/tex]Decide whether enough information is given to prove that △RSV≅△UTV. If so, state the theorem you would use.
Answers
In the diagram we are given that angle S = angle T
We are given that side SV = side TV
We know that vertical angles are equal so angle RVT = angle UVT
WE have 2 angles and the included side so we can use the ASA Congruence theorem which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
There is enough information to use the ASA Congruence Theorem.
the number of employees Forrester company of vindication each year by 4% of the company currently k670 employees and this rate continues from the number of employees in 16 years
Answers
The expression for number of employee after n year if population, P decreases at rate of r % is,
[tex]p=P(1-\frac{r}{100})^n[/tex]Substitute the values in the formula to determine the population after 16 years.
[tex]undefined[/tex]What is the inverse operation for addition?additionsubtractiondivisionmultiplication
Answers
The inverse operation for addition is subtraction.
Hence, the answer is Subtraction.
Jack has $205 and he is spending $2 each day. Which algebraic expression describes this situation, where d represents the number of days?
Answers
M= 205 - 2d
1) We can write a mathematical sentence for that situation, considering Jack's initial amount of money: $205 and the fact that we don't know the number of days (d). But we do know that each day costs Jack $2, i.e. minus 2 dollars per day.
2) Therefore, we can write out the following:
[tex]M_{}=205-2d[/tex]Where M stands for Jack's money and "d" stands for the number of days.
3) Hence the answer is
M= 205 - 2d
Change 0.005 to equivalent fraction. ANS. _________.
Answers
You can identify that the following is a Decimal number:
[tex]0.005[/tex]In order to convert a Decimal number to an Equivalent fraction, you can follow the steps shown below:
1. You need to write the Decimal number 0.005 as the numerator of the fraction and the denominator must be 1:
[tex]=\frac{0.005}{1}[/tex]2. Now you can multiply the numerator and the denominator by 1,000, in order to remove the decimal places of the numerator (notice that it has three decimal places):
[tex]=\frac{0.005\cdot1,000}{1\cdot1,000}=\frac{5}{1,000}[/tex]3. Finally, you have to reduce the fraction. Notice that you can divide the numerator and the denominator by 5. Then, you get:
[tex]=\frac{1}{200}[/tex]The answer is:
[tex]\frac{1}{200}[/tex]find the value 24÷(1 to the 5th power+5)
Answers
Given
[tex]\frac{24}{(1^5+5)}[/tex]When you power a number by a determined exponent "n" it means that you are multiplying said number n-times by itself. We know that if you multiply 1 by 1 the result is 1, no matter how many times you do it, then 1 multiplied 5 times by itself is also equal to 1:
[tex]1^5=1\cdot1\cdot1\cdot1\cdot1=1[/tex]Then, you can write the calculation as:
[tex]\frac{24}{(1+5)}[/tex]Solve the addition in the denominator's place and then solve the division
[tex]\frac{24}{6}=4[/tex]The result of the calculation is 4
Drag the tiles to the boxes to form correct pairs.
Answers
Given that
The vertices of the polygon ABCD are A(1,1), B(2,3), C(3,2), and D(2,1). ANd it is reflected about the x-axis.
So we have to find the vertices of the polygon A'B'C'D'.
Explanation -
Since the reflection is about the x-axis, the x-axis will be unchanged and the y-axis will be changed.(sign will be changed)
And it will be changed by the factor +2 in upwards directions.
So if A, B, C, D are reflected across x-axis.
The new points will be A' = (1,-1)
B' = (2,-3)
C' = (3,-2)
D' = (2,-1)
Now we have to add 2 in the y axis as they move upwards.
Then, the required points will be
A' = (1, -1+2) = (1,1)B' = (2, -3+2) = (2,-1)C' = (3,-2+2) = (3,0)D' = (2, -1+2) = (2,1)So these are the required answers.
(3x-3)
[6(x - 10)] What is the value of x?
Answers
3(x - 1)
[6(x - 10)]
6x + 6 times -10
simplify 6 times -10 to -60
6x - 60
The original price of a pair ofjeans was $40. The price wasmarked down to $35. What is thepercent of decrease in the price?
Answers
SOLUTION
From the question, the original price of the jeans was $40, then the price was reduced to $35. Decrease in price becomes
[tex]40-35=5\text{ dollars }[/tex]Percent decrease becomes
[tex]\begin{gathered} =\frac{decrease\text{ in price}}{original\text{ price}}\times100 \\ =\frac{5}{40}\times100 \\ =\frac{1}{8}\times100 \\ =12.5 \end{gathered}[/tex]hence the answer is 12.5%
The quotient of forty three abs a number m
Answers
Explanations:
Answer:
mason used a 30% coupon to buy a new computer. after the discount, the cost of the computer was $728. determine the original price of the computer . show your work . calculate how much money Mason saved by using the coupon . show your work .
Answers
Let's call x to the original price.
Given that Mason used a 30% coupon, then he paid 0.3x dollars less.
After the discount, the cost of the computer was $728, then
x - 0.3x = 728
0.7x = 728
x = 728/0.7
x = 1040
The original price of the computer was $1040
Mason saves 30% of $1040, which is computed as follows:
[tex]1040\cdot\frac{30}{100}=312[/tex]Mason saves $312
i gave away 10% of my summer job earnings. If i give away $256, how much did i earn over the summer?
Answers
ok
$256 --------------------------- 10%
x --------------------------100%
x = (100 x 256) / 10
x = 25600 / 10
x = $2560
I earned $2560 over the summer
What is the Center and radius of x2+67+y2=8y+20x
Answers
Let's rewrite the expression as:
[tex]\begin{gathered} x^2+67+y^2-8y-20x=0 \\ so\colon \\ (x-10)^2+(y-4)^2-49=0 \\ (x-10)^2+(y-4)^2=49 \end{gathered}[/tex]Which is the standard equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) is the coordinates of center of the circle and r is the radius
Therefore, the center is:
[tex]\begin{gathered} (h,k)=(10,4) \\ \end{gathered}[/tex]And the radius is:
[tex]r=\sqrt[]{49}=7[/tex]at work one day, erica recieved 18 packages. speed delivery delivered three times as many as ralphs express, while ralphs express delivered two more than send quick service. how many packages did each service deliver to erica
Answers
Answer:
Let the number of packages delivered by Ralph's Express be x.
The number of packages delivered by Speedee Delivery would then be 4x.
The number of packages delivered by Send Quick Package Service would be x-5.
Adding all of these together,
x + 4x + (x - 5) = 6x -5
6x - 5 = 55
6x = 60
x = 10
Hence,
Ralph's Express delivered 10 packages.
Speedee Delivery delivered 40 packages.
Send Quick Package Service delivered 5 packages. Hope this help's you
Step-by-step explanation:
which expression is equivalent to 7y + 7y?
Answers
Evaluate the value of expression.
[tex]7y+7y=14y[/tex]So answer is 14y.
Solve the system: y = 12 + 4x y = -33 - 5x
Answers
The equation system is:
[tex]\begin{gathered} y=12+4x \\ y=-33-5x \end{gathered}[/tex]So we can made the equation equal so:
[tex]\begin{gathered} 12+4x=-33-5x \\ 4x+5x=-33-12 \\ 9x=-45 \\ x=-\frac{45}{9} \\ x=-5 \end{gathered}[/tex]Now we can replace the value of x to find y in the first equation so:
[tex]\begin{gathered} y=12+4(-5) \\ y=12-20 \\ y=-8 \end{gathered}[/tex]so the solution is:
[tex](-5,-8)[/tex]one to the sixth power
Answers
sixth power is the exponent of 1.
To obtain the result, multiply 1 by itself 6 times:
1x1x1x1x1x1=1
1^6 = 1