Answer:3x • (2x2 - 3)
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 3 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
((3•(x3))+(4•(x2)))+(((3•(x3))-22x2)-9x)
STEP
2
:
Equation at the end of step
2
:
((3•(x3))+(4•(x2)))+((3x3-22x2)-9x)
STEP
3
:
Equation at the end of step
3
:
((3 • (x3)) + 22x2) + (3x3 - 4x2 - 9x)
STEP
4
:
Equation at the end of step
4
:
(3x3 + 22x2) + (3x3 - 4x2 - 9x)
STEP
5
:
STEP
6
:
Pulling out like terms
6.1 Pull out like factors :
6x3 - 9x = 3x • (2x2 - 3)
Trying to factor as a Difference of Squares:
6.2 Factoring: 2x2 - 3
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
3x • (2x2 - 3)
SCENARIO: ROAD CONSTRUCTION: Your state highway department hires high school students every summer to help with road construction projects. The hourly rate is $11.75 with the possibility of up to 10 hrs per week in overtime, for which you would be paid time and a half. Of course, the work is totally dependent on good weather, so the number of hrs you would work per week could vary. A road construction worker earns $11.75 per hour with up to 10 hours overtime. Write an equation, create a table, and create a graph for a road construction worker's weekly earnings with NO overtime, f(x), where x represents the total number of hrs the road construction worker would work. Is it Proportional or Non-proportional? Using the equation, table or graph, how much will a road construction worker earn for a typical 40 hr week
Answer:
Step-by-step explanation:
LET
x be the number of regular work hours
overtime paid time and a half :(11.75+1/2(11.75))= 17.625 dollars
max time =10 hours
max overtime paid = 10*17.625=170.65 dollars per week
f(x) or y =11.75x
the graph is proportional because it passes through the origin( no work hours, no earning)
with no overtime the workers if the workers work 40 hours then :
y=11.75*40=470 dollars
Order of Operations.
if a turtle moves at 1 1/3 kilometers per hour how long would it take for the turtle to travel 9 kilometers.
Answer:
33 hours
Step-by-step explanation:
[tex]\frac{11}{3} *9 =33[/tex]
Answer:
6 3/4 hours
Step-by-step explanation:
divide 9 by 1 1/3. You get 6.75 which is converted to 6 and 3/4 hours.
An airport offers two shuttles that run different schedules. If both leave the airport at 4:00 pm, at what time will they next leave the airport together
Answer:
4:18 pm
Step-by-step explanation:
An airport offers two shuttles that run on different schedules.If both shuttles leave the airport at 4:00 p.m.,at what time will they next leave the airport together.
Shuttle A leaves every 6 minutes
Shuttle B leaves every 9 minutes
Shuttle A: 4:00 pm
Leaves every 6 minutes
Next 4:06 pm
Next: 4:12 pm
Nex: 4:18 pm
Next: 4:24 pm
Shuttle B: 4:00 pm
Leaves every 9 minutes
Next: 4:09 pm
Next: 4:18 pm
Next: 4:27 pm
Next: 4:36 pm
The next time both shuttles will leave the airport together is 4:18 pm
what is the opposite of -1,679?
Answer:
1679 ?
Step-by-step explanation:
Do you have more information?
What is thr answer of (a-b) (a+2b)
Answer:
Step-by-step explanation:
Use FOIL method
F -> First
O Outside
I inside
L Last
(a - b)(a + 2b)= a*a + a *2b + (-b)*a + (-b)*2b
= a² + 2ab - ab - 2b²
Combine like terms
= a² + ab - 2b²
the definition of theorem?
Answer:
In mathematics, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems. A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system. As a result, the proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.
Step-by-step explanation:
On monday jan made withdrawals of 25 45 75 from her savings account. On the same day her twin sister julie made withdrawals of 35 55 and 65 dollars from her savings account. Write a sum of negative integers to show jans withdrawals on monday. Find the total amount jan withdrawal.
Answer:
(-25) + (-45) + (-75)
-145
Step-by-step explanation:
Given that :
jan made withdrawals of 25 45 75 from her savings account
Sum of negative integers to show Jan's withdrawals :
Expression to showing sun of negative integers to represent Jan's withdrawals :
(-25) + (-45) + (-75)
The result of the sum will give the total amount of Jan's withdrawal.
(-25) + (-45) + (-75) = - 145
Hence, total amount Jan withdrew is - 145
1
2
3
4
Resistance to British rule in southern Africa was led by the
Ethiopians
Egyptians.
Liberians.
Zulus.
O
o
What is it
Answer:
Zulus.
Explanation:
The Zulus are a group of ethnic people from the Bantu tribe in Southern Africa. They also constitute the largest ethnic group in South Africa and were a separate kingdom before the attack by the Britishers in 1879.
Therefore, it is only reasonable to say that the resistance to the British rule in Southern Africa was led by the Zulus as it was their land. The Ethiopians, Egyptians, and Liberians were African nations but not a part of the Southern African area. Ethiopia is in the East, Liberia in the West, and the Egyptians in the North part of Africa.
Samuel currently has an account balance of $3,439.96. He opened the account five years ago with a deposit of $3,104.31. If the interest compounds quarterly, what is the interest rate on the account?
Answer:
The interest rate on the account is 2.1%
Step-by-step explanation:
Compound interest is one that is added to the initial capital and on which new interests are generated. Money, in this case, has a multiplier effect because interest produces new interest. In other words, the initial capital increases in each period because the interests add up.
To calculate the final capital, the initial capital is multiplied by one plus the interest, raised to the number of periods:
[tex]A=P*(1+\frac{r}{n}) ^{n*t}[/tex]
where
A = Accumulated amount (principal + interest) P = Principal amount r = the interest rate n = the number of times the interest is compounded per year t = Time Involved in yearsIn this case:
A = $3,439.96P = $3,104.31r = ?n = 4t = 5Replacing, you get:
[tex]3,439.96=3,104.31*(1+\frac{r}{4}) ^{4*5}[/tex]
Now, solving:
[tex]\frac{3,439.96}{3,104.31} =(1+\frac{r}{4}) ^{20}[/tex]
[tex]\sqrt[20]{1.1081} =(1+\frac{r}{4})[/tex]
[tex]1.00514 =1+\frac{r}{4}[/tex]
[tex]1.00514 -1=\frac{r}{4}[/tex]
[tex]0.00514=\frac{r}{4}[/tex]
r=0.0051*4
r= 0.02056
In percentage it is expressed as: r= 2.056 %≅ 2.1 %
The interest rate on the account is 2.1%
please solve and explain!!!
Answer:
I think thats false
Step-by-step explanation:
Tell them false there isn't much evidence and if you tried to search it up thats not correct or the correct way to solve it theyre trying to trick you.
What would be a good lower bound for the number of jelly beans in the jar?
Answer:
I think you need to link the question or a picture of the jar
Step-by-step explanation:
stephanie has a recipe that calls for 2/3 tablespoons of vanilla to make 3 1/2 dozen cookies how many tablespoons of vanilla are needed per dozen cookies
Answer:
4 / 21 spoonful of vanilla
Step-by-step explanation:
3 1/2 dozens = 42 cookies
Let x = spoonful of vanilla for 1 dozen of cookies
2/3 : 42 cookies
x : 12 cookies
2/3 ÷ 42 = x ÷ 12
2/3 × 1/42 = x / 12
2 / 126 = x / 12
Cross product
2*12 = 126*x
24 = 126x
Divide both sides by 126
x = 24 / 126
= 4 / 21
x = 4 / 21 spoonful of vanilla
Per dozen of cookies requires 4/21 spoonful of vanilla
Check:
4/21 per dozen × 3 1/2 dozens
4/21 × 7/2
28 / 42
2/3 spoonful for 3 1/2 dozens
The total amount of dozen cookies = [tex]3\dfrac{1}{2}[/tex]
Stephanie requires [tex]\dfrac{2}{3} \ tablespoons[/tex] to make [tex]\mathsf{3\dfrac{1}{2}\ dozen \ cookies}[/tex]
Let assume that:
(x) represents the amount of the tablespoons Stephaine needs to prepare 1 dozen cookies:Then; we can equate both equations together as follows:
[tex]\dfrac{2}{3} \ tablespoons[/tex] = [tex]\mathsf{3\dfrac{1}{2}\ dozen \ cookies}[/tex]
x tablespoon = 1 dozen cookies
By cross multiply and making (x) the subject of the formula, we have:
[tex]\mathbf{x \times 3\dfrac{1}{2} dozen \ cookies = \dfrac{2}{3} \ tablespoons \times 1 \ dozen \ cookies}[/tex]
[tex]\mathbf{x =\dfrac{ \dfrac{2}{3} \ tablespoons \times 1 \ dozen \ cookies}{3\dfrac{1}{2} dozen \ cookies}}[/tex]
[tex]\mathbf{x =\dfrac{ \dfrac{2}{3} \ tablespoons}{3\dfrac{1}{2} }}[/tex]
[tex]\mathbf{x =\dfrac{ \dfrac{2}{3} \ tablespoons}{\dfrac{7}{2} }}[/tex]
[tex]\mathbf{x = \dfrac{2}{3} \ tablespoons} \div {\dfrac{7}{2} }[/tex]
[tex]\mathbf{x = \dfrac{2}{3} \ tablespoons} \times {\dfrac{2}{7} }[/tex]
[tex]\mathbf{x = \dfrac{4}{21} \ tablespoons}}[/tex]
Therefore, the amount of tablespoons Stephaine will need to prepare a dozen cookies is: [tex]\mathbf{ = \dfrac{4}{21} \ tablespoons}}[/tex]
Learn more about solving fractions here:
https://brainly.com/question/6201432?referrer=searchResults
Write a polynomial that represents the area of the shaded region
=========================================
Explanation:
The larger rectangle has area of (x+1)(x+1) = x^2+2x+1 through the use of the FOIL rule or distribution
If you use distribution, then it might help to let y = x+1 so we'd have y(x+1) lead to xy+1y which becomes x(x+1)+1(x+1). From there it might be easier to see how to get x^2+2x+1 after everything distributes again and simplifies.
The smaller rectangle has area 5x-35 which is found by distributing 5(x-7)
To get the shaded area, we subtract the two rectangle areas found above
shaded area = (larger area) - (smaller area)
shaded area = (x^2+2x+1) - (5x - 35)
shaded area = x^2+2x+1 - 5x + 35
shaded area = x^2-3x+36
A boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is ___ km/hr.
Answer:
The speed of the stream is 5 km/hr.
Step-by-step explanation:
- Let's assume that the speed of stream is = x km/h
- Speed of boat in still water v = 15 km/h
- Total time taken = 4 hour and 30 mins or 9/5 hrs
- Distance covered (one way) = 30 km/s
Then,
Speed of boat downstream =( 15 + x ) km/h
Time taken downstream = (30/15 + x ) hrs
As time = distance / speed
Speed of boat upstream = ( 15 - x ) km/h
Time taken upstream =( 30/15 - x ) hrs
Now,
Total time taken = Time taken downstream + Time taken upstream
or, 9/2 = (30/15 + x ) + (30/15 - x )
or, x = 5 km/h
The speed of the stream is 5 km/h
I hope my answer helps
Use the graph below to evaluate, f(1): A f(1)=4 B f(1)=3.5 C f(1)=2 D f(1)=3
F(1) would be the y value of where the line is at x =1
At x = 1, the line is at y =3
The answer is D. F(1) = 3
Simplify (2 raised to- 1 x 3 raised to 2 )/ (2 raised to 2 x 3 raised to -4 )the who raised to 7/2 x (2 raised to -2 multiplied by 3 raised to 3 )/ (2 raised to 3 multiplied by 3 raised to -5) whole raised to -5/2
Answer:
12
Step-by-step explanation:
Given the expression:
[tex](\dfrac{(2^{-1}\times 3^2)}{(2^{2}\times 3^{-4})})^\frac{7}{2} \times (\dfrac{(2^{-2}\times 3^3)}{(2^{3}\times 3^{-5})})^\frac{-5}{2}[/tex]
We have to simplify the above expression.
Let us have a look at a few formulas:
[tex]1.\ a^b = \dfrac{1}{a^{-b}}[/tex]
[tex]2.\ a^b\times a^c = a^{b+c}[/tex]
[tex]3.\ (a^b ) ^c = a^{bc}[/tex]
Now, let us try to solve the given above expression using the formulas:
[tex]\Rightarrow (\dfrac{(3^{4}\times 3^2)}{(2^{2}\times 2^{1})})^\frac{7}{2} \times (\dfrac{(3^{5}\times 3^3)}{(2^{3}\times 2^{2})})^\frac{-5}{2}[/tex]
[tex]\Rightarrow (\dfrac{(3^{4+2})}{(2^{2+1})})^\frac{7}{2} \times (\dfrac{(3^{5+3})}{(2^{3+2})})^\frac{-5}{2}\\\Rightarrow (\dfrac{3^{6}}{2^{3}})^\frac{7}{2} \times (\dfrac{3^{8}}{2^{5}})^\frac{-5}{2}\\\Rightarrow (\dfrac{3^{\frac{42}{2}}}{2^{\frac{3\times 7}{2}}})\times (\dfrac{2^{5}}{3^{8}})^\frac{5}{2}\\\Rightarrow (\dfrac{3^{21}}{2^{\frac{21}{2}}})\times (\dfrac{2^{\frac{5\times 5}{2}}}{3^{\frac{8\times 5}{2}}})[/tex]
[tex]\Rightarrow (\dfrac{3^{21}}{2^{\frac{21}{2}}})\times (\dfrac{2^{\frac{25}{2}}}{3^{20}})\\\Rightarrow {3^{1}}\times {2^{\frac{25-21}{2}}}\\\Rightarrow 3\times 4 \\\Rightarrow \bold{12}[/tex]
When a negative and positive number is added, is the sum going to be negative or positive?
Answer:negative
Step-by-step explanation:
Answer:
It depends on the values of the numbers.Step-by-step explanation:
If the positive number has a greater value than the negative number,adding them together will give you a positive answer.But,if the negative number has a greater value than the positive number, adding them together will give you a negative answerThe sum of three consecutive even integers is 108 what is the largest number
Answer:
38
Step-by-step explanation:
if x is an even integer then the two other even integers are x+2 and x+4.
x+x+2+x+4=108
3x+6=108
3x=108-6
3x=102
x=102/3
x=34.
⇒the largest number from x, x+2 and x+4 is x+4.
x+4=34+4=38
Answer:
38
Step-by-step explanation:
good luck on your assignment
Is 10 closer to 3 or 4?
Answer:
4
Step-by-step explanation:
Answer:
If there's a zero in the tenths place and your round down, keep the zero in your answer. For example, 4.03 rounded to the nearest tenth in 4.0.
Which property was used to write the equation in step 2? Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18. distributive property addition property of equality subtraction property of equality division property of equality
Answer:
Distributive property
Step-by-step explanation:
Answer:
Distributive property
Step-by-step explanation:
I got it rigth on edge
hope this helps!
A basketball player scored 8 points in the 1st quarter 5 points during 2nd quarter 2 points in the 3rd quarter and 20 in the 4th quarter
Answer: 25
Step-by-step explanation: He scored 25 in the game
A motorist is pumping gas into a car at a rate of 5/12 of a gallon every 1/24 of a minute. At this rate, how many gallons of gas will he have pumped into his car on 1/2 of a minute?
Answer:
5 gallons
Step-by-step explanation:
times both the rate of the gas pumping and the time it takes by 12/1
so you could get half a minute.
then you get 60/12 gallons pumped per 1/2 min
then you just simplify it to 5 gallons per half minute
4 + 2x2(3x-5)
number of terms
5a+6b-10d=15c SOLVE FOR B
What is the difference between -4 and 6?
-10
-2
2
10
Answer:
the answer is 10
Step-by-step explanation:
*please give me brainliest, i only need four more*
Answer:
-10
I did the math
(-4)-6
Someone please help me
algebraic expression for x more than 5.
Answer:
5 + x
Step-by-step explanation:
x more than 5 is 5 + x
Answer:
5+x
Step-by-step explanation:
x more than 5.
More than means it comes after
5+x
A line passes through the points (−4, −18) and (0, 2). Which is an equation of the line?
Answer:
y=5x+2
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-4,-18), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-4 and y1=-18.
Also, let's call the second point you gave, (0,2), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=0 and y2=2.
Now, just plug the numbers into the formula for m above, like this:
m= (2 - -18)
------------
(0 - -4)
or...
m= 20
-------
4
or...
m=5
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=5x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-4,-18). When x of the line is -4, y of the line must be -18.
(0,2). When x of the line is 0, y of the line must be 2.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=5x+b. b is what we want, the 5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-4,-18) and (0,2).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(-4,-18). y=mx+b or -18=5 × -4+b, or solving for b: b=-18-(5)(-4). b=2.
(0,2). y=mx+b or 2=5 × 0+b, or solving for b: b=2-(5)(0). b=2.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(-4,-18) and (0,2)
is
y=5x+2
Please help me one this question
Answer:
the volume is 7 because there is 7 blocks