Answers
The factor of the polynomial, the area of the pool and the simplified expression are all algebraic expressions
How to simplify the expressions?Factor of the polynomial
The polynomial is given as:
2x^3 + 6x^2 + 6x + 18
Factor out 2
2x^3 + 6x^2 + 6x + 18 = 2(x^3 + 3x^2 + 3x + 9)
Factorize
2x^3 + 6x^2 + 6x + 18 = 2(x^2(x + 3) + 3(x + 3))
Factor out x + 3
2x^3 + 6x^2 + 6x + 18 = 2(x^2 + 3)(x + 3)
Expand
2x^3 + 6x^2 + 6x + 18 = (2x^2 + 6)(x + 3)
Hence, 2x^2 + 6 is a factor of the polynomial 2x^3 + 6x^2 + 6x + 18
The length of the pool
The given parameters are:
Area = 2x^3 - 29x + 12
Width = x + 4
The length is calculated as:
Length = Area/Width
This gives
Length = 2x^2 - 29x + 12/x + 4
Factorize the numerator
Length = (2x^2 - 8x + 3)(x + 4)/x + 4
Cancel out x + 4
Length = 2x^2 - 8x + 3
Hence, the length of the pool is 2x^2 - 8x + 3
Simplify the expression
The expression is given as:
(3s^2 - 2s + 1) [tex]\div[/tex] (s^2 - s + 2)
Evaluate the quotient
3 + (s - 5)/(s^2 - 5 + 2)
Hence, the simplified expression is 3 + (s - 5)/(s^2 - 5 + 2)
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Related Questions
15<96–q
what is the value of q
Answers
Answer: q < 81
Step-by-step explanation:
isolate q
15 < 96 - q
-81 < -q
divide by negative 1 but flip inequality because you are dividing by a negative
81 > q so
q < 81
Express the difference between 0.35 and 2/5 as a decimal
Answers
0.05
Explanation:
2/5 is as a decimal, 0.4
The difference between them is 0.05
Choose the ratio that is equivalent to this one: 4/7
Answers
Answer:
4:7
Step-by-step explanation:
4:7 is the same as 4/7
Fill in the table using this function rule. (Fill Y side)
Y=10x+3
X Y
-1
0
1
5
Answers
Answer:
[tex]y = -7[/tex]
[tex]y = 3[/tex]
[tex]y = 13[/tex]
[tex]y = 53[/tex]
you bought 4 jumbo cookies for $5. whats the cost per cookie?
Answers
Answer:
80 Cents for each jumbo cookie
Cual es la velocidad de un carro si su masa es de 1,2 toneladas y genera energía cinética de 905 J
Answers
Answer:
75 kilómetros por hora creo no estoy muy seguro
last year a company made a profit of one and a quarter million dollars.Each year the company reinvests 1/3 of the profit How much of this profit eill they reinvest
Answers
Answer:
$83,333
Step-by-step explanation:
1 000 000*1/4
250 000
250 000*1/3 = 83 333.33
If 25 workers can complete a work in 48 days, then in how many days 20 workers will complete the same work?
Answers
Answer:
heya! ^^
given that ,
25 workers together complete a certain piece of work in 48 days.
here , we've to find the number of days in which 20 workers can complete the same work ~
_____________________________
so let's start ~
★ 25 workers complete the work in = 48 days
★ 1 worker will complete the work in = 25 × 48 days
now ,
29 workers will complete the work in =[tex] \frac{\cancel{25} \times 48} {\cancel{20}} \: \: days \\ \\ \dashrightarrow \: \frac{5 \times \cancel{48}}{\cancel{4}} \\ \\ \dashrightarrow \: 5 \times 12 \\ \\ \dashrightarrow \: 60 \: days[/tex]
hope helpful :D
Answer:
60 days
Step-by-step explanation:
Thing to Remember
Number of workers is inversely proportional to the number of daysSolving
25 men can do a certain amount of work in 48 days25 men is reduced to 20 men ⇒ x 4/5Therefore, no. of days = inverse of rate of workers x 48⇒ 5/4 x 48 = 5 x 12 = 60 dayscan some one help me do this question
just give me e and f
Answers
Answer:
I believe the answer should be 90:90:180. I may be wrong.
HELP The recursive rule for a sequence is shown An=An-1 +4 a1=14 write the explicit rule in simplified form for the sequence An=
Answers
Answer:
aₙ = 4n + 10Step-by-step explanation:
Given is the AP with
The first term of 14The common difference of 4Explicit rule for the sequence is
[tex]a_n=a_1+(n-1)d=14+(n-1)(4)=14+4n-4=4n+10[/tex]Answer:
[tex]\sf a_n=4n+10[/tex]
Step-by-step explanation:
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
Given recursive rule:
[tex]\begin{cases} \sf a_n=a_{n-1}+4\\ \sf a_1=14\end{cases}[/tex]
Therefore, the next two values in the sequence are:
[tex]\begin{aligned} \implies \sf a_2 & = \sf a_{2-1}+4\\& = \sf a_1+4\\& = \sf 14+4\\& = \sf 18\end{aligned}[/tex]
[tex]\begin{aligned} \implies \sf a_3 & =\sf a_{3-1}+4\\& = \sf a_2+4\\& = \sf 18+4\\& = \sf 22\end{aligned}[/tex]
Explicit formula
[tex]\sf a_n=a+(n-1)d[/tex]
where:
[tex]\sf a_n[/tex] is the nth terma is the first termn is the number of the termd is the common difference between termsGiven:
[tex]\sf a = a_1=14[/tex][tex]\sf d = 22-18=4[/tex]Substituting the given values into the formula:
[tex]\sf \implies a_n=14+(n-1)4[/tex]
[tex]\sf \implies a_n=14+4n-4[/tex]
[tex]\sf \implies a_n=4n+10[/tex]
Therefore, the explicit rule in simplified form for the sequence is:
[tex]\sf a_n=4n+10[/tex]
Learn more about arithmetic sequences here:
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The value of the expression in standard nation is ….. of( 0.00032)(5.2 times 10^6) divided by 6.4 times 10^5
Answers
Answer:
The answer is 0.0026
Step-by-step explanation:
0.00032 x 5200000 = 1664
1664 divided by 640000 is 0.0026
Find the distance between the two points in simplest radical form.
(-8,3) and (-2,-5)
Answers
Here we would be using distance formula to calculate the distance between those two points.
Points are,
(-8,3) (-2,5)★ Distance Formula :
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]We have :
x1 = -8 x2 = -2 y1 = 3 y2 = -5Substituting the values in the formula :
Refer the attachment.The distance between the pair of points (-8,3) and (-2,-5) in radical form is √100.
What is the distance between the pair of points?The distance formula can be expressed as:
[tex]d = \sqrt{( x_2 - x_ 1 )^2 + ( y_2 - y_1 )^2}[/tex]
Given the coordinates of the pair of points:
Point 1( -8,3 )
x₁ = -8
y₁ = 3
Point 2( -2,-5 )
x₂ = -2
y₂ = -5
Plug the coordinates into the distance formula and simplify.
[tex]d = \sqrt{( x_2 - x_ 1 )^2 + ( y_2 - y_1 )^2}\\\\d = \sqrt{( -2 - (-8) )^2 + ( -5 - 3 )^2}\\\\d = \sqrt{( -2 + 8 )^2 + ( -5 - 3 )^2}\\\\d = \sqrt{( 6 )^2 + ( -8 )^2}\\\\d = \sqrt{36 + 64}\\\\d = \sqrt{100}[/tex]
Therefore, the distance is √100 units.
Learn more about the distance formula here: brainly.com/question/24509115
#SPJ3
In what fraction of their games did Darnel's team score 2 or more runs?
Answers
Answer:
0.75 or 3/4Step-by-step explanation:
According to the given box plot, the 25% point matches the number 2.
It means the rest of the scores are 2 or more runs:
100% - 25% = 75% = 0.75 = 3/4 of all the runsSimplify the expression by
combining like terms:
-3a + 1 + a +5
Enter the number that belongs in the green box.
[? ]a +[ ]
Enter
Answers
-2a+6
Solution:Let's simplify this expression by combining like terms.The like terms are-3a, a1, 5Combine them:-3a+a+1+5-2a+6Hope it helps.
Do comment if you have any query.
please answer fast and you get points
Answers
Answer:
[tex]\frac{3}{6}=\frac{3*4}{6*4}=\frac{12}{24}[/tex]
Step-by-step explanation:
How may twenty-fourths equal 3/6
Well, we know that 6 * 4 = 24
So, we will be multipying the numerator and denominator with 4/4:
[tex]\frac{3}{6}=\frac{3*4}{6*4}=\frac{12}{24}[/tex]
Therefore, twelve twenty-fourths (12/24) is equivalent to three-sixths (3/6)
Hope this helps!
Given that Cos0=5/13,find a)Tan0,b)Sin0,c)Sec0,d)Co sec0,e)Cot0,
Answers
Step-by-step explanation:
cos 0=5/13. B/H
p=√h2 - b2
= √13 square -5 square
=√169 -25
=√144
=12 Ans
Tan0=p/b =12/5. , sin0=p/h =12/13,. sec0= h/b =13/5 ,. Co sec0 =h/p =13/12 , cot0 =b/p=5/12
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Find the perimeter of the figure to the nearest hundredth.
perimeter: about
ft
Answers
Can somebody please help with 7 and 8
Answers
Answer:
Point Form:
(−4,−9)
Equation Form:
x=−4, y=−9
Step-by-step explanation:
I need this answer fast please factorise the following 16gh2 – 8hi + 24h =
Answers
Answer: 8h(2gh - i + 3)
Step-by-step explanation:
factorise 8 out as 8 is a comon factor of 16, 8 and 24
factorise h out together with 8 because all of them have h
A student is interested in the depth of the water off the
end of the local pier. Starting at midnight, he measures
the depth of the water every three hours for an entire
day and records the results in the table.
The equation of the least-squares regression line is
9 = 13.0 -0.259x, where y is the depth of the water
and x is the number of hours past midnight. Which
shows the residual plot?
For edge
Answers
The residual plot regarding the depth of the water is the difference between the observed response and the fitted response values.
What is a residual plot?Your information is incomplete. Therefore, an overview of a residual plot will be given. A residual plot is a graph that shows the residual on the vertical axis while the independent variable is on the horizontal axis.
Here, the equation of the least-squares regression line is 9 = 13.0 -0.259x, where y is the depth of the water and x is the number of hours past midnight.
In this case, the residual plot regarding the depth of the water is the difference between the observed response and the fitted response values.
Learn more about residual plot on:
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Answer: C
Step-by-step explanation: Edge '23 Trust me
A window has the shape of a rectangle with a semicircle at the top.
Find the approximate area of the window using the dimensions shown.
Answers
Answer:
8+pi/2
Step-by-step explanation:
The area of the rectangle on the bottom is 8, or 2*4. The area of the top is half (because it's a semi circle) of pi*r^2, or just 1/2 pi
If a floor plan has a key for 1 graph paper line = 5 ft in real life, what is the area of a rectangular room in real life if the area on the floor plan is 44?
*HINT: the key is for a dimension, but your answer is an area.*
Answers
=======================================================
Explanation:
1 unit along the grid represents 5 feet in real life.
A 1 unit by 1 unit square on the graph paper represents a 5*5 = 25 square foot area in real life.
This means we multiply by 25 when going from the floor plan's area to the real world area.
44*25 = 1100 square meters is the area of the room in real life when the floor plan says the area is 44 sq units.
PLEASE HELP PLEASE PLEASE HELP
Answers
Reason:
Choices A through C all result in 8/3 = 2.667 approximately
In contrast, choice D becomes 2/3 + 4/3 = (2+4)/3 = 6/3 = 2; showing that choice D is not equivalent to choices A through C.
Use the product-to-sum formula to convert the expression to a sum or difference. Simplify where is possible.
Answers
Answer:
sin3t*cos(s)*cos(t)+sin3t*sin(s)*sin(t).
Step-by-step explanation:
sin3t*cos(s-t);
1) cos(s-t)=cos(s)cost+sin(s)sint; then
2) sin3t*cos(s-t)=sin3t*cos(s)*cos(t)+sin3t*sin(s)*sin(t).
The circumcenter of a triangle can lie on one of the edges if the triangle is:
Select the best choice from the answers provided.
A.
Right
B.
Acute
C.
Obtuse
D.
none of the above choices are correct.
Answers
Answer:
B. Acute
Step-by-step explanation:
the hypotenuse for right triangles and lies outside the triangle for obtuse triangles. The circumcenter coincides with the midpoint of the hypotenuse if it is an isosceles right triangle.
Simplify the polynomial then evaluate for x=-1 3x^2-4+2x-1+x^2
Answers
Answer:
-3
Step-by-step explanation:
Simplified polynomial: 4x^2 + 2x - 5
Plug in -1: 4(-1)^2 + 2(-1) - 5
= -3
Help picture below problem 9
Answers
Answer:
i think the answer might be E.
the answer is A option that is Angle M
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
EG = 6 in.
Step-by-step explanation:
EG is congruent to DF and DF is 6 in. so EG would be 6 in.
Answer:
6 in.
Step-by-step explanation:
DF's length is congruent ( same ) to EG's length which is shown by the one mark on each side
Since DF's length is 6 inches, EG's length is also 6 inches.
Therefore,the answer is 6 in( inches )
Hope this helps!
Please mark as brainliest!!!
Please Expand the following y( y + 2)
Answers
Answer:
[tex]y^{2} + 2y[/tex]
Step-by-step explanation:
y times y is [tex]y^{2}[/tex]
2 times y is 2y
PLS HELPP- I NEED AN ANSWER ASAP BRAINLY WILL BE GIVEN~
