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
Betty has some bottles.
4
7
of the bottles are big and
4
5
of the remaining bottles are small. The rest of the bottles are tiny.
What fraction of the bottles are tiny?
Answers
MAX POINTS PLEASE HELP Will make Brainliest
What is the period and frequency of the function graphed and how would the equation be written??
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The required equation is :
[tex]\qquad \sf \dashrightarrow \:y =a \cos(bx) + k[/tex]
Now, let's find the required values :
period (p) = 6
[distance between any successive Crest or trough]
a = - 4 (flipped)
b = 2π/p = 2π/6 = π/3
k = -2
Distance of starting position from origin = k
Now, plug in the values ~
[tex]\qquad \sf \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]
There is not crest given so use distance between troughs
Period (T):-
Distance between two troughs|3-(-3)|6Frequency:-
[tex]\\ \rm\dashrightarrow \dfrac{1}{T}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{1}{6}[/tex]
[tex]\\ \rm\dashrightarrow 0.17Hz[/tex]
convert the following units to the units in bracket 12m (to cm)
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We are converting 12 meters into centimeters.
A meter is a larger unit of messurment then centimeter. In fact, a meter is made up of many centimeters
How many centimeters are in a meter?
We can look at the word composition of the word centimeter to figure this out:
centimeter
centi = 100
There are 100 centimeters in 1 meter.
In this problem, we have 12 meters. That is twelve 100 cm or:
12 × 100 = 1,200
12 meters is the same as 1,200 centimeters
1 meter = 100 centimeter
So ,
12 m = 12 × 100 = 1,200 centimeter
The hands of a clock suggest an angle whose measure is continually changing. How many degrees does a minute hand move through during 4 -minute time interval?
In 4 -minute time interval a minute hand moves __ degrees.
Answers
Step-by-step explanation:
oh, come one ! you can literally see that one ...
a full rotation on a clock is a full circle and stands therefore for 360°.
for the minute hand these 360° represent 60 minutes.
4 minutes of 60 is a fraction, a ratio, and the same ratio applies then also to 360°.
4/60 = 1/15
360 × 1/15 = 24°
so, 4 minutes represent 24°.
Answer:
Wow no reasonable explanaition for why you don't know this answer but here it is.
360*
Step-by-step explanation:
Moderne Furniture Company had sales of $2,000,000 during its first year of operation. If the sales increased by $200,000/year thereafter, find Moderne's sales in the fifth year and its total sales over the first 5 years of operation.
Answers
The graph of the relation H is shown below.
Give the domain and range of
H
Write your answered using set notation
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Using the concepts of domain and range, it is found that:
The domain of the relation is {-1, 2, 3, 4}.The range of the relation is {-1, 0, 2, 4}.What are the domain and range of a relation?The domain of a function is the set that contains all possible input values. On a graph, it is given by the values of x.The range of a function is the set that contains all possible output values. On a graph, it is given by the values of y.In this graph, the points represented are given by: {-1, 2}, {2,0}, {3,-1} and {4,4}. Hence:
The domain of the relation is {-1, 2, 3, 4}.The range of the relation is {-1, 0, 2, 4}.More can be learned about the concepts of domain and range at https://brainly.com/question/10891721
How do you solve this
Answers
A + B = 12 miles
Beth and Candace combined ran 34% of the total distance.
B + C = 10.2 miles
Candace and John combined ran 40% of the total distance.
C + J = 12 miles
John and Pat combined ran 41% of the total distance.
J + P = 12.3 miles
A + B + C + J + P = 30
A + (10.2-C) + C + J + (12.3-J) = 30
A + 10.2 + 12.3 = 30
A = 7.5 miles
B = 12 - 7.5 = 4.5 miles
C = 10.2 - 4.5 = 5.7 miles
J = 12 - 5.7 ] = 6.3 miles
P = 12.3 - 6.3 = 6 miles
3125 - [72 - 4(11 - 4)]} =
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Answer:
25
Because its right
also I just took a test that has this problem.
6. following activities: has 9 hours of free time on Sunday, find how much time he spends on the The circle graph shows the percentage of Nathan's free time on Sunday. If Nathan 1. Percent spent on Reading: Free Time % 2. Time spent on Reading: Drawing Reading 25% 3. Time spent on Drawing: 4. Time spent Exercising: Watching Television 25% Exercising 30% 5. Time spent watching TV:
Answers
Answer: add them
Step-by-step explanation: your welcome to get a tutor
what is the slope of the line that passes through the points (-1,1) and (1,-15)
Answers
Answer:
[tex]\boxed{\text{The slope is -8.}}[/tex]Step-by-step explanation:
To find the slope of the line, you have to use a slope formula.
Slope formula:
[tex]\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
⇒ y2=(-15)
⇒ y1=1
⇒ x2=1
⇒ x1=(-1)
Rewrite the whole problem down.
[tex]\Longrightarrow: \sf{\dfrac{-15-1}{1-\left(-1\right)}=\dfrac{-16}{2}=\boxed{\sf{-8}}[/tex]
So, the slope is -8, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Can someone help me?
Answers
Answer:
(i) [tex]y = 2x(x-5)[/tex]
(ii) zeros: x = 0 and x = 5
axis of symmetry: x = 2.5
(iii) vertex: (2.5, -12.5)
(iv) see attached
Step-by-step explanation:
Part (i)
Factor: [tex]y=2x^2-10x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies y=2x(x-5)[/tex]
Part (ii)
Zeros occur when [tex]y=0[/tex]
[tex]\implies 2x(x-5)=0[/tex]
Therefore:
[tex]\implies 2x=0 \implies x=0[/tex]
[tex]\implies (x-5)=0 \implies x=5[/tex]
So the zeros are x = 0 and x = 5
The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.
[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]
Therefore, the axis of symmetry is [tex]x=2.5[/tex]
Part (iii)
The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.
[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]
So the vertex is (2.5, -12.5)
Part (iv)
Plot the zeros and the vertex.
As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.
Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.
*see attached*
A triangle is graphed on the coordinate grid below.
What are the coordinates of the image of this triangle after a dilation, with a center of dilation at the origin and a scale factor of 2.
Explanation please!! Thank you
Answers
Answer:
The answer is D
Still stuck? Get 1-on-1 help from an expert tutor now.
Step-by-step explanation:
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
y = -x - 4
Step-by-step explanation:
Help picture below problem 18
Answers
Answer:
X⁶
Step-by-step explanation:
x⁹/x³
= x⁹-³
= x⁶ is the answer
Answer:
E. [tex]x^{6}[/tex]
Step-by-step explanation:
To divide two fractions we subtract the power of second expression from the first one:
[tex]x^{(9-3)} = x^{6}[/tex]
help me help me help me
Answers
Answer:
For the third one,
3, 8, 15, 24, 35, 48, 63
For the fourth one,
4, 6, 10, 18, 30, 46, 66
Step-by-step explanation:
Prove. An odd number cubed is an
odd number.
Answers
Answer:
If you're looking for the equation, it's:
[tex](2n+1)^3=8n^3+12n^2+6n+1=2(4n^3+6n^2+3n)+2=[/tex] an odd
I know because I got it right on acellus.
A rectangle has a length of 15 cm and a width of 11 cm. What is its perimeter?
54 cm
52 cm
165 cm
26 cm
Answers
Answer:
52 cm
Step-by-step explanation:
perimeter = 2(length) + 2(width) for a rectangle.
2(15)+2(11)=52 cm
Answer:
52
Step-by-step explanation:
i got 100% on the quiz i got all the answers
1. Mark practices the piano for 2/3 of an hour, 6 times a week. How many hours does
he practice each week?
Answers
Answer:
4 hours
Step-by-step explanation:
2/3*6/1= 12/3
12/3 simplified is 4
Explanation: 2/3 of an hour = 40 minutes
40 times 6 = 240 minutes
240 (minutes) / 6 (hours) = 4 hours practiced each week
Hope this helps :)
in 1977, Pistol Pete Maravich led the NBA with 2273 points. In 2006, Kobe Bryant led the NBA with 2832 points. However, there were many differences between basketball in 1977 and basketball in 2006, including the number of teams and possibility of a three-point shot. The mean number of points for the top 110 players in 1977 was 1198 points with a standard deviation of 379 points. The mean nimber of yards for the top 150 players in 2006 was 1123 points with a standard deviation of 433 points. Who had the better performance, Maravich or Bryant? Explain your reasoning.
Answers
Using z-scores, it is found that due to the higher z-score, Bryant had the better performance.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The above bullet point means that higher z-scores mean a better performance.For Maravich, we have that the parameters are [tex]X = 2273, \mu = 1198, \sigma = 379[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2273 - 1198}{379}[/tex]
Z = 2.84.
For Bryant, we have that the parameters are [tex]X = 2832, \mu = 1123, \sigma = 433[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2832 - 1123}{433}[/tex]
Z = 3.95.
Due to the higher z-score, Bryant had the better performance.
More can be learned about z-scores at https://brainly.com/question/24663213
I need help with this please
Answers
Answer:
4 and 7
2 and 5
Step-by-step explanation:
4 and 7 are co interior angles
2 and 5 are co interior angles
sum of co interior angles are 180° hence they are Supplementary
Find the value of x
A. 4
B. 10
C. 17
D. 25
Answers
Answer:
X can be any of those numbers depending on which equation it is in
Step-by-step explanation:
Which of the following numbers is the smallest?
1/3
3/10
2/5
3/8
Answers
Answer:
3/10
Step-by-step explanation:
Taking the decimal values (upto the thousandths place)
1/3 = 0.333/10 = 0.32/5 = 0.43/8 = 0.375Clearly,
0.3 < 0.33 < 0.375 < 0.40.3 is the smallest3/10 is the smallest3/10 is the smallest number among the given options.
Given that are numbers we need to check which is the smallest from this,
To determine which of the given numbers is the smallest, we can compare them by finding a common denominator and then comparing the numerators.
The common denominator for 1/3, 3/10, 2/5, and 3/8 is 120 (the least common multiple of 3, 10, 5, and 8).
Now, let's convert each fraction to have a denominator of 120:
1/3 = 40/120
3/10 = 36/120
2/5 = 48/120
3/8 = 45/120
Comparing the numerators, we can see that 36/120 (3/10) is the smallest.
Therefore, 3/10 is the smallest number among the given options.
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Which shows how to determine the volume of the pyramid?
10 cm
8 cm
12 cm
V-3(1268)(10)
OV-2(12)(10)
8
V-=(12(B)(10)
Answers
Answer:
V = 1/3(12×8×10)
Step-by-step explanation:
V= 1/3×base area×height
V = 960/3
V = 320cm^3
The volume of the pyramid is,
⇒ V = 320 cm³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Height of pyramid = 10 cm
Length of pyramid = 12 cm
Width of pyramid = 8 cm
Hence, We get;
The volume of the pyramid is,
V= 1/3 × base area × height
V = 1/3 (12×8×10)
V = 960/3
V = 320 cm³
Thus, The volume of the pyramid is,
⇒ V = 320 cm³
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Find the equation of the line that contains the point (4, - 2) and is perpendicular to the line y = - 2x + 5.
Answers
y=1/2x
Solution:The slopes of perpendicular lines are opposite reciprocals of each other.The simplest way to determine a number's reciprocal is to flip it over, like so:[tex]-2 ~ - > -\displaystyle\frac{1}{2}[/tex]Now, change the sign:[tex]\displaystyle\frac{1}{2}[/tex]So we have the slope of the line that's perpendicular to the given line.Now, let's find the line's equation.First, let's write it in Point-Slope Form:y-y1=m(x-x1)y-(-2)=1/2(x-4) y+2=1/2x-2 (Point slope)Now, convert to slope-intercept:y=1/2x+2-2y=1/2xHope it helps.
Do comment if you have any query.
Answer:
y=1/2x
Step-by-step explanation:
Solve the system using the linear combination method:
x + 5y= -3
2x + 7y=3
Answers
Answer:
3x+12y=0
Step-by-step explanation:
x+2x=3x
5y+7y=12y
-3+3=0
If 12% of a number is 30, find 4% of that number.
Answers
12%= 30
-> 100%= 30÷12×100
-> 100%= 250
4% of 250
-> 4%=250÷100×4
-> 4%= 10
Bethany is making a rectangular fenced-in area for her rabbit in her yard. The area measures 4 3/4 feet wide by 2 yards long. What is the total length of fencing, in feet, that Bethany will need?
Answers
PLEASE HELP PLEASE HELP PLEASE
Answers
Answer:
False
Please make this brianliest so others can learn from this answer
Happy to help :)
Step-by-step explanation:
The segments shown below could form a triangle.
д
C
B
9
11
B
C
O A. True
B. False
Answers
Answer:
hi the answer is true
Step-by-step explanation:
hope it helps
The triangle can be formed using the given line segments. Therefore, the given statement is true.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, line segments AC=9 units, BC=4 units and AB=11 units.
If a, b and c are the lengths of the sides of a triangle then
If a ≤ b ≤ c, then a + b > c.
9+4>11
13>11
Therefore, the given statement is true.
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Find the surface area of the pyramid.
Answers
Answer:
i think the answer is 87.
Step-by-step explanation:
i think its 87.