Simplify by combining like terms. Write the answer with the variables in alphabetical order and any constant term last.
a+ ab^3 + ab^3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. a+ ab^3 + ab^3 simplifies to [ ]
O B. The expression cannot be simplified.
Answers
a+ ab³ + ab³ simplifies to 2ab³+a.
For simplifying the terms first we have to add Like Terms.
Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.
In Algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
So hence we will add ab³ + ab³= 2ab³
For any given term, we almost always list the variables in alphabetical order and any constant terms last — this is helpful in identifying common terms, a topic discussed in the next section. So, for example, it is simply not cool to write 15yx, 15 y x , we want to stay alphabetical and write 15xy. Exponents play no role in this decision.
Therefore a+ ab³ + ab³ simplifies to 2ab³+a.
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Related Questions
Brian earns $5 per hour babysitting. He makes a graph and plots what he
earns for different numbers of hours. He places the number of hours he
works on the x-axis and his earnings on the y-axis. What is the slope of the
line that Brian graphs?
Answers
Answer:
The slope of the line is 5
Step-by-step explanation:
When we talk of the slope of a straight line graph, we refer to the rate at which the values on the y-axis changes as a ratio of the changes we have on the x-axis
Now, from the question, number of hours is placed on x-axis, while we have the amounts on the y-axis
having $5 per hour means the rate of change of what is earned to number of hours worked is 5 and this is the slope of the line
Exercise 10
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. What is the probability of the compound event? Write your answer as a fraction or percent rounded to the nearest tenth.
Answers
The probability of choosing a 5 and then a 6 is 1/49
Finding the probability of the compound eventFrom the question, we have the following parameters that can be used in our computation:
The tiles
Where we have
Total = 7
The probability of choosing a 5 and then a 6 is
P = P(5) * P(6)
So, we have
P = 1/7 * 1/7
Evaluate
P = 1/49
Hence, the probability of choosing a 5 and then a 6 is 1/49
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Question
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6
They are selling lollipops for $0.50 and candy bars for $1.50
Lydia buys 6 lollipops and some candy bars.
If she spends $15.00 in total, how many candy bars, b, did Lydia buy?
Answers
If you times 6 by 50 then you get $3.00 that is the answer for the lollipop you have to minus $15.00 by $3.00 which is $12.00
A rectangular box with a square base, an open top, and a volume of 32,000 cm3 is to be made. What is the minimum surface area for the box
Answers
the minimum surface area for the box is 4800 cm².
Forming the Equation of SurfaceArea
It is given that the given rectangular box is square-based and top is open. hence, it consists of square and 4 rectangles.
Let the side of the square be a, and height of the box be h.
Then, the total surface area of the box will be given by,
S = a² + 4ah _________ (1)
Also, it is given that the volume of the box is, V = 32000 cm³
The volume of the rectangular box, V = a² h
Eliminating One of the Variables From the Equation
The volume of the rectangular box, V = a² h
⇒ a² h = 32000
⇒ h = 32000/a² _______ (2)
Substituting this value of h in equation (1), we get,
S = a² +4a(32000/a²)
S = a²+128000/a
Minimizing the Surface Area Equation
To find the minima, put, dS/da = 0
dS/da = 2a-128000/a²
⇒ 2a-128000/a² = 0
Multiplying the whole equation with a², we get,
2a³-128000 = 0
⇒ 2a³ = 128000
⇒ a³ = 128000/2
⇒ a³ = 64000
⇒ a = 40 cm
Calculating the Minimum Surface Area
From, equation (2), h = 32000/(40)²
h = 32000/1600
h = 20 cm
Now, substituting the computed values of a and h in equation (1), we get,
S = (40)² +4(40)(20)
S = 1600 +3200
S = 4800 cm²
∴ The minimum surface area of the box is 4800 cm².
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let x(t) = cos(75t). if we sample x(t) at the nyquist frequency, what is the resulting discrete frequency
Answers
If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.
In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.
Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.
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High clouds are those that form at altitudes of at least:
65,617 ft (20,000 m).
32,800 ft (10,000 m).
6500 ft (2000 m).
20,000 ft (6000 m).
Answers
High clouds are those that form at altitudes of at least 20,000 ft (6000 m).
At high altitudes, ice crystals form due to which cloud formation occurs. Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.
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Please help!
Thank you!
Answers
Answer: i think the answer is C
maybe this will work
Step-by-step explanation:
Rewrite the following equation in slope-intercept form.4x – 3y = -12please show how
Answers
The equation of line in slope-intercept form is,
\(y=mx+c\)Here, m is slope of line and c is y-intercept.
Simplify the equation to obtain the slope-intercept form.
\(\begin{gathered} 4x-3y=-12 \\ 4x+12=3y \\ y=\frac{4x}{3}+\frac{12}{3} \\ =\frac{4}{3}x+4 \end{gathered}\)A cylindrical swimming pool is approximately 12 feet wide and 4 feet deep. About how many gallons of water can the swimming pool contain? Remember that 1 cubic foot is approximately 7.48 gallons.
Answers
Answer:
Step-by-step explanation:
Since the swimming pool is cylindrical, we would find its volume by applying the formula for determining the volume of a cylinder which is expressed as
Volume = πr²h
Where
r represents radius of the cylinder
h represents height
π = constant = 3.14
From the information given,
Diameter = 12 feet
Radius, r = diameter/2 = 12/2 = 6 feet
h = 4 feet
Volume = 3.14 × 6² × 4 = 452.16ft³
Since 1 cubic foot is approximately 7.48 gallons, the number of gallons of water that the swimming pool can contain is
452.16 × 7.48 = 3382.16 gallons
Find the slope of a line with the cordnates of (6,1) and (-3,5)
Answers
Answer:
Answer:
Slopem=−49
As a decimal:
m = -0.444444
Step-by-step explanation:
Slope m with two points
Graph of the line for y = mx + b
Point Slope Form y - y1 = m(x - x1)
Slope Intercept Form y = mx + b
Standard Form Ax + By = C
y-intercept, when x = 0
x-intercept, when y = 0
The smaller triangle is dilated to create the larger triangle. The center
of dilation is plotted, but not labeled.
Answers
Answer:
Point D is the point of dilation.
Step-by-step explanation:
If the smaller triangle A'B'C' is dilated to form a larger triangle ABC by the dilation about point D,
Ratio of the DA and DA' will be equal to the ratio of DB and DB'.
Length of DA = 3 units
Length of DA' = 1 unit
Coordinates of D → (3, 0)
Coordinates of B → (9, 3)
Coordinates of B' → (5, 1)
Use the formula of distance between the two points to find find the length of DB and DB'
Length of DB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(3-0)^2+(9-3)^2}\)
\(=\sqrt{45}\)
\(=3\sqrt{5}\)
Length of DB' = \(\sqrt{(5-3)^2+(1-0)^2}\)
\(=\sqrt{5}\)
Ratio of DB and DB' = \(\frac{3\sqrt{5} }{\sqrt{5} } =3:1\)
Ratio of DA and DA' = 3 : 1
Since, \(\frac{DA}{DA'}=\frac{DB}{DB'}\)
Therefore, smaller triangle is dilated by a scale factor of 3 to form the bigger triangle about the point D.
What is the volume of the following rectangular prism?
Answers
Answer:
1/10 units ^3
Step-by-step explanation:
The formula for the volume is given by
V = Bh where B is the area of the base and h is the height
V = 3/20 units ^2 * 2/3 units
= 3/20 * 2/3
= 1/10 units ^3
Determine the magnitude of the resultant vector of two forces of \( 54 {~N} and \( 34 {~N} acting at an angle of \( 55^{\circ} to each other. Show all your work. [ 10 marks]
Answers
The magnitude of the resultant vector of the two forces is approximately 67.84 N.
To find the magnitude of the resultant vector, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the included angle.
Let's denote the two forces as \(F_1 = 54~N\) and \(F_2 = 34~N\), and the angle between them as \(\theta = 55^\circ\).
Using the law of cosines, we can calculate the magnitude of the resultant vector (\(R\)) as follows:
\(R^2 = F_1^2 + F_2^2 - 2 \cdot F_1 \cdot F_2 \cdot \cos(\theta)\)
Substituting the given values, we have:
\(R^2 = 54^2 + 34^2 - 2 \cdot 54 \cdot 34 \cdot \cos(55^\circ)\)
\(R^2 = 2916 + 1156 - 2 \cdot 54 \cdot 34 \cdot 0.5736\)
\(R^2 = 4072 - 3716.4168\)
\(R^2 \approx 355.5832\)
Taking the square root of both sides, we find:
\(R \approx \sqrt{355.5832}\)
\(R \approx 18.87~N\)
Therefore, the magnitude of the resultant vector is approximately 18.87 N.
The magnitude of the resultant vector of two forces, one with a magnitude of 54 N and the other with a magnitude of 34 N, acting at an angle of 55 degrees to each other, is approximately 18.87 N. This value was obtained using the law of cosines to calculate the magnitude of the resultant vector. It is important to note that the direction of the resultant vector is not determined by this calculation, as it only provides the magnitude. To determine the direction, one would need to consider the angles and orientations of the individual forces.
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1) What is the simple interest if Principal = $100, Rate = 5% and time = 3 months?
2) Find the simple interest given that Principal = $900, Rate = 5% andd Time =1 year 4 months.
Answers
Answer:
1. 1.25, 2. $60
Step-by-step explanation:
1. 100 x .05=$5 interest/year
$5/12=.42 interest per month
.42x3 =1.25 interest for 3 months
2. 900 x .05=$45 interest/year
$45/12=3.75 interest/month
$3.75 x 16 months=$60 interest/16 months
please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6
Answers
Answer:
Below.
Step-by-step explanation:
Step 1: it is 5 x 10^-6 not 5 x 10^-5.
Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.
Answer: yes that is correct explanation:
A standard subdivision consists of subdivisions with ___________ parcels. ten or fewer four or fewer exactly two five or more
Answers
A standard subdivision consists of subdivisions with four or fewer parcels.
In a standard subdivision, the number of parcels is limited to four or fewer. This means that each subdivision within the standard subdivision will have a maximum of four parcels.
So, if you are looking for a standard subdivision, you can expect to find subdivisions with four or fewer parcels.
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What are pyramidal sequences? How do they work, and can I have some examples of ones? What are their recursive and explicit formulas, and how do solve them with and without knowing the number of layers?
For context, I was faced with a problem earlier. The issue with it is that I knew how many balls were in the pyramid(300) but not how many layers, I had no clue how to solve it.
the problem goes as such:
As a project for his high school's science fair, Miguel wants to construct a stack of ping-pong balls in the shape of an ancient pyramid. For a budget of $30, he can purchase 300 balls. how many layers are in the tallest pyramid he can build?(He will have some balls left over.)
Answers
Answer:
See belowStep-by-step explanation:
This is about the arithmetic progression.
The sequence will be:
1, 3, 5, 7, ...The common difference here is d= 2
Recursive formula:
a₁ = 1, aₙ = aₙ₋₁ + 2Explicit formula:
aₙ = 1 + (n - 1)*2 = n - 1Sum of the first n terms:
Sₙ = (a₁ + aₙ)*n/2 = (2a₁ + (n - 1)d)*n/2 = (2 + 2n - 2)*n/2 = 2n*n/2 = n²We need to find the nearest perfect square smaller than 300.
This is 289 = 17².
There will be 17 layers and 11 balls left over.
When conducting a scientific investigation, how many variables should be tested?.
Answers
An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.
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Do y’all know the answer of (3 ^ 4) ^ 5 in exponential form
Answers
Answer:
\(3^{20}\)
Step-by-step explanation:
Answer: Hi that would be 3^9, but since it has a parantheses it becomes 3^20, hope this helps.
A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.
Answers
Slope is $0.15 of the equation of cost C=$0.15t+$35.00.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that A cell phone company uses the equation C=$0.15t+$35.00
C is the total cost for a month of service.
t is the number of text messages.
We have to find the slope of the equation.
slope is 0.15 and 35.00 is the y intercept of the equation given.
Hence, slope is $0.15 of the equation of cost C=$0.15t+$35.00.
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What is the role of parentheses in expressions containing exponents?
Answers
Step-by-step explanation:
the quantity inside the parentheses is being multiplied by itself the number of times the outside exponent
pls help I’m stuck on this
Answers
Answer:
Step-by-step explanation:
Find the distance to walk along the arc NQ
⇒I think it will be 12Find the area inside one of the 4 sectors
⇒ Circle area = π * r² = π * 36 [cm²] ≈ 113.1 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 6 [cm] * 2 = 12 [cm]
= 113.1Find the distance to walk along the following path: Start at point P and go to R then to Q and over to N then back to P:
= 36 Hope this helps Mark me as Brainelist PleaseFind three solutions of the equation. y=-2x-1 a. (–2, 3), (1, –3), (2, –4) c. (1, –3), (0, –1), (–1, 0) b. (–2, 3), (1, –3), (0, –1) d. (0, –1), (3, –9), (–2, 3)
Answers
The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).
To find the solutions, we substitute different values of x into the equation and solve for y.
For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).
For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).
For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).
These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.
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can I please get help with this question
Answers
Answer:
I think B honestly because when your doing slope you want each dot to add up and still go on the line
Step-by-step explanation:
Answer:
A. -1/3 y-intercept 3
Step-by-step explanation:
Slope Formula: y2-y1/x2-x1
Find 2 coordinates
(-3,4) (3,2)
y2=2
y1=4
y2-y1
2-4=(-2)
x2=3
x1=-3
3-(-3)=(6)
-2/6= -1/3
Hope this helps!
Study Island Congruence Which series of transformations shows that hexagon A is congruent to hexagon B? A. Rotate hexagon A 180° counterclockwise about the origin, reflect it over the y-axis, and translate it 3 units to the right. B. Translate hexagon A 3 units down, rotate it 90° counterclockwise about the origin, and translate it 3 units to the right. C. Reflect hexagon A over the x-axis, reflect it over the y-axis, and translate it 3 units down. D. Reflect hexagon A over the x-axis, rotate it 90° counterclockwise about the origin, and translate it 3 units to the right.
Answers
The series transformation that shows congruency is D, Reflect hexagon A over the x-axis, rotate it 90° counterclockwise about the origin, and translate it 3 units to the right.
How to describe congruency?To show that two polygons are congruent, we need to perform a series of rigid transformations (translations, rotations, and reflections) that will map one polygon onto the other.
In this case, hexagon A can be mapped onto hexagon B through the following transformations:
Reflect hexagon A over the x-axis
Rotate the resulting polygon 90° counterclockwise about the origin
Translate the resulting polygon 3 units to the right
These transformations preserve the size and shape of the polygon, and they map every point of hexagon A onto the corresponding point of hexagon B. Therefore, we can conclude that hexagon A is congruent to hexagon B.
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PLS HELP WILL GIVE BRAINLY!!
What is the weight (in grams) of a liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135grams over milliliter? Round to the nearest hundredth when necessary, and only enter numerical values, which can include a decimal point
Answers
Answer:
Step-by-step explanation:
1 milli liter = 0.135 grams
182.8 ml = 0.135 * 182.8 = 24.678 grams
Answer:
24.678
Step-by-step explanation:
Hope this helps :)
Diana had a coupon for c dollars off of
each box of crackers. Diana bought 2
boxes of crackers for 4.50 – c dollars
each. She also bought 8 cans of soup
for s dollars each. The total amount, in
dollars, she spent on the cans of soup
and boxes of crackers is represented by
the expression below.
2(4.50 – c)+8s
Which expression also represents the
total amount, in dollars, she spent?
A.6.50 – 2c + 8s B. 6.50 – 2c + 10s
C. 9 – c + 8s D. 9–2c + 8s
Answers
Answer:
d. 9 - 2c + 8s
Step-by-step explanation:
we can distribute the two by multiplying it by both 4.50 and -c. our result will be 9 and -2c. simply combine that with the 8s that we already had, and we end up with 9 - 2c + 8s.
An engineer at Shoefactory, Inc. wants to calculate the cycle time (time to make one unit) for a process based on work sampling observations of workers performing the job. The standard deviation for the process times is 0.4 minutes, based on a small sample of observations which she took. If the engineer wants to be 95% confident of being in error by only 0.125 minutes, what sample size should she take?
For continuous data:
E=(zα2)(σn)
For attribute data:
E=(zα2)p(1-p)n
Answers
The engineer should take a sample size of approximately 40 to be 95% confident of being in error by only 0.125 minutes.
To calculate the sample size for estimating the cycle time, the engineer can use the formula for continuous data:
E = (zα/2) * (σ / √n)
where:
E is the maximum allowable error (0.125 minutes),
zα/2 is the z-value for a 95% confidence level (which corresponds to a 0.025 alpha level),
σ is the standard deviation (0.4 minutes), and
n is the sample size (unknown).
Rearranging the formula, we have:
n = (zα/2)^2 * (σ^2 / E^2)
Plugging in the given values, we get:
n = (1.96)^2 * (0.4^2 / 0.125^2)
Simplifying the equation, we have:
n ≈ 3.8416 * (0.16 / 0.015625)
n ≈ 3.8416 * 10.24
n ≈ 39.494
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The table shows the number of minutes Jalen talks on his mobile phone and the cost of the phone calls. Jalen’s Mobile Phone Cost Number of minutes, x 150 220 250 275 Cost, y $7. 50 $11. 00 $12. 50 $13. 75 If the cost varies directly with the number of minutes Jalen talks on the phone, which equation represents the variation? y = 0. 05 x y = 20 x y = 157. 5 x y = 1125 x.
Answers
If the cost varies directly with the number of minutes Jalen talks on the phone, we can use the equation y = kx, where y represents the cost, x represents the number of minutes, and k is the constant of variation.
To determine the value of k, we can choose any of the given data points to substitute into the equation.
Let's use the first data point: Number of minutes, x = 150 and Cost, y = $7.50.
Substituting these values into the equation, we have:
$7.50 = k * 150
To solve for k, we divide both sides of the equation by 150:
k = $7.50 / 150
k = 0.05
Therefore, the equation that represents the variation is y = 0.05x.
Out of the given options, the equation y = 0.05x is the correct representation of the variation between the cost and the number of minutes Jalen talks on his mobile phone.
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HELP PLEASE!!!!!!!!!!!
Answers
Answer:
i think the answer should be c