a(n)= 2 3 (−2) n−1
Determine the product of (x-2)^3
The profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).
What are expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical expression for "4 added to 2" will be 2+4.So, (x-2)³:
Do, the product as follows:
(x-2)³Perfect cube root formula: (a - b)³ = a³ - 3a²b + 3ab² -b³
x³ - 3x² · 2 + 3x · 2² -2³Simplify:
x³ - 6x² + 12x - 8Therefore, the profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).
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Jacinda works at Super Shoes and earns
a commission for her sales. A customer
purchases $259.50 in shoes, and
Jacinda receives $31.14 in commission.
What percent commission does Jacinda
earn?
Jacinda get 12% of commission
How to find percentage :
The cost of shoe that customer purchased is $259.50
The amount that Jacinda get commission is $31.14
To calculate the percentage of commission divide 31.14 by 259.50 and multiply by 100.
That is percentage of commission = 31.14/259.50 * 100
= 12%
Jacinda get 12% of commission.
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%. To find 50 apples as a percentage of 1250 apples, one first computes the ratio 50/1250 = 0.04, and then multiplies by 100 to obtain 4%.To learn more about percentage refer :
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6 more than the difference of p and 3
Do not simplify any part of the expression.
I'm pretty sure it's 6>p-3
2x²-11x-21=0.using factorization method
The factors of the quadratic equation are found as the 7 and -3/2
What is termed as the factorization method?To factorize a number, use the factorization formula. Factorization is defined as the process of converting one entity into the a product of another entity, as well as factors, that when multiplied together yield the original number. The factorization method employs the basic factorization formula to simplify any algebraic and quadratic equation, where the equations are depicted as the product of factors rather than expanding the brackets.For the given question, the quadratic equation is give as;
2x² - 11x - 21 = 0
Find the factors of -21×2 = 42 such that on subtraction it gives -11.
2x² - 14x + 3x - 21 = 0
Take 2x common from the first two terms and 3 from the last two terms.
2x(x - 7) + 3(x - 7) = 0
Take (x - 7) common from the terms.
(x - 7)(2x + 3) = 0
Then,
x - 7 = 0
x = 7
and, 2x + 3 = 0
x = -3/2
Thus, the factors of the quadratic equation are found as the 7 and -3/2.
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b
2x - 15
3x + 5
Line a || Line b.
Use the diagram to write an equation and solve for x
Answer:
x= −20
Step-by-step explanation:
The solution is x = 38
The equation to measure the value of x is ( 2x - 15 )° + ( 3x + 5 )° = 180° and the value of x = 38 from the two angles
What are angles in parallel lines?
Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Same side exterior angles are supplementary
Given data ,
Let the first angle be represented as A
Now , the value of A is = ( 2x - 15 )°
Let the second angle be represented as B
Now , the value of B is = ( 3x + 5 )°
The angles A and B are on the same side of the exterior angles
And , lines a and b are parallel
So , When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary
Substituting the values in the equation , we get
( 2x - 15 )° + ( 3x + 5 )° = 180°
On simplifying the equation , we get
2x - 15 + 3x + 5 = 180
5x - 10 = 180
Adding 10 on both sides of the equation , we get
5x = 190
Divide by 5 on both sides of the equation , we get
x = 190/5
x = 38
Therefore , the value of x is 38
Hence , the value of x from the equation is 38
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A 12-ft-by-15-ft rectangular swimming pool has a 3-ft-wide no-slip surface around it. What is the outer perimeter of the no-slip surface?.
The outer perimeter of the no-slip surface is equal to 78 feet.
Perimeter is a term used to describe the sum of the outside edge lengths or it can also be described as the whole of the outer edge or boundary.
The outer perimeter of this swimming pool can be determined by adding 3 feet twice to all the sides of the rectangular swimming pool and then adding these sides together.
Since it is a 12-ft-by-15-ft rectangular swimming pool, this means that two sides of this swimming pool are 12 feet and two sides of this pool are 15 feet, therefore;
12 + 6 = 18
15 + 6 = 21
Now the perimeter can be determined by adding all the sides as follows;
18 + 21 + 18 + 21 = 78 feet
Hence, the outer perimeter of the no-slip surface is calculated to be 78 feet.
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Which rational number also belongs to the set of whole numbers
A 0.3333
B. -9
C. 0
D. 5/6
Answer:
0
Step-by-step explanation:
Whole numbers are 0.1.2.3... Follows that pattern forever.
What is the area of trapezoid ABCE?A20 mB16 mEDC25 msq m
Given data:
The given figure of the trapezium.
The expression for the area of the trapezium is,
[tex]\begin{gathered} A=\frac{1}{2}(20\text{ m+25 m)(16 m)} \\ =360m^2 \end{gathered}[/tex]Thus, the area of the given trapezium is 360 sq-m.
x/5 > 8 solve the inequality for x and simplify your answer as much as possible
Answer:
x = 40
Step-by-step explanation:
x = 8 x 5
x = 40
that's it
due wensday but prefered be done now
The correct statement about the function is the y-intercept is (0.71), and 71 represents the starting temperature.
What is the y-intercept?
A graph can be described as a pictorial representation of data. A graph has a y-axis and a x-axis. The x-axis in this question represents time and the y-axis is the temperature.
The function shown in the graph is a linear function. This is because the curve is a straight line. The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero. The y-intercept represents the initial temperature or the starting temperature.
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Which expression is equivalent to 4x - 2y = 6
Answer:
2y-4x=6
Step-by-step explanation:
it can be correct i dk
Solve for m/UVX.
Answer: m/UV X =
O
72°
42°
Submit Answer
The measure of angle UVX is 30°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. The arc is centered at the vertex and defined by the sides in the case of a geometric angle.
Given, measure of angle UVW = 72°
measure of angle XVW = 42°
So, the measure of angle UVX = 72° - 42° = 30°
Hence, the measure of angle UVX is 30°
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I need help 9th grade math
Answer:
A. y - 2 = 2/3 (x - 0)
Step-by-step explanation:
Find the equilibrium concentrations of a and b for a=2 and b=2 . assume that the initial concentration of a is 1.0 moll−1 and that no b is present at the beginning of the reaction.
The concentration of A 0.29M and Concentration B 0.755M that the initial concentration of a is 1.0 moll−1 and that no b is present at the beginning of the reaction.
a A (g)⇔ b B (g) k =2.4
when a= 1 and b= 1
A⇔B
initial 1 0
concentration
change -x +x
equilibrium 1-x x
concentration
so, k = [tex]\frac{B}{A}[/tex] = [tex]\frac{x}{1-x}[/tex]= 2.4
x = 2.4 (1-x)
x = [tex]\frac{2.4}{3.4}[/tex] = =0.755
The equilibrium concentration are
concentration of A = 1-x = 1- 0.755 = 0.29M
Concentration B = x = 0.755M
What is initial concentration?The first measured the concentration of the compound in the substance.
The best way to determine the rate constant k for a first-order half-life is to determine the half-life using experimental data. This is because the first-order half-life is independent of the initial concentration of its initial value. So based on the above relationship, the half-life of a first-order reaction does not depend on the initial concentration.
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Question 2 of 10
Use the quadratic formula to find the solution to the quadratic equation given
below.
9
ײ − 3x + 9/4 =0
PLEASE HELP
Answer:
using the quadratic formula
Step-by-step explanation:
x= 3/2
In a class of 20 students, 5 have a brother and 11 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who does not have a brother has a sister?
attempt 1 out of 2
Answer:
45%
Step-by-step explanation:
In a class of 20 students, 5 have a brother and 11 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who does not have a brother has a sister?
P (no bro / yes sis) = P(no bro) - P(sis and bro)
= 12/20 - 3/20
= 9/20
or 45%
Hi can i get help with this precal question please
Using a piecewise function, it is found that:
a. The rule is:
C(w) = 0.75w, 0 ≤ w ≤ 50.C(w) = 0.35w + 10, 51 ≤ w ≤ 75.C(w) = 0.2w + 7, w > 75.b. C(75) = 36.25.
c. C(100) = 27.
d. A practical domain for the function is integer values of w ≥ 0
e. A practical range the function is C(w) ≥ 0.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For 0 to 50 wristbands, which is the first definition of the function, the cost is of $0.75 per each wristband, hence the definition is:
C(w) = 0.75w, 0 ≤ w ≤ 50.
From 51 to 75 wristbands, which is the second defition of the function, the cost is of $0.35 per each wristband plus the $10 shipping fee, hence:
C(w) = 0.35w + 10, 51 ≤ w ≤ 75.
For more than 75 wristbands, which is the third definition of the function, the cost is of $0.2 per wristband plus the $7 shipping fee, hence:
C(w) = 0.2w + 7, w > 75.
The numeric values are as follows:
C(75) = 0.35 x 75 + 10 = 36.25.C(100) = 0.2(100) + 7 = 27.The domain and the range of the function are as follows:
Domain -> input values -> number of wristbands, which is a countable amount, hence integer numbers of 0 or greater.Range -> Output values -> cost of purchasing w wristbands, real values greater than 0.More can be learned about piecewise functions at https://brainly.com/question/19358926
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w + 2 < 24 solve for w and simplify your answer as much as possible
Answer: w<22
1. Group all constants on the right side of the inequality
2. Subtract from both sides
3. Simplify the arithmetic
4. Simplify the arithmetic
Answer:
w < 22
Step-by-step explanation:
w + 2 < 24
Step 1 : Subtract 2 on both sides.
w + 2 - 2 < 24 - 2
w < 22
Hence, simplified
Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days, she had nine
more than five times as many fruit flies as when she began the study. If she observes 20 fruit flies on the first
day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after
6 days.
The expression to find the population of fruit flies on 6th day in Lavania's laboratory can be (9+5x) where x is the number of fruit flies on the first day. After evaluating the expression, the number of fruit flies on 6th day will be 109.
According to the question,
We have the following information:
Lavania observes 20 fruit flies on the first day of her study.
On 6th day, the number of fruit flies would be nine more than 5 times as many fruit flies as when she begun her study.
Now, let's take the number of fruit flies on first day to be x.
So, we have:
x = 20
Now, the expression to find the number of fruit flies on 6th day would be:
9+5x
Now, putting the value of x:
9+5*20
9+100
109
Hence, the required expression is (9+5x) and the number of fruit flies on 6th day are 109.
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How does the graph of 2y−x=1 compare with the graph of 3y−x=1?
a.
The graph of 2y−x=1 has a steeper slope than the graph of 3y−x=1.
b.
The graph of 3y−x=1 has a steeper slope than the graph of 2y−x=1.
c.
The graph of 2y−x=1 crosses the x-axis farther to the left than the graph of 3y−x=1.
d.
The graph of 2y−x=1 crosses the x-axis farther to the right than the graph of 3y−x=1.
The way in which the graph of 2y − x = 1 compare with the graph of 3y − x = 1 is that: A. the graph of 2y − x = 1 has a steeper slope than the graph of 3y − x = 1.
What is a steeper slope?In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.
How to interpret the slope?Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m is the slope or rate of change.c is the intercept.For the graph of 2y − x = 1, the slope is given by:
2y − x = 1
2y = x + 1
y = x/2 + 1/2
Slope, m₁ = 1/2 or 0.5.
For the graph of 3y − x = 1, the slope is given by:
3y − x = 1
3y = x + 1
y = x/3 + 1/3
Slope, m₂ = 1/3 or 0.3.
Therefore, m₁ > m₂ (steeper slope).
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Round your answer to the nearest hundredth.A = 8.4 in²Calculate the diameter of the circle.O 3.27 inO 4.20 inO 1.75 inO2.89 in
The area of a circle can be calculated as follows:
[tex]A=\pi r^2[/tex]Using the area given in the problem and solving for the radius r:
[tex]\begin{gathered} A=8.4 \\ 8.4=\pi r^2 \\ \frac{8.4}{\pi}=r^2 \\ \sqrt{\frac{8.4}{\pi}}=r \\ 1.635=r \end{gathered}[/tex]Finally, the diameter is twice the radius:
[tex]\begin{gathered} d=2r \\ d=2*1.635 \\ d=3.27\text{ in} \end{gathered}[/tex]Then the answer is the first option 3.27 in
A television normally
costs $1,420. Due to
a store sale, the
television is now $994.
What was the
percentage taken off
the television?
A 30% percentage of the total price was taken off the TV.
What is the percentage?By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%. A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.So, the percentage is taken off from TV:
$1,420 - $994 = $426
Formula: (original price - decreased price)/original price × 100
Now, substitute values as follows:
(1420 - 994)/1420 × 100994/1420 × 1000.7 × 10070%Now, 100% - 70% = 30%
Therefore, a 30% percentage of the total price was taken off the TV.
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Simplify. 14(3x−7)+34x Responses 34x−1 3 over 4 end fraction x minus 1 334x−134 3 and 3 over 4 end fraction x minus 1 and 3 over 4 34x+212 3 over 4 end fraction x plus 2 and 1 half 112x−134
The simplified form of the given expression is option c 1 1/2x - 1 3/4
Given,
The expression; 1/4 (3x - 7) + 3/4x
We have to simplify this expression;
Simplification of expressions;
To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.
Then,
1/4 (3x - 7) + 3/4x
= 1/4 × 3x - 1/4 × 7 + 3/4x
= 3/4x - 7/4x + 3/4x
= 6x/4 - 7/4
= 3x/2 - 7/4
= 1 1/2x - 1 3/4
Therefore,
The simplified form of the given expression is option c 1 1/2x - 1 3/4
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Find the indicated measure. Assume that all segments that appear to be tangent are tangent.
We are asked to determine the arc length of HJ. To do that we will use the following formula:
Given two secant lines that intercept outside a circle as follows:
We have the following relationship:
[tex]\angle x=\frac{1}{2}(\text{mCD-mAB)}[/tex]Substituting the values we get:
[tex]29=\frac{1}{2}(96-\text{mHJ)}[/tex]Now, we multiply both sides by 2:
[tex]58=96-mHJ[/tex]Now, we subtract 96 from both sides:
[tex]58-96=-\text{mHJ}[/tex]Solving the operations:
[tex]-38=-\text{mHJ}[/tex]Now, we multiply both sides by -1:
[tex]38=\text{mHJ}[/tex]Therefore, the measure of the arc length of HJ is 38.
this is a super hard one
Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.
Answer: last option.
14. In exercise 13, suppose grapes cost
$2.35 per pound, oranges cost $0.99 per
pound, and apples cost $1.65 per pound.
Estimate how much Adrian paid for all
the fruit.
Assume grapes cost $2.35 per pound, oranges cost $0.99 per pound, and apples cost $1.65 per pound in exercise 13. Adrian paid a total of $5 for the fruits.
What is Estimation?Calculations are made easier and more realistically when a number is estimated, which is a plausible estimation of its true value.To estimate something is to approximate it as accurately as possible.To acquire a quick and approximate response, this is obtained by rounding off the values used in the calculation. Rounding integers to the closest whole number is the simplest method for estimating. Rounding off makes getting a rough answer quicker. Koel, for instance, makes a 3950 monthly deposit toward the cost of her new home. This value can be rounded out to 4000 to make the calculation easier. To round a number, determine its nearest required digit. To avoid working with fractions or decimals, numbers are frequently rounded to the next whole number.Therefore,
The cost of Grapes = $2.35 per pound
The cost of Oranges = $0.99 per pound
The cost of Apples = $1.65 per pound
If Adrian purchased one pound of each fruit,
He paid:
$2.35 + $0.99 + $1.65 = $4.99 = $5 (Approx.)
So, Adrian paid $5 in total for the fruits.
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Hello, I just need help with part b and it's dealing with combinations
According to the combination method, there are 6 ways for the selection to be made if one worker is to be a receptionist, one a secretary, and one a technical typist.
Combinations:
A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations.
The standard form for calculating the combinations is,
[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
where,
0 ≤ r ≤ n.
This formula is sometimes also called as ncr formula.
Given,
An executive hires 3 office workers from 8 applicants.
Here we need to find how many ways can the selection be made if one worker is to be a receptionist, one a secretary, and one a technical typist.
Here we have to split the problem like the following,
We know that the total number of office workers is 3.
Like, if one worker is to be a receptionist, the the combination is like,
So, the value of n = 3 and r = 1.
Then, according to the ncr formula,
=> ³C₁ = [tex]\frac{3!}{1!(3-1)!}[/tex]
=> 3!/1!2!
=> (3 x 2 x 1) / 1 x 2 x 1
=> 3
Similarly, if one worker is to be a secretary,
Here the value of n = 2 (Because we have already select one person as receptionist) and r = 1
So,
=> ²C₁ = (2!)/1!(2-1)!
=> (2x1)/ 1 x 1
=> 2
Similarly, if one worker is to be a technical typist,
Here the value of n = 1 (Because we have already select one person as receptionist) and r = 1
So,
=> ¹C₁ = 1
Therefore, the total number of possible ways are,
=> 3 x 2 x 1
=> 6
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PLEASE HELP MUST SHOW HAND WRITEN WORK
1. Kim's age is twice that of her sister.
(a) How can you represent Kim’s age with a mathematical sentence? (2pts)
When you add Kim's age to her sister's age, you get 36. How old is each sister?
(b) Write a mathematical equation that represents the situation above. Make sure to use part “a” to help you fill in Kim’s age. (4pts)
(c) Solve the equation in the space below for Kim’s sister’s age. (4pts)
(d) What is Kim’s sister’s age? (2pts)
(e) Use that information to solve for Kim’s age. What is Kim’s age? (3pts)
Answer:
a.) Let x be Kim's sister's age. Kim's age would therefore be 2x.
b.) 2x + x = 36
c.) 2x + x = 36
3x = 36
x = 12
d.) So Kim's sister (x) is 12.
e.) Since Kim's age is 2x, Kim is 24.
Step-by-step explanation:
See above.
a student reflects four point across the y ax is and recorded his work
Reflection across the y axis the y coordinate values remains the same but the x coordinates value changes sign. For example
[tex](x,y)\rightarrow(-x,y)[/tex]Therefore,
[tex]\begin{gathered} (6,8)\rightarrow(-6,8) \\ (1,1)\rightarrow(-1,1) \\ (0,3)\rightarrow(0,3) \\ (3,2)\rightarrow(-3,2) \end{gathered}[/tex]Set D has an error.