Expressions → Type of factoring
3x³ + 15x² + 2x + 10 → Grouping
x³ + 27 → Sum of cubes
2x² + 6x → Greatest common factor
x² - 25 → Difference of squares
x² + 6x + 8 → Unfoil
x³ - 1 → Difference of cubes
What is factorization?'Factor' is a term used to express a number as a product of any two numbers. Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.
Given expressions
3x³ + 15x² + 2x + 10Using grouping method
= (3x³ + 15x²) + (2x + 10)
= 3x²(x + 5) + 2(x + 5)
Factoring out common term
= (x+5)(3x² + 2)
x³ + 27It can be written as
= x³ + 3³
Which is sum of cubes
2x² + 6xit can be written as
= 2x.x + 2x.3
GCF (greatest common factor) = 2x
= 2x (x + 3)
x² - 25It can be written as
= x² - 5²
which is difference of squares
x² + 6x + 8= x² + 4x + 2x + 8
= x(x + 4) + 2(x + 4)
= (x + 4) (x + 2)
Which is unfoil.
x³ - 1it can be written as
= x³ - 1³
which is difference of cubes.
Hence, the factoring of expressions 3x³ + 15x² + 2x + 10, x³ + 27, 2x² + 6x, x² - 25, x² + 6x + 8, x³ - 1 refers to grouping, sum of cubes, greatest common factor, difference of squares, unfoil and difference of cubes respectively.
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(d) If every unit that the Acme factory produces is sold for $4, write a function R(x) that gives the
cumulative revenue of the Acme factory where x is the number of days since the start of 2018.
Include the units of the function's output.
Revenue is calculated by multiplying the number of units sold by the price per unit. Multiply the output level by the price function to get the revenue function.
What is revenue function?R is expressed as a function of x. Remember that revenue = price quantity. Because we want the revenue to be a function of x, we must express the price and quantity in terms of x. The number is straightforward; it is x.If x is the number of units sold, we will refer to these two functions as: R(x) denotes the revenue function, while C(x) denotes the cost function. As a result, our profit function equation will be: P(x) = R(x) - C (x).Profit is a function. P(x) is the profit made from selling x units of the commodity and is represented by the difference.So here R(x) = 4(x)
Where x = number of days.
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After 16 years in an account with a 5.9% annual interest rate compounded continuously, an investment is worth a total of $37,950.24. What is the value of the principal investment? Round the answer to the nearest penny. $14,765.24 $14,859.72 $23,185.00 $23,090.52
Answer: We can use the formula A = Pert to find the value of the principal investment P
Where A is the future value of the investment, r is the annual interest rate, t is the number of years, and e is the mathematical constant approximately equal to 2.718
In this case,
A = 37950.24, r = 0.059, t = 16
We can plug in the given values into the formula and solve for P:
37950.24 = P * e^(0.059 * 16)
To find the value of P we will divide both sides by e^(0.059 * 16)
P = 37950.24 / e^(0.059 * 16)
using the calculator to find the value of e^(0.059 * 16) gives 1.966862298
P = 37950.24 / 1.966862298
The value of P is $19,169.99.
Rounded to the nearest penny $19170
Therefore, the answer is $19,170.00
Step-by-step explanation:
Integer of 56 how many units is it away from 12
The number of units that the integer 56 is away from 12 is 44.
How to calculate the value?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The integer will be expressed as:
= 56 - 12
= 44
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Select the correct answer. Which statement best defines a circle? A. the set of all points in a plane that are the same distance from a given point called the center B. points in a plane that surround a given point called the center C. the set of all points that are the same distance from a given point called the center D. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
The statement that best defines a circle is A. the set of all points in a plane that are the same distance from a given point called the center.
what is a circle?A circle is a shape produced by all points on a plane that are at a fixed distance from the center. It is the curve sketched out by a point moving in a plane so that its distance from a given point is constant. The radius is the distance between any two points on a circle and its center.
A circle is a basic closed curve that splits the plane into two regions: inner and exterior. In daily parlance, the phrase "circle" can refer to either the figure's boundary or the entire figure, including its inside; in pure technical parlance, the circle is simply the boundary and the entire figure.
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If x and y are positive integers less than 10, and 3x + 2y = 13, using a guess-and check method, what could be the value of y?
Find one of the two possible correct answers. Enter a number for y only!
Hint: Substitute numbers in for x and y and find a pair that works!
y = ____
Step-by-step explanation:
we can do even a little bit better than wild guessing and trying.
3x + 2y = 13
tells us that the sum of 2 terms is an odd number.
that means one term has to be odd and the other even, as only then their sum will be odd.
2y is because of the included factor 2 an even number. always.
so, 3x has to be odd.
and that means x has to be odd too. because an even number multiplied with any number is always even.
so, x can only be 1 or 3. because 3×5 = 15 (3×7 = 21, 3×9 = 27) and already too big for the sum 13.
so, for x = 1 we have
3×1 + 2y = 13
3 + 2y = 13
2y = 10
y = 5
for x = 3 we have
3×3 + 2y = 13
9 + 2y = 13
2y = 4
y = 2
so, the answer is either y = 2 or y = 5.
Suppose that the world's current oil reserves is R = 2200 billion barrels. If, on average, the total reserves
are decreasing by 15 billion barrels of oil each year, answer the following:
A.) Give a linear equation for the total remaining oil reserves, R, in billions of barrels, in terms off, the
number of years since now. (Be sure to use the correct variable.)
R=-15t+2200
B.) 15 years from now, the total oil reserves will be 1975
✓billions of barrels
C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted all
used up) approximately 146.60
x years from now.
(Round your answer to two decimal places.)
age instructor
Answer:
54637737636553363666
Margaret has a monthly clothes budget of $50. She maps the amount of money she spends each month to the number of items of clothes she buys. what constraints are there on the domain?
Answer:The domain of Margaret's budget is the number of clothes she can buy.
The constraint on the domain is between 0 and the maximum number of clothes $50 can buy.
From the question, we understand that her budget is: $50.
The number of clothes she can buy is 0 or more.
And she cannot buy more than what $50 can afford.
This means that, the constraint on the domain is the amount of cloth she can purchase.
Step-by-step explanation:
becasue i know and i know i know
dividing complex numbers simplify
Answer:
Step-by-step explanation:
Determine the average rate of change of B from t = 0 $ to t = 332 s. Time (s) Concentration of A (M) 0 0.670 166 0.415 332 0.160
A -> 2B rateB =__________________ M/s
The rate of B is -0.003072 M/s.
The average rate of change is a measure of how much a quantity changes over a certain period of time. In this case, we are looking at the concentration of B, and we want to know how much it changes over the time interval from 0 to 332 seconds. To calculate this, we first need to determine the initial and final concentrations of B at these two points in time.
From the given data, we know that
the initial concentration of B at t = 0 is 0.670 Mthe final concentration of B at t = 332 s is 0.160 M.Once we have these values, we can calculate the change in concentration of B by subtracting the initial concentration from the final concentration: 0.160 M - 0.670 M = -0.510 M. This tells us that the concentration of B decreases by 0.510 M over the time interval from 0 to 332 seconds.
Next, we need to divide this change in concentration by the length of the time interval to get the average rate of change. The length of the time interval is the difference between the final and initial time: 332 s - 0 s = 332 s. So, the average rate of change of B is (-0.510 M) / (332 s) = -0.001536 M/s. This tells us that the concentration of B decreases by 0.001536 M per second on average over the given time interval.
As we know that the reaction is of form A -> 2B, the rate of formation of B is equal to twice the rate of A.
So, Rate of B = 2* Rate of A = 2*(-0.001536) = -0.003072 M/s
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Help Me please It's geometry
Answer:
D) [tex]28^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle EDQ+m\angle QDC=m\angle EDC \\ \\ 8x+4+31x-3=118 \\ \\ 39x+1=118 \\ \\ 39x=117 \\ \\ x=3 \\ \\ m\angle EDQ=8(3)+4=28^{\circ}[/tex]
In a classroom 1\6 of the students are wearing blue shirts,and 2/3 are wearing white shirts .There are 36 students in the classroom. How many students are wearing a shirt other than blue or white ?
b. As part of the assignment, you need to make a ratio table using the scale factor 0.5 nm
to 10 inches. A partially completed ratio table is shown. What value can be placed
where the question marks (?) are? Show all your work.
Nanometers Inches
? 5
0.5 10
1 20
3 ?
Answer: The ratio between the units of measurement of nanometers and inches is 0.5 nm to 10 inches. This means that for every 0.5 nanometers, the equivalent measurement in inches is 10 inches.
We can use this ratio to find the conversion of other values from nanometers to inches as well.
We know that 1 nm = 20 inches, we can multiply the value 1 by 20 to get 20 inches
So 3 nm will be 3 * 20 = 60 inches
so, the value that can be placed in the ratio table where the question marks (?) are would be 1 nm = 20 inches
and 3 nm = 60 inches.
Step-by-step explanation:
uhhh pls put the process of how u got the answer
Answer:
Here is a process on how to solve it:
Step-by-step explanation:
The midline theorem states that a seg that connects the midpoints of 2 sides is parallel and equal to 1/2 (50%) of the other side.
Look for the line that is drawn from one midpoint of another (you can see because it is usually drawn or you can see bisected segs) then multiply it by 2 to find the value of the other side.
Hope this helps!
Consider the matrices.
A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢53−1−468⎤⎦⎥
What is the result of A−B?
The subtraction of the given martix B from A given as:
A - B = | -1 11 |
| -6 2 |
| -4 -10 |
Explain the term matix and its subtraction?When a matrix is subtracted, its equivalent elements from two or more other matrices are also subtracted. Data can be organized mathematically into rows and columns using matrices.A = | 4 7 | B = | 5 -4 |
| -3 8 | | 3 6 |
| -5 -2 | | -1 8 |
A - B = | 4 - 5 7 + 4 |
| -3 - 3 8 - 6 |
| -5 + 1 -2 - 8 |
A - B = | -1 11 |
| -6 2 |
| -4 -10 |
Thus, the subtraction of the given martix B from A given as:
A - B = | -1 11 |
| -6 2 |
| -4 -10 |
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Write the inequality using interval notation
a movie theater can sell as little as 425 tubs of popcorn and as many as 800 tubs of popcorn on a friday night
Interval notation: [0, ∞). To arrange the intervals in interval notation, use brackets and parenthesis.
Write the inequality using interval notation ?To arrange the intervals in interval notation, use brackets and parenthesis.The number at the extremity of the interval is included when it is enclosed in brackets [or], and it is not included when it is enclosed in parentheses (or). We always use parentheses for infinite.For instance:Numbers higher than a and less than or equal to b are not included in this interval, so a x b applies.In this case, the expression x > 0 refers to numbers greater than or equal to zero.Since there is no upper bound specified, we must use a right parenthesis with an infinite symbol and a left bracket for zero in interval notation (since it includes the integer). Therefore, this is [0,] in interval notation.We first create a number line on which the extremes of the interval or intervals can be seen before graphing this.If one of them is an endless symbol, we must indicate that with an arrow, using a left arrow for - and a right arrow for. Then, we can use a bracket or parenthesis for the extremes.To learn more about interval notation refer
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What two numbers multiply to give you 56 and add up to give you negative -30
Answer:
The two numbers that multiply to give 56 and add up to give -30 are -8 and 7.
-8 * 7 = 56
-8 + 7 = -1
simplify the expression 5x^(2n-1)+(2x^(3n+1))^2
Hey there!
Given:
[tex]5x^(^2^n^-^1^)+(2x^(^3^n^+^1^))^2[/tex]
Simplified Solution:
[tex]5x^2^n^-^1+4x^6^n^+^2[/tex]
Hope this helps!
Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
The graph of g is a vertical translation 2 units up of the graph of f.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Here, the two functions are f(x) = -2x
and Now, g(x) = f(x) + 2
g(x) we obtained by translating the graph f(x).
g(x) = -2x + 2
Implies f(x) is increased by 2 or graph translated 2 units upwards.
Thus, the graph f(x) is translated vertically upward by 2 units to g(x).
Hence, the graph of g is a vertical translation 2 units up of the graph of f.
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PLEASE HELPPP <3
What is the domain of the square root function graphed below
The given graph function is a radical function. The domain of the function is [-4,∞). It can represent as x≥-4. Option A is the correct option.
What is a function?
A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. Originally, functions were the idealization of how a varying quantity depends on another quantity.
The graph starts at point (-4,0).
Then graph extended the upward direction vertically and the positive x-axis horizontally.
Since the graph extended the positive x-axis, thus x-coordinates of the points on the graph are also increasing.
The x-coordinate of the points on the graph are the domain of the graph.
Since (-4,0) is a point on the graph, thus the domain of the graph starts from -4.
The domain is [-4,∞).
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when using matrix bands on these teeth, the band should be trimmed to which of the following dimensions?
Height and contour: The matrix band should not extend more than 2 mm beyond the occlusogingival height of the crown of the tooth.
A dental matrix band can be defined as a properly shaped piece of metal, or other material, inserted. To support and give form to the restoration during placement, and hardening of the restorative material.
The primary function of a matrix band is to compensate for missing walls and thus provide containment of the filling material.
Matrix band systems have evolved over time and newer systems are made to give ease of use to operators and also cover for flaws and difficulties in older systems.
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Find the difference by subtracting the polynomial 4a^3+6a^2-11a-3 from the polynomial 2a^3-4a^2-6a+1
The difference of the polynomials 4a^3+6a^2-11a-3 and 2a^3-4a^2-6a+1 is given as follows:
2a³ + 10a² + 5a - 4.
How to obtain the difference of polynomials?The difference of polynomials in this problem is defined as follows:
4a^3+6a^2-11a-3 - (2a^3-4a^2-6a+1)
To subtracted the polynomials, we combine the like terms, hence:
4a³ - 2a³ = 2a³.6a² - (-4a²) = 6a² + 4a² = 10a²-11a - (-6a) = -11a + 6a = -5a.-3 - 1 = -4.Hence the difference of the polynomials is given as follows:
2a³ + 10a² + 5a - 4.
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Help me, please pls pls pls
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting a black marble.
A. 0.27
B. 0.33
C. 0.40
D. 0.60
The required probability of selecting the black marble is given as 0.40. Option C is correct.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of marbles in the bag = 15
Number of black marble = 6 [from the table]
Now,
The experimental probability of selecting a black marble,
= Number of black marble/Total number of marbles
= 6/15 = 0.40
Thus, the required probability of selecting the black marble is given as 0.40. Option C is correct.
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169 divided, simplified
The number 169 is called the numerator or dividend, and the number 3 is called the denominator or divisor. The quotient of 169 and 3, the ratio of 169 and 3, as well as the fraction of 169 and 3 all mean (almost) the same: 169 divided by 3, often written as 169/3.
What is denominator or divisor?The number that is on top is called the numerator, and the number on the bottom is called the denominator (the prefix 'de-' is Latin for reverse) or divisor. These two numbers are always separated by a line, which is known as a fraction bar. This way of representing fractions is called display representation.
When we divide two numbers, the number that is being divided is the dividend, whereas the number by which we divide is the divisor. For example, 12 candies are to be divided among 3 children. So we have 12 ÷ 3. Here, 12 is the dividend, and 3 is the divisor.
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question- What is 169 when divided by 3 ? also write the remainder, and with decimal .
time-ordered plot of representative sample statistics called a(n): Gantt chant. simo chart
control chart
p-down matrix
standard deviation table
An example of time-ordered typical sample statistics is shown in the Control chart. It is used to process the Mean bar.
A control chart is a statistical tool for monitoring the effectiveness of a process over time. It has the form of a graph with two additional lines representing the upper control limit and lower control limit. The central line in the graph represents the mean or average of the data.
Control charts are a type of graph used in production control to assess the effectiveness of exceptional production procedures under challenging circumstances. Control charts are actually the tools used in control strategies. These curves were produced using historical data.
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The Morris family is planning to carpet the entire home. The type of carpet the family wants is sold at two different stores. store A sells 50 square feet of carpet for $325. The equation y=7.25x represents the cost of buying x square feet of carpet from store B
So, on solving the question we can say that - the equation is y=7.25x; y = 2356.25
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
y=7.25x
x = 325
y = 2356.25
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I need the answer please
Answer:ok
Step-by-step explanation:
ol
Evaluate the iterated integral by converting to polar coordinates_ J" La 6x2y dx dy a2 y2
The iterated integral by converting to polar coordinates is [tex]\frac{2a^{2} }{5}[/tex]
Evaluating an iterated integral by converting it to polar coordinates involves the following steps:
Identify the region of integration in the xy-plane.Convert the region of integration to polar coordinates. This typically involves finding the bounds for r and theta in terms of x and y.Write the iterated integral in terms of polar coordinates, with the outer integral being with respect to r and the inner integral being with respect to theta.Evaluate the integral by using the bounds found in step 2 and the appropriate substitution.Here, [tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]
Now, converting it into the polar form:
[tex]\int\limits^\pi _\frac{\pi }{2} \int\limits^a_0} {6\cos^{2}\theta}\ {sin\theta\ r^{4} dr\ d \theta[/tex]
[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6cos^2\theta}{5}\ r^5 sin\theta]^{a}_{0} \, d\theta[/tex]
[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6\ a^2 \cos^2\theta sin\theta}{5}] \, d\theta[/tex]
[tex]= [-\frac{2a^{2} }{5}\ cos^{3}\theta ]^{{\pi} }_\frac{\pi}{2}[/tex]
[tex]= \frac{2a^{2} }{5}[/tex]
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The complete question is:
Evaluate the iterated integral by converting it to polar coordinates:
[tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]
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A line ray or segment that intersects a segment at its midpoint is said to bisect the segment and is called
When a line, ray or segment intersects another segment at its midpoint, such a line, ray or segment is called a segment bisector.
What is a segment bisector?As the name implies, When a line or a ray intersects another segment at its midpoint, such a line or ray is called a segment bisector.
More specifically, A line or ray is termed a perpendicular bisector when the ray or line intersects a given line segment at 90°, and also passes through the midpoint of the line segment.
Ultimately, the term which best describes such line or ray as described in the task content is; Segment bisector.
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PENTAGONS
If ABCDE PQRST, find the
scale factor of ABCDE to PQRST and the
perimeter of each polygon.
The perimeters of ABCDE and PQRST are 65 and 91, respectively, and their respective scale factors are 5/7.
what is perimeter ?The perimeter of a form is its circumference. The interior space of a form is measured by area. The perimeter is the space around a shape's edge. Discover how to calculate the perimeter of various forms by multiplying their side lengths. The whole length of a shape's boundary is referred to in geometry as the perimeter of that shape. The length of each side and edge that surrounds a shape is added to find its perimeter. It is measured in linear distances such as centimeters, meters, inches, or feet.
given
the scale factor in the following format: a: b = 5/7 for ABCDE and PQRST
ABCDE's perimeter is equal to the total of its sides,
which is 65 (10 + 10 + 10 + 20 + 15).
the sum of all the sides of PQRST equals 91.
The perimeters of ABCDE and PQRST are 65 and 91, respectively, and their respective scale factors are 5/7.
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