C) 6p³ – 23p² + 9p + 28 is the product obtained when Iliana multiplied
3p – 7 and 2p² – 3p – 4.
What is mathematical equation?A mathematical equation is a statement of equality between two expressions that can contain numbers, variables, and mathematical operators. Equations are often used to describe relationships between different quantities, and can be used to solve problems and make predictions. They can also be represented graphically. Equations can be simple or complex, with one or multiple variables. They are used in various fields like physics, chemistry, engineering, economics etc.
In order to find the result we multiply both mathematical equation together
(3p – 7)*(2p² – 3p – 4).
=> 6p³ - 9 p² - 12p - 14p² + 21p +28
=> 6p³ - 23 p² + 9p + 28
so the product of both mathematical equation is 6p³ - 23 p² + 9p + 28
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Complete question:
Iliana multiplied 3p – 7 and 2p² – 3p – 4. Her work is shown in the table.
Which is the product?
A) 6p³ + 23p² + 9p + 28
B) 6p³ – 23p² – 9p + 28
C) 6p³ – 23p² + 9p + 28
D) 6p³ + 23p² – 9p + 28p-
Identify the coefficient in the expression below.
6h²-9
1.) -9
2.) h
3.) 2
4.) 6
6 will be the Coefficient of the given expression.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, the expression below.
6h²-9
To find the coefficient of this expression:
A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constants and variables.
Thus, in our case,
Coefficient = 6
Constant = 9
therefore, the Coefficient of the given expression will be 6.
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Tanner measured a house and made a scale drawing. The scale of the drawing was
1 inch : 4 feet. If the actual length of a rug in the hallway is 8 feet, how long is the rug in the
drawing?
inches
If the scale for the drawing is 1 inch : 4 feet , then the length of the rug in the drawing is 2 inches .
the actual length of the rug in the hallway is = 8 feet ;
the scale factor for the drawing is given as 1 inch : 4 feet ;
that means 4 feet of actual length is represented by 1 inch in the drawing ,
So , 1 feet in the actual length will be = [tex]\frac{1}{4}[/tex] inch in the drawing ;
that means , 8 feet of the actual length will be = [tex]\frac{8}{4} =2[/tex] inch in drawing .
Therefore , the length of the rug in the drawing is 2 inches .
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Can someone help me please
The 25th percentile for the given dataset is 5, and the 80th percentile is 16.
What is the percentile?
A percentile is a measure used in statistics that indicates the value below which a given percentage of observations in a group of observations fall. Percentiles divide a set of observations into 100 equal parts, where each part represents 1% of the observations.
To find the 25th percentile (also known as the first quartile) and 80th percentile (also known as the fourth quartile) for a set of data, you can use the following steps:
Arrange the data in increasing order:
1, 3, 5, 9, 10, 11, 14, 15, 16, 18, 20, 22, 24, 25, 27, 29, 31, 37
To find the 25th percentile, use the following formula:
25th percentile = (N+1) x 25%
where N is the number of observations. In this case, N = 18.
Plugging in the values, we get:
25th percentile = (18+1) x 25% = 19 x 25% = 4.75
So, the 25th percentile is the 4.75th value in the ordered list. Rounding up to the nearest whole number, we get 5 as the 25th percentile.
To find the 80th percentile, use the following formula:
80th percentile = (N+1) x 80%
where N is the number of observations. In this case, N = 18.
Plugging in the values, we get:
80th percentile = (18+1) x 80% = 19 x 80% = 15.2
So, the 80th percentile is the 15.2th value in the ordered list. Rounding up to the nearest whole number, we get 16 as the 80th percentile.
Hence, the 25th percentile for the given dataset is 5, and the 80th percentile is 16.
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The first term of a geometric Sequence is 3 and the sum of the Second and third term is 60 Determine the first term and the general term
the general term will be a,ar,ar², .... i.e 3, 12, 48..
What is geometric sequence?
The sequence where another varies each word by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.
Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.
Given,
a = 3
ar+ar² = 60
r+r² = 20
r(r+1)=20
r = 4
So the general term will be a,ar,ar², .... i.e 3, 12, 48..
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for every camera sold in february the store donated 2$ to a charity how much did the store donate ?
The amount that the store donate will be $50
How to calculate the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, for every camera sold in February the store donated $2 to a charity. If 25 cameras are sold, the amount that the store donate will be:
= 25 × $2
= $50
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Complete question
For every camera sold in February the store donated $2 to a charity. If 25 cameras are sold, how much did the store donate ?
How do you name a graph?
How to Name a Graph: Tips for Writing Great Chart Captions
Summarize Your Data in Plain English.Left Justify Chart Captions Below Figure.Keep Chart Captions Simple and Short.Simplify Your Information.Include Units of Representation.Don't Forget Time Period!Now, According to the question:
The title should concisely tell the reader what is in the graph. Avoid the obvious use of “vs.” or “versus” or the word “plotted” in the title. Graphs that will appear as a figure in a publication or in a formal laboratory report will not have a title (the information is given in the figure caption).
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7. -60 + 5/13p
p = -26
Please help me show the work giving 20 points need in 20mins
The simplification of the given expression would be = -60
What is simplification of an expression?The simplification of an expression is defined as the representation of a large number or sophisticated equation into a simpler one.
The given expression = -50 + 5/13P
where P.= -26
Therefore, -50 + 5/13(-26)
Solve for; 5/13(-26) = 5/13 × -26 = -130/13 = -10
= -50 -10 = -60.
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-3,3/4,0,2, what are non real numbers
Answer:
0
Step-by-step explanation:
1. Review the definition for a real number: Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers
2. Review the definition for a non real number: The numbers which are not real and are Imaginary (such as i or a square root)
3. Your question may be missing an answer choice
4. Since all 4 of these numbers are positive, negative, whole, fraction, or decimal numbers, they are all real. Unless you are missing a number in the answer choices, there are no non real numbers.
But, wait! I may have missed something here. '0' is technically both an imaginary and real number, so it may be the answer to your problem!
how can you determine the coordinates of S(-7,1) after a reflection in the line y=3
The coordinates of S(-7,1) after a reflection over the line y = 3 is given as follows:
(-7,5).
How to obtain the coordinates after the reflection?The coordinates of the original point in this problem are given as follows:
S(-7,1).
The reflection line is given as follows:
y = 3.
The reflection line is an horizontal line, meaning that:
The x-coordinate will remain constant.The y-coordinate will be the same distance from the reflection line, but in an opposite direction.The y-coordinate of S is 2 units below of the reflection line, hence after the reflection it will be two units above, as follows:
3 + 2 = 5.
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Why do we use log function?
Logarithmic functions are important largely because of their relationship to exponential functions.
What is logarithm ?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
The first section explains the meaning of the logarithmic function f (x) = c·loga(x - h) + k. It describes how to evaluate logarithms and how to graph logarithmic functions. This section also addresses the domain and range of a logarithmic function, which are inverses of those of its corresponding exponential function.
The next section presents two special logarithmic functions--the common logarithmic function and the natural logarithmic function. The common logarithm is log10x, and it corresponds to the "log" button on most calculators. The natural logarithm is logex, and it corresponds to the "ln" button on most calculators. The natural log has a particular use in economics--it is used to perform calculations involving compound interest.
Logarithmic functions are important largely because of their relationship to exponential functions.
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A polygon ABCDE in which the measures of the interior angles are (6x)°, (4x+13)°, (x+9)°, (2x−8)°, and (4x−1)°.
SOLVED
Answer:
Solution
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = \frac{rise}{run}
run
rise
= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }
x
2
−x
1
y
2
−y
1
with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line
m = \frac{1-(-5)}{2-(-1)}
2−(−1)
1−(−5)
= \frac{1+5}{2+1}
2+1
1+5
= \frac{6}{3}
3
6
= 2
solving a formula for a variable means rewriting the formula so that the variable is ___
Solving a formula for a variable means rewriting the formula so that the variable is Isolated to one side.
Solving a formula for a particular variable entails placing that variable alone with a coefficient of 1 on one side of the equals sign. The other side of the equals sign represents all other variables and constants.
A formula is a mathematical representation of how two variables relate to one another. In the sciences, including physics, biology, and chemistry, formulas are also employed. They are employed in medicine to do computations for calculating body mass index or distributing medication. Calculations are done using formulas in spreadsheet systems.
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In what ratio is the line segment joining the points (- 2?
Y-axis divides the line segment joining the given points (-2, -3) and (3, 7) in the ratio is equal to 2 : 3.
As given in the question,
Given points of the line segments are :
( x₁ , y₁ ) = ( -2 , -3 )
( x₂ , y₂) = ( 3, 7 )
When y-axis divides the line segment its coordinate are ( 0, y)
Let the ratio which divides the line segment be m : n
( 0 , y ) = [ ( mx₂ + nx₁) / ( m + n) , ( my₂ + ny₁) / ( m + n)]
⇒( 0 , y ) = [ ( 3m -2n) / ( m + n) , ( 7m -3n) / ( m + n)]
⇒( 3m -2n) / ( m + n) = 0
⇒ 3m -2n = 0
⇒3m = 2n
⇒ m : n = 2 : 3
Therefore, the y-axis divides the given line segment in the ratio equals to 2 : 3.
The above question is incomplete , the complete question is:
In what ratio is a line segment joining the points (-2, -3) and (3, 7) divided by y-axis?
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Solve for X, Leave in simplest radical form.
When the number under the root sign has no square factors, a radical is said to be in its simplest form.
Why is it called a radical?In the 14th century, the term radical was first used. It was derived from the Late Latin radicalis, which was derived from the Latin radic-, radix, which meant "root." The definition "of, connected to, or proceeding from a root" underlies the first usage of the word "radical," which are all about actual roots.
Radical: The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions. The radical symbol's "radicand" is a number or phrase. A radical equation is one that uses variables as radicands in radical expressions.
Using the Pythagorean theorem, x = 27:
7² + ?² = 9²\sx² = 81 - 49\x = √32\x = 4√2
For the lower portion:
x² + 2² = (4√2)
²\x² + 4 = 32\x² = 28\x = √28\x = 2√7
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just need some help.
The side length of BC in ∠ABC is 11.
How to find side length of triangle using angle?To find the side length of a triangle using angle, first determine the angle measurement of the triangle. Then, depending on the type of triangle, use a trigonometric ratio to find the side length. For example, if the triangle is an equilateral triangle, all three angles are equal and measured at 60 degrees. Using the sine function, the side length can be found by plugging in the angle and solving for the side length. The equation would look like sin(60)=x/side length, and when solved, the side length will be equal to the square root of 3. Alternatively, if the triangle is an isosceles triangle, two angles will be equal. To find the side length, use the cosine function and plug in the angle measurement. The equation would look like cos(angle)=x/side length, and when solved, the side length will be equal to the inverse cosine of the angle. Lastly, if the triangle is a right triangle, one of the angles is equal to 90 degrees. To find the side length, use the Pythagorean Theorem, which states that the sum of the squares of the two legs of the triangle will be equal to the square of the hypotenuse. The equation looks like side length1^2 + side length2^2 = hypotenuse^2. When solved, the side length can be determined by taking the square root of the hypotenuse. In conclusion, to find the side length of a triangle using angle, the type of triangle must be determined, then a trigonometric ratio or Pythagorean Theorem can be used to solve for the side length.Solution:
∠A = 32°
∠C = 39°
∠B = 180°-39°-42°
∠B = 99°
side length of AC = 16
a / sin A = b / sin B = c / sin C
a / sin42° = 16 / sin99°
a = 16 sin42°/ sin99°
a = 10.84
a = 11
The side length of BC = 11
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Among the following countries, which country is not in Asia?AIndiaBUSACIranDChina
Answer:
B) USA
Step-by-step explanation:
USA is in North America
What is the derivative of ln 3x?
ln 3x = ln (3x). The derivative of ln (3x) is 1/3x. in this case, f(x) = ln (x) and g(x) = 3x. The derivative of ln (x) is 1/x and the derivative of 3x is 3. Therefore, the derivative of ln (3x) is 1/3x which is equal to 1/(3x).
in this case, f(x) = ln (x) and g(x) = 3x. The derivative of ln (x) is 1/x and the derivative of 3x is 3. Therefore, the derivative of ln (3x) is 1/3x which is equal to 1/(3x). Using the chain rule, the derivative of ln (3x) can be found. The chain rule states that the derivative of a function f(g(x)) is f'(g(x)) * g'(x). In this case, f(x) = ln (x) and g(x) = 3x.ln 3x = ln (3x). The derivative of ln (3x) is 1/3x.
ln 3x = ln (3x). The derivative of ln (3x) is 1/3x.
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What is the function f/x )= 1 x called?
The mathematical function f/x= 1 x is known as the reciprocal function.
It is a mathematical operation that takes a number and produces its reciprocal, or inverse, as the result.
For example, if you input the number 2 into the reciprocal function, it will return the result of 1/2, or 0.5. The reciprocal function is also known as the multiplicative inverse, since multiplying a number by its reciprocal will always result in the number 1.
The reciprocal function is an important mathematical tool used to calculate the inverse of a given number. It is an essential element of many algebraic equations, and can be used in a variety of ways to simplify complex problems.
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How many solutions does the system have y =- 2x 4 7y =- 14x 28?
The given system of equations y = -2x + 4 and 7y = -14x + 28 have Infinite solutions.
We have two equations are y = -2x + 4 and 7y = -14x + 28
We have to find the number of solutions for this set of equations
Let us first solve the given equations
y = -2x + 4 eqn 1
7y = -14x + 28 eqn 2
Substitute eqn 1 into eqn 2
7(-2x + 4) = -14x + 28
-14x + 28 = -14x + 28
0 = 0
This means that given equations y = -2x + 4 and 7y = -14x + 28 have infinitely many solutions.
Therefore, The two lines may have an infinite number of intersecting points (infinite solutions).
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Write the fraction as a percent. If neccessary, Round to the nearest tenth of a percent. 6 4/5
Answer: 644.99999
Step-by-step explanation:
6 4/5 = 34/5 = 6.8
6.8 as a percent is 680%
Hope this helps!
Write an equation for the proportional relationship shown in the table.
x 0.5 1 1.5 2
y 7 14 21 28
Y=?X
Answer: hopefully this helps
The relationship between x and y in the table appears to be a linear, proportional relationship. One way to write an equation for this relationship is using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula: m = (y2 - y1) / (x2 - x1).
Using any two points from the table, like (x1, y1) = (0.5, 7) and (x2, y2) = (1, 14)
m = (14 - 7) / (1 - 0.5) = 7 / 0.5 = 14
So the slope (m) = 14, which means that y increases by 14 units for every unit increase in x.
Then we can use any point in the table to find the y-intercept (b)
Using the point (1,14)
14 = 14*1 + b
b=0
So the equation for the proportional relationship shown in the table is : y = 14x
Step-by-step explanation:
Identify the triangle as scalene isosceles or equilateral A(0,-4) B(0,-9) C(-2,-5)
The triangle that has the coordinates as A(0,-4) B(0,-9) C(-2,-5) is; A scalene Triangle
How to find the distance between two coordinates?The formula for the distance between two coordinates is;
D = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus;
Distance AB = √[(-9 + 4)² + (0 - 0)²]
Distance AB = √25
Distance AB = 5
Distance BC = √[(-5 + 9)² + (-2 - 0)²]
Distance BC = √20
Distance CA = √[(-4 + 5)² + (-2 - 0)²]
Distance CA = √5
Since the three sides all have different lengths, then they the triangle is said to be a scalene triangle.
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Find out how many weed killer cans are needed and the price for all
The number of weed killer cans needed is 2.4 cans and it will cost $ 47.4
What is area of trapezium?A trapezium is a quadrilateral with at least one pair of parallel lines. The two parallel lines are named a and b. The area of a trapezium is given as:
A = ½( a+b) h
where a and b are the parallel sides and h is the height of the trapezium.
since the lawn takes the shape of a trapezium,
The height of the lawn is calculated as:
h² = 17²- 8²
h² = 289-64
h² = 225
h = √225 = 15m
therefore A = ½(12+20)15
A = ½×32× 15
A = 16×15
A = 240m²
If one can will go for 100m², then the number of can that will be needed for the lawn = 240/100 = 2.4 can of weed killers.
If one weed killer cost $19.75, then
2.4 weed killers will cost 19.75 × 2.4 = $47.4
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The set of polynomials is ___ closed under division.
The set of polynomials is not closed under division.
A polynomial is a mathematical statement made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division operations. Polynomial means "many terms" since it combines the words poly-, which means "many," and -nomial, which in this context means "term." A polynomial may have exponents (like the 2 in y2), constants (like x and y), variables (like the x and y exponents), and other terms, but only those that can be mixed using addition, subtraction, multiplication, and division are permitted. Constants, variables, and exponents are all permitted in polynomials, but variable division is never permitted.
In addition, they are now only limited to a finite number of terms, which can be one or more.
The dividend appears at the top of the division at first, similar to how long multiplication is written.
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What is the first step to writing an expression in factored form?
Answer:
factor out the GCF
Step-by-step explanation:
The equation y = 10x + 15 represents a gym that charges. What is the slope and y-intercept?
The required values of slope and y-intercept are 10 and 15.
What is equation of line?The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.
According to question:We have,
y = 10x + 15
On comparing with general equation of line.
Y = mx + c
m is slope of line, c is y-intercept.
Then,
m = 10
And
y-intercept = 15
Thus,the required values of slope and y-intercept are 10 and 15.
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Please help, I don't quite understand. I'm offering 30 points with Brainliest answer!
Answer:
-4
Step-by-step explanation:
a1 is 2
a2 = a1^2-5 = 4-5 = -1
a3 is a2^2-5 = 1-5 = -4
write -23 27/50 as a decimal number.
Answer:
Step-by-step plotttt
Answer:
23.54
Step-by-step explanation:
What is the average speed of a car that travels 150 m in 5 s?
Answer:
30 m/s
i believe
Answer:30 m/s
Step-by-step explanation:It travels 150 m in 5 seconds. What is its average speed ? Thus, the average speed of the car is 30 m/s.
Determine a possible second point with a y-coordinate of 8.
A possible second point with a y-coordinate of 8 is equal to 5.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following slope and data points on the line:
Points on x-axis = (1, 2).
Points on y-axis = (_, 8).
Slope, m = 3/2
Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
3/2 = (8 - 2)/(x₂ - 1)
3/2 = 6/(x₂ - 1)
Cross-multiplying, we have:
3(x₂ - 1) = 12
x₂ - 1 = 12/3
x₂ - 1 = 4
x₂ = 4 + 1
x₂ = 5
In conclusion, we can logically deduce that the second point (x₂) is 5.
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