factorials with algebraic expressions still be correct if you substitute the letter with a number.
What are factorials?Factorial is a mathematical operation denoted by the exclamation mark (!). It is used to find the product of all positive integers from 1 to a given number. For example, the factorial of 4 (written as 4!) is:
4! = 4 × 3 × 2 × 1 = 24
Given by the question.
if you substitute a numerical value for the algebraic expression, the resulting factorial can be computed and evaluated as a numerical expression.
For example, consider the factorial expression n! where n is an algebraic expression such as n = x + 2. Substituting a numerical value for x, say x = 3, we get n = 3 + 2 = 5, and hence we can compute 5! = 5 x 4 x 3 x 2 x 1 = 120.
Similarly, if we have an expression like (n+1)! /(n-1)! where n is an algebraic expression, we can substitute a numerical value for n and compute the resulting value. For example, if we substitute n = 4, we get (4+1)!/(4-1)! = 5!/3! = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 60.
It's important to note that substituting numerical values for algebraic expressions only works if the resulting expression is well-defined and doesn't lead to any undefined or indeterminate forms (such as division by zero).
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Mary used a graph to solve this system of equations:
y = 3/1 x + 2 (blue line)
y = -1/1 x - 2 (red line)
Explain the error she made when graphing the equations
Creating your own graph, what is the correct solution to this system of equations
The system of equations are solved graphically and the value of x and y are -1 and -1 respectively
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the first equation be be P
y = 3x + 2 be equation (1)
Let the second equation be Q
y = -x - 2 be equation (2)
Now , the slope of the line P is m₁ = 3
The slope of the line Q is m₂ = -1
On simplifying the equations , we get
3x + 2 = -x - 2
Adding x on both sides , we get
4x + 2 = -2
Subtracting 2 on both sides , we get
4x = -4
Divide by 4 on both sides , we get
x = -1
Substitute the value of x in equation (1) , we get
y = -3 + 2
y = -1
Hence , the equations are plotted on the graph value of x and y are ( -1 , -1 )
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Which expression means “3 decreased by the quotient of 11 and a number n”?
The option A is correct because the value of the statement is 6+3/n-8.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
According to the statement
we have given that the statement and we have to write the statement in the numerical form.
So, For this purpose
we know that the given statement is
"Six more than the quotient of three and a number, decreased by eight".
In this statement "Six more than" indicates the sum between the quotient and 6.
And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.
"Decreased by eight" indicates a subtraction between the quotient an 8 units".
If we unit all parts of the statements, we would have
6+3/n-8
So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.
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solve by using substitution
write it as a point
show work
The solution of the equations -4x-2y= -12 and 4x+8y= -24 is {6, -6).
Solve by using substitutionThe question above has 2 equation.
Equation I = -4x-2y= -12
Equation II=4x+8y= -24.
Equation I = -4x-2y= -12, replace to 4x= -2y+12
then substituted 4x= -2y+12 into the second equation, namely 4x+8y= -24.
4x+8y= -24
=(-2y+12) +8y= -24
6y+12= -24
6y = -24-12
6y= -36
y = -6
found the value of y is -6.
The next, substitute the value y= -6 into the equation II
4x+8y= -24
4x+8(-6) =-24
4x-48=-24
4x=-24+48
4x=24
x=24/4
x=6
found the value of x is 6.
Therefore the x and y values of those equation in question are 6 and -6.
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find three solutions to the equation 2x+6y=-12 for the following values of x or y. Enter your answers as an ordered pair in the form (x,y).
Enter the solution when
x=0
Enter the solution when
y=0
Enter the solution when
y=2
Answer:
Step-by-step explanation:
Use the slope formula to find the slope of the line that travels through the given points (4, 4) and (5, 3)
Answer:
The slope of the line that travels through the points (4, 4) and (5, 3) is -1.
Step-by-step explanation:
The slope formula is:
m = (y2 - y1) / (x2 - x1)
where m is the slope of the line, (x1, y1) and (x2, y2) are the given points. Plugging in the values for (4, 4) and (5, 3):
m = (3 - 4) / (5 - 4)
m = -1 / 1
m = -1
The slope of the line that travels through the points (4, 4) and (5, 3) is -1.
Someone please help it’s an emergency!!
Answer:
-3
Step-by-step explanation:
Look at x. Go right until you see 3. Now look below to see what y is.
When x is 3, y is -3.
Nakeisha is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 6 t-shirts, and 3 pairs of shoes. How many different outfits does Nakeisha have to choose from?
Answer:36
Step-by-step explanation: 2x6x3=36
Nakeisha has 36 different outfits to choose from.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1[/tex] ,[tex]n_2[/tex] , [tex]n_3[/tex], ..... [tex]n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
N= [tex]n_1[/tex] x [tex]n_2[/tex] x [tex]n_3[/tex] x.....x [tex]n_n[/tex]
Given:
We have 2 pairs of pants, 6 t-shirts, and 3 pairs of shoes.
For the pants we have [tex]n_1[/tex] = 2
For the t-shirts we have [tex]n_2[/tex] = 6
For the shoes we have [tex]n_3[/tex] = 3
Thus, the total number of outfits is given by:
= 2 x 6 x 3
= 36
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Hertz has a processing fee of R115,00 and charges R210 per day for car rental. Avis Car Rental has a processing fee of R255,00 and charges R190 per day for a car. When will the cost of the rentals be equal?
The cost of the rentals be equal after 2 days
What is a word problem?A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.
Let d represent the he number of days for which the car is rented
The cost for Hertz can be represented will be
= 115 + 210d,
The cost for Avis will be
= 255 + 190d.
We can set the two costs equal to each other and solve for d:
115 + 210d = 255 + 190d
95 = 45d
d = 95 / 45
d = 2
Hence, the cost of the rentals will be equal after 2 days.
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what minus 2/3 = 5/7
yoseph wants to surprise his wife a birthday party at her favorite restaurant .it will cost birr 56.50 per person for dinner,including tip and tax.his budget for party is birr 735.what is the maximum number of people yoseph can have at the party.
The required, maximum number of people Yoseph can have at the party is 13 people.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As mentioned in the question, Joseph wants to surprise his wife with a birthday party at her favorite restaurant .it will cost birr 56.50 per person for dinner, including tips and taxes. his budget for the party is birr 735.
So, the ratio of the budget to the cost per person defines the maximum number of people Yoseph can have at the party,
= 735 / 56
= 13 people
Thus, the required, maximum number of people Yoseph can have at the party is 13 people.
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the diagram shows two lighthouse a and b and a port p
a) The position of boat is shown by red point.
b) About 78 degree should the boat sail on to enter the port.
What is Angle?A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.
Given:
From point 'a', measure around 340 degrees bearing and then put the line there.
Then, from point 'b' measure around 245 degrees when measuring north.
The position of boat is shown by red point.
b) About 78 degree should the boat sail on to enter the port.
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The question attached here is seems to be incomplete and inappropriate The complete question is attached below.
The diagram shows two lighthouses A and B and a port P
A boat is on a bearing of 340° from lighthouse A and 245° from lighthouse B.
a) Mark, with a cross, the position of the boat on the map.
b) What bearing should the boat sail on to enter the port?
Find the value(s) of c guaranteed by the mean value theorem for integrals for the function over the given interval. (enter your answers as a comma-separated list. ).
The value(s) of c guaranteed by the mean value theorem for integrals for the function over the given interval is proved.
The mean value theorem for integrals states that if a continuous function f is defined on a closed interval [a, b], then there exists a number c in the interval (a, b) such that the average value of the function over the interval is equal to the value of the function at c.
Mathematically, this can be expressed as:
[tex]\frac{1}{b-a} \int_{a}^{b} f(x) dx = f(c)[/tex]
where c is a number in the interval (a, b) and the integral sign represents the area under the function from a to b.
The mean value theorem for integrals tells us that there is always a point in the interval where the average value of the function is equal to the function's value at that point. However, it does not tell us the value of c. To find the value of c, we need to solve for it in the equation above.
In conclusion, the mean value theorem for integrals is a useful tool for understanding the average value of a function over an interval and finding the value of c where the average value is equal to the function's value at that point.
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Suppose that some resource x is necessary to produce some good y. If the price of x rises.
This implies that the QS of good Y increases at the same price and as such, the S curve of good Y will experience a rightward shift.
The quantity provided (QS) of the good Y at different prices would be determined by the supply (S) curve of the good Y. (P). The fact that resource X is utilized in the supply of good Y suggests that resource X is an input employed in the creation of good Y. When a result, as the P of resource X declines, the cost of producing good Y increases, and in response, the producers of good Y raise the QS of good Y. This suggests that the QS of good Y grows at the same rate, leading to a rightward shift in the good Y S curve
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In a small forest, a certain species of tenrecs doubles in number every
year. Write a function, f(x), that models the number of tenrecs after X
years if there were originally 698 tenrecs.
The function, f(x), that models the number of tenrecs after x years is f(x) = 698(2)^x
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
Initial value, a = 698
Rate, b = 2 i.e. doubles
Using the above as a guide, we have the following:
f(x) = ab^x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 698(2)^x
Hence, the function is f(x) = 698(2)^x
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Mr. Carter gives a 30 point quiz.
cody scored 8 points less than twice
of what Erica Scored, the sum of
Codys and Ericas score was 37,
how many points did each student
Score?
The points scored by Cody will be 22 and by Erica be 15.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that Mr Carter administers a 30-point test. Cody scored 8 points less than Erica, and the total of Cody and Erica's scores was 37.
The two equations can be written as:-
C = 2E - 8
C + E = 37
2E - 8 + E = 37
3E = 45
E = 45 /3
E = 15
C = 30 - 8
C = 22
Therefore, Cody will score 22 points, while Erica will score 15.
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Joan bought 5 yards of fabric for $2.85 a yard, including tax. Which expression will find the change John received if she gave the cashier $50
The solution is, the change John received if she gave the cashier $50 is,
$50 - ($2.85 * 5)
=$50 - $ 14.25
=$ 35.75 , the required expression.
What is Subtraction?
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
Joan bought 5 yards of fabric for $2.85 a yard, including tax.
i.e. he spend = $2.85 * 5
= $14.25
so, the change John received if she gave the cashier $50 is,
$50 - ($2.85 * 5)
=$50 - $ 14.25
=$ 35.75
Hence, The solution is, the change John received if she gave the cashier $50 is,
$50 - ($2.85 * 5)
=$50 - $ 14.25
=$ 35.75 , the required expression.
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At&t claims you can download 58 gigabytes every 2. 3 mins. If this is true how many years would it take to download 122 terabytes of data?
Answer:
3,076.5 rounded
Step-by-step explanation:
58 divided by 2.8 = 25.2173913043 for the unit rate. Then multiply by 122 = 3,076.5217391246.
what is the answer to –56/y − 11 ≤ –28
The inequality equation is 0 < y ≤ 56/17
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( -56 / y ) - 11 ≤ -28 be equation (1)
On simplifying the equation , we get
Adding 11 on both sides of the equation , we get
-56 / y ≤ -17
On further simplification , we get
( -56 + 17y ) / y ≤ 0
Therefore , the inequality equation is 0 < y ≤ 56/17
Hence , the inequality is 0 < y ≤ 56/17
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What is the result when the number 28 is increased by 25%?
Answer:
Step-by-step explanation:
To increase a number by a certain percentage, we can multiply the number by (1 + the percentage as a decimal).
To find 25% of 28, we can convert 25% to a decimal by dividing by 100:
25% = 25/100 = 0.25
Now, to find what 28 is increased by 25%, we can multiply 28 by (1 + 0.25):
28 * (1 + 0.25) = 28 * 1.25 = 35
So, the result when 28 is increased by 25% is 35.
Answer: 35
Step-by-step explanation:
we know 28 / 4 = 7
so, 7 is 25% of 28, therefore, we can add 7 to 28 and the answer is 35.
-2x+y=12
y=-26-9x
Solve by elimination
Show work
The values of x and y after solving the simultaneous equations are; x = 37/11 and y = 17⁸/₁₁
How to solve Simultaneous Linear Equations?The two simultaneous equations given are;
-2x + y = 12 -------(1)
y = -26 - 9x ------(2)
Let us make y the subject in eq 1 to get;
y = 2x + 12 -----(3)
Subtract eq 2 from eq 3 to get;
0 = 2x + 12 + 26 + 9x
11x + 37 = 0
11x = 37
x = 37/11
Similarly;
y = 2(37/11) + 12
y = 74/11 + 12
y = 6⁸/₁₁ + 12
y = 18⁸/₁₁
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In the knitting pattern,
m/1 = 42°.
Find the
measure of 2
in the knitting pattern, since the m<2 is the exterior angle, the measure of the exterior angle is 132°
Calculating exterior angles.Exterior angles of a right-angled triangle are calculated by the sum of the opposite interior angles. It can also be calculated by using the sum of angles in a triangle, followed by using the sum of angles on a straight line to determine the exterior angles.
Here, m < 1 = 42°, and the other angle is 90°
Thus, if the sum of the two opposite interior angles equals the exterior angles, then:
m< 2 = 42° + 90°
m< 2 = 132
Therefore, in the knitting pattern, since the m<2 is the exterior angle, the measure of the exterior angle is 132°
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in 2006 was 85% of the number at
the school in 2005. In 2006 the number of students was 1020.
How many students were there in 2005?
Answer:
In 2005, there were 1,200 students at the school.
Step-by-step explanation:
In 2005, there were 1,200 students at the school. This can be calculated by taking 85% of 1020 (the number of students in 2006) and multiplying it by 100. 85% of 1020 is 861. Multiplying this by 100 gives us 86,100. Dividing this by 85 gives us 1,200. Therefore, in 2005 there were 1,200 students at the school.
what is percentage is as common fractions in simplest form 40% 32% 15% 37% 96%
Answer:
2/5, 8/25, 3/20, 37/100, 24/25
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If we know that percentages are fractions of 100, we can convert these percentages:
40% = [tex]\frac{40}{100}[/tex]32% = [tex]\frac{32}{100}[/tex]15% = [tex]\frac{15}{100}[/tex]37% = [tex]\frac{37}{100}[/tex]96% = [tex]\frac{96}{100}[/tex]Simplifying these fractions:
[tex]\frac{40}{100} = \frac{2}{5}[/tex][tex]\frac{32}{100} = \frac{8}{25}[/tex][tex]\frac{15}{100}=[/tex] [tex]\frac{3}{20}[/tex][tex]\frac{37}{100}=\frac{37}{100}[/tex][tex]\frac{96}{100} =\frac{24}{25}[/tex]Therefore, the percentages as simplified fractions are listed above.
The total area covered by 6 rectangular openings is 1.3 square meters, calculate the total amount of area of rectangular openings which should be painted
The total area of the rectangular openings which should be painted is 1.3 sq meters.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
Given that, the total area covered by 6 rectangular openings is 1.3 square meters, we need to calculate the total amount of area of rectangular openings which should be painted,
Since, it is already given that the area of the rectangular opening is 1.3 m²
Therefore, the area which need to be painted is 1.3 m²
Hence, the total area of the rectangular openings which should be painted is 1.3 sq meters.
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A potassium hydroxide (koh) solution has a molar concentration of 0. 065 m, calculate the and ph of the solution. Remember that kw= 1. 0 x 10-14m2.
The pH of the solution is 12.81.
1) [OH⁻] = 0.065 M
2) [H₃O⁺] = 1.54 x 10⁻¹³ M.
3) pH = 12.81.
HCl is completely dissociated into its ions in solution:
KOH + H₂O → H₃O⁺ + K⁺ + OH⁻,
1) [OH⁻] = 0.065 M.
2) [H₃O⁺]:
∵ [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [H₃O⁺] = [tex]\frac{10^{-14}}{OH^-}[/tex] = [tex]\frac{10^{-14}}{0.065}[/tex] = 1.54 x 10⁻¹³ M.
3) pH:
Typically, a pH meter is used to measure pH, which converts the difference in electromotive force (electrical potential or voltage) between appropriate electrodes put in the solution under test into pH measurements. A pH meter's basic components are a voltmeter connected to an electrode that responds to pH and an electrode that is constant. The reference electrode is typically a mercury-mercurous chloride (calomel) electrode, however a silver-silver chloride electrode is occasionally used. The pH-responsive electrode is often made of glass.
For strong acids like HCl:
pH = - log[H₃O⁺] = - log[1.54 x 10⁻¹³ M] = 12.81
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Find the inverse of the following functions?
Y=x^2+2
Therefore, the inverse of the function y = x^2 + 2 is: y = ±√(x - 2)
To find the inverse of the function y = x^2 + 2, we need to switch the roles of x and y, and then solve for y.
Step 1: Write the function with x and y swapped:
x = y^2 + 2
Step 2: Solve for y. To do this, we'll need to isolate the y variable on one side of the equation. We can start by subtracting 2 from both sides:
x - 2 = y^2
Step 3: Take the square root of both sides. When we do this, we'll need to include both the positive and negative square root, since a square can have two possible roots:
±√(x - 2) = y
Step 4: Simplify the answer by using the ± symbol to show that there are two possible inverses:
y = ±√(x - 2)
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Using your calculator, determine the value
of the car in 2020.
y = 20,000(0.85) ¹0
(Be careful rounding)
Answer: $7,291.14
Step-by-step explanation: To calculate the value of the car in 2020, you can use the formula y = 20,000(0.85)^10.
Here, y represents the value of the car in 2020, 20,000 is the initial value of the car, and 0.85 is the depreciation rate. The exponent 10 represents the number of years that have passed, so the formula calculates the value of the car after 10 years by multiplying the initial value by the depreciation rate raised to the power of 10.
To perform this calculation, you can calculate 0.85^10 first, and then multiply that result by 20,000:
0.85^10 = (0.85)(0.85)(0.85)...(0.85) (10 times)
= 0.364569708
y = 20,000 * 0.364569708
= 7,291. 139416
So the value of the car in 2020 would be approximately $7,291.14.
I need help with this please and thank you.
Answer:
11x-11x+9 it's the answer the number having same value in top add then or sub them ok bro
Find the ratio of triangles to total shapes in the diagram below.
The ratio of triangles to total shapes is 4:10.
For every two triangles, there are 5 total shapes.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
Number of triangles = 4
The number of shapes.
= 4 triangles + 6 squares
= 10
Now,
The ratio of triangles to total shapes.
= 4 : 10
Now,
4 : 10
= 4/10
= 2/5
= 2 : 10
This means,
For every two triangles, there are 5 total shapes.
Thus,
The ratio of triangles to total shapes is 4:10.
For every two triangles, there are 5 total shapes.
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In a box of marbles, 25% are blue, 35% are red and the rest are yellow. If there are 112 yellow marbles in the box, how many red marbles are there?
please tell me the whole process, thank you
Answer:
98 red marbles
Step-by-step explanation:
112 yellow marbles is 40% of total. If we divide 112 by 5 then that is 5% of total, which is 14. Since the red marbles is 35% of total we can multiply 14(which is 5% of total) and 7, which gives the answer of 98.