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Related Questions
The following expression models the total money earned by setting up a food stall at a funfair, where x represents the number of cheeseburgers sold.
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Answer:
C is correct option.
The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
Step-by-step explanation:
We are given expression [tex]\dfrac{6x}{x+3}+10[/tex]
Let us suppose f(x) is total money earned by setting up a food stall at a funfair.
where, x represents the total number of cheeseburger were sold.
Therefore, [tex]f(x)=\dfrac{6x}{x+3}+10[/tex]
We need to collect the information about constant 10.
If we put x=0 into f(x)
f(0)=10
10 is a money earn when no cheeseburger sold.
It means 10 would be initial cost of setting up of Food stall.
Thus, The constant 10 represents the cost of setting up the food stall even if no cheeseburger were sold.
I need to make a matrix in reduced row echelon form
A real estate agency offers three apartments for rent in New Mexico City. The expected total revenue per month from monthly rentals for the three apartments is $1,600. The individual owners of these apartments bear the monthly maintenance costs of 20% of the rent for the first two apartments and 25% of the rent for the third apartment, which is a total amount of $345. The agency charges a monthly fee equal to 10% of the rent for apartments 1 and 3 and a fee equal to 20% of the rent for apartment 2. The monthly rent plus agency fees totals $1,820. Let x, y, and z represent the monthly rental for the first, second, and third apartments, respectively.
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Let the three apartments be A, B & C
The rent of A is $x
The rent of B is $y
The rent of C is $z
So x + y + z = 1600 .......(1)
Now
Maintenance of A is 20% of x = 0.20x
Maintenance of B is 20% of y = 0.20y
Maintenance of C is 25% of z = 0.25z
0.20x + 0.20y + 0.25z = 345
Multiplying by 100 we get
20x + 20y + 25 z = 34500
Dividing by 5 we get
4x + 4y + 5z = 6900 .......(2)
Monthly fee of A is 10% of x = 0.10x
Monthly fee of B is 20% of y = 0.20 y
Monthly Fee of C is 10% of z = 0.10z
Now
0.10x + 0.20y + 0.10 z= 1820 - 1600
0.10x + 0.20y + 0.10z = 220
Multiplying by 100 we get
10x + 20y + 10z = 22000
Dividing by 10
x + 2y + z = 2200 ....(3)
Making a Matrix of equation (1), (2) & (3)
[tex] \left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right] [/tex]
is the required matrix
The sum of three consecutive odd integers is 153. what is the value of the largest of the integers?
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The value of the largest of the integers will be 53.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of three consecutive odd integers is 153.
Let x be the odd number. Then the other two odd numbers will be x + 2 and x + 4. Then the equation will be
x + x + 2 + x + 4 = 153
3x + 6 = 153
3x = 147
x = 49
Then the other two odd numbers will be
x + 2 = 49 + 2 = 51
x + 4 = 49 + 4 = 53
The value of the largest of the integers will be 53.
More about the Algebra link is given below.
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what are the four main ideas of physical science,
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Tabitha defines a sphere as the set of all points equidistant from a single point. Is Tabitha's definition valid?
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YES it is VALID.
Explanation.
In 3 dimension, it can be seen that a sphere is a round solid. It is a round object where the distance from the centre to every point on the surface is equal.
Tabitha says that a sphere is a set of all points equidistant from a single point. This single point must be the centre of the sphere for that definition to be true. This definition is correct.
Answer: Yes, Talid's definition is valid.
Step-by-step explanation:
Definition of sphere:- In geometry , a sphere is a perfectly round three-dimensional shape . It is defined as the set of points that are all at the same distance which is known as radius from a given point in a 3-dimensional space. Talid's definition:- A sphere as the set of all points equidistant from a single point.
Hence, Talid's definition is valid.
Please help asap! 44 pts (:
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Answer choice A is wrong because y-y^1=m(x-x^1) remember, you cannot subtract a negative so it becomes posotive which means that answer choice C is your best bet
Have a nice day!
The second step in the process for factoring the trinomial x2-5x-36 is to
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Write -5x as a sum or difference.
x²+4x-9x-36
Factor out x from the expression.
x(x+4)-9(x+4)
Factor out x+4 from the expression.
(x+4)(x-9)
Answer: The second step is to factor out x.
Answer:
Find the sum of the factors of 36
Step-by-step explanation:
Which expression is a factor of 4ab + 4a − 3b − 3?
b − 1
4a − 3
3b + 1
4a + 3b
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=4a(b + 1) - 3(b+1)
= (b+1)(4a - 3)
(b+1) and (4a - 3) are factors
answer
4a − 3
(4a − 3) is a factor of 4ab + 4a − 3b − 3. Option B is correct. It is obtained by solving the given expression and taking the common terms.
What is the factored form of an expression?When an expression is written as the result of multiplication of some terms, then that multiplication form is called the factored form of that expression.
From the given expression;
[tex]= \rm 4ab + 4a - 3b - 3\\\\ =4a(b + 1) - 3(b+1) \\\\ = (b+1)(4a - 3)[/tex]
From the expression, (b+1) and (4a—3) are factors.
Hence, option B is correct.
Learn more about factored form of an expression here:
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For this question, any non-integer answers should be entered as decimals, rounded to the hundredths place. Consider this data set. 25.5 26 18.2 15.3 28.5 27 20.7 20.2 26.1 18.2 21.4 17.9 24.3 22.6 19.6 The mean of the data set is , and the sample proportion of numbers less than the mean is .
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The mean of the data set is 22.1 , and the sample proportion of numbers less than the mean is 0.53
Explanation:
.
1) Mean
Formula: mean = sum of values / number of data
sum of values = 25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6 = 331.5
number of data = 15
mean = 331.5 / 15 = 22.10
2) proportion of numbers less than the mean
This is easier if you order the data. These are the data in growing order:
15.3
17.9
18.2
18.2
19.6
20.2
20.7
21.4
---------
22.6
24.3
25.5
26
26.1
27
28.5
The discontinues line shows the split of the data that are less than the mean.
Those are 8 numbers less than 22.1 and the proportion is:
8 / 15 = 0.53
Answer:
Step-by-step explanation:
this is it
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. What is the rectangle’s width and length?
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l = 2x - 1
wl = 100
(5x+2)(2x-1) = 100
10x^2 - x - 2 = 100
10x^2 - x - 102 = 0 <--this is a quadratic equation so use the quadratic formula
x = 3.24144...
w = 5(3.24) + 2 l = 2(3.24) - 1
width = 18.2 ft length = 5.48 ft
Final answer:
To find the width and length of the rectangle, set the equation (5x + 2)(2x - 1) = 100, simplify to 10x² - x - 102 = 0, factor to find x = 6, then substitute back to find the dimensions: 32 feet by 11 feet.
Explanation:
A rectangle with a width of (5x+2) feet and a length of (2x-1) feet has an area of 100 square feet. To find the rectangle’s width and length, we need to solve for x using the area of a rectangle, which is the product of its length and width. The equation is:
(5x + 2)(2x - 1) = 100
First, expand the left side of the equation:
10x²- 5x + 4x - 2 = 100
Combine like terms:
10x² - x - 2 = 100
Subtract 100 from both sides to set the equation to zero:
10x² - x - 102 = 0
Now, we can use the quadratic formula, factorization, or a graphing utility to find the values of x that satisfy the equation. For simplicity, we are looking for integer solutions because the setup of the problem suggests that such solutions are likely.
Factoring the quadratic equation, we get:
(10x + 17)(x - 6) = 0
Setting each factor to zero gives us two potential solutions for x:
10x + 17 = 0 or x - 6 = 0
Solving these, we find:
x = -17/10 or x = 6
Since a negative width does not make practical sense for a rectangle, we discard the negative solution and keep x = 6.
Inserting x = 6 into the original expressions for width and length, we find:
Width = 5(6) + 2 = 32 feet
Length = 2(6) - 1 = 11 feet
Therefore, the rectangle's dimensions are 32 feet by 11 feet.
Which trigonometric function is equivalent to sec(-270) ? a. sec(-120) c. sec(-30) b. sec(60) d. sec(90)
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we add our angle to 360°
-270+360
=90
But sec(-270) is a positive value, this implies that the angle that will give us the same answer as sec (-270) should also give us the positive value. This means that 90 is our answer since it will give us the positive sec value.
The answer is d. sec(90)
Answer: d
Step-by-step explanation: edge 2021
state if the polygons are similar
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Since you didn't provide a picture of the exact thing you're working on I'm not sure if this will help you but it will help anyone who has the same project as me
in 56 years, kevin will be 9 times as old as he is right now. how old is he right now?
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This is because
m + 56 = 9m
9m – m = 56
56/8
7
56+9A
A=7
he will be 7 years old he is pretty old
The pentagons JKLMN and PQRST are similar find the length x of TP
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Answer:
the answer is 2.8 assuming you had the same messurments and questions as me
Step-by-step explanation:
y = 2x2 - 3x - 20?
A) x = -5 and 2
B) x = 5 and -2
C) x = -2.5 and 4
D) x = 2.5 and -4
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40
2 20
4 10
5 8
2x² - 8x 5x - 20
2x(x - 4) 5(x - 4)
(2x + 5) (x - 4)
2x + 5 = 0 x - 4 = 0
2x = -5 x = 4
x = -5/2
C) x = -2.5 and 4
Use a graphing calculator to solve the equation in the interval from 0 to 2π Round your answers to the nearest hundredth. 1.21, 2.26, 3.31, 4.35, 5.40 3.64 1.21, 4.35 0.404, 1,452.5, 3.55, 4.59, 5.64
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The solution to the equation at the given interval is x = 3.64
Using a graphing calculator to solve the equation
From the question, we have the following parameters that can be used in our computation:
[tex]3\tan(\dfrac 13\theta) = 8[/tex]
This can be expressed as
[tex]y = 3\tan(\dfrac 13\theta)[/tex]
y = 8
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection of the lines
This point is located at x = 3.64
Hence, the solution to the equation at the inverval is x = 3.64
Question
Use a graphing calculator to solve the equation
[tex]3\tan(\dfrac 13\theta) = 8[/tex]
in the interval from 0 to 2π Round your answers to the nearest hundredth.
Find the second of 3 consecutive integers if the sum of the first and the third is 26
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x+1= 2nd integer
x+2= 3rd integer
Add the 1st and 3rd set equal to 26.
x + (x+2)= 26
combine like terms
2x + 2= 26
subtract 2 from both sides
2x= 26
divide both sides by 2
x= 13
Substitute x=13 to find 2nd integer.
= x+1
= 13 + 1
= 14 second integer
ANSWER: The second integer is 14.
Hope this helps! :)
x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)
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hope it helps!!
Answer: The correct answer is (1,-1).
Explanation:
The given equations are,
[tex]x-2y=3[/tex] ..... (1)
[tex]5x+3y=2[/tex] ..... (2)
Use elimination method to solve the equations.
Multiply equation (1) by 5.
[tex]5(x-2y)=5(3)[/tex]
[tex]5x-10y=15[/tex] ..... (3)
Subtract equation (3) from equation (2).
[tex]5x+3y-(5x-10y)=2-15[/tex]
[tex]5x+3y-5x+10y=-13[/tex]
[tex]13y=-13[/tex]
[tex]y=-1[/tex]
The y-coordinate is -1.
Put y=-1 in equation (1).
[tex]x-2(-1)=3[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
The x-coordinate is 1.
Therefore the intersection point is (1,-1).
50x = 100 what does x equal??
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Divide 50 by each side.
X= 2
To find out what x equals, you can divide the numbers 100 and 50 . . .
100 divided by 50 = 2
2 x 50 = 100
x=2 <--------
Hope this helps you.
Have a great day!
You are a lab technician and it takes you 1 hour 30 minutes to complete a lab test. At this rate, how many hours would it take you to complete 5 of the lab tests?
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write the equation of the line that passes throughout (-1,5) and has a slope of 3 in point-slope form
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[tex]y - k = m(x-h)[/tex]
So, here, you just plug in values:
[tex]y - 5 = 3(x+1)[/tex]
It would be + 1 because remember, the '-' sign just means the opposite of, not subtraction in this case. Also, m = slope.
Find the missing lengths of the sides
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Answer:
a) a = 9d, c = 18 yd
Step-by-step explanation:
The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.
Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.
In given figure, we are given the longer leg.
√3x = 9√3
From this we can find the value of x, which is the shorter leg.
Dividing both sides by √3, we get
x = 9
The shorter side, a = 9 yd
Now let's find the hypotenuse.
Plug in x = 9, in 2x, we get
= 2*9
= 18 yd
The hypotenuse "c" = 18 yd.
So the answer is a) a = 9d, c = 18 yd
The time it takes runners to complete a certain marathon are normally distributed with a mean of 4.6 hours and a standard deviation of 1.1 hours what is the time for a runner with a score of -1.2? Round to the nearest hundredth
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The equation for the z-score is
z-Score = (Time - Mean) / Standard Deviation
Given:
mean = 4.6 hours
standard deviation = 1.1 hours
z-Score = -1.2
∴ -1.2 = (x - 4.6) / 1.1
x - 4.6 = -1.32
x = 3.28 hours
The time would be 3.28 hours for a z-score of -1.2.
Explanation:
The formula for a z-score is
z = (X-μ)/σ,
where μ is the mean and σ is the standard deviation.
For our problem, we know that z = -1.2, μ = 4.6 and σ = 1.1:
-1.2 = (X-4.6)/1.1
Multiply both sides by 1.1:
-1.2(1.1) = ((X-4.6)/1.1)*1.1
-1.32 = X-4.6
Add 4.6 to both sides:
-1.32+4.6 = X-4.6+4.6
3.28 = X
List the coordinates of the image after a rotation of the figure below of 180° about the origin. 20 points
(__ , __)
(__ , __)
(__ , __)
(__ , __)
Find the measures of the segment and its image:
AD = √___, A'D' = √___
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B' (-5,-4)
C' (-7,-2)
D' (-4,0)
AD = sqrt(2)
A'D' = sqrt(2)
Answer: The co-ordinates of the image quadrilateral areA'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
Step-by-step explanation: We are given to list the co-ordinates of the image after a rotation of the figure below of 180° about the origin.
From the figure, we note that
the co-ordinates of the vertices of quadrilateral ABCD are A(3, 1), B(5, 4), C(7, 2) and D(4, 0).
We know that
the co-ordinates of the image of a point (x, y) after rotation of 180° about the origin is given by (-x, -y).
Therefore, after rotating the quadrilateral ABCD through an angle of 180° about the origin, then the co-ordinates of the image A'B'C'D' are
A(3, 1) ⇒ A'(-3, -1),
B(5, 4) ⇒ B'(-5, -4),
C(7, 2) ⇒ C'(-7, -2)
and
D(4, 0) ⇒ D'(-4, 0).
And, the lengths of the line segments AD and A'D' can be calculated using distance formula as follows :
[tex]AD=\sqrt{(4-3)^2+(0-1)^2}=\sqrt{1+1}=\sqrt{2}~\textup{units},\\\\A'D'=\sqrt{(-4+3)^2+(0+1)^2}=\sqrt{1+1}=\sqrt 2~\textup{units}.[/tex]
Thus, the co-ordinates of the image quadrilateral are A'(-3, -1), B'(-5, -4), C'(-7, -2) and D'(-4, 0). The length of the segments AD and A'D' are both √2 units.
The Jensen family took a road trip in September.the dad fills up the tank,he records the miles on the SUV as 24,033.he pays $83.58 to fill up the tank. what is the size of the SUV's tank in gallons, rounded to the nearest whole number. One gallon of gas cost $3.79,
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what is (-5.62x - 0.8) + (1.12+ 1.4x)
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Mark has a bag containing a mixture of 30 green and white marbles. Without looking, he guesses that half of the marbles in the bag are green. He randomly selected 1 marble from the bag, recorded the color, and returned the marble to the bag. After 15 trials, Mark has drawn 10 green marbles and 5 white marbles. Which of the conclusions below is BEST supported by his data?
The bag contains more white than green marbles.
The bag contains 10 green marbles and 20 white marbles.
The bag contains an equal amount of each color.
The bag contains more green than white marbles.
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How use zero product property to solve equations
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In words: if two numbers multiply to 0, then one (or both) of the values must be zero.
So in terms of algebra, if we had
-0.2*(x-1.9)*(x-3.5) = 0
then
x-1.9 = 0 or x-3.5 = 0
Now solve each individual equation for x
x-1.9 = 0
x-1.9+1.9 = 0+1.9 ... adding 1.9 to both sides
x = 1.9
x-3.5 = 0
x-3.5+3.5 = 0+3.5 .... adding 3.5 to both sides
x = 3.5
The two solutions are x = 1.9 or x = 3.5
These two x values, when plugged into f(x), will make f(x) = 0
These are the x intercepts because this is where the graph crosses the x axis.
Note: "root" is another term for "x intercept"
Dimension of triangle A are three times the dimensions of triangle
b. The area of triangle A is 252 cm squared. What is the area of triangle B?
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Answer:
28 cm2
Step-by-step explanation:
I did this question
What is the ratio of pennies to dimes in a dollar
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You need 10 dimes to make a dollar
ratio of pennies to dimes is 100:10, or 10:1 simplified
hope this helps