Answer:
a) System of equations will be: [tex]x+y=500\: and\:5x+2y=1789[/tex]
b) Number of adult tickets sold = 263
Number of students tickets sold = 237
Step-by-step explanation:
Let:
Number of adult tickets sold = x
Number of students tickets sold = y
a)
As Marc sold total 500 tickets, the expression will be: [tex]x+y=500[/tex]
Student tickets cost $2 and adult tickets cost $5. Marc's sales totalled $1,789.
The expression will be: [tex]5x+2y=1789[/tex]
So, system of equations will be: [tex]x+y=500\: and\:5x+2y=1789[/tex]
b)
Solve the system to find value of x and y
Let:
[tex]x+y=500--eq(1)\\5x+2y=1789--eq(2)[/tex]
Multiply equation 1 by 2 and subtract
[tex]2x+2y=1000\\5x+2y=1789\\-\:\:\:-\:\:\:\:\:\:\:\:\:-\\------\\-3x=-789\\x=\frac{-789}{-3}\\x=263[/tex]
We get value of x = 263
Now finding value of y by putting value of x in eq(1)
[tex]x+y=500\\263+y=500\\y=500-263\\y=237[/tex]
We get value of y = 237
Number of adult tickets sold = x = 263
Number of students tickets sold = y = 237
k/3+16 algebraic expression
Answer: -48
Step-by-step explanation:
k/3 + 16
find the roots by factoring
which leads to -48
k/3 + 16
To add or subtract expressions, expand them so their denominators are the same. Multiply 16 by 3/3.
k/3 + 16 × 3/3
Since k/3 and 16 × 3/3 have the same denominator, we join their numerators to add them.
k + 16 × 3/3
We perform the multiplications in k+16×3.
k + 48/3
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grafica
[tex]5y-15=-4x[/tex]
El grafico de la ecuación lineal se puede ver en la imagen al final.
¿Como graficar la ecuación lineal?En este caso queremos graficar la ecuación lineal:
5y - 15 = -4x
Para ello debemos encontrar dos puntos en la linea, y para hacer eso podemos evaluar en dos valores de x.
Sí x = 0 obtenemos:
5y - 15 = -4*0
5y = 15
y = 15/5 = 3
Sí x= 5 obtenemos:
5y - 15 = -4*5
5y = -20 + 15
5y = -5
y = -5/-5 = -1
Entonces solo tenemos los dos puntos (0, 3) y (5, 1), ahora debemos graficar estos en un eje de coordenadas y trazar una linea que pase por ambos, como en el ejemplo de abajo.
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pls help it's due for a grade
find all values of x in the interval [0, 2????] that satisfy the inequality. (enter your answer using interval notation.)
A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).
What does a math inequality mean?A relation in mathematics that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.
According to the given information:5 sin(x) > 5 cos(x)
To removing constant we divide both the side by 5:
5sin(x) > 5 cos(x)
sin(x) > cos(x)
sin x > cos x;
sin x = cos x; tan x = 1; x = π/4 or x = 5π/4
sin x > cos x for x ∈ (π/4, 5π/4)
A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).
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I understand that the question you are looking for is:
Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)
which expression simplifies to 41? choose all that apply! question 14 options: 10 2³ ∙ 4 - 1 10 2³ ∙ (4 - 1) (10 2³) ∙ 4 - 1 10 (2³ ∙ 4) - 1
The expressions that simplifies to 41 are:
a) 10 + 2³ * 4 - 1
d) 10 + (2³ * 4) - 1
Information about the problem:
a) 10 + 2³ * 4 - 1
b) 10 + 2³ * (4 - 1)
c) (10 + 2³) * 4 - 1
d) 10 + (2³ * 4) - 1
We solve the equations respecting the level of hierarchy:
First the operations in parentheses, then brackets and finally braces.Of the arithmetic operations, first the multiplication and divisions and then the additions and subtractions.a) 10 + 2³ * 4 - 1
10 + 8*4 - 1
10 + 32 - 1
42 - 1
41 (it applies)
b) 10 + 2³ * (4 - 1)
10 + 8 * (3)
10 + 24
34 (it doesn't applies)
c) (10 + 2³) * 4 - 1
(10 + 8) * 4 - 1
18*4 - 1
72 - 1
71 (it doesn't applies)
d) 10 + (2³ * 4) - 1
10 + (8*4) - 1
10 + 32 -1
42 - 1
41 (it applies)
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Please help me I dont understand this! its due soon by the end on class omg!
The number of people who would prefer Choco chocolate chip is 120.
How many people would prefer Choco chocolate chip?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
In order to determine the number of people who would prefer Choco chocolate chip , multiply the given ratio of people who prefer Choco chocolate chip by the total number of people in the group.
The number of people who would prefer Choco chocolate chip = (ratio of people who prefer choco / sum of ratios) x number of people
(3/5) x 200 = 120
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Carrie is packing her clothes in moving boxes that are in the shape of a cube. Each box has a volume of 3 cubic feet. The moving truck has shelves that are 12 inches in height. Will the moving boxes fit? Explain.
Yes, the moving boxes will fit in this volume.
What is volume ?The current volume of box :
Volume = height * width * depth
Volume = 12 * 9 * 2
Volume = 216 in³
New dimension :
Height and volume are the same
Width = 9 - 1 = 8
Depth = x
Volume = height * width * depth
216 = 12 * 8 * x
216 = 96x
x = 216 / 96
x = 2.25 inch
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.
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Simplify the difference.
One rectangle has an area of ((7x² - 4x +12) ft². A second rectangle has an area of
(4x² + 2x − 1) ft².
How many more square feet is the first rectangle ?
O 3x² - 2x + 11
O 11x² - 6x + 11
O 3x²- 6x + 13
O-4x²-5x-9
Answer:
The first rectangle is 3x² - 6x + 13 more square feet then the second rectangle
Step-by-step explanation:
A rule for subtracting polynomials
Keep the first term the same Change the subtraction sign to addition Change the sign for every termSteps
Keep the polynomial 7x²- 4x + 12 the same Change the subtraction sign to addition Change the sign for every term 4x² + 2x - 1 becomes -4x² - 2x + 13At the end of the expression is (7x²- 4x + 12) + -4x² - 2x + 1
At this point you combine like terms like you do with adding polynomials so ( 7x² + (-4x²) is 3x², (-4x) + (-2x) is (-6x), and 12 + 1 is 13) so the final answer would be 3x²-6x+13
Miles driven
120
300
380
480
Gas Use
20
24
33
39
Gallons of
gasoline used
If the car always uses the same amount of gasoline each mile, how many gallons of gasoline would be needed to
travel 480 miles?
6
15
18
2
Answer:
the answer is 70,007
Step-by-step explanation:
again the answer is 102,002
Answer:
Step-by-step explanation:
70007
Sophia need to earn at least 1,800 each month to cover her living expenses.what is the minimum amount she needs to sell in order to earn at least 1,800 if she earn a 10.75commission on everything she sells?round to the nearest dollar
In a condition where Sophia needs to earn at least $1800 as a part of her living expenses, she will need to sell goods worth at least $16,745 if she earns 10.75% commission on everything she sells.
What is the significance of living expenses?
Living expenses of an individual can be referred to or considered as the amount of expenditure made by a person for living for a predefined period of time. The living expenses also include the spending towards the necessities of an individual.
In the condition given above, the provided information can be used in order to find out about the living expenses as,
Living Expenses = Sales x Commission
1800 = Sales x 10.75%
Sales = 1800 / 10.75%
Sales = $16,744.12
Therefore, the significance regarding the living expenses has been aforementioned.
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if the mean of a set of 12 numbers is 13 , then the summer of the numbers is
Answer:
156, because the mean is 13, and the mean in equal to all of the numbers added up and divided by how many numbers there are.
Which expressions describe the end behaviors of the function f(x)=2^x+3. modeled by the graph attached to this. Choose all that are correct.
As x increases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 3.
As x increases without bound, f(x) increases without bound.
The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3 therefore option (C) and (D) will be correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand behavior of the graph.
Given the function,
f(x) = [tex]2^{x}[/tex] + 3
At x = 0 → f(0) = 2⁰ + 3 = 3
This is an exponential function as shown below which will be increasing as x increase while it will gain the value y = 3 as x decrease.
Hence "The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3".
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Given −47.01 × 6.2, find the product.
−291.462
−282.02
−37.608
29.1462
Step-by-step explanation:
-282.02 its korrect now
How do i do this? This is all due tomorrow
1.2 because you take 2 congruent sides of each shape and divide the larger one by the small one. in this example you could do
8.4÷7
36.6÷30.5
19.2÷16
they all give you 1.2
the equation is -5 = -8+v/3 help
Step-by-step explanation:
could it be that the equation is rather
-5 = (-8 + v)/3
?
that is a huge difference ...
to solve such an equation we keep transforming it (every change we make we have to do on both sides of the equation to keep the equality), until we have only the variable on one side, and everything else (which is then the solution) on the other side.
1st step : we get rid of the "/3" by multiplying both sides by 3.
that gives us
-5×3 = ((-8 + v)/3)×3 via the multiplication property.
2nd step : we simplify
-15 = -8 + v
3rd step : we get rid of the -8 on the side of the variable by adding 8 to both sides.
that gives us
-15 + 8 = -8 + 8 + v via the addition property.
4th step : we combine like terms (or simplify, if we can use it a second time) :
-7 = 0 + v
-7 = v
that's it.
0.00015797 in scientific notations
Answer:
1.5797 x 10^-4
Step-by-step explanation:
2000, 200, 20, 2, ... what 3 numbers come next pls help
Answer:
2, 20, 200, 2,000, 20,000, 200,000
Answer: 0.2, 0.02 0.002
What is the image of (8, -12) after a dilation by a scale factor of 1/4 centered at the origin?
Answer: (2, -3)
Step-by-step explanation:
To get these points, you just need to multiply the coordinates by 1/4, or divide by 4
Order numbers from least to greatest: 4 3/4, -2 1/2, -8/3, 9/2
Answer:
-8/3 < -2 1/2 < 9/2 < 4 3/4
Step-by-step explanation:
-2.667 < -2.5 < 4.5 < 4.75
14.2 in scientific notation
Answer: 1.42 x 10^1
Step-by-step explanation:
Answer: 1.42x10
Step-by-step explanation:
Please someone answer this question points.
(05.03)bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. calculate the area of the polygon. be sure to show all your work and explain your answer. six-sided polygon that includes two isosceles right triangles, one with height and base of 15 feet, the other height and base of 4 feet, and one rectangle measuring 25 feet by 4 feet.
The area of the six-sided polygon = 220.5 square ft.
Given that the six-sided polygon consists of two isosceles triangles and a rectangle. So the total area to be cut will be equal to the sum of areas of the triangles and the rectangle.
First triangle has base = 15 ft and height = 15 ft
Area of a 1st triangle = 1/2 x base x height
= 1/2 x 15 x 15
= 112.5 square feet
Second triangle has base = 4 ft and height = 4 ft
Area of the 2nd triangle = 1/2 x base x height
= 1/2 x 4 x 4
= 8 square ft
The rectangle has length = 25 ft and width = 4 ft
Area of the rectangle = length x width
= 25 x 4
= 100 square ft
So the total area of the six-sided polygon = 112.5 + 8 + 100
= 220.5 square ft.
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A party will have hexagonal tables placed together with space for one person on each open side:
n
12
a. Complete this table showing the number of people P (n) who can sit at n tables.
If n =12 then there are 50 person who can sit .
Hexagonal - In geometry, a hexagon is a closed two-dimensional six-sided polygon. It is made up of six line segments and six vertices that form six internal angles. The sum of all the internal angles of a hexagon is 720°.
Each table seats 4 people, which can be represented with n,plus two more people at either end of the set of tables. The table is hexagonal and so can seat 6 people. So, the given equation defines this situation.
The number of people who can sit at the tables increases by 4 each time a table is added
P=4n+2
the given equation to find the number of tables n.
P=4n+2
Where P = person
and n= no of tables .
given that
n=12
put value of n in equation to find the no. of person .
P = 4(12) +2
P = 48 +2
P = 50.
Hence,in this given seating arrangement 50 person can sit on 12 tables. .
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question 11(multiple choice worth 5 points) (01.06 mc) the length of a blue whale is approximately 3 × 104 millimeters; the length of an otter is 2 × 103 millimeters. how many times longer is the blue whale than the otter? 1.5 2 10 15
Blue whale is 15 times longer than otter.
To find how many times the blue whale is longer than the otter, we will perform division. We will divide the length of blue whale by length of otter, which we will give us the desired result.
Now, performing calculation as per the above statements -
Number of times longer length = [tex]\frac{3*10^{4} }{2*10^{3} }[/tex]
Performing division of numbers. Also, as we know, on division the exponents are subtracted. Hence, subtracting the exponents to get the desired result.
Number of times longer length = 1.5*[tex]10^{4-3}[/tex]
The result will be -
Number of times longer length = 1.5*10
Performing multiplication -
Number of times longer length = 15
Hence, we get that blue whale is 15 times longer than otter.
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Marie has 2 boxes for numbered ping
pong balls, labeled A and B, as shown
in the figure above. Box A is for ping
pong balls that are multiples of 2 and
box B is for ping pong balls that are
multiples of 7. If Marie were to move
all the balls that could go in either one
of these boxes into a third box, which
best describes the ping pong balls this
third box would have?
A) Multiples of 2
B) Multiples of 7
C) Multiples of 14
D) Multiples of 42
Answer:
multiples of 14
Step-by-step explanation:
we multiply 7×2
Please help as fast as you can!!!!
-2 1/3 - 1 3/4=
Write the answer as a fraction please!!
Answer:-41/4 try that
hint: since there are 100 terms in the sum, it isn’t a good idea to write them all out and add. use the formula for the sum of terms of a geometric sequence. leave the answer with exponents rather than using a calculator to try to get a decimal approximation of the answer.
Final answer obtained is 2/3
What is a geometric sequence?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.
Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is
[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]
where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.
A series is a sum, whereas a progression is a sequence. This is the difference between the two.
∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]
We see that n= 99, r= -1/2, a=1
∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]
[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]
[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]
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8. Find the equation of the lines passing through the origin and (a) parallel (b) perpendicular to the lines represented by 6x² - 5xy + y2 + 5x - 2y + 1 = 0. .
Answer:
Hello,
Step-by-step explanation:
1. We must decompose the conic into 2 lines.
[tex]f(x,y)=x^2-5xy+y^2+5x-2y+1=0\\\\We\ are\ going\ to\ find\ the\ center\\\\\left\{\begin{array}{ccc}\dfrac{ \partial{f} }{\partial{x} }&=&12x-5y+5=0\\\\\dfrac{ \partial{f} }{\partial{y} }&=&-5x+2y-2=0\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x=0\\y=1\\\end {array} \right.\\\\We\ must\ find\ an\ other\ point\ of\ f(x,y).\\\\if\ y=0\ then\ x=\dfrac{-1}{2} \ or\ x=\dfrac{-1}{3}[/tex]
The 2 lines are: 2x-y+1=0 and 3x-y+1=0
Paralleles are y=2x and y=3x
Perpendiculars are x+2y=0 and x+3x=0
What does mx or mx = b mean in math pls explain from like your knowledge
Step-by-step explanation:
In the equation y = mx + b for a straight line, the number m is called the slope of the line. In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.
If 1/2 cup of soup equals 120 milliliters, then how many milliliters are in 3 1/4 cups of soup?
If 1/2 cup of soup equals 120 milliliters, then there are 780 milliliters in
3 1/4 cups of soup.
A milliliter is a metric unit that is abbreviated as ml and is used to measure volumes for liquid and gas states. It is usually used to measure smaller volumes of liquids as it is equal to 1/1000 of a liter.
We can find the milliliters in 3 1/4 cups of soup as follows:
1/2 cup of soup = 120 milliliters
As 1/2 = 0.5
We can rewrite it as:
0.5 cup of soup = 120 milliliters
3 1/4 cups = 3.25 cups
Consider milliliters in 3 1/4 cups = x
Therefore,
0.5 cup = 120 ml
3.25 cups= x
Cross multiply to find x,
0.5 x = 120x3.25
0.5 x = 390
x= 390/0.5 = 780 milliliters
Hence it is found that 3 1/4 cups of soup is equal to 780 milliliters.
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