The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $11. The auditorium can hold a maximum of 130 people. The drama club must make a minimum of $1100 from ticket sales to cover the show's costs. Also, they can sell at least 90 adult tickets. If x x represents the number of student tickets sold and y y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
The graph for the inequality is attached below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Each student ticket sells for $6.50 and each adult ticket sells for $11.
let the number of student ticket sold be x and number of adult ticket sold be y.
so, the inequality is
x + y < 130
and, 6.5x + 11y >1100.
Solving the inequality we get
x= 73.33 and y = 56.667
Now, if they sell at least 90 adult tickets then they sell at most 40 children ticket.
Hence, the solution is (73.33, 56.667).
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Is an example of a zero pair?
The Zero pairs is defined as the pair where the sum of all the elements is zero and one such example of zero pair is (-5,5) .
What is Zero Pair ?
The Zero Pair is defined as the pair of element (a,b) , where the sum of elements "a and b" are zero , that means ⇒ [tex]a+b=0[/tex] .
Few Examples of Zero Pairs are :
(i) the ordered pair (2,-2) is a Zero Pair because ,
⇒ [tex]2+(-2)[/tex]
⇒ [tex]2-2[/tex]
⇒ 0 .
(ii) the ordered pair (8,-8) is a Zero Pair because ,
⇒ [tex]8+(-8)[/tex]
⇒ [tex]8-8[/tex]
⇒ 0 .
(iii) the ordered pair (5,-5) is a Zero Pair because ,
⇒ [tex]5+(-5)[/tex]
⇒ [tex]5-5[/tex]
⇒ 0 .
Therefore , the examples of zero Pair are (2,-2) , (5,-5) and (8,-8) .
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If grapes are $1.99/pound and you buy 2.25 pounds of grapes, how much change will you receive if you hand the cashier a $5 bill
Using simple mathematical operations, we know that we will get a change of $0.5.
What are mathematical operations?An operation is a function in math that transforms zero or more input values into a strictly delineated output value.
The operation's arity is influenced by the number of operands.
For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "×" Finding the quotient in division ("÷)
So, we know that:
Grapes cost $1.99.
We purchased 2.25 pounds of grapes.
The change we will receive if we gave a $5 bill will be:
5 - (1.99*2.25)
5 - 4.4775
0.5225
Rounding off: $0.5
Therefore, using simple mathematical operations, we know that we will get a change of $0.5.
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What are the 3 exponent properties?
The 3 main exponent properties are:
The product of powers property: (a^m) * (a^n) = a^(m+n)The quotient of powers property: (a^m) / (a^n) = a^(m-n)The power of a power property: (a^m)^n = a^(m*n)The product of powers property states that when you multiply two numbers with the same base, you can add the exponents to find the result. For example, (2^3) * (2^4) = 2^(3+4) = 2^7
The quotient of powers property states that when you divide two numbers with the same base, you can subtract the exponents to find the result. For example, (2^5) / (2^3) = 2^(5-3) = 2^2
The power of a power property states that when you raise a power to another power, you can multiply the exponents to find the result. For example, (2^3)^2 = 2^(3*2) = 2^6
These three properties help simplify algebraic expressions that include exponents and make it easier to solve equations and perform other mathematical operations.
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Erisa collected quarters. After a year he had quite a few of them. In fact, when he counted them in groups of two, three, four, and so on, up to groups of 16, there was always one left over. What is the smallest number of quarters Erisa could have collected
Erisa collected quarters. After a year he had quite a few of them. The smallest number of quarters that Erisa could have collected is 17.
What is the smallest number?Generally, Erisa collected quarters. After a year he had quite a few of them.
The smallest number of quarters that Erisa could have collected is 17.
This is because 17 is a prime number, and when it is divided into groups of 2, 3, 4, and so on, up to 16, there will always be one left over.
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What is the first step to solving quadratic equations in factored form?
Transform the equation using standard form in which one side is zero is the first step to solving quadratic equations in factored form.
What is quadratic equations in factored form?Form factored (of a quadratic expression) A quadratic expression is said to be in factored form if it can be represented as the sum of a constant and two linear factors. If and only if its discriminant is a perfect square, a quadratic equation with integer coefficients can be factored over integers. To begin factorising an expression, "take away" any shared factors that the terms have. As x appears in both terms, if you were asked to factor x2 + x, you would write x(x + 1). It is common to refer to a polynomial as "irreducible" if it cannot be factored. It might not be factorable if the coefficients lack common components or are not reasonable.Use standard form to transform the equation so that one side is zero.Factor the non-zero side, step 2.3. Reset each component to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).Solve each of the ensuing equations.To learn more about quadratic equations refer to:
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URGENT!!!
In the figure [FD]=[FE] and [DM]=[NE] prove that the triangle FMN is two sided
Therefore , the solution of the given problem of congruences comes out to be [FD]=[FE] and [DM]=[NE]
What is congruency?SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.
SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.
SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.
Here,
SSS – side, side, and side. ...
SAS – side, angle, and side. ...
ASA – angle, side, and angle. ...
AAS – angle, angle, and side. ...
HL – hypotenuse and leg.
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Use a trigonometric ratio to solve for b. Round to two decimal places as necessary!!
HELP
Write “Lana put one third of the fence (f) around her yard” in expression
Answer:
1/3
Step-by-step explanation:
one third= 1/3
. The points (–5, 26) and (3, 26) are located on the same parabola. What is the equation for the axis of symmetry for this parabola?
The equation for given two points of parabola will be (x+1)^2=y-10.
What is parabola?
A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
In general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as:
y^2 = 4ax
If the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes,
x^2 = 4ay
Apart from these two, the equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.
Now,
the parabola having points (–5, 26) and (3, 26) is given in graph
and the equation will be (x+1)^2=y-10
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A farm has 14 cows and 10 horses. Write the
ratio of cows to horses as a fraction in lowest
terms.
Answer: 7:5
Step-by-step explanation: 14/2 = 7 and 10/2 = 5
I am truly sorry if it was wrong or i did not understand ty.
- ♥ Roxy ♥
The table shows the length and width of proportional rectangles. Length (in inches) 4 6 12 16 width (in inches) 10 15 30 40 using the table, find the width of a rectangle that has a length of 24.
The width of a rectangle that has a length of 24 inches would be 60 inches.
According to the data, we can assume that all the rectangles in the table have the same ratio of measurement.
To find unknown width of the rectangle, we can use this equation:
A/B = C/D
Where:
A represents the length of the first rectangle
B represents the width of the first rectangle
C represents the length of the second rectangle
D represents the width of the second rectangle
In this case, we are going to use 12 as the length of the first rectangle, and 30 as its width.
12/30 = 24/D
12D = (30 x 24)
12D = 720
D = 60
Thus, the width of the rectangle that has a length of 24 inches is 60 inches.
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Please help me with my work
In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.
In algebra, what does a fraction mean?The components of a whole or group of objects are represented by fractions. A fraction consists of two parts. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the whole or collection. The denominator is the figure that appears below the line.
What are the Algebra Fundamentals?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.
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The temperature is -3F at 7:00 a.m during the next 4 hours,the temperature increases to 21F.what is the temperature at 11:00 a.m?
Answer:
I believe it is 24°F
Step-by-step explanation:
I'm just cool like that
On the third grid, create a graph of the set of points (2+5t, 3-4t) for -2 ≤ t ≤ 7 pm the xy-plane
The graph of the set of the points has the constraints -8≤2+5t≤37 & -25≤3-4t≤11
What is an inequality?An inequality is an inequation separated by <,>≥,≤
Given here: The set of points (2+5t,3-4t) in the xy-plane
when -2≤t≤7 set of points (2+5t,3-4t)
then 2+5×-2≤2+5t≤2+5×7
-8≤2+5t≤37
Again, 3-4×-2≤3-4t≤3-4×7
-25≤3-4t≤11
We can construct a graph using the above accordingly
Hence, The graph of the set of the points has the constraints -8≤2+5t≤37 & -25≤3-4t≤11
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I don’t understand this very well, help me with an explanation please?
Answer:
what is this on
Step-by-step explanation:
Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.
Please select the best answer from the choices provided.
T
F
True, Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.
What is Recreational water illnesses?
Recreational water infections (RWIs) are contracted by ingesting, inhaling mists or aerosols from, or coming into touch with contaminated recreational water and are brought on by microorganisms.
In addition to swimming pools, hot tubs, water slides, water play zones, interactive fountains, lakes, rivers, and seas are all examples of recreational water.
What exactly is a recreational water?
Incorporated into this are swimming, diving, water skiing, and surfing. Recreation involving secondary touch, where you come into direct contact with the water but are unlikely to ingest it Paddling, wading, boating, and fishing all fall under this category.
without any physical interaction with the water, passive recreation.
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What are exponents for Grade 7?
Exponents are a way to represent the repeated multiplication of a number by itself. The exponent is written as a small number raised to the right of the base number.
For example, in the expression 2^3, 2 is the base and 3 is the exponent. This means 2 multiplied by itself 3 times, equal to 2 x 2 x 2 = 8. The exponent tells how many times the base is multiplied by itself.
In grade 7, students typically learn the basic rules of exponents such as how to multiply and divide numbers with the same base, and how to raise a power to a power. They also learn about scientific notation, which is a way of writing very large or tiny numbers using exponents.
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The reflection rule is (x,y) = _____ where the equation of line t is _
The reflection rule is (x, y) = (y, x)) where the equation of line t is y = x
How to find the equation of line tThe slope, m of the linear function is calculated using the points on the graph (4, 4) and (2, 2)
m = (y₀ - y₁) / (x₀ - x₁)
m = (4 - 2) / (4 - 2)
m = (2) / (2)
m = 1
Equation of the line t passing through point (0, 0) applying the point slope formula
(y - y₁) = m' (x - x₁)
y - 0 = 1(x - 0)
y = 1(x)
y = x
The equation of the line is y == x
Refection rule for line y = x, on the positive sides is to interchange the positions of the x and y values
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the festival organizers expect 10,000 people to attend the four day festival at the end they have exceeded their attendance by 2000 people determine the average number of people that attended the festival per day
Answer:
500 people came each day
Step-by-step explanation:
2000 divide by 4= 500
Classifying Triangles Card
The triangle problem's solution is given by the relationship amongst x,y and z, which is z²= x²+y² .
Explain the triangle.Due to its three vertices and three sections, a triangles is a polygon. It has a simple geometric form. Triangle ABC refers to a triangular with the points A, B, and C. When three factors are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By summing three triangle angles, one gets 180 degrees.
Here,
Given: In this situation, triangle XYZ is a right triangle.
Thus,
We discover:
Z, X, and Y components
They are linked in the following ways:
It being a right triangle,
So,
According to the Pythagoras Theorem,
=>z²= x²+y²
The triangle problem's solution can be found by using the relationship among z, x, and y, which is given by z2=x2+y2.
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Which phrase represents this expression? (30 - 10) × 5 PLEASE ANSWER NOW!!! DUE TOMORROW
Answer:
I can only give you the answer to the equation which is 100 but I can't help you with finding the phrase because you did not include the answer choices.
Step-by-step explanation:
Hello! Please help I need this done tonight! I have no clue on how to do this! I have included a picture of the problem.
Answer: x = 1, y = -1
Step-by-step explanation:
The elimination method is a technique for solving systems of linear equations.
1) 4x-6y=10
2) 9x+2y=7
in the second equation
it multiply with 3
then
3×(9x+2y=7)
= 27+6y= 21
We notice that the first equation has a 6y term and the second equation has a -6y term. These terms will cancel if we add the equations together—that is, we'll eliminate the x terms:
then add 1 + 2 equations
4x-6y = 10 _____1)
27+6y= 21 _____2)
then we will get
31x+0 = 31
31x= 31
where x = 31/31= 1
then x = 1
if value of x substitute in the equation ____1)
4x+6y = 10
4×1+6y = 10
6y = -6
y = -6/6
y = -1
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someone help please thank you
Answer:
distance = (62t) + 22
Step-by-step explanation:
Distance = speed * time
distance = (62*t) + 22
Hope this helps!
Find the additive inverse of the linear expression. −2x+5 __
The answer is 2x-5
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: linear expression. −2x+5
Thus the additive inverse is -2x+5+2x-5=0
Hence, the additive inverse is 2x-5
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Find the value of x .
X=
Answer:
65°+106°+78°+*°=360°
249°+ *°=360°
*°=360°-249°
*°=111°
The bar chart below shows the monthly energy bill for Wally's tackle shop.
Which of the listed months had bills between $40 and $50? Scroll down to
see all six answer options and check all that apply.
Energy bill (S)
70
60
50
40
30
20
10
January
February
March
April
Months
August
September
October
ՅզաaAON
December
Answer:
March, June, and November
Step-by-step explanation:
See attached image for the utility bills by month. Draw a line along the $40 and $50 lines on the y axis and select the months that fall within these two lines.
p) find the sum of the infinite geometric series:
a1 = -20 a5 = -1650 r = 3
The sum of the infinite geometric series is 10
How to solve for the infinite geometric seriesFrom the values that we have, the first term a1 = - 20, the common ratio r = 3
From the above we can get the first 5 terms of the geometric series. We do this by multiplying each number derived by 3
this would be :
-20, -60, -180, -540 , -1650 ...
The formula for the sum of the infinite geometric series is given as
S = a1 / 1 - r
from the question we have
a1 = -20
r = 3
we would put the values into the formula
S = -20 / 1 - 3
S = -20 / -2
s = 10
Hence the sum is given as 10
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Simplify (s^-5)^3 write your answers using only positive exponents
how do u write y=e^-1.5t into y=ab^x
Consequently, the exponential function y=e-1.5t can be changed to y=abx. The transcendental number is the most popular exponential-function base.
what is exponential function ?The formula for a mathematical function called an exponential function is f (x) = an x, where x is a variable and an is a fixed quantity known as the function's base. The exponential-function base that is most frequently used is the transcendental number e, or approximately 2.71828. An example of an exponential function is the growth of bacteria. Some bacteria can multiply by two in one hour. There will be twice as many germs around after x hours as there were at the beginning. F(x) = 2x is the formula for this.
given
y=e^-1.5t
f(x) = 2. x
f(x) = 1/ 2x = 2. -x
f(x) = 2. x+3
f(x) = 0.5. x
y=ab^x
Consequently, the exponential function y=e-1.5t can be changed to y=abx. The transcendental number is the most popular exponential-function base.
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